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Masterarbeit, 2006
218 Seiten, Note: A
Title Page
Approval
Certification Page
Dedication
Acknowledgements
Abstract
Table of Contents
List of Tables
List of Figures
CHAPTER ONE: GENERAL INTRODUCTION TO THE STUDY
1.0 Introduction and Background
1.1 Capital Market Efficiency
1.2 Market Efficiency And Rational Expectations
1.3 Approaches to Security Evaluation
1.4 The Stock Valuation Model
1.5 Economic Determinants of Security Prices
1.6 Investment Decisions And The Fisher Separation Principle: The State Preference Theory
1.7 Statement of Problem
1.8 Purpose of The Study
1.9 Objectives of The Study
1.10 Research Questions
1.11 Statement of Hypotheses
1.12 Scope of The Study
1.13 Significance of The Study
1.14 Definition of Terms
References
CHAPTER TWO: LITERATURE REVIEW AND THEORETICAL FRAMEWORK
2.0 Introduction
2.1 Stock Valuation Models
A. Balance Sheet Valuation Methods
B. Dividend Valuation Model
C. Earnings Valuation Model
D. Cash Flow Valuation Model
E. Capitalization Approach
2.2 Price/Earnings (P/E) Ratio.
2.2.1 P/E Ratios And Stock Risk
2.2.2 Pitfalls In P/E Analysis
2.3 The Nigerian Stock Market
2.4 Capital Structure And Cost Of Capital: Theory and Empirical Evidence
2.4.0 Introduction
2.4.1 Miller’s Hypothesis With Corporate And Personal Taxes
2.4.2 The DeAngelo And Masulis Model
2.4.3 Bankruptcy Costs/Costs Of Financial Distress
2.4.3.1 Application of The State Preference Model
2.4.4 Signaling Hypotheses
2.4.5 Agency Costs And Financial Structure
2.4.6 Empirical Evidence On Capital Structure
2.4.7 Section Summary
2.5 Dividend Policy Impact
2.5.1 Toward A Theory Of Optimal Dividend Policy
2.5.2 Behavioural Models Of Dividend Policy
2.5.3 Information Content Of Dividends Hypothesis
2.5.4 The Relationship Between Dividends And Value
2.5.5 Section Summary
2.6 Empirical Tests Of The CAPM
2.6.1 Recent Tests Of The CAPM
2.6.2 Roll’s Critique
2.7 Common Stock Performance and Systematic Factors: Some Theoretical Issues.
2.8 The CAPM and The APT
2.9 Volatility and Asymmetries In Stock Returns
2.10 Hedging Against Inflation
2.10.1 Theory
2.10.2 Common Stocks and Inflation
2.10.3 Empirical Results and Discussion
2.11 Chapter Summary
References
CHAPTER THREE: METHODOLOGY
3.0 Introduction
3.1 Research Design
3.2 Data Issues
3.3 Population of Study
3.4 Sample
3.5 Methodological Issues And Modeling
3.6 Evaluation of Estimates
3.7 Limitations of the Methodology
References
CHAPTER FOUR: DATA ANALYSES AND RESULTS
4.0 Introduction
4.1 Results on Capital Structure Relevance
4.2 Results on Information Content of Dividends
4.3 Common Stock Performance and Systematic Factors
4.4 Applicability of the CAPM
4.5 P/E Ratio - Growth Relation
4.6 Inflation Hedging Capacity of Common Stocks
References
CHAPTER FIVE: SUMMARY OF FINDINGS, CONCLUSIONS AND RECOMMENDATIONS
5.0 Introduction
5.1 Major Findings
5.2 Discussion of Findings
5.3 Conclusions
5.4 Recommendations
BIBLIOGRAPHY
APPENDICES
APPENDIX A: Modeling Risk Aversion
APPENDIX B: Market Clearing and the CAPM
2.1 Stock Market Statistics, 1988-2005
2.2 Volatility of Nigerian and United States Stock Markets, 1989-1992
2.3 Inter-Sector Return Correlation Matrix for The Nigerian Stock Market Jan 1989-Dec, 1992
2.4 Regression Results Of Sectoral Returns on The Market Index
2.5a Symbols Used in The SPM Analysis of Capital Structure Decisions
2.5b Amounts Received Under Alternative Outcomes
2.5c Formulas for The Value of The Firm Under Alternative Outcomes
2.5 Fama-Schwert Study on Sensitivities of Assets to Expected and Unexpected Inflation, 6-Month Holding Periods July 1959-July 1971
4.1a Regression Results on Capital Structure Impact
4.1b Regression Equations Using Four Bank Stocks.
4.1c Debt Ratios of Four Banks (1990-2004)
4.1d Return on Bank Capital Employed (%) 1990-2004)
4.1e The Cost of Equity and Debt-Equity (D/E) Ratio
4.1f Earnings Per Share (EPS) and D/E Ratio
4.2a Descriptive Statistics (Hypothesis Two)
4.2b Intercorrelation Matrix of Prices, Dividends and Retentions
4.2c Model summary - Prices, Dividends and Retentions
4.3a Descriptive Statistics (Hypothesis Three)
4.3b Correlations of All-Share Index with Systematic Variables
4.3c Coefficients Derived from the NSE All-share Index Regression.
4.3d Descriptive Statistics
4.3e Correlations of Return Index with Systematic Variables
4.3f Coefficients from Total Return Regression
4.4 Market Model Test of CAPM
4.5a Descriptive Statistics (Hypothesis five)
4.5b Intercorrelation Matrix of P/E, Payout and Growth
4.5c Model Summary - P/E, Payout and Growth
4.6a Descriptive Statistics (Hypothesis 6)
4.6b Correlations of Return Index with Expected Inflation and Unanticipated Inflation
4.6c Model Summary - Return Index and Inflation Components
2.1 MM Theory Versus The Traditionalists
2.2 Aggregate Debt Equilibrium With Heterogeneous Corporate And Personal Tax Rates
2.3 Value Of Levered Firm Under Corporate Taxes and Financial Distress.
To the Almighty God, the Source and Essence of life, the Custodian of wisdom, the Giver of a sound and fertile mind and the Strength of my passionate commitment to excellence.
To my family and my church family for continually providing the incentive for the exercise and development of my potential.
To the pioneers in the development of the modern theory of finance without whose intellectual leadership, this project could not exist.
To all those individuals whom I have had the privilege to meet and have encouraged me to strive to be all I could be.
My greatest appreciation is to my Lord and Saviour, Jesus Christ, who has shown me so much mercy and grace. I appreciate Him especially for the inspiration and the flow of ideas in the course of executing this project. He is also my link to all of the great personalities that have encouraged me to strive for excellence.
I thank my parents, Chief and Mrs J. A. Paseda and siblings for their love, sacrifice, patience, support, prayer and for providing the necessary environment for the development of my potential. My brother, ‘Dayo Paseda Esq and sister, ‘Funmi Paseda provided inspiration, financial support and encouragement in the critical process of my Master’s Programme. They continue to be guiding light. To the duo and our parents I extend fraternal gratitude.
To an educationist par excellence and my high school Principal, Mr ‘Segun Osiboye for inculcating in me enduring values in the pursuit of excellence in life.
To Professor Afolabi Soyode, a Distinguished Service Professor, an accomplished academic and former Vice-Chancellor, O.O.U., Ago-Iwoye for providing the terrain and incentives for the development of my career and for the powerfully-worded letter that he wrote in support of my application for postgraduate scholarship. I’m highly delighted to be associated with you.
To my Vice-Chancellor, Prof. Chinedu Nebo for providing excellent and purposedriven leadership that has guaranteed stability in our academic calendar.
To my supervisor, Prof. Chibuike Uche for taking interest in me and for providing not only continuous intellectual stimulation but also painstaking care in reading the various preliminary drafts. I am very proud of you.
To the pioneers in the development of what has come to be known as the ‘modern’ theory of finance: Hirshleifer, Arrow, Debreu, Stigler, Roberts, Durand, Solomon, Miller, Modigliani, Markowitz, Tobin, Sharpe, Lintner, Jensen, Fama, Roll, Black, Scholes, Merton, Myers, Ross and others cited in the pages that follow. Without their intellectual leadership this Dissertation could not exist.
This study has also profited from the criticisms, suggestions, and technical assistance of several other people such as Professors Francis Okafor, Uche Modum, D.A. Nnolim, Dr. Sunday Owualah, Dr. Sam Isitor, Dr. (Mrs) Ebele Ogamba, Dr. (Mrs) O.J. Nnabuko, Dr. B.E. Chikeleze, Dr. U.F. Amaeshi, D.N. Asomugha, E.O.C. Onah, F.C. Ahio, Mrs. N.J. Modebe and others too numerous to mention. Many of the ideas in the study arose out of the teachings of Professors Francis Okafor, Olaseni Akintola-Bello, Chibuike Uche and Mrs Nwanneka Modebe and I have profited from many invaluable discussion sessions. I wish especially to thank Professor Akintola-Bello for stimulating my interest in finance. Professor Akintola- Bello is more than my teacher; he was also a model.
To these eminent Professors; Wole Adewunmi, ‘Kayode Ajayi, Ademola Ariyo, David Ekpenyong, Cyril S. Ige, Eno L. Inanga, W. Iyiegbuniwe, Gini Mbanefo, Ben Osisioma, T. Ademola Oyejide, Kayode Oyesiku, Charles C. Soludo and Adedoyin Soyibo and for their liberal minds towards youngsters in the attainment of their potentials.
To the management of Covenant University Library (Centre for Learning Resources), Obafemi Awolowo University Library and University of Ibadan Library for providing me access to key journals and up to date articles.
To Dr. (and Mrs) David Oyedepo, an ardent Pan-Africanist, social reformer, educationist and preacher, founder of Living Faith Church Worldwide, Chancellor of Covenant University and a recipient of distinguished fellowships and awards, for providing a church home for me.
To my classmates at the M.Sc. class for the exciting time we had together. We questioned many things, learnt to begin analysis with first principles and worked on a host of fascinating problems. Intellectually, it opened new worlds.
A special thanks to Mr. Adeoye Ogunbanjo for assistance in producing the work in several copies.
To all of those individuals who assisted in one way or the other but whose names are inadvertently omitted. Many thanks to all.
Within the last decade, the Nigerian Stock Exchange (NSE) has witnessed remarkable growth mainly due to privatization, new minimum capital requirements, improvements in market infrastructure, amongst a host of other factors. The vast potential of the nation ’ s secondary market is clearly indicated in its high rating by the International Finance Corporation (IFC) and Standard and Poors with respect to investment returns in dollar terms. Despite the growth in market capitalization, it is noted that when measured as a percentage of the Gross Domestic Product (GDP), it is still quite low. The investment performance of capital market securities should enhance the contribution of the capital market to economic development. This study investigates the investment performance of common stocks in Nigeria. In particular, this study examines the empirical conformity of some finance theories in Nigeria since most of such evidence are based on developed markets and evidence on emerging markets like Nigeria remains scanty.
Secondary data, obtained from official sources, were utilized. Employing correlation and regression analyses, this study confirms the Modigliani- Miller (MM) capital structure theorem, information content of dividends ’ hypothesis, stock returns-systematic factors relation, and inflation- hedging capacity of common stocks. However, the Capital Asset Pricing Model (CAPM) and Price Earnings (P/E) Ratio- Growth relation lack strong empirical support. The implications of these findings are discussed.
Economists, for many years, have been concerned with the problem of selecting optimal portfolios of risky assets. Most of the developed models, in this regard, assume investors’ possession of a preference ordering over all possible portfolios with the intention of maximizing the value of this preference ordering subject to a budget constraint, taking the prices and probability distributions of yield for the various available assets as given data. In essence, the pervasive influence of risk in the investment environment has necessitated the development of models for the purpose of assessing prices and returns movements generally and by extension, investor behaviour.
The problem of valuing any asset is simplified by the existence of an active market in which all kinds of such an asset are traded. For many purposes, no formal theory of value is needed. We can take the market’s word for it.
This study examines the investment performance of a risky financial asset- common stock- in Nigeria. It intends to do this within the framework of some modern finance theories to ascertain their empirical conformity or otherwise. Most of the empirical evidence on some of these theories are essentially foreign and predominantly based on the capital markets of the western world. This study is particularly considered of interest to the researcher because of the recent wave of massive investments on the Nigerian stock market, which has been attributed primarily to increased confidence in the environment. Moreso, equities represent the largest portion of listed securities on the Nigerian Stock Exchange (NSE). The phenomenal growth in turnover, in recent times, has been attributed partly to investors’ willingness to persevere in times of uncertainty for long-term rewards.
In particular, the last decade has witnessed privatization and new minimum capital requirements. The proactive innovation of the management of the NSE has also been applauded, especially with respect to making the Nigerian Capital Market competitive globally. The Exchange had automated its delivery, clearing and settlement system in line with international practice. Despite the growth in the Nigerian Stock Exchange’s Market Capitalization it is noted that when measured as a percentage of the Gross Domestic Product (GDP), it is still quite low. For instance, it was 9.39 percent of GDP in 1999, 9.77 percent in 2000, 12.07 percent in 2001, 14.0 percent in 2002, 18.9 percent in 2003, 29.1 percent in 2004 and 35.1 percent in 2005. The performance of capital market securities should determine largely the prospects of capital inflow into the nation’s economy via portfolio investments.
In addition, the primary role of the capital market is allocation of ownership of the economy’s capital stock. In general terms, an ideal market is presumed to have prices which provide accurate signals for resource allocation such that security prices at any time reflect all “relevant” information. Such a market is described as “efficient”. As a result, most of the finance theories are built on this assumption. Specifically, this study examines the capital structure impact argument, dividend policy impact, capital asset pricing model (CAPM) and attempts to present a simplified form of arbitrage pricing theory (APT). It also examines the extent to which the price-earnings (P/E) ratio points to a stock’s growth potential as well as the inflation hedging capacity of common stocks.
Thus, the first chapter is the introduction and general background of the study. Chapter two reviews some related theories and empirical studies that are considered pertinent to this research. Chapter three presents the study methodology and data issues. Chapter four will present our data analysis, results and discussion while chapter five will summarize our findings with directions for future research.
The attributes of capital market efficiency are similar to those of efficiency in the factor or product market. Thus, capital market efficiency does not admit of monopoly or monopsony pressures. It demands the existence of effective competition amongst participants. Specifically, a capital market that is efficiently operated has two broad categories of characteristics: those relating to market conditions and those relating to investor behaviour (see, for example, Okafor, 1983:185). The former includes:
(a) Absence of any restraining influences on the price-setting mechanism i.e no price regulation and no entry and exit barrier.
(b) Unrestrained access to all relevant information about traded securities for market participants.
(c) Absence of (or, at least, minimal) transaction and information costs so as not to jeopardize investment activities that could arise from slight shifts in market opportunities.
(d) Large investors do not dominate the market.
(e) Continuity in market transactions in the sense that investors are able to execute, buy or sell orders with minimum delay.
The assumptions of market efficiency which reflect investor behaviour include the following:
(a) Investors are presumed to be risk-averse and rational (utility maximizers), so that their investment decisions are based on rational considerations and not on sentiments.
(b) Investors have adequate knowledge themselves or can secure enough advice to appreciate the significance of relevant and available information.
(c) Investors have homogeneous expectations
Based on the above restrictive assumptions, the efficient market theory (EMT) makes specific postulations regarding the behaviour of stock prices, portfolio selection, asset diversification and the pricing of capital assets (Elton et al, 2005; Cohen, et al, 2005; Brooks & Katsaris, 2003; Haliassos & Michaelides, 2003; Heaton and Lucas, 2000; Bajeux- Besnainou, et al, 2003; Fama, 1965; Fama, et al, 1969; Sharpe, 1964; Lintner, 1965a; Cecchetti, et al, 2000; Brealey and Myers 2003; etc).
We intend to gain an understanding of how the marginal investor’s decision -making process, given the receipt of information, is reflected in the market prices of securities. However, it is difficult to observe the quantity and quality of information or the timing of its receipt in the real world. Even the issue of what information is relevant to investors has been a contentious matter amongst theorists. Forsythe, Palfrey, and Plott (1982) identify four different hypotheses in this regard. Each hypothesis assumes that investors know with certainty what their own payoffs will be across time, but they also know that different individuals may pay different prices because of differing preferences.
The first hypothesis, known as naive hypothesis, asserts that asset prices are completely arbitrary and unrelated either to how much they pay out in the future or to the probabilities of various payouts. The second hypothesis, known as the speculative equilibrium hypothesis, implies that all investors base their investment decisions entirely on their anticipation of other individuals’ behaviour without any necessary relationship to the actual payoffs that the assets are expected to provide. The third hypothesis is that asset prices are systematically related to their future payouts. Called the intrinsic value hypothesis, it says that prices are determined by each individual’s estimate of the payoffs of an asset without consideration of its resale value to other individuals. The fourth hypothesis may be called the rational expectations hypothesis. It predicts that prices are formed on the basis of the expected future payouts of the assets, including their resale value to third parties. Thus, a rational expectations market is an efficient market because prices will reflect all information. In the rational expectations model, differential payoffs indicate heterogeneous expectations. Heterogeneous expectations could result from information asymmetry amongst individuals. Also, it is contentious whether market efficiency implies full aggregation or averaging of information in pricing.
A fully aggregating market is said to be consistent with the Fama’s (1970) definition of strong-form efficiency. In a fully aggregating market, even insiders who possess private information would not be able to profit by it. However, empirical evidence on insider dealing suggests that insiders can and do make abnormal returns. On this basis, it was said that capital markets do not instantaneously and fully aggregate information (Copeland and Weston, 1988).
Three broad approaches were identified by Okafor (1983:121) viz: the fundamental approach, the technical approach and the efficient market approach.
The fundamental approach assumes that every security has an intrinsic value, which is reflected by its market price. The approach assumes that basic economic facts about a firm determine the intrinsic value of securities issued by it. Without agreeing on specifics, fundamentalists use three basic performance indicators in predicting intrinsic values. These are the earnings record, some index of risk and a time-value conversion rate for funds.
The technical approach believes that security-price movements follow identifiable and recurring patterns, which could constitute a sound basis for formulating trading rules. Emphasis is laid on price movements and on the intensity and direction of such movements. The most common technique under this is charting. Although there are many different chartist theories, they all make the same basic assumption. That is, they all assume that the past behaviour of a security’s price is rich in information concerning its future behaviour. History repeats itself in that “patterns” of past price behaviour will tend to recur in the future. Thus, if through careful analysis of price charts, one develops an understanding of these “patterns, ” this can be used to predict the future behaviour of prices and in this way increase expected gains.
The efficient market approach is based on assumptions of capital market efficiency, as were earlier enumerated. Several scholars, as advocates of this approach, have assembled empirical evidence to demonstrate that trading rules based on public information do not yield abnormal returns on stock market transactions. The most vocal exposition of the approach is embodied in the random walk hypothesis, which states that the future path of the price level of a security is no more predictable than the path of a series of cumulated random numbers. In statistical terms, the theory states that successive price changes are independent, identically
distributed random variables. Most simply, this implies that the series of price changes has no ‘memory,’ that is, the past cannot be used to predict the future in any meaningful way. The random walk theory actually involves two separate hypotheses: (1) successive price changes are independent, and (2) the price changes conform to some probability distribution. Suffice to note that, of the two hypotheses, the former is the most important (Fama, 1965).
It is useful to think of stock price, Pt, as the discounted present value of expected future cash flows to stockholders:
Abbildung in dieser Leseprobe nicht enthalten
Where Et-1 denotes conditional expectation, Dt+k denotes capital gains plus dividends paid to stockholders in period t+k and 1/(1+Rt+k) captures the stockholders’ marginal rate of time and risk preference and is the cut-off rate for assessing the profitability of investment projects when the objective is to maximize the wealth of the stockholders, wealth being interpreted as their utility from consumption. This discount rate is based on information available at time t-1 (See Inanga, 1987; Schwert, 1989).
The model above clearly indicates the inverse relationship between a stock’s price and its discount rate.
Copeland and Weston (1988:116) have shown that the prices of securities depend on:
(a) Time preferences for consumption and the productivity of capital;
(b) Expectations as to the probability that a particular state will occur;
(c) Individuals’ attitudes toward risk, given the variability across states of aggregate end-of-period wealth.
The state-preference theory (SPT) is a useful way of looking at investment decisions under uncertainty. Individuals save by purchasing firm securities and firms obtain resources for investment by issuing securities. Securities are precisely defined as conditional or unconditional payoffs in terms of alternative future states of nature. All individual and firm decisions are made, and all trading occurs at the beginning of the period. Consumers maximize their expected utility of present and future consumption and are characterized by their initial endowments (wealth) and their preferences. Firms are characterized by production functions that define the ability to transform current resources into state-contingent future consumption goods; for example, where Ij is initial investment, [Abbildung in dieser Leseprobe nicht enthalten]. Total state-contingent output produced by a firm must equal the sum of the payoffs from all securities issued by a firm.
Firms maximize an objective function that, in its most general form, is maximization of the expected utility of its shareholders. To do this, managers need not be concerned with the specific preferences of their shareholders but need only know the market discount rate and the cash flows of their investment projects to make optimal investment decisions. This separation of investment/operating decisions of firms from shareholder preferences or tastes is termed the Fisher separation principle. This principle basically rests upon the assumption of efficient capital markets.
At this juncture, it suffices to present some analyses of our research problem.
Wealth is held over periods of time, and different states of nature will change the value of a person’s wealth position over time. Securities represent positions with regard to the relation between present and future wealth. Since securities involve taking a position over time, they inherently involve risk and uncertainty. This assertion aptly describes the Nigerian investment terrain, which is characterized by macro- economic instability (as depicted by high level of inflation) and policy shocks resulting, in some cases, from inconsistency in government policy formulation. Also, government policies, especially during the present democratic system, have been directed towards stimulating the pace of capital formation (economic growth) via capital inflow by encouraging expatriates to invest in Nigeria. This position is consistent with the deregulation and liberalization of the activities of market participants. The increased local and international awareness of available opportunities in the market has been cited as being partly responsible for the recent burst of investment activities in the Nigerian securities market. Furthermore, as globalisation eases cross-border capital flows and makes financial markets to assume an international posture, investors have become increasingly intolerant of the unproductive use of capital. As a result, CEOs have been under severe pressure to adopt strategies that emphasize the continued creation of shareholder value as a licence to assuring the continued provision of needed capital for their companies (Elumelu, 2003:45; Nwokoma and Olofin, 2004).
At the macro level, the foregoing issues imply that the success of the government economic reform programmes aimed at stimulating growth is contingent on the investment performance of securities in general and common stocks in particular.
In addition, the best managers as well as prudent investors, who are able to respond rationally to change, have recognized that they need more than time-honoured rules of thumb to guide them on the path of optimal decisions.
This point makes it imperative to examine, for instance, the objectivity of security values within the framework of existing finance theories. For example, studies by Fama and French (1992), Jegadeesh (1992), Kothari, et al (1995), Chan and Chui (1996), Jagannathan and Wang (1998) and Liew and Vassalou (2000) find that the relation between beta and average asset returns is not positively linear even when beta is the only regressor, and that size and book-to-market equity can help to explain the cross- sectional variation in average asset returns. However, little is known whether the evidence provided by these scholars can be found in other markets particularly the Nigeria stock market. All theories make valid points but they cannot all be true at the same time and environment.
In addition, the extent to which market indices provide accurate signals for resource allocation has been questioned in recent times. Bodie, et al (1998) in a study, quoting an article in the Wall Street Journal ( February 7, 1995) captioned “Flaws in Market Gauges Make Stocks Seem Expensive,” indicate that the justifiable P/E ratio depends on the levels of both interest and inflation rates. To a curious researcher, this creates hypothetical statements on interest and inflation rates’ impact on the P/E ratio in Nigeria; the inflation -hedging capacity of common stocks; and the significance of the P/E ratio in general.
Further, opponents of the efficient market theory (EMT) sometimes cite examples of market movements that seem inexplicable in terms of conventional theories of stock price determination. It has been argued that market perceptions could be biased or affected by opinions and sentiments. Along these lines, a number of studies in the finance literature have proposed behavioural theories to account for asset pricing anomalies. Examples include theories of overconfidence (Barberis, et.al 1998; Daniel, et. al 1998; etc), loss aversion (Barberis and Huang, 2001), and the house-money effect (Barberis, et al, 2001). Although behavioural finance has recently become a rather popular area for asset pricing research, relatively little empirical evidence exists to directly support behavioural theories and assumptions. This is due in part to the fact that behavioural models cannot be tested as easily as traditional asset pricing models. Moreover, proper assessment of behavioural theories requires detailed information on the trading strategies of various market participants (Campbell, 2000 and Coval and Shumway, 2005).
Consequently, the asymptotic assumption in this study is that capital markets are efficient.
This study attempts to present some factors that impact on the performance of common stocks (i.e. factors that affect common stock returns and prices) in the Nigerian stock market.
Specifically, the researcher aims to determine the applicability of some finance theories in the pricing of common stocks in Nigeria. In pursuance of this, an attempt would be made to resolve the capital structure impact argument, the dividend policy controversy especially through the signaling hypothesis, the CAPM debate and the inflation - hedging capacity of common stocks in Nigeria, among other issues.
The specific objectives of this research are as follows:
1) To examine, if any, the relationship between corporate financial structure and common stock returns.
2) To establish if there is any information-signaling effect of dividend payout policy in Nigeria.
3) To determine the empirical conformity of the CAPM in the Nigerian Capital Market.
4) Examination of the impact of systematic factors on equity returns and presentation of a simple model for portfolio analysis.
5) To determine the extent to which the P/E ratio captures growth opportunities rather than assets in place.
6) To examine the inflation-hedging capacity of common stocks in Nigeria.
1. Does the financial structure of companies affect the value of (or return on) common stocks?
2. What message does the corporate dividend payout policy convey to market participants in Nigeria?
3. How applicable is the CAPM in the determination of the required rate of return on equity and ultimately on the values of stocks traded on the Nigeria Stock Exchange (NSE)?
4. How do systematic factors relate to returns on equity in Nigeria?
5. How significant is the P/E ratio on the NSE?
6. To what extent does common stock investment serve as hedge against inflation?
1. Gearing is independent of common stock valuation.
2. The information content of dividend hypothesis does not hold in Nigeria.
3. Systematic factors do not jointly affect the riskiness and thus, equity returns in Nigeria.
4. A CAPM-determined price does not conform to common -stock pricing on the NSE.
5. The P/E ratio is independent of a stock’s growth potential.
6. Common stocks are not effective inflation -hedgers.
This study is restricted to the examination of the investment performance of selected common stocks in Nigeria. Fourteen (14) stocks were selected across four broad sectors of Financial, Manufacturing, Commercials and Services for the 15-year period from 1990 to 2004. The study attempts to provide answers only to issues pertinent to the specified questions. In pursuance of this, the research does not intend to:
-examine the context of marginalization of new ordinary shares in the Nigerian primary stock market.
-determine the impact of mergers and acquisition on common stock price movements.
-examine the impact of technological breakthroughs on equities or investments generally .
-determine the extent to which the stock market indices point to the nation’s economic power.
-analyse the effect of personal taxes on equity returns.
The basic issues, which form the subject of this research, have, of course, been given some attention in the fairly extensive and rapidly growing literature of finance. As far as is known, however, there is a dearth of current studies on such issues globally and particularly in Nigeria. Consequently, the research will serve as a review of such issues with specific application to Nigeria. Furthermore, in the specification of cues of assessment, this study would serve as one of the most-widely developed work on appraisal of common stock performance. More importantly, it will educate the modern day investor and financial manager about the items of information, which should constitute critical inputs in the decision process.
In addition, the study itself will serve as an input and stimulate issues for further academic discourse. It may also impact on the discerning faculties of the regulatory bodies, to grasp the nature, context and coverage of regulation as it relates to capital market investment.
Abnormal Return: Part of return that is not due to systematic influences, e.g., market wide price movements.
Absolute Priority: Rule that establishes priority of claims under liquidation.
Adverse Selection: A situation in which a pricing policy causes only the less desirable customers to do business.
Agency Theory: Theory of the relationship between principals and agents. It involves the nature of the costs of resolving conflicts of interest between principals and agents.
APT: Arbitrage Pricing Theory. An alternative to the CAPM, which assumes that returns are generated by a number of industry wide and market wide factors.
Arbitrage: Purchase of an asset and simultaneous sale of another to earn a risk-free profit.
CAPM: Capital Asset Pricing Model.
Call Option: The right - but not the obligation - to buy a fixed number of shares of stock at a stated price within a specified time.
Correlation: A standardized statistical measure of the dependence of two random variables. It is defined as the covariance divided by the standard deviations of two variables.
Cost of Equity Capital: The required return on the company’s common stock in capital markets. It is also defined as equity holders’ required rate of return because it is what equity holders can expect to obtain in the capital market. It is a cost from the firm’s perspective. Covariance: A statistical measure of the degree to which random variables move together.
Debt Capacity: Ability to borrow. The amount a firm can borrow up to the point where the firm value no longer increases.
Debt Ratio: Total debt divided by total assets.
Defeasance: A debt-restructuring tool that enables a firm to remove debt from its balance sheet by establishing an irrevocable trust that will generate future cash flows sufficient to service the decreased debt. Disintermediation: Withdrawal of funds from a financial institution in order to invest them directly.
Efficient Market Hypothesis (EMH): The prices of securities fully reflect available information. Investors buying bonds and stocks in an efficient market should expect to obtain an equilibrium rate of return. Firms should expect to receive the “fair” value (present value) for the securities they sell.
Financial Leverage (Gearing): Use of debt to increase the expected return on equity. Financial Leverage could be measured by the ratio of debt to debt plus equity.
Financial Signal: Change in market perception of a stock’s worth following variation in capital structure.
Free Cash flow: Cash not required for operations or for reinvestment.
Growth Stock: Common stock of a company that has an opportunity to invest money to earn more than the opportunity cost of capital.
Homemade Dividends: An individual investor can undo corporate dividend policy by reinvesting excess dividends or selling off shares of stock to receive a desired cash flow.
Homemade Leverage: Idea that as long as individuals borrow (and lend) on the same terms as the firm, they can duplicate the effects of corporate leverage on their own. Thus, if levered firms are priced too high, rational investors will simply borrow on personal accounts to buy shares in unlevered firms.
Idiosyncratic Risk: An unsystematic risk.
Income Stock: Common stock with high dividend yield and few profitable investment opportunities.
Inflation-Hedging: An asset is said to be an effective inflation-hedge if its actual nominal rate of return moves one-for-one with the actual rate of inflation.
Information-content Effect: The change in the stock price following a dividend signal.
Inside Information: Nonpublic knowledge about a corporation possessed by people in special (or privileged) positions.
Lintner ’ s Observations: John Lintner’s work (1956) suggested that dividend policy is related to a target level of dividends and the speed of adjustment of change in dividends.
MM Proposition I: A proposition of Modigliani and Miller (MM) which states that a firm cannot change its total value by changing its capital structure proportions. Same as Irrelevance Proposition. MM Proposition II: A proposition of Modigliani and Miller (MM) which states that the cost of equity is a linear function of the firm’s debt-equity ratio.
Market Capitalization: Price per share of stock multiplied by the number of shares outstanding.
Market Model: A one-factor model for returns where the index that is used for the factor is an index of the returns on the whole market. Multiple-discriminant Analysis (MDA): Statistical technique for distinguishing between two groups on the basis of their observed characteristics.
Pecking Order in long-term Financing: Hierarchy of long-term financing strategies, in which using internally generated cash is at the top and issuing new equity is at the bottom.
Performance Shares: Shares of stock given to managers on the basis of performance as measured by earnings per share and similar criteria-a control device used by shareholders to tie management to the selfinterest of shareholders.
Perquisites: Management amenities such as a big office, a company car or expense account meals. “Perks” are agency costs of equity, because managers of the firm are agents of the stockholders.
Pie Model of Capital Structure: A model of debt-equity ratio of the firm graphically depicted in slices of a pie that represents the value of the firm in the capital markets.
Price-to-earnings (P/E) Ratio: Current market price of common stock divided by current annual earnings per share.
Q ratio or Tobin ’ s Q ratio: Market value of firm’s assets divided by replacement value of firm’s assets.
Random Walk: Theory that stock price changes from day to day are at random; the changes are independent of each other and have the same probability distribution.
Refunding: Replacement of existing debt with a new issue of debt.
Security Market Line (SML): Line representing the relationship between expected return and market risk.
Security Market Plane (SMP): A plane that shows the equilibrium relationship between expected return and the beta coefficient of more than one factor.
Short Sale: Sale of a security that an investor doesn’t own but has instead borrowed.
Signaling Approach: Approach to the determination of optimal capital structure asserting that insiders in a firm have information that the market does not; therefore the choice of capital structure by insiders can signal information to outsiders and change firm value. This theory is also called the asymmetric information approach.
Static Theory of Capital Structure: Theory that the firm’s capital structure is determined by a trade-off of the value of tax shields against the costs of bankruptcy.
Term Structure: Relationship between interest rates on loans of different maturities.
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In the first chapter, we stated the background of this study as well as the issues of interest to this research. Again, the intention of this study is to find how certain finance theories fit well to the data in Nigeria. In achieving this noble task, reference would be made to several studies that have raised certain issues, which the researcher considers as cogent. To this end, an attempt would be made to review empirical studies and some methodologies on the wide range of issues covering this research.
The fundamental issues considered in this chapter include stock valuation models; price-earnings ratio analysis; the Nigerian stock market; theory and empirical evidence on the capital structure and cost of capital nexus; theory and empirical evidence on the dividend policy impact argument with specific emphasis on the ‘information content of dividends’ hypothesis, empirical tests of the capital asset pricing model (CAPM), some theoretical issues on common stock performance and systematic (macroeconomic) factors; comparison of the CAPM and the APT as equilibrium pricing models; volatility and asymmetries in stock returns; and the general theory of hedging against inflation with particular application to common stocks.
It is important to stress that answers to some of these phenomena depend on the assumptions of the models employed to study the problems. Under different sets of assumptions, different and even opposite answers are possible. This is extremely puzzling to the study of finance. Therefore, an attempt is made to present empirical evidence related to each of the theoretical hypotheses.
Hence this chapter is divided into ten main sections that discuss the foregoing issues, with an eleventh, which summarizes the chapter.
This section draws essentially from the fundamentalists’ approach to valuation of securities. The basic approach is to determine the intrinsic value of a security and compare such a value with the market price. The basic approach to valuation of common stock is to ascertain what constitutes the true index of common stock income, which must be capitalized or discounted to derive its intrinsic value. The finance literature documents a number of variables that qualify for consideration: dividends, capital gains, earnings, cash flow, net asset values.
Each of the above indices has been justified on the basis of the circumstances of the firm, the income orientation of the investor and his relative ability to influence the decision-making in the firm (Okafor, 1983:154).
Here, finance scholars talk about book value, liquidation value, Tobin’s q and so on (see Bodie, et al 1998:355; Tobin, 1998:146-161). The book value is the networth of a common stock according to the firm’s balance sheet. It reflects the historical value of the common stock from an accountant’s viewpoint. In effect, it reflects the net asset value of a firm as the critical variable that determines the value of its shares. Mathematically expressed:
V = f(A,L) and V_{ps} = 1/N (A - L)
Where V represents the firm value, Vps indicates the value per share, A represents the historical value of assets (which atimes could be adjusted for market realizable values), L total liabilities, and N indicates the number of outstanding shares.
The liquidation value represents the net amount that can be realized by selling the assets of the firm and paying off outstanding debt obligations. The reasoning of investment analysts along this line is that if the market price of equity drops below the liquidation value of a firm, such a firm becomes attractive as a takeover target.
Replacement value represents the cost to replace a firm’s existing assets in the current condition. Some analysts believe the market value of the firm cannot get too far above its replacement cost because, if it did, competitors would try to replicate the firm. The competitive pressure of other similar firms entering the same industry would drive down the market value of all firms until they came into equality with replacement cost (Bodie, et al; Brealey and Myers, 2003). The ratio of the market value of a firm (MV) to replacement cost (RC) is known as Tobin’s q after the Nobel prize-winning economist James Tobin. Expressed mathematically, q = MV/RC. Denoting the gross marginal product of capital by MPK and the depreciation rate by δ, the return on capital r for an interval is.
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Equilibrium in the capital market obtains when the expected return on capital E(r) is equal to the rate of return required by investors rk. This can be written from the definition of return in (2.1),
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Integrating (2.2) forward yields the familiar present value relationship.
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Equilibrium in the capital market can be viewed interchangeably as determining rk or MV, which are inversely related.
The marginal efficiency of capital R is defined implicitly by the net rate of return on replacement cost, that is,
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In the special case where MPK is constant over time RC = MPK/(R+ δ),
and MV = MPK/(rk + δ), so q can be expressed as a function of the marginal efficiency of capital and the discount rate:
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Tobin (1998) gives certain points for emphasis. First, the statistic q is observable as a ratio of market valuation to replacement cost, whereas R, rk, and δ are not easily measured. Second, the hurdle rate (discount rate) is not any observed interest rate on long-term bonds or other fixed- income value obligations. Those interest rates are the discount factors for streams of payments with the risks and other characteristics of those instruments, while rk is the discount rate for streams of return with the characteristics of earnings on business capital. The rates are related but not identical. Third, the rates rk and R are in the same interest- rate numeraire. As discount for a stream of earnings, they both would be nominal rates. As discount for a stream of earnings in constant amounts, they would be real rates. The ratio q is the same either way (Tobin, 1998: 151).
The going concern value is the amount that a company could realize if it sold its business as an operating business. Going concern value is normally expected to be higher than the liquidation value, the difference accounting for the usefulness of assets and value of intangibles (Pandey, 1999:300).
The current line of thinking among some scholars is that all these valuation parameters, subsumed under balance sheet valuation models, would constitute the critical consideration by any (potential) investor who intends to buy the bulk or majority shares in any company (refer to Maug, 1998; Allen, et al, 2000; Gompers and Metrick, 2001; Dennis and Strickland, 2002; Hotchkiss and Strickland, 2003; etc). Okafor (1983) argues that a majority shareholder could exercise a dominant influence over corporate policies. He could, through the power of his voting rights chart a fresh course for a firm’s activities. He could re-order the use of the company’s resources towards what he opines to be more viable investment outlet for the firm. Therefore, such a prospective investor would be more interested in the earnings potential (asset base) rather than in the historical earnings of a firm. By extension, this bias would be reflected in his choice among stock valuation models toward any (or all) of the aforementioned parameters. Also, the implication is that the comparison of the investor’s estimate of a stock’s real worth with the market price (or offer price for new issues or for firms going public) enables him/her to determine whether such a security is appropriately priced or not. Where the investor’s estimate exceeds the market price, the stock is considered undervalued and a good investment vehicle and vice versa (see Akintola - Bello, 2003).
This model recognizes dividends as the true index of common stock income, which must be discounted to determine the investment worth of a share of stock. This model in addition, recognizes the impact of capital appreciation on common stock values. As indicated in chapter one, this model could be expressed mathematically as.
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Where all the terms are as earlier defined. Equation (2.6) states that the stock price should equal the present value of all expected future dividends into perpetuity. This formula is also called the dividend discount model (DDM). A variant of (2.6) is where the investor has a limited investment horizon. Then
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While PH represents the expected price at the end of the desired investment horizon.
Further, depending on the trend of annual dividends, certain variations of (2.6) are recognized namely: zero-growth model; constant growth formula, super normal growth model and constant- decay model.
A zero-growth model is appropriate when the dividends are expected to be constant indefinitely or over contemplated investment horizon. In effect a stock with such a feature would be valued as perpetuity.
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A constant - growth model measures the value of a stock whose dividends are expected to grow at a constant rate, where this growth rate represents the capital gains yield and is as well the expected growth rate in stock price. This model is referred to as Gordon model, after Myron J. Gordon, who popularized the model. In this case, the stock (under the assumption of an infinite life) is valued as a growing perpetuity thus.
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The implication of (2.9) is that stock price rises as growth rate increases. Specifically, the Gordon model is built on the following assumptions (see Ross, Westerfield & Jordan 1996:164 & Akintola-Bello, 2003):
1. That the growth rate of dividends is constant
2. That the stock price grows constantly at the dividend growth rate (g)
3. That the growth rate in dividends is less than the required rate of return by stockholders (cost of equity).
4. The total rate of return is the summation of the dividend yield (defined as Et - 1 Dt/Pt-1) and the capital gains yield (defined as Et-1 Pt-Pt-1 Pt-1).
5. The expected rate of price appreciation in any year will equal the constant growth rate. Following point 4 above, E(R) = dividend yield + capital gains yield
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Many finance researchers opine that once a firm has profitable investment opportunities, it is better to lower the payout ratio, to reinvest the earnings that would otherwise have been distributed to shareholders via dividends. Such reinvestment, as they assert, would guarantee growth in the value of the company as well as its (future) earnings capacity. To these proponents, growth is a function of the retention ratio as well as the company’s rate of return on its investments. Mathematically, g = br where b is the retention ratio and r is the rate of return on the firm’s investment (or ROE if the firm is wholly equity financed). Such reinvestment of earnings is thereby seen as the myth behind the subsequent growth in a firm’s assets, which should generate growth in future dividends and is expected to be reflected in today’s share price.
In contrast, the firm whose dividends are expected to be declining as investment opportunities become less numerous, the growth rate would be negative implying the declining or decay trend.
Further, companies at early stages of their lifecycles with numerous investment opportunities are expected to achieve a supernormal growth (i.e growth in excess of what is normal from macroeconomic perspective e.g growth in excess of GDP growth rate) as a result of low payout. As investment opportunities reduce, the earnings will start growing at a decreasing rate until it reaches what is normal from industrial average or macro-economic perspective.
To value companies with temporarily high growth, analysts use a multistage version of the dividend discount model. Dividends in the early high-growth period are forecast and their combined present value is calculated. Then, once the firm is projected to settle down to a steady growth phase, the constant growth DDM is applied to value the remaining stream of dividends.
In sum, some financial analysts see the dividend valuation model as being more appropriate for valuing income stocks, defined as stocks that guarantee constant stream of income and characterized with higher dividend yield relative to capital gains.
This model emphasizes the importance of earnings as the “correct” indicator of common stock worth. It is similar in all respects, but for this difference of income index, with the dividend valuation model. Therefore, under the assumption of infinite horizon, it could be expressed thus:
Abbildung in dieser Leseprobe nicht enthalten
Where [Abbildung in dieser Leseprobe nicht enthalten] represents earnings plus capital appreciation and other terms as earlier defined.
Relative to the dividend valuation model, some investment analysts propose this model for the valuation of growth stocks defined as stocks whose payouts are low but guarantee high capital gains yield.
The underlying logic of this model is that investments should be valued by reference to the present value of expected future cash flows. In particular, it presupposes the use of expected net cash flows of the company to generate the value for total outstanding equity of a company (see Ward, 1993:53). The logical concept for valuing the company’s equity is the “free cash flow” defined as:
Free cash flow = Net operating cash flow - net investment. The free cash flow model is generally formulated in an equivalent form to the dividend based model.
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Ward opines that both dividend growth and free cash flow models allow for current cash flows to be reinvested and swapped for greater cash flows in the future. He points to the critical relationship existing between the rate of return on the reinvestment and the required (expected) return of the investors as the underlying factor that determines shareholder value creation. In particular, where the former is greater than the latter, the investors will be better off.
Various studies indicate that the cash flow valuation model helps to circumvent the problem associated with the plethora of complex accounting procedures and principles.
This approach relies on maintainable level of earnings (or dividends or cash flows) of firms in the derivation of value. In cases of infinite investment horizons, the maintainable earnings could be assumed to be an annuity in perpetuity. In that case, the maintainable earnings per share are capitalized using an appropriate rate to derive a value for the stock.
On a historical note, when the authority for price-fixing of new issues was vested in the Nigerian Securities and Exchange Commission (SEC), the SEC used this method in fixing prices for equity securities. The profit per share would be capitalized to arrive at an offer price for a new issue of equity shares. The Commission has applied the following rates of capitalization, in determining the appraised values of equity shares of companies in different sub-sectors (Okafor 1983:87-9):
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The usual practice by the Commission was to derive an average after-tax profit of a firm for a five-year track period preceding the offer. This was then used as a surrogate for the maintainable profit until the deregulation of the capital market when the function of price determination was transferred to the issuing houses.
The major distinction between this approach and the earlier discussed approaches is that it relies on historical record of earnings as against forecasts of future benefits.
In practice, Okafor opines that considerations other than straightforward accounting may be involved. A weighting system could, for instance, be applied in deriving the maintainable level of earnings, especially where trend in profit performance so justifies. Modifications could also be made to reflect the analyst’s opinion regarding a company’s asset and capital structure, inflationary levels in the economy and other qualitative variables.
The price/earnings ratio is the ratio of a stock’s price to its earnings per share. The P/E ratio determines the multiple of earnings per share (EPS) paid by a potential investor to buy a unit of equity share. In other words, it measures the price that investors are prepared to pay for each naira of earnings.
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Where Po represent stock’s price today and E1 represents expected earnings, R represents required return by stockholders and PVGO indicates the present value of growth opportunities.
Many analysts note that the P/E ratio is a reflection of the market’s optimism concerning a firm’s growth prospects. In the use of a P/E ratio, analysts normally decide whether they are more or less optimistic than the market. If they are more optimistic, they will recommend buying the stock. Looking again at the constant DDM formula, Pt = Dt+1/ (Rt - g). If 100 per cent payout is assumed, Dt+1 = Et+1 (1-b). Recall also that g = br. Hence, substituting for Dt+1 and g, we find that
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Implying that the P/E ratio for a firm growing at a long-run sustainable pace is
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It is easy to verify that the P/E ratio increases with ROE. This makes sense, because high ROE projects give the firm good opportunities for growth. Also, we can also verify that the P/E ratio increases for higher b as long as ROE (or r) exceeds R. When a firm has good investment opportunities, the market will reward it with a higher P/E multiple if it exploits those opportunities more aggressively by ploughing back more earnings into those opportunities.
Bodie, et al, summarizing the relationship between P/E ratios and growth opportunities, note that the higher the retention ratio, the higher the growth rate, but a higher retention ratio does not necessarily translate to a higher P/E ratio. A higher retention ratio is said to increase P/E only if investments undertaken by the firm offer an expected rate of return higher than the equity (market) capitalization rate. Otherwise, higher retention hurts investors because it means more money is sunk into prospects with inadequate rates of return. P/E ratios are commonly taken as proxies for the expected growth in dividends or earnings - this fact, in particular, is a common Wall Street rule of thumb in America (see also Sharpe, et al. 1999, Brealey and Myers 2003).
Some studies also indicate that one important implication of any stock valuation model is that (holding all else equal), riskier stocks will have lower P/E multiples. This can be seen in the context of the constant growth model by examining the formula for the P/E ratio.
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This fact is also said to hold well even outside the context of the constant growth model. For any expected earnings and dividend stream, the present value of those cash flows will be lower when the stream is perceived to be riskier. Hence, the stock price and the ratio of price to earnings will be lower.
In sum, an inverse relationship is said to hold between the riskiness of firms and their P/E ratios, holding all else equal. Holding growth projection fixed, the P/E multiple will be lower when the risk is perceived to be higher.
This first pitfall in P/E analysis that is usually cited in financial research is the denominator, which is accounting earnings, which are influenced by arbitrary accounting rules such as use of historical cost in depreciation and inventory valuation. Some scholars have noted that historic cost depreciation and inventory costs will tend to under- represent true economic values because the replacement cost of both goods and capital equipment will rise with the general price level.
Another confounding factor in the use of P/E ratios is related to the business cycle. There is the assumption that earnings rise at a constant rate or on a smooth trend in deriving the DDM. In contrast, earnings can fluctuate dramatically around a trend line over the course of the business cycle. The P/E ratio reported in the financial pages is the ratio of current price to the most recent earnings. Current accounting earnings can differ considerably from future economic earnings. Because ownership of stock conveys the right to future as well as current earnings, the ratio of price to most recent earnings can vary substantially over the business cycle, as accounting earnings and the trend value of economic earnings diverge by greater and lesser amounts. Because the market values the entire stream of future dividends generated by the company, when earnings are temporarily depressed, the P/E ratio should tend to be high - that is the denominator of the ratio responds more sensitively to the business cycle than the numerator.
The Nigerian Stock Exchange (NSE) was launched in 1960 as the Lagos Stock Exchange. A specific exchange floor was established on 5th June 1961. It became the Nigeria Stock Exchange in 1977 and currently has five (5) other trading floors across the country in Kaduna, Port Harcourt, Kano, Onitsha and Ibadan.
As at December 2004, there were 276 securities listed on the Exchange made up of 207 equities, 52 industrial loans/debentures, and 17 government bonds/development stock. Quoted companies represent almost every sector of the economy, due largely to a large scale privatization/commercialization programme which started around the early 1990s and has continued till now, resulting in large number of government-run enterprises being listed on the Stock Exchange.
Dealing on the NSE are made through the brokers who themselves must be approved members of the Exchange. Dealing members must be registered with the Securities and Exchange Commission (SEC) to carry on business as Issuing and/or Stockbrokerage Houses. According to the International Finance Corporation (IFC), the NSE ranked as one of the best performing markets in the world in terms of returns for 1995. This was attributed to the removal of government restrictions on investment that year. In particular the Exchange Control Act of 1962 and the Nigerian Enterprises Promotion Decree (NEPD) of 1989 were removed that year. The market grew by 128% in value in 1995 and 38% in 1996. The All-share index was 2205.0 in 1994, 5092.15 in 1995, 6992.10 in 1996 and by October 2005, it had grown to 25,871. 47 while the market capitalization closed N2.574 trillion. Some summary statistics of the stock market from 1988 to 2005 are given in table 2.1 below.
Table 2.1 Stock Market Statistics (1988-2005).
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SOURCE: THE NSE FACTBOOK (VARIOUS YEARS)
The Automated Trading System (ATS), introduced in 1999, through which trading is carried out daily is said to have improved the liquidity of the market by facilitating the matching of bid and offer prices between traders and thereby speeding up the entire trading process. The impact of automation on stock market informativeness and liquidity, and by extension a reduction in the cost of equity for listed firms has been documented in studies such as Pastor and Stambaugh (2003), O’Hara (2004), Kalay, et al, (2002) and Easley and O’Hara (2004). In a recent survey, Jain (2005) assembles the announcement and actual introduction dates of electronic trading by the leading exchanges of 120 countries to examine the impact of automation, controlling for risk factors and economic conditions. Employing dividend growth models and international CAPM, the author finds a significant decline in the equity premium, especially in emerging markets. The findings serve to establish an important linkage between market microstructure and asset prices. The results implore inclusion of both market design factors and liquidity factors into asset pricing models (Jain, 2005: 2983).
In a survey by Akpan (1995), using stock market price indices published in the Central Bank of Nigeria (CBN) Monthly and Annual Reports and Statements of Accounts (1989-1992), the author finds that share price movements tend to be systematic over time. In essence, his results refute the ‘random walk hypothesis.’ He compared the relative volatility of share prices and quantities on the NSE and the New York Stock Exchange (NYSE), using the coefficient of variation (standard deviation/mean). His results indicate that the Nigerian stock market was more volatile than the United States stock market over the period.
The results are presented hereunder:
Table 2.2 Volatility of Nigerian and United States Stock Markets, 1989-1992.
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Source: Akpan, O.E. (1995) Table 1, page 77.
Akpan also regressed the mean returns (m) of securities of seven major index portfolios (namely industrial, transport, banks, petroleum/oil, building, construction and services) against the standard deviations(s) to obtain an estimate of Nigerian investors’ risk attitude, as proxied by the slope coefficient. The results indicate an extremely high risk-return trade-off of about 3 per cent in returns per one per cent increase in risk. Further, he computes the correlation coefficients amongst sectoral returns. The correlation matrix is presented hereunder.
Table 2.3. Inter-Sector Return Correlation Matrix
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Notes: RA = Monthly return for all-shares index
R_{1} = Monthly return for industrial index
R_{T} = Monthly return for transport index R
R_{F} = Monthly return for banks index
R_{P} = Monthly return for petroleum/oil index
R_{B} = Monthly return for building index
R_{C} = Monthly return for construction index
R_{S} = Monthly return for services index
Source: Akpan, page 82
Also, regression results of each of the sectoral returns on the all-share market index (Rmt) to give a market model [as described in Paseda ,2005a) indicate opportunities for efficient diversification as encapsulated in table 2.4 below.
Table 2.4 Regression Results of Sectoral Returns on the Market Index (Rmt)
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SOURCE: Akpan, page 83.
Where
*** indicates that the coefficient is significant at 1% level.
** significant at the 5% level
* significant at the 10% level.
The implication of low coefficient of determination for returns on banks, building and construction is that risk on these securities is wholly unsystematic and as a consequence diversifiable when held in an investor’s portfolio. The portfolios with beta > I indicate a higher risk relative to the market portfolio.
Nwokoma (2002), in a recent survey on the probable long-term equilibrium relationships between a group of macroeconomic variables (such as industrial production index, the consumer price index, narrowly defined money supply-MI, and the interest rate) and the NSE all-share index, indicates that the stock market responds more to developments within it than to the changes in the macroeconomic variables.
In the light of the current wave of globalization of the world’s economies, Nwokoma and Olofin (2004) investigate the extent to which the Nigerian stock market, particularly in the post-automation era, has been financially integrated with the stock markets of the world’s key financial centres. The study rests on the notion that the existence of financial integration determines the extent to which the Nigerian capital market can offer international investors portfolio diversification benefits based on risk-return characteristics. The authors indicate positive signs of integration with other major stock markets. In addition, the impulse response analysis conducted indicates some lagged response to the US market relative to the other major stock markets, with the least effect emanating from Germany. They also suggest “the need for a greater focus by the authorities on strengthening domestic macroeconomic management, to ensure a stable macro environment as a buffer against any negative effects that may result from the ever growing trend of globalization.”(Nwokoma and Olofin, 2004:76). Other studies on Globalization and stock market nexus, though foreign based, include Kaminsky and Schmukler (2002), Masson (1998), Reinhart (2001), Stulz (1999), and Guasch and Hahn (1999).
Other Nigerian -based studies on stock market performance include Udegbunam & Oaikhenan (1999), Oludoyi (1999, 2000, 2001), Udegbunam & Eriki (2001), Edo (1997), Omole and Falokun (1999), Akintola-Bello (1993), Soyode (1991, 1993), and so on.
Soyode (1991, 1993) studied the effects of the announcements of the Structural Adjustment Programme (SAP) on the Nigerian Stock Market. His studies covered the period between 1980 and 1989. Soyode used annual data to examine the impact of macroeconomic variables, such as the exchange rate, minimum bank lending rate, and inflation rate on the average share price in the Nigerian stock market. He found that the announcement of SAP in 1986 affected the Nigerian stock market.
Oludoyi (2001) examines the extent to which share prices adjust to earning announcements in the Nigerian stock market, with the objective of assessing whether or not there is a post earnings announcement drift of returns in the market. The study indicates evidence of post earnings announcement drift because the drift persisted for at least ten weeks after firms’ earnings became public knowledge.
These selected studies that have been carried out on the capital market and other related issues are follow-ups to the existing arguments on the impact of some corporate financial policies and / or macro-economic factors and their transmission to the market. These issues constitute the main review in this chapter.
Modigliani and Miller (1958, 1963) wrote the seminal paper on cost of capital, corporate valuation and capital structure. It was David Durand who initially specified the basic issues to be considered in solving the cost of capital - capital structure linkage problem. MM assumed either explicitly or implicitly that:
- Capital markets are frictionless.
- Individuals can borrow and lend at the risk-free rate.
- There are no costs to bankruptcy
- Firms issue only two types of claims: risk-free debt and (risky) equity.
- All firms are assumed to be in the same risk class.
- Corporate taxes are the only form of government levy (i.e there are no wealth taxes on corporations and no personal taxes).
- All cash flow streams are perpetuities (i.e no growth).
- Corporate insiders and outsiders have the same information (i.e, no signaling opportunities)
- Managers always maximize shareholder’s wealth (i.e., no agency costs).
In spite of the restrictive nature of these assumptions, empirical evidence has found that relaxing many of them does not really change the major conclusions of the model of firm behaviour that was provided by Modigliani and Miller. Relaxing the assumption that corporate debt is risk-free will not change the results (see Copeland and Weston, 1988: 462-471). However, the assumptions of no bankruptcy costs and no personal taxes are critical because they alter the implications of the model. The last two assumptions rule out signaling behaviour-because insiders and outsiders have the same information; and agency costs - because managers never seek to maximize their own wealth (Bushman , et.al, 2005; Chae, 2005; Piotroski and Roulstone, 2004;Cohen, et al, 2003 and so on).
Specifically, the MM theorem states that a firm’s valuation should be independent of its financial structure, implying that a firm could theoretically estimate the required rate on a new investment just by looking at the stock market and observing the market’s valuation of equities whose distribution of earnings are proportional to those on the contemplated investment. Again, Tobin asserts that there are important reasons why the valuation of a firm’s assets cannot be divorced from its financial structure. These include corporate income taxation, which is not neutral regarding debt interest and dividends; the implications of leverage for probability of bankruptcy and loss of control; and economies of scale in borrowing, which enable stockholders to borrow more cheaply through the corporation than individually.
In contrast to the traditionalist view which assumes the presence of an optimal capital structure (with a judicious use of debt), the MM theory posits that no such optimal structure exists -- all structures being equivalent from the point of view of the cost of capital (Modigliani and Miller, 1958:278).
The MM hypotheses can be best explained by their propositions I and II. Their proposition I asserts that the market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the rate P k appropriate to its class. Equivalently stated , the average cost of capital to any firm is completely independent of its capital structure and is equal to the capitalization rate of a pure equity stream of its class. In essence VL = VU (however, with corporate taxes, MM assert that VL = VU + (plus) the present value of the interest tax shield on debt). Proposition II, derived from Proposition I, states thus:
the expected yield of a share of stock is equal to the appropriate capitalization rate P k for a pure equity stream in the class, plus a premium related to financial risk equal to the debt-to-equity ratio times the spread between P k and r D . In essence, the expected yield on a share of stock increases linearly with leverage. That is, rE = P k + (P k - rD) Dj/Ej without corporate taxes; or rE = P k + (1 - c) (P k - rD) Dj/Ej with corporate taxes.
Figure 2.1 below compares the MM theory with the traditionalists’ position (without taxes)
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Traditionalists believe there is an optimum D-E ratio that minimizes rA Figure 2.1: MM Theory vs the Traditionalists.
Note: the thick lines show MM’s view of the effect of leverage on the expected return on equity (rE) and the weighted average cost of capital
(rA). The dashed lines show the traditional view. Traditionalists say that borrowing at first increases rE more slowly than MM predict but that r_{E} shoots up with excessive borrowing. If so, a prudent use of debt would minimize the overall cost of capital.
MM’s tax-corrected view suggests that firms would adopt a target debt ratio so as not to violate debt limits imposed by lenders. In addition, the existence of personal taxes and costs of financial distress have been cited in the finance literature as possible offsetting measures to the interest tax shield advantage of corporate debt.
Consequent on the ‘tax corrected’ version of the MM hypothesis, the gain from leverage, G is the differences between the value of the levered and unlevered firms, which is the product of the corporate tax rate and the market value of debt. Miller (1977) modifies this result by introducing personal as well as corporate taxes into the model, in an attempt to bring it closer to the real world. The basis for the argument is that the firm’s objective is no longer to minimize the corporate tax bill but to minimize the present value of all taxes paid on corporate income. “All taxes” include personal taxes paid by bondholders and stockholders. Under this stated assumption, the value of a levered firm can be expressed as
Abbildung in dieser Leseprobe nicht enthalten
Where Vu represents value of an unlevered firm of equivalent risk,[Abbildung in dieser Leseprobe nicht enthalten] represents corporate tax, PD represents the personal tax rate on bond income and D = INT [Abbildung in dieser Leseprobe nicht enthalten], the market value of debt. Consequently, with the introduction of personal taxes, the gain from leverage is the second term in (2.14) (see Copeland and Weston, 1988:497). It is important to emphasize that where both debt and equity income are taxed at the same effective personal rate (i.e where pe = PD), the gain from leverage equals the product of the corporate tax rate and the market value of debt (hence, the impact of personal taxes can be ignored). Further, (2.14) implies that the gain from leverage vanishes when:
Abbildung in dieser Leseprobe nicht enthalten
When personal tax rate on stock is nil, then gain from leverage becomes
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Miller’s argument has important implications for capital structure. First, the gain to leverage may be much smaller than previously thought. Consequently, optimal capital structure may be explained by a trade off between a small gain to leverage and relatively small costs such as expected bankruptcy costs. Second, the observed market equilibrium interest rate is seen to be a before - tax rate that is “grossed up” so that most or all of the interest rate tax shield is lost. Finally, Miller’s theory implies there is an equilibrium amount of aggregate debt outstanding in the economy that is determined by relative corporate and personal tax rates.
Thus, we can summarise MM’s and Miller’s models as follows. Under MM’s model, the existence of corporate taxes provides a strong incentive to borrow. In fact, it is ideal for a company to have 100 per cent debt ratio. They ignore personal taxes. Miller’s model considers both the corporate as well as the personal taxes. It concludes that the advantage of corporate leverage is reduced by the personal tax loss (resulting from higher personal tax rate on bond income relative to personal tax rate on common stock income). The important implication of the model is that there is no optimum capital structure for a single firm, although for the macro-economy, there exists equilibrium amount of aggregate debt. From a single firm’s point of view, therefore, the capital structure does not matter. Miller’s perpetual tax shield formula has served as one of the major references for those evaluating whether taxes can explain observed financing patterns. This formula is a cornerstone of the static trade-off theory, which posits that firms weigh the tax benefits of debt against the costs associated with financial distress and bankruptcy. This model has provided intuition and guidance for much of the empirical literature on corporate capital stricture, which has uncovered several patterns in the data that are inconsistent with the static trade-off theory (Hennessy and Whited, 2005:1129).
Graham (2000), for instance, finds that, “paradoxically, large, liquid, profitable firms with low expected distress costs use debt conservatively.” By debt ‘conservatism’, Graham means that firms fail to issue sufficient debt to drive their expected marginal corporate tax rate down to that consistent with a zero/low net benefit to debt based on the Miller formula. Also, Baker and Wurgler (2002) reject the trade-off theory on different grounds stating, “the trade-off theory predicts that temporary fluctuations in the market to book ratio or any other variable should have temporary effects.” Based on finding a negative relationship between leverage and an “external finance weighted average market to book ratio,” they conclude that “capital structure is the cumulative outcome of attempts to time the equity market.”
Miller’s model has certain limitations (Pandey, 1999:702): First, it implies that tax exempt persons/institutions will invest only in debt securities and ‘high-tax bracket’ investors in equities. In practice, investors hold portfolio of debt and equity securities. Second, the personal tax rate on equity income is not zero. As long as tpe is positive, more investors can be induced to hold debt securities. Third, investors in high-tax brackets can be induced to invest in debt securities indirectly. They can invest in those institutions wherefrom income is tax exempt. These institutions, in turn, can invest in the corporate bonds.
Those ‘controversial assumptions’ upon which Miller’s model is said to be built make most scholars still believe that in balance, there is a tax advantage to corporate borrowing (DeAngelo and Masulis, 1980; Graham, 1996a; 1996b; 2000;Graham, et al, 2002;Graham and Rogers, 2002; Korajczyk and Levy, 2003; Johnson, 2003; Lamont and Polk, 2001; etc).
DeAngelo and Masulis (1980) extend Miller’s work by analyzing the effect of tax shields other than interest payments on debt, e.g, non cash charges such as depreciation, oil depletion allowances, and investment tax credits. They are able to demonstrate the existence of an optimal (nonzero) corporate use of debt while still maintaining the assumption of zero bankruptcy (and zero agency) costs.
Their original argument is illustrated in figure 2.2. The corporate debt supply curve is downward sloping to reflect the fact that the expected marginal effective tax rate, ic, differs across corporate suppliers of debt. Investors with personal tax rates lower than the marginal individual earn a consumer surplus because they receive higher after-tax returns. Corporations with higher tax rates than the marginal firm receive a positive gain to leverage, a producer’s surplus in equilibrium because they pay what is for them a low pre-tax debt rate.
The idea that investment tax credits and depreciation expenses do serve as tax shield substitutes for interest expenses has a deal of theoretical appeal. The DeAngelo and Masulis model predicts that firms will select a debt level that is inversely related to the level of available tax shield substitutes. Also, with increase in leverage, the likelihood of winding up with zero or negative earnings will increase, thereby causing the interest tax shield to decline in expected value. They further show that, with bankruptcy costs, there will be an optimum tradeoff between the marginal expected benefit of interest tax shields and the marginal expected cost of bankruptcy.
Abbildung in dieser Leseprobe nicht enthalten
Figure 2.2: Aggregate Debt Equilibrium with Heterogeneous Corporate And Personal Tax Rates.
Where ro represents the rate paid on debt of tax-free institutions (e.g return on municipal bonds).
Financial distress occurs when promises to creditors are broken or honoured with difficulty (Brealey and Myers, 2003:497). Sometimes, financial distress leads to bankruptcy. Sometimes, it only means, “skating on thin ice.” Financial distress could be very expensive. The firm may have to sell its assets at distress’ prices. More important consideration is the inflexibility of raising funds when needed if the firm has a heavy ‘debt overhang.’ Non-availability of funds on acceptable terms could adversely affect the operating performance of the firm.
Financial distress has many indirect costs as well. It has a great effect on management’s attitude. The shareholders may like the management to invest in risky, marginal projects so that debtholders’ wealth is transferred. Management may also avoid investment in profitable projects since, under an insolvency or distress, debtholders are likely to benefit more from such investments. A financially distressed firm also has a tendency to emphasize short-term profitability at the cost of longterm solvency and stability (Pandey, 1999:703).
Copeland and Weston (1988) document some attempts made by scholars such as Baxter in 1967, Stiglitz in 1973, Kraus and Litzenberger in 1973, Warner in 1977, Kim in 1978, among others, to demonstrate the impact and significance of bankruptcy costs on the optimal capital question. Most of the evidence obtained suggests an optimal leverage as determined by taking on increasing amounts of debt until the marginal gain from leverage is equal to the marginal expected loss from bankruptcy costs. The optimal capital structure minimizes the weighted average cost of capital and maximizes the firm value. Thus, the value of a levered firm is given as follows:
Abbildung in dieser Leseprobe nicht enthalten
This is the traditional trade-off theory of capital structure (see Brealey and Myers, 2003: 508-10; Fama and French, 1998; Wald, 1999; Shyam - Sunder and Myers, 1999).
Expressed diagrammatically.
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Figure 2.3: Value of levered firm under corporate taxes and financial distress.
Figure 2.3 shows that the present value of the interest tax shield (PVINT) increases with leverage but so does the present value of the costs of financial distress (PVFD). However, the costs of financial distress are quite insignificant with moderate level of debt, and therefore, the firm value increases with debt. With more and more debt, the costs of financial distress increases and therefore, tax benefit shrinks. The optimum point is reached when the present value of the tax benefit becomes equal to the present value of the costs of financial distress.
Evidence on indirect bankruptcy costs is provided by Altman (1984). Admittedly, because indirect costs are opportunity costs (what might have happened in the absence of bankruptcy proceedings), they are difficult to estimate. Altman provides an estimate (for a sample of 19 firms, 12 retailers and 7 industrials, that went bankrupt between 1970 and 1978) that compares expected profits, computed from time series regressions with actual profits. The arithmetic average indirect bankruptcy costs were 8.1% of firm value three years prior to bankruptcy and 10.5% the year of bankruptcy. A second method uses unexpected earnings from analysts’ forecasts for a sample of 7 firms that went bankrupt in the 1980-1982 interval. Average indirect bankruptcy costs were 17.5% of value one year prior to bankruptcy. Altman’s evidence suggests that total bankruptcy costs (direct and indirect) are sufficiently large to give credibility to a theory of optimal capital structure based on the trade-off between gains from leverage-induced tax shields and expected bankruptcy costs. Also Weiss, 1990 who studied 31 firms that went bankrupt between 1980 and 1986 and found average costs of about 3 percent of total book assets and 20 percent of the market value of equity in the year prior to bankruptcy. Further, a study by Andrade and Kaplan (1998) of a sample of troubled and highly leveraged firms estimated costs of financial distress amounting to 10 to 20 percent of predistress market value (see also Weiss and Wruck, 1998). Graham and Rogers (2002) show that risk-management activities impact firms’ debt choice and can cause a firm engaged in risk management to respond differently to a change in its fundamental risk. Korajczyk and Levy (2003) find that only unconstrained firms are able to adjust their capital structures to time their issue choice. Baker, et al. (2003) provide a rationale for why endogeneity might be less severe when firms are financially constrained (or equity dependent). Johnson (2003) uses a simultaneous equation approach to find that shorter debt maturity attenuates the negative effect of growth opportunities on leverage. In an attempt to investigate whether firms are indeed underleveraged or whether there are alternative explanations, Molina (2005) studies the effect of firms’ leverage on default probabilities as represented by the firms’ ratings. Using an instrumental variable approach, the author finds that the leverage’s effect on ratings is three times stronger than it is if the endogeneity of leverage is ignored. This stronger effect, according to the author, results in a higher impact of leverage on the ex ante costs of financial distress, which can offset the tax benefits estimated by Graham (2000). The results in Graham and Harvey’s(2001) survey are consistent with the view that leverage and ratings are jointly determined; managers refer to ratings as one of the most important factors that they take into account when making capital structure decisions.
Hirshleifer and Myers were among the first authors to apply state preference theory to corporate finance problems. Banz and Miller in 1978 have demonstrated, through estimates of “state prices,” that the SPM can be used to analyze financing decisions. Table 2.5A presents some symbols employed in such analysis.
Table 2.5A. Symbols Used in the SPM Analysis of Capital Structure Decisions
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In the capital structure analysis, three broad categories of alternative outcomes are usually identified. The outcomes are defined by the amount of net operating income achieved in relation to the amount of the debt obligations incurred (Copeland and Weston, 1988:140). These three alternative outcomes are specified by column (1) in Table 2.5B below. Table 2.5B Amounts Received Under Alternative Outcomes
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Under outcome 1, the state-dependent net operating income, Xs, is equal to or greater than the amount of the debt obligations, D. Debt holders will receive the total amount of promised payments, D. Equity holders will receive the after -tax income remaining after the debt payments. The amounts received by debt holders and equity holders are listed in columns (2) and (3) respectively.
Under outcome 2, the state-dependent net operating income is less than D but non-negative. Debtholders will receive the net operating income less bankruptcy costs that may be incurred. Shareholders will receive nothing. If the state dependent income is negative, neither debt holders nor stockholders will receive anything.
In Table 2.5C, the applicable state prices are multiplied times what the debt holders and shareholders receive under alternative outcomes to determine the respective values of receipts in each state. The value of the firm in each state is the sum of the market value of debt and the market value of equity.
Table 2.5C Formulas For the Value of the Firm Under Alternative Outcomes.
Abbildung in dieser Leseprobe nicht enthalten
The first application of signaling to finance theory has been put forth by Ross (1977). He suggests that implicit in the MM irrelevancy proposition is the assumption that the market knows the (random) return stream of the firm and values this stream to set the value of the firm. What is valued in the market place, however, is the perceived stream of returns for the firm. This raises the possibility that changes in the capital structure may alter the markets perception. In MM terminology, by changing the financial structure, the firm alters its perceived risk class even though the actual risk class remains unchanged.
Managers, as insiders who have monopolistic access to information about the firm’s expected cash flows, will choose to establish unambiguous signals about the firm’s future if they have the proper incentive to do so. It’s a known fact that managers are prohibited (perhaps by capital market regulations) from insider dealing. This prevents them from profiting by issuing false signals, such as announcing bad news and selling short even though they know the firm will do well.
In a simple one-period model, the manager’s compensation, M, paid at the end of the period may be expressed as:
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Where y_{o}, y_{1} = positive weights,
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The incentive-signaling approach suggests that management might choose real financial variables such as financial leverage or dividend policy as the means of sending unambiguous signals to the public about the future performance of the firm. These signals cannot be mimicked by unsuccessful firms because such firms do not have sufficient cash flow to back them up and because managers have incentives to tell the truth. Without management incentives to signal truthfully, there would be no signaling equilibrium. Chowdhury and Miles (1990) apply the concept to financial structure and dividend policy and provide strong support for the signaling role of dividends and firms’ debt-equity changes. This is consistent with Ross’s paper, which suggests that greater financial leverage can be used by managers to signal an optimistic future for the firm.
Myers and Majluf (1984) present a signaling model that combines investment and financing decisions. Managers are assumed to know more about their companies’ prospects, risks and values than do outside investors. Further, they are assumed to act in the interest of “old” stockholders, i.e; those who hold shares in the firm at the time a decision is made. Finally, the ‘old’ shareholders are assumed to be passive in that they do not actively alter their personal portfolios to undo the management’s decision ( see Copeland and Weston, 1988:503-507 for details of the analysis). The Myers-Majluf paper points out that if the firm uses its available liquid assets to finance positive NPV projects, then all positive NPV projects would be undertaken because no new equity is issued and the information asymmetry problem is thereby resolved. They suggest that this may be a good reason for carrying excess liquid assets. They also suggest that debt financing, which has payoffs less correlated with future states of nature than equity, will be preferred to new equity as a means of financing. Myers (1984) suggests a pecking order theory for capital structure. Asymmetric information yet accounts for the choice between internal and external financing and between new issues of debt and equities. Pecking order theory implies that investment is financed first with internal funds (primarily retained earnings/available liquid assets); then by new issues of debt, and finally with new issues of equity. New equity issues are a last resort when the company runs out of debt capacity, that is, when the threat of costs of financial distress brings regular ‘insomnia’ to existing creditors and to the financial manager.
The pecking order theory does not specify a well-defined target debt- equity mix, because there are two kinds of equity, internal and external, one at the bottom of the pecking order and one at the top. Each firm’s debt ratio reflects its cumulative requirements for external finance (Myers, 2001:81; Brealey and Myers, 2003:513). This theory is said to explain why the most profitable firms generally borrow less - not because they have low target debt ratios but because they don’t need ‘outside’ funds. Less profitable firms issue debt because they do not have internal funds sufficient for their capital investment programs and because debt financing is first on the pecking order of external financing. Further, in this theory, the attraction of interest tax shields is assumed to be a second-order effect. Debt ratios change when there is an imbalance of internal cash flow, net of dividends, and real investment opportunities. Highly profitable firms with limited investment opportunities work down to low debt ratios. Firms whose investment opportunities outrun internally generated funds are driven to borrow more and more. This theory also explains the inverse intra-industry relationship between profitability and financial leverage. Suppose firms generally invest to keep up with the growth of their industries, then rates of investments will not be dissimilar within an industry. However, given sticky dividend payouts, the least profitable firms will have less internal funds and will end up borrowing more.
The pecking order seems to predict changes in many mature firms’ debt ratios. These debt ratios increase when the firms have financial deficits and decline when they have surpluses. (Shyam-Sunder and Myers, 1999).
However, the pecking order is less successful in explaining interindustry differences in debt ratios. Along this line, Brealey and Myers note, for example, that “debt ratios tend to be low in high-tech high-growth industries, even when the need for external capital is great. There are also mature, stable industries - electric utilities, for example - in which ample cash flow is not used to pay down debt. High dividend payout ratios give the cash flow back to investors instead .”
Implicit in the assumptions made thus far is that the interests of the firm’s managers and its shareholders are perfectly aligned, and that corporate financial decisions are in the shareholders’ interest. This may be implausible in theory and far from practice. Michael Jensen and William Meckling, in 1976, have used agency costs to argue that the probability distribution of cash flows provided by the firm is not independent of its ownership structure and that this fact may explain the case for optimal leverage. They suggest that, given increasing agency costs with higher proportions of equity on the one hand and higher debt proportions on the other, there is an optimum combination of outside debt and equity that will be chosen because it minimizes total agency costs. In this way, it could be argued that an optimum financial structure can exist even in a world without taxes and bankruptcy costs. (Copeland and Weston, 1988; Myers, 2001:95). Agency costs of external equity are assumed to decrease as the percentage of external equity decreases, and the agency costs of debt are assumed to increase. If the agency costs of external equity are very low, as may be the case for a widely held firm, then optimal capital structure can result as a trade-off between the tax shelter benefit of debt and its agency cost.
It is within this framework of agency costs that the free cash flow theory evolved. The free cash flow theory says that dangerously high debt levels will increase value, despite the threat of financial distress, when a firm’s operating cash flow significantly exceeds its profitable investment opportunities. The free cash flow theory is designed for mature firms that are prone to overinvest (Myers, 2001:81). Myers (2001) considered the costs of probable conflicts between debt holders and stockholders on one hand and managers and stockholders on the other. A pervasive recent manifestation is that debt, by restricting the availability of free cash flow at a manager’s disposal, serves to constrain the manager’s incentive to pursue personal agenda at the expense of value maximization. This fact has been expressed in Jensen (1986) and underlies studies such as Zwiebel (1996), Stulz (1990), Hart and Moore (1995) and Novaes (2003).
Michael Jensen stressed the tendency of managers with ample free cash flow (or unnecessary financial slack) to plough too much cash into mature businesses or ill-advised acquisitions. “The problem,” Jensen says, “is how to motivate managers to disgorge the cash rather than investing it below the cost of capital or wasting it in organizational inefficiencies.” (Jensen, 1986:323).
Zwiebel (1996) develops a model in which managers voluntarily choose debt to creditably constrain their own future empire building. Dynamically consistent capital structure is derived as the optimal response in each period of partially entrenched managers’ trading-off empire-building ambitions with the need to ensure sufficient efficiency to prevent control challenges. He argues that if debt serves to constrain managers’ access to free cash, one should never expect to see managers voluntarily making dividend payments. Managerial optimality rather than shareholder optimality was used as the basis of deriving an optimal capital structure. A policy of dividend payments coordinated with debt follows, cum implications for the level, frequency, and maturity structure of debt as a function of outside investment opportunities. Additionally, the Zwiebel model yields new testable implications for security design, and changes in debt and empire-building over managerial careers.
Novaes (2003) indicates that in the value-maximizing approach, antitakeover amendments reduce the sensitivity of leverage to entrenchmentrelated variables. Other recent studies on capital structure theory include Booth, et al, 2001; Goldstein, et al, 2001; Green and Hollifield, 2003; Morellec, 2004; Datta, et al, 2005; Leary and Roberts, 2005; Berger, et al, 2005; and Miao, 2005.
There are two broad approaches to empirical tests of capital structure. First are cross-sectional studies that attempt to explain observed financial leverage as a function of the firm’s tax rate, its non-debt tax shields, its potential for agency costs (e.g., whether it produces durable goods or has specialized labour), its operating leverage, its systematic risk, etc. Here, the incremental impact of each of these variables on financial leverage helps to separate the conflicting theories of capital structure. The second broad approach is time series data that looks at the relationship between changes in leverage and simultaneous changes in the value of debt and equity on the announcement of a leverage changing event.
Modigliani and Miller (1958) use cross-section equations on data taken from 43 electric utilities (Allen’s utilities) during 1947-1948 and 42 oil companies (Smith’s oil companies) during 1953. They estimate the weighted average cost of capital as net operating cash flows after taxes divided by the market value of the firm. When regressed against financial leverage (measured as the ratio of the market value of debt to the market value of the firm), the results were:
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Oil companies: WACC = 8.5 + .006d, r = .04
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where d is the financial leverage and r is the correlation coefficient. Figures in parentheses are standard errors. These results suggest that the cost of capital is not affected by capital structure and therefore that there is no gain to leverage. This test confirms their proposition 1.
Next, to test the proposition II, MM regressed the expected yield on common stock (defined as average net income divided by average market value of common stock) on the debt -equity ratio
The results were:
Electric utilities: r_{E} = 6.6 + .017h, r = .53
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Oil companies: r_{E} = 8.9 + .051h, r = .53
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where h is the debt -equity ratio. These results suggest that the cost of equity increases linearly with leverage (debt-equity ratio). In order to test for the direction of curvature, MM add a square term and obtain the following estimates (MM, 1958:288):
Electric utilities r_{E} = 4.6 + .004h - .007h^{2}
Oil companies r_{E} = 8.5 + .072h - .016h^{2}
For both cases, the curvature is negative, implying rising cost of borrowed funds and runs counter to the traditional hypothesis.
However, the authors emphasize caution interpreting their results especially with regard to the proposition II test, “partly because of possible statistical pitfalls and partly because not all factors that might have a systematic effect on stock yields have been considered.”
Several studies have criticized the MM results on at least two counts. First, the oil industry is seen as heterogeneous in business risk (operating leverage); second, the valuation model from which the cost of capital is derived assumes that cash flows are perpetuities that do not grow. Copeland and Weston report Weston’s study in 1963, which took account of the stated omissions. The result for electric utilities, with growth inclusion, becomes:
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where A is the book value of assets (a proxy for firm size), and E is the compound growth in earnings per share (1949-1959). Since WACC decreases with leverage, the results are consistent with the existence of a gain from leverage i.e., that the tax shield on debt has value. A subsequent study by Miller and Modigliani (1966) also found results (based on a sample of 63 electric utilities in 1954,1956 and 1957) that were consistent with a gain from leverage (see Copeland and Weston, 1988: 517-518). Several empirical evidence indicate that the tax subsidy on debt does contribute a significant amount to the value of the firm. This is consistent with the notion that the firm’s WACC falls as leverage increases.
Cordes and Sheffrin (in 1983) use Treasury Department data to examine cross-sectional differences in effective tax rates that may be caused by tax carry-backs and carry-forwards, by foreign tax credits, by investment tax credits, by the alternate tax on capital gains, and by the minimum tax. They found significant differences across industries with the highest effective rate for tobacco manufacturing (45%) and the lowest rate (16%) for transportation and agriculture. This tends to support the DeAngelo- Masulis (1980) contention that the gain from leverage-induced tax shields can be positive.
Hamada (in 1972) tests proposition II by combining MM theory with the CAPM. He finds that on average, the systematic risk of the levered firm is greater than that for the unlevered firm [Abbildung in dieser Leseprobe nicht enthalten]. This is consistent with the increased risk associated with higher leverage.
Bradley, Jarrell and Kim regressed leverage against
(1) earnings volatility as a proxy for bankruptcy risk, (2) the ratio of depreciation plus investment tax credits to earnings as a proxy for non-debt tax shields, and (3) the ratio of advertising plus research and development expenditures to net sales as a proxy for noncollateralizable assets.
The first and third variables were significantly negative, supporting the importance of bankruptcy costs and collateral; but the second variable was significantly positive, seeming to be inconsistent with debt as a tax shield. Long and Malitz estimate a similar regression but add several explanatory variables. They obtain results similar to Bradley, et al but find non-debt tax shields to be negatively related to leverage, although not significant. Titman and Wessels employ linear structure modeling to explicitly accommodate explanatory variables as proxies for their theoretical counterparts. Their results show that asset uniqueness and profitability were significantly negatively related to leverage. This result supports the Myers- Majluf (1984) pecking order theory, because more profitable firms will tend to use less external financing. It also supports the Titman (1984) idea that firms with unique assets can carry less debt owing to agency costs (Copeland and Weston, 1988:519).
The time-series studies have emphasized the announcement effects of changes in leverage. This underlies the plausibility of the signaling hypothesis. Empirical studies document that leverage-increasing exchange offers have significant positive announcement effects. Exchanges of debt-for-debt, studied by Dietrich have no significant effect on shareholders’ wealth, and leverage-decreasing exchange offers have a significant negative effect.
Stock repurchases and seasoned equity offerings are at the opposite end of the scale. Evidence by Masulis and Kowar, Asquith and Mullins, Mikkelson and Partch, and Kolodny and Suhler indicates that issue of seasoned equity are interpreted as bad news by the marketplace, with significantly negative announcement date effects on equity prices. This result is consistent with the pecking order theory. Firms will resort to equity issues only as a last resort. The negative announcement date residuals are large for industrial firms that issue equity infrequently (- 3.2%) and small for utilities that are frequent issuers (-.6%). This is also consistent with the pecking order theory. Shyam-Sunder and Myers (1999) use a panel of 157 firms from 1971 to 1989 and found support for both the pecking order and tradeoff theories. Each showed impressive statistical significance. Stock repurchases are at the opposite end of the spectrum. They increase leverage and they are interpreted as favourable signals about the future prospects of the firm (Myers, 2001:93-94, Copeland and Weston:522).
All leverage-decreasing events have negative announcement effects, and all leverage-increasing events, save one, have positive announcement effects. The exception is the new issue of debt securities where Dann and Mikkelson; Eckbo; and Mikkelson and Partch found negative but insignificant announcement effects. This result is also consistent with the pecking order theory. The majority of corporate events with no leverage change had insignificant announcement effects.
Announcements with favourable (unfavourable) implications for the future cash flows of the firm such as investment increases (decreases) and dividend increases (decreases) were accompanied by significant positive (negative) effects on shareholders’ wealth. Events that both increase leverage and provide a favourable signal about the future prospects of the firm, common stock repurchases, and debt-for -common exchange offers seem to have the largest positive announcement effects (Copeland and Weston:523).
The capital structure relevance is one of the most difficult empirical issues in finance. This section has attempted to review the theory and application in different contexts. The broad issues relate to the relevance and optimality in financial structure decisions of corporations. In a world without taxes, MM (1958) posit that the value of a firm is independent of its capital structure. With taxes, MM (1963) imply optimality in capital structure at 100% debt. Miller’s (1977) study indicates that when personal taxes are also introduced, the value of any specific firm is unaffected by leverage. The DeAngelo- Masulis (1980) study indicates the existence of optimal capital structure arising from available tax shield substitutes while assuming zero bankruptcy and zero agency costs. With positive bankruptcy costs, they indicate an optimum trade off between the marginal expected benefit of tax shields and the marginal expected cost of bankruptcy. This tradeoff issue underlies the traditional trade-off theory, which emphasizes taxes and financial distress. The personal tax disadvantage of debt is said to offset to some degree the corporate tax advantage. The trade-off theory, by balancing the tax advantages of borrowing against the costs of financial distress, suggests that firms with safe, tangible assets and plenty of taxable income to shield ought to have high targets. On the other hand, unprofitable companies with risky, intangible assets ought to rely primarily on equity financing. This theory of capital structure successfully explains many industry differences in capital structure, but it does not explain why the most profitable firms within an industry generally have the most conservative capital structures. Under the trade-off theory, high profitability should mean high debt capacity and a strong corporate tax incentive to use that capacity.
The pecking order theory states that firms use internal financing when available and choose debt over equity when external financing is needed. This explains why the less profitable firms in an industry have high debt ratios - not because they have higher target debt ratios but because they need more external financing and because debt is next on the pecking order when internal funds are exhausted. The pecking order is a consequence of asymmetric information. Managers are assumed to know more about their firms than outside investors do, and they are reluctant to issue stock when they believe the price is too low. They try to time issues when shares are fairly priced or overpriced. Investors are said to understand this and interpret a decision to issue shares as bad news. That explains why stock price usually falls when a stock issue is announced. In sum, the pecking order theory says that equity will be issued as a last resort (i.e., when debt capacity is running out and financial distress threatens). Refer to Heron and Lie (2004) for an empirical evidence on this.
However, while this theory does explain why most external financing comes from debt and why changes in debt ratios tend to follow requirements for external financing, it does not explain cases of equity issues by firms that could easily have borrowed.
The pecking order theory stresses the value of financial slack (i.e. abundant liquid assets). Without sufficient slack, the firm may be caught at the bottom of the pecking order and be forced to choose between issuing undervalued shares, borrowing and risking financial distress, or passing up positive-NPV investment opportunities (Almeida, Campello and Weisbach, 2004).
The free cash flow theory identifies the “dark side” of financial slack. Surplus cash or credit could tempt managers to overinvest or to indulge an easy and glamorous corporate lifestyle. Given the latter, a high debt ratio is said to help disgorge cash and prods managers and organizations to try harder to be more efficient. The free cash flow theory says that dangerously high debt levels will increase value, despite the threat of financial distress, when a firm’s operating cash flow significantly exceeds it profitable investment opportunities.
These three theories of optimal capital structure (trade-off theory, pecking order and free cash flow) differ in their relative emphases on, or interpretations of, taxes, information asymmetry and agency costs. The trade-off theory emphasizes taxes, the pecking order theory emphasizes differences in information and the free cash flow theory emphasizes agency costs. The interested reader is referred to Myers (2001) and Fama and French (2002) for an orderly review of these theories cum the basis for empirical tests.
Other matters of empirical studies include issues such as the effect of other financial instrument (i.e., warrants, convertible bonds, call provisions, preferred stock, committed lines of credit, etc) on the cost of capital; unification of MM and the CAPM; the maturity structure of debt; option pricing implications for capital structure - the bondholder wealth expropriation hypothesis, contractual methods for reducing agency costs; bond indenture provisions and bond ratings among other issues. It’s important however, to note that the major empirical issue is the impact of the capital structure on the value of the firm and on the weighted average cost of capital.
The capital structure theory shows that in a world without taxes, agency costs, or information asymmetry, repackaging the firm’s net operating cash flows into fixed cash flows for debt and residual cash flows for shareholders has no effect on the value of the firm. The dividend policy argument is a variant of the impact of financing decision on the firm’s value. Miller and Modigliani (1961) present an argument that a firm’s value is unaffected by dividend policy. This was based on assumption of absence of taxes, agency costs and information asymmetry. Even when their argument was extended to a valuation model with growth and corporate taxes, the result does not change. Dividend payout is said to be independent of firm value. When the assumptions are relaxed further, it has been shown that personal as well as corporate taxes, presence of agency costs and information heterogeneity are possible explanations for dividend policy relevance.
The Miller-Modigliani (1961) paper proved the irrelevance of dividend policy in a world with no taxes or transaction costs and where everyone was fully informed about the distribution of the firm’s uncertain future cash flows. Once corporate and personal income taxes were introduced, then the theory suggested that perhaps it would be optimal to pay no dividends at all because of the tax disadvantage of ordinary income over capital gains. Miller and Scholes (1978) modified this point of view and demonstrated how dividend income could, to a large extent, be sheltered from taxation. Theories, which seek to explain benefits as well as costs of dividend payout, in an effort to evolve a theory of optimal dividend policy, abound in the finance literature. According to Copeland and Weston (1988), these theories could be grouped into three: theory based on taxes and investment opportunities, theories based on the informativeness of dividend payout (information signaling), and agency costs and sourcing costs of funds (see Ross, 1977; Bhattacharya, 1979; Copeland and Weston, 1988:561-72 Veronesi, 2000; Grullon and Michaely, 2002; and Pastor Veronesi, 2003). Rozeff in 1982 reports strong cross-sectional regularities in dividend payout. Accordingly, there might be optimal dividend policies that result from a tradeoff between costs and benefits of paying dividends. The list of possible costs includes (1) tax disadvantages of receiving income in the form of dividends rather than capital gains, (2) the cost of raising external capital if dividends are paid out, and (3) the foregone use of funds for productive investment. The possible benefits of dividend payout are (1) higher perceived corporate value because of the signaling content of dividends, (2) lower agency costs of external equity, and (3) the ability of dividend payments to help complete the markets (Copeland and Weston:573). Specifically, Rozeff hypothesized a relation between dividend payout and five proxy variables as below:
Abbildung in dieser Leseprobe nicht enthalten
Where DP represents dividend payout ratio, INS represents the percentage of insiders, GROWI represents the actual growth rate in revenues within the study period, GROW2 indicates Value Line’s forecast of the growth of sales revenue. GROW 1 and GROW 2 are an attempt to measure the impact of costly external financing. The variable INS and STOCK are proxies for agency relationship. STOCK represents the number of shareholders. BETA measures the riskiness of the firm. Of course, o , 1 , …., 5 represent the parameters of the regression. The results obtained are consistent with his predictions, though cannot be used to distinguish among the various theories of optimal dividend policy. A more recent study by La Porta, et. al (2000) is consistent with the Rozeff model. Specifically, La Porta, et al state that the relation between agency costs and dividend policy rests on the stringency (or otherwise) of a country’s law on corporate policies especially in connection with management’s over investment and empire building.
A classic analysis of how companies set their dividend payments is provided in Lintner (1956). Lintner conducted interviews with 28 carefully selected companies to investigate their thinking on the determination of dividend policy. His fieldwork suggested that (1) managers focused on the change in the existing rate of dividend payout, not on the amount of the newly established payout as such; (2) most managements sought to avoid making changes in their dividend rates that might have to be reversed within a year or so; (3) major changes in earnings “out of line” with existing dividend rates were the most important determinants of a company’s dividend decisions; and (4) investment requirements generally had little effect on modifying the pattern of dividend behaviour. In essence, managers try to smooth dividends (see Akintola-Bello, 2003). Lintner suggests that corporate dividend can be described on the basis of the equation.
Abbildung in dieser Leseprobe nicht enthalten
The target dividend payout, Div^{*} it, is a fraction, r_{i}, of this period’s earnings, NIit. Upon fitting the equations to annual data from 1918 through 1941, Lintner finds that the model explains 85% of the changes in dividends for his sample of companies. The average speed of adjustment is approximately 30% per year, and the target payout is 50% of earnings. Fama and Babiak in 1968 investigate many different models for explaining dividend behaviour. They use a sample of 201 firms with 17 years of data (1947-1964), then test each explanatory model by using it (1) to explain dividend policy for a hold out sample of 191 firms and (2) to predict dividend payments one year hence. Of the many models selected, the best two are Lintner’s model and a similar model that suppresses the constant term and adds a term for the lagged level of earnings.
That second model, as proposed by Fama and Babiak, may be written as follows:
Abbildung in dieser Leseprobe nicht enthalten
It is contended that dividends are relevant because they have informational value. A company can make statements about its expected earnings growth to inform shareholders in order to create a favourable impression on them. The payment of dividends is said to convey information to shareholders that the company is profitable and financially strong. When a firm changes its dividend policy, investors assume that it is in response to an expected change in the firm’s profitability which will last long (Pandey, 1999:764; Bhana, 2002). Ezra Solomon contends that dividends may offer tangible evidence of the firm’s ability to generate cash, and as a result, the dividend policy of the firm affects the share price. He states that the “dividend action does provide a clearcut means of ‘ making a statement’ that speaks louder than a thousand words.” The theoretical implication of the ‘information content’ hypothesis is that the announcement of a dividend (or a change in dividend) conveys information about management’s assessment of the firm’s prospects, that this information is different from other information provided by management, and that this information may cause an immediate investor reaction, including but not limited to share price changes. It is argued that the announcement of changes in dividend policy influences share prices, and that managers use the dividend changes to convey information about the future earning of their companies. They may also influence the perceptions of the investors about the riskiness of the company by following a stable dividend policy where the actual riskiness of the company remains unchanged. This sort of argument is also known as the dividend signaling hypothesis. (Ross, 1977).
The validity of the dividend information hypothesis hinges on the belief that a firm’s management often possesses privileged information about the firm’s future earnings potential and communicates this to the general investment community by altering the expected dividend. The difference between the actual dividend declared and that “expected” by the market i.e., the unexpected change in dividends, purportedly is a signal that investors use to reassess their estimates of a security’s value.
Empirical studies on the ‘information content of dividends’ hypothesis include Bhattacharya (1979), Benartzi, et. al (1997), Brickley (1983), Aharony and Swary (1980), Woolridge (1982, 1983), Handjinicolaou and Kalay (1984), DeAngelo, et. al (1996, 2000), Dewenter and Warther (1998), Conrad, et al,(2003), Grullon, et al, (2002), and so on.
One way for a company to increase its cash distribution in periods of prosperity is to declare a special (extra) dividend in addition to the regular annual or semi annual dividend. By declaring a special dividend, the company attempts to prevent investors from expecting that the dividend represents an increase in the established dividend rate. The declaration of a special dividend is particularly suitable for companies with fluctuating earnings. Gold mining companies in South Africa, for instance, usually declare special dividends when the bullion price is high (Bhana, 2002).
The use of the special dividend enables the company to maintain a stable record of regular dividends but also to distribute to shareholders some of the rewards of prosperity. By paying special dividends only when earnings are higher than usual, the company will not lead investors to count on the increased dividends in future periods. However, a company cannot pay special dividends continuously without conveying to the market some impression of permanency. As soon as a certain level of dividends is recurrent, investors begin to expect that level regardless of the distinction between regular and special dividends.
The rationale for special dividends is based on the hypothesis that dividend changes convey information. Aharony and Swary (1980) separate the information content of quarterly earnings reports from that of unexpected quarterly dividend changes. They examine only those quarterly dividend and earnings announcements made public on different dates within any given quarter. Their findings strongly support the hypothesis that changes in quarterly cash dividends provide useful information beyond that provided by corresponding quarterly earnings numbers. Brickley (1983) studies the announcement effect of specially designated dividends - those labeled by management as “extra,” “special,” or “year-end,” and compares them to surrounding regular dividend increases. Specially designated dividends are interesting because they are not intended to be a part of continuing higher dividend payout and may therefore not be interpreted by the market as a signal about higher future cash flows. Since a special dividend is a labeled dividend increase, Brickley argues that the increase is a temporary phenomenon and will not be repeated. His results support the notion that management uses the labeling of dividends to convey information to the market about future dividends and earnings. In addition, given the magnitude of the change in share price, he finds that regular dividend increases provide a more positive message than special dividends. Brickley finds additional support for the information content hypothesis in the earnings patterns surrounding the announcements of special dividends and regular dividend increases. Specifically, he documents that the group of firms with regular dividend increases has statistically larger earnings changes in the year following the dividend announcement. In essence, though the market reacts positively to the information content of specially designated dividends, regular dividends convey more information. This result was also confirmed by DeAngelo, et. al, (2000).
Handjinicolaou and Kalay (1984) and Woolridge (1983) have argued that one cannot infer that dividend increases convey positive information about the firm by examining share prices alone, since unexpected dividend increases could cause wealth transfers from bondholders to shareholders by reducing the asset base of the firm (expropriation argument). Therefore, the observed increase in share price is consistent with both wealth redistribution and positive information. To distinguish between the relative importance of these two effects, Handjinicolaou and Kalay and Woolridge analyze the changes in bond prices around dividend announcements since the two hypotheses (information and wealth transfer) have different predictions for bond price behaviour. In particular, the wealth transfer hypothesis predicts a negative bond price reaction, while the information content hypothesis predicts a positive reaction. The findings of both studies are consistent with the hypothesis that informational effects dominate wealth redistribution effects wherever there are unexpected dividend increases.
In sum, share price reactions to special announcement for firms that declare special dividends infrequently may differ from those for firms with repetitive declarations. The normal expectation here, is that the former group would exhibit a larger abnormal return around the announcement period than the latter if repetition generates anticipation. Specifically, if repeated announcements of special dividends are anticipated, then the wealth transfer hypothesis predicts that announcement period reactions will be smaller for repetitive special dividends since returns in the announcement period capture unanticipated wealth transfers only. The same prediction is obtained from the information content hypothesis since the market already anticipates the special dividend announcement, and the announcement effect has already been impounded into the share price at some previous date.
Benartzi, et. al (1997) provide evidence that managers do look to the future when they set dividend payment. They found that dividend increases generally followed a couple of years of unusual earnings growth. Similar results are reported in DeAngelo, et. al (1996). Further, it seems that in some countries investors are less preoccupied with dividend changes. For example, in Japan there is a much closer relationship between corporations and major stockholders , and therefore information may be more easily shared with investors. Consequently, Japanese corporations are more prone to cut their dividends when there is a drop in earnings, but investors do not mark the stocks down as sharply as in the United States (Dewenter and Warther, 1998). Grullon, et al (2002) relate dividend changes to variation in systematic risk. They indicate that the positive market reaction to a dividend increase is significantly related to the subsequent decline in systematic risk. Accordingly, in the long run, the dividend-increasing firms with the largest decline in systematic risk also experience the largest increase in price over the next three years, suggesting that the market reaction to dividend changes may not incorporate the full extent of the decline in the cost of capital associated with dividend changes.
The evidence in support of the informational content of dividends is overwhelming. Unexpected dividend changes do convey information to the market about expected future cash flows. The Miller- Modigliani proposition suggests that dividend policy is irrelevant to value. However, when personal taxes are introduced with a capital gains rate that is less than the rate on ordinary income, the picture changes. Under this set of assumptions,. The firm should not pay any dividends. One way to test these theories is to examine the relationship between dividend payout and the price per share of equity.
In pursuance of this, the usual cross-section equation was:
Abbildung in dieser Leseprobe nicht enthalten
Where P_{it} = the price per share, Div_{it} = aggregate dividends paid out, REit = retained earnings εit = the error term.
Friend and Puckett in their 1964 study, criticize the above approach on three major points. First, the equation is said to be misspecified because it assumes that the riskiness of the firm is uncorrelated with dividend payout and price/earnings ratios. However, a look at the data suggests that riskier firms have both lower dividend payout and lower price/earnings ratios. Consequently, the omission of a risk variable may cause an upward bias in the dividend coefficient in (2.22). Second, there is almost no measurement error in dividends, but there is considerable measurement error in retained earnings. + It is well known that accounting measures of income often imprecisely reflect the real economic earnings of the firm. They argue that the measurement error in retained earnings will cause its coefficient to be biased downward. Third, Friend and Puckett argue that even if dividends and earnings do have different impacts on share prices, we should expect their coefficients in (2.22) to be equal. It is stated that in equilibrium, firms would change their dividend payout until the marginal effect of dividends is equal to the marginal effect of retained earnings. This is said to provide the optimum effect on their price per share (Copeland and Weston, 1988: 589).
A study by Black and Scholes (1974) uses capital asset pricing model to control for risk. Their conclusion is as follows: “It is not possible to demonstrate, using the best empirical methods, that the expected returns on high yield common stocks differ from the expected returns on low yield common stocks either before or after taxes.” They begin by pointing out that the assumption that capital gains tax rates are lower than income tax rates does not apply to all classes of investors. Some classes of investors might logically prefer high dividend yields. They include: (a) Corporations, because they usually pay higher taxes on realized capital gains than on dividend income (because of the 80% exclusion of dividends); (b) Certain trust funds in which one beneficiary receives the dividend income and the other receives capital gains; (c) Endowment funds from which only the dividend income may be spent; and (d) Investors who are spending from wealth and may find it cheaper and easier to receive dividends than to sell or borrow against their shares. Alternatively, investors who prefer low dividend yield will be those who pay higher taxes on dividend income than on capital gains. With all these diverse investors, it is possible that there are clientele effects that imply that if a firm changes its dividend payout, it may lose some shareholders but they will be replaced by others who prefer the new policy. Thus, dividend payout will have no effect on the value of an individual firm.
The Black and Scholes (1974) study presents empirical evidence that the before-tax returns on common stock are unrelated to corporate dividend payout policy. They assume, among other things, that there are no differential tax effects that would affect investors’ demands for different securities. Brennan has shown that if effective capital gains tax rates are lower than effective rates on dividend income, then investors will demand a higher rate of return on securities with higher dividend payout. Using annual data, Black and Scholes test this hypothesis by adding a dividend payout term to an empirical version of the CAPM:
Abbildung in dieser Leseprobe nicht enthalten
dividends paid during the previous year divided by the end-of-year stock price,
DY_{m}= the dividend yield on the market portfolio measured over the prior 12 months,
z_{j}= the error term.
The Black -Scholes (1974) study posits that if the coefficient, γ1, of the dividend yield is significantly different from zero, we would reject the null hypothesis that dividend payout has no impact on the required rate of return for securities. The results of Black and Scholes indicate that the dividend impact coefficient is not significantly different from zero.
The Black-Scholes study has been criticized that their test is not very powerful. Had the null hypothesis been that dividend yield does not matter, it could not have been rejected either. Their test has been described as inefficient in that they grouped stocks into portfolios instead of using individual returns (Copeland & Weston: 591).
Litzenberger and Ramaswamy (1979) also test the relationship between dividends and security returns. They use the Brennan model below with monthly data for individual securities:
Abbildung in dieser Leseprobe nicht enthalten
Litzenberger and Ramaswamy (LR) conclude that risk-adjusted returns are higher for securities with higher dividend yields. The implication is that dividends are undesirable; hence higher returns are necessary to compensate investors in order to induce them to hold high dividend yield stocks.
Because investors use dividend announcements to estimate expected returns, E(Rjt) ; i.e, there is an information effect, the LR study was criticized by Miller and Scholes (1982) for their handling of the information effect of dividend announcements. Miller and Scholes, using the LR methodology, but adjusting for announcement and dividend tax effects, show that the dividend impact coefficient drops to insignificance implying the irrelevance of dividend payout decisions on securities risk- adjusted returns.
Litzenberger and Ramaswamy (1982) have responded to the Miller - Scholes criticism by rerunning their regressions. The level revised dividend yield gave the highest coefficient ( 3 ), and it is slightly higher than the Miller-Scholes estimate. Their “predicted dividend yield” model avoids the Miller-Scholes criticism and continues to give a statistically significant estimate of the dividend effect.
Thus, the Brennan and LR studies point towards the conclusion that shareholders express their displeasure with high dividend payout. However, the Friend and Puckett, Black and Scholes, and Miller and Scholes studies tend to support the conclusion that the value of the firm is independent of dividend yield.
Another camp of thought as to dividend relevance was provided by Long in 1978. His conclusion supports that dividends are desirable to shareholders i.e they will require a lower rate of return on shares that pay a high dividend yield. A recent signaling argument, developed by Allen, Bernardo and Welch (2000) is that well-managed companies want to signal their worth and they can do so by having a high proportion of demanding institutions among their stockholders. They achieve this by paying high dividends and those shareholders in the high-income tax brackets do not object to these high dividends as long as the effect is to encourage institutional investors who are prepared to put the time and effort into monitoring the management. ( Brealey and Myers, 2003:453).
Yet another area of interest to finance researchers has been the ex- dividend-day price behaviour of stocks. Almost all research on the movement of stock prices on ex-dividend days has found that prices decline by less than the dividend. Studies such as Green and Rydqvist (1999), McDonald (2001), Bell and Jenkinson (2002), Elton, et al (1998) and Elton, et al, (2005) posit that this phenomenon is consistent with tax effects i.e. differential taxes on dividends and capital gains. Numerous articles have appeared, however, questioning the tax explanation of ex- dividend-day price behaviour. Alternative explanation for the tax hypothesis includes changes in tax policy (e.g. Graham, Michaely and Roberts, 2003), arbitrage (by short-term traders) argument (e.g. Karpoff and Walking, 1990), and perhaps most damaging to the tax explanation is a series of articles that attempt to show that even in the absence of differential taxes, the price of common stocks should fall by less than the dividend on ex-dividend days because of market-microstructure characteristics. The first of the microstructure arguments is presented by Dubofsky (1992). He argues that price falls by less than the dividend due to limit-order adjustments. Bali and Hite (1998) state that the drop in price less than the dividend is really due to discreteness in prices rather than taxes. They hypothesize that because of discreteness in prices the ex-dividend-day price should fall by an amount equal to or smaller than the amount of the dividend. A further microstructure analysis is presented by Frank and Jagannathan (1998). They hypothesize that the collection and reinvestment of dividends is bothersome for individual investors but not for market makers. This means that individuals want to sell the stock before it goes ex-dividend and are anxious to buy it back after it goes ex-dividend. They argue that because of this, market makers can purchase stock at the bid price before the stock goes ex-dividend and sell at the ask price after it goes ex-dividend. They then state that in the absence of taxes, this means that the fall in price on the ex-dividend date will be less than the dividend. They argue that this bid-ask bounce contributes to, if it does not totally explain, a phenomenon others attribute to tax effects.
Empirical analyses of this conjecture include Koski and Scruggs (1998) and Graham, Michaely, and Roberts (2003). Microstructure arguments, however, merely explain price decline by less than dividend. None of them explains a price drop more than the dividend. A price drop by more than dividend explanation is provided in Elton, et al (2005) using taxable and non taxable closed-end funds.
Dividends come in several forms. The most common is the regular cash dividend, but sometimes companies pay stock dividends (scrip issue). Lintner’s work suggests that managers try to smooth dividends. On dividend policy impact, there are three broad schools viz: the Leftists (who favour low payouts), the Rightists (who favour high payouts) and the Middle-of-the-roaders (who argue that dividend payout has no effect on the value of a firm). The Leftists derive their argument from the differential tax rates (in most countries) that favour capital gains over dividend income and in some places (like Germany) where capital gains tax is nil; existence of high transaction costs associated with new issues of securities; and preference for capital gains by wealthy investors. The Rightists’ argument hinges on factors such as: the dynamics of some tax laws which permit exclusion of dividends from taxes; the presence of institutional investors (as against unsophisticated and more docile stockholders) in well-managed companies; shareholders’ preference for current income and the resolution of uncertainty and agency costs. The ‘information content of dividends’ is also cited as a factor that either supports the Leftists or Rightists depending on the market reaction to a change in dividend payout policy (Akintola-Bello, 2003). Akintola-Bello indicates that the clientele theory supports the dividend policy irrelevance school. The theory states that high dividend stocks will be favoured by “poor” individuals, tax-free institutions and corporations while low dividend stocks will be favoured by “wealthy” individuals. This point underlies the migration of investors to their most convenient firms such that in equilibrium, no unsatisfied clientele exists.
Dividend payout policy, as it relates to this research, emphasizes the information content of dividends hypothesis or signaling hypothesis. Other possible, but not mutually exclusive, hypotheses are: the leverage tax shield hypothesis; the dividend tax avoidance hypothesis; the bondholder expropriation hypothesis; and wealth transfers among shareholders.
The CAPM as developed by Sharpe(1964), Lintner (1965b) and Mossin (1966) is a simple model that expresses the expected return on a security or portfolio as a linear function of its systematic risk proxied by beta. Expressed mathematically,
Abbildung in dieser Leseprobe nicht enthalten
Many empirical extensions of the model include the assumption of no ‘riskless’ asset, non-normality in the distribution of returns, the existence of non-marketable assets (such as human capital), the existence of taxes (differential taxes on dividends and capital gains), the model in continuous time, the existence of heterogeneous expectations and information, etc. Most of these extensions support the simple linearity formulation. However, some studies suggest that return-risk relation may not be linear, and that other factors other than beta may be needed to explain returns.
When the CAPM is empirically tested, it is usually written in the ex post form as follows:
Abbildung in dieser Leseprobe nicht enthalten
The predictions made by the CAPM is expected to meet the following criteria.
a) Yo = 0 i.e. the intercept them should not be significantly different from zero
b) Beta should be the only factor that explains the rate of return on a risky asset. If other terms such as residual variance, dividend yield, price/earnings ratio, firm size, or beta squared are included in an attempt to explain return, they should have no explanatory power i.e. Y2 = 0
c) The relationship should be linear in beta. I.e. Y3 = 0
d) The coefficient of beta, Y1, should be equal to [Abbildung in dieser Leseprobe nicht enthalten]
e) When the equation is estimated over very long periods of time, the rate of return on the market portfolio should be greater than the risk-free rate i.e. [Abbildung in dieser Leseprobe nicht enthalten]
Some of the empirical tests of the CAPM were published by Friend and Blume in 1970, Black, Jensen and Scholes in 1972, Blume and Husick in 1973, Fama and Macbeth in 1973, Basu in 1977, Reinganum in 1981, Litzenberger and Ramaswamy in 1979, Banz in 1981, Gibbons in 1982, Stambaugh in 1982, Shanken in 1985, Fama and French in 1992, Black in 1993, Fama and French in 1993, etc. (see Copeland/Weston: 214-217; Ross, Westerfield and Jaffe, 1996: 289-90; Brealey and Myers, 2003; Cochrane,1999:36-58 for a review of the empirical tests).
Some of the studies use monthly total returns (dividends are reinvested) on listed common stocks as their database. A frequently used technique is to estimate the betas of every security during a five-year holding period, by computing the covariance between return on the security and a market index that is usually an equally weighted index of all listed common stocks. The securities are then ranked by beta and placed into N portfolios (where N is usually 10,12 or 20). By grouping the individual securities into large portfolios chosen to provide the maximum dispersion in systematic risk, it is possible to avoid a good part of the measurement error in estimating betas of individual stocks. Next, the portfolio betas and returns are calculated over a second five-year period and a regression similar to (2.26) is run.
In the first set of empirical tests of the CAPM, using data from 1930s to the 1970s, researchers agree on the following conclusions.
a) The intercept term, Yo, is significantly different from zero, and the slope, Y1, is less than the difference between the return on the market portfolio and the risk-free rate. The implication is that low beta securities earn more than the CAPM would predict and high beta securities earn less.
b) Versions of the model that include a squared beta term or unsystematic risk find that at best these explanatory factors are useful only in a small number of the time periods sampled. Beta dominates them as a measure of risk.
c) The simple linear empirical model fits the data best. It is linear in beta. Also, over long periods of time, the rate of return on the market portfolio is greater than the risk-free rate (i.e. Y1 > 0).
d) Factors other than beta are successful in explaining that portion of security returns not captured by beta. Basu found that low price/earnings portfolios have rates of return higher than could be explained by the CAPM. Banz and Reinganum found that firm size is important. Smaller firms tend to have high abnormal rates of return. Fama -French (1992) study is consistent with this finding. Litzenberger and Ramaswamy (1979) found that the market requires higher rates of return on equities with high dividend yields (as earlier indicated in the dividend impact discussion). Keim in 1983 and 1985 reports seasonality in stock returns - a January effect.
Researchers such as Gibbons, Stambaugh and Shanken have severally tested the CAPM by first assuming that the market model is true - i.e., that the return on the ith asset is a linear function of a market portfolio proxy such as an equally weighted market portfolio (Yoon, 2005:372):
Abbildung in dieser Leseprobe nicht enthalten
The market model (2.27), is merely a statistical statement. It is not the CAPM. The CAPM - e.g. Black’s (1972) two-factor version - actually requires the intercept term, E (Rz) in (2.28), to be the same for all assets. The two-factor CAPM is true across all assets at a point in time.
Abbildung in dieser Leseprobe nicht enthalten
Gibbons pointed out that the two-factor CAPM implies the following constraint on the intercept of the market model.
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for all se curities during the same time interval. When he tests restriction (2.29), he finds that it is violated and that the CAPM should be rejected. The empirical form of the model, which has come to be known as the empirical market line,
Abbildung in dieser Leseprobe nicht enthalten
does provide an adequate model of security returns (Copeland and Weston : 216).
While a large body of empirical work developed three decades ago (and before), often with varying results, the CAPM was not seriously called into question until recently. Two papers by Fama and French (1992, 1993) (yes, the same Fama whose joint paper in 1973 with James Macbeth supported the CAPM) present evidence inconsistent with the model. Their work has received a great deal of attention, both in academic circles and in the popular press, with newspaper articles displaying headlines such as “Beta is Dead!” in the United States. These papers make two related points. First, they conclude that the relationship between average return and beta is weak over the period from 1941 to 1990 and virtually nonexistent from 1963 to 1990. Second, they argue that the average return on a security is negatively related to both the firm’s price -to -earnings (P/E) ratio and the firm’s market value -to-book value (M/B) ratio. After all, the CAPM states that the expected returns on stocks should be related only to beta, and not to other factors such as P/E and M/B.
However, a number of researchers have criticized the Fama-French papers (including Fama and French, 1996). A summary of the salient issues raised are as follows: “First, although Fama and French cannot reject the hypothesis that average returns are unrelated to beta, one can also not reject the hypothesis that average returns are related to beta exactly as specified by the CAPM. In other words, while 50 years of data seem like a lot, they may simply not be enough to test the CAPM properly. Second, the result with P/E and M/B may be due to a statistical fallacy called a hindsight bias. Third, P/E and M/B are merely two of an infinite number of possible factors. Thus, the relationship between average return and both P/E and M/B may be spurious, being nothing more than the result of data dredging. Fourth, average returns are positively related to beta over the period from 1927 to 1990. There appears to be no compelling reason for emphasizing a shorter period than this one. Fifth, average returns are actually positively related to beta over shorter periods when annual data, rather than monthly data, are used to estimate beta. “Ross, Westerfield and Jaffe (1996) opine that ‘there appears to be no compelling reason for preferring either monthly data over annual data or vice versa. Thus, we believe that, while the results of Fama and French are quite intriguing, they cannot be viewed as the final word.” (Ross, Westerfield and Jaffe, 1996:289-90).
For more on the CAPM and beta, the interested reader is referred to Gauer (1999), Fama and French (1996), Groenewold and Fraser (2000), Martin (2000), Philip (2004), Jagannathan and McGrattan (1995), Duffee, (2005), Markellos and Mills (2001), Campbell & Vuolteenaho (2004), Yoon (2005) and so on.
Roll (1977) takes exception to the interpretation of the residual term, Ejt, as abnormal performance measure in the empirical tests of the CAPM in general. In brief, his major conclusions are:
1) The only legitimate test of the CAPM is whether or not the market portfolio (which includes all assets) is mean-variance efficient.
2) If performance is measured relative to an index that is ex post efficient, then from the mathematics of the efficient set, no security will have abnormal performance when measured as a departure from the security market line.
3) If performance is measured relative to an ex post inefficient index, then any ranking of portfolio performance is possible, depending on which inefficient index has been chosen.
Roll implies that even if markets are efficient and the CAPM is valid, then the cross-section security market line cannot be used as a means of measuring the ex post performance of portfolio selection techniques. Furthermore, the efficiency of the market portfolio and the validity of the CAPM are joint hypotheses that are almost impossible to test because of the difficulty of measuring the ‘true’ market portfolio.
In interpreting the Roll critique, it is noted that it does not imply that the CAPM is an invalid theory. However, great caution has been called in interpretation of the CAPM tests (Copeland and Weston: 219). On a macro perspective, some articles have appeared in the literature to investigate the relevance of idiosyncratic risk via the existence of a trade- off between stock market returns and idiosyncratic volatility of individual stocks. Campbell, et al (2001) find a “strong evidence of a positive deterministic trend in idiosyncratic firm-level volatility. There is no similar trend in industry or market volatility.” In addition, the scholars find that the trend increase in idiosyncratic volatility relative to market volatility implies that the correlations among individual stock returns have declined over the past few decades. The R^{2} of the market model for a typical stock has also declined, while the number of stocks needed to obtain any given amount of portfolio diversification has increased. They further indicated that their volatility measures help to forecast GDP growth and greatly diminish the significance of stock index returns in forecasting GDP (Campbell, et al, 2001:40-41). Other related papers on the relevance of idiosyncratic risk include: Goyal and Santa-Clara (2003), Xu and Malkiel (2003), and Bali, et al (2005).
Studies on the interrelationship of the stock market with macroeconomic variables have been conducted for various economies. These studies have arisen because of the notion of inadequacies in the explanation of common stock returns as depicted in single-factor models such as the CAPM. The stock market is said to be influenced by a myriad of events in an economy such that for instance, if the economy is sick, the market may not grow at a desired pace. It was in realization of this that the Arbitrage Pricing Theory (APT) was developed by Professor Stephen Ross in 1976, as a testable alternative to the CAPM. Nwokoma (2002) reports some Indian studies on the relationship of the stock market with macroeconomic variables such as Sharma and Kennedy, 1977; Sharma, 1983; Poterba and Summers, 1988; Darrat and Mukherjee, 1987. The work of Darrat and Mukherjee was said to have employed the Vector Autoregressive (VAR) model to find a causal relationship between stock returns and some macroeconomic indicators. Most authors have adopted cointegration tests to determine the existence of possible long-term relationship between key macro-economic variables and the stock market index. The Nwokoma study in addition, demonstrates the effects of factors in the macroeconomy on the Nigerian stock market through the investigation of impulse responses.
In brief, the evolution of a multifactor model (such as the APT) on security returns has led to the pursuance of two lines of inquiry. First, researchers analyze security returns statistically to discern the significant factors and to construct portfolios that are highly correlated with those factors. They then estimate the average returns on these portfolios to determine whether these factors command risk premiums. The second approach is to prespecify likely economic factors and identify portfolios that are highly correlated with these factors. The risk premiums on these portfolios are thereafter estimated from sample average returns.
Chen, Roll and Ross (1986) hypothesized several macro-variables that might proxy for systematic factors such as: the monthly growth rate in industrial production, changes in expected inflation measured by changes in short-term (T-Bill) interest rates; unanticipated inflation defined as the difference between actual and expected inflation; unexpected changes in default risk premiums measured by the difference between the returns on corporate Baa bonds and long-term government bonds; and unanticipated changes in the term premium measured by the difference between the returns on long and short-term bonds.
The economic logic underlying these variables has been widely accepted. According to the basic discounted cash flows model, the price of a common stock depends on the future stream of cash flows and the required rate of return. In other words common stock prices are the present values of expected cash flows. The industrial production index is said to relate to cash flow while the remaining variables relate to the discount rate. This fact underlies Nwokoma’s statement that “the stock index of a country is affected by factors that influence its economic growth or bring about changes in its real rates of interest, expected rate of inflation, and risk premium”. (Nwokoma, 2002:233).
Given the likelihood of a positive correlation between the nominal interest rate and the risk-free rate of the ‘conventional’ valuation model, a change in nominal interest rate should move asset prices in the opposite direction. Despite other possibilities, cash flows may not rise with inflation Actual inflation will be positively correlated with unanticipated inflation and will ceteris paribus move asset prices in the opposite direction. Any growth in output should generally affect the future cash flows of firms in the same direction alongside stock prices, all things being equal. According to Fama (1981), there is a positive relationship between monetary growth and inflation rate, implying that monetary growth will adversely affect stock prices. On the other hand, it may also be argued that growth in money stock brings about increased cash flows and thus increased stock prices. In Nigeria, the level of money supply has been on the increase over the years, implying that since money supply has a negative relationship with interest rates, then stock prices would be expected to grow with the level of money supply.
In Nigeria, before the advent of SAP in July 1986, interest rates were closely regulated and monitored. On August 1 1987, interest rates were deregulated in the country. In 1989, all deposits of government and its parastatals were withdrawn from banks to the Central Bank of Nigeria (CBN). A serious liquidity squeeze gripped the economy.
The Interbank rates reached unprecedented heights of over 30 percent (Umoh, 1997:55). Deposits rates were in the range of 20 to 30 percent while inflation rate was over 40 percent. Given the conventional perception that capital market investments constitute effective inflation - hedgers, such situation should have precipitated series of disintermediation as depositors divest their interests in banks to the capital market. However, increase in market index may be dependent on the strength of the offsetting movements in interest rates - stock prices relation on one hand and increase in securities investment on the other. With the advent of SAP, the interest rate regime was largely deregulated with financial institutions allowed to charge interest freely within specified bounds from time to time. In summary, it could be hypothetically stated that there is an inverse relation between inflation or interest rates and stock prices, and positive relation between output growth and stock prices.
A direct comparison of the CAPM and the APT was performed by Chen (1983). First, the APT was fitted to the data as in the following equation
Abbildung in dieser Leseprobe nicht enthalten
Then, the CAPM was fitted into the same data.
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Next, the CAPM residuals, ni, were regressed on the arbitrage factor loadings, ˜k , and the APT residuals, ˜I, were regressed on the CAPM coefficients.
The results showed that the APT could explain a statistically significant portion of the CAPM residual variance, but the CAPM could not explain the APT residuals. Thus, Chen presents some support of the technical superiority of the APT when explaining cross-sectional variation in asset returns.
Several extensions of these (two) equilibrium-pricing models have led to attempts by some researchers to unify the two models. Essentially, the APT states that, under certain assumptions, the single-period expected return on any risky asset is approximately linearly related to its associated factor loadings (i.e. systematic risks). The assumptions that are generally employed in the APT derivation are that (a) all investors exhibit homogenous expectations that the stochastic properties of capital asset returns are consistent with a linear structure of K factors, (b) either there are no arbitrage opportunities or the capital markets are in competitive equilibrium, and (c) the number of securities in the economy is either infinite or so large that the law of large numbers may be applied. An additional assumption necessary to test the theory correctly is that (d) the number of factors, K, is known in advance or can be correctly estimated by the investigator. The assumptions that asset returns are generated by a factor structure and that no arbitrage opportunities exist (or that capital markets exists in a state of competitive equilibrium) are typically regarded as acceptable approximations to reality. Connor in 1984 employed a competitive equilibrium assumption to show that the elimination of the infinite-securities assumption does not change the pricing relation if the market portfolio is well diversified in a given factor structure.
Unfortunately, as noted by Connor, the assumption that the market portfolio is well diversified in a given factor structure is very restrictive in a finite economy since asset supplies must exist in exactly the correct proportion for their nonsystematic risks to net to zero in the market portfolio. The assumption is also nongeneric since even a minor perturbation of asset supplies would almost destroy the net-zero position. Similarly, the assumption of the existence of a well-diversified portfolio that is at least one utility-maximizing investor’s optimal portfolio in a given factor structure also appears too restrictive. These problems, combined with the fact that the assumption of a known number of factors in empirical tests of the APT is also not likely to be satisfied, have led some researchers to question the merits of the APT from both theoretical and empirical standpoints (see Wei, 1988).
Wei’s (1988) paper represents an extension and integration of Connor’s; Cragg and Malkiel’s; Dybvig’s and Grinblatt and Titman’s contributions on the APT and Stapleton and Subrahmanyam’s contribution on the CAPM. Wei shows that the competitive equilibrium version of the APT may be extended to develop an exact model if idiosyncratic risks obey the Ross separating distribution. The results indicate that the addition of the market portfolio as an extra factor produces an exact asset pricing relation. The ‘empirical’ APT, as shown in the Wei-study, allows for omission of some factors from the econometric model employed to test the theory. The ‘robust’ model, reducible to the CAPM , may be extended to approximate Ross’s APT depending on the number of omitted factors. Further, the importance of the market portfolio is shown to be a monotonic increasing function of the number of omitted factors. Finally, the author demonstrates that, in a finite economy, the pricing error bound of the Ross APT in a correlated-residuals factor structure is an increasing function of the absolute value of market-residual beta, rather than the weight of the asset in the market portfolio as is the case for uncorrelated factor residuals.
Kubler and Schmedders (2003) formulate an asset-pricing model with infinitely lived heterogeneous agents, collateral constraints, and incomplete markets. Their paper proves the existence of a Markov equilibrium and show how one can describe this equilibrium numerically. The practical advantage of their approach is that the ‘curse of dimensionality’ in the member of securities is avoided.
Predictability of the mean and volatility of stock returns has been reported in a growing body of empirical studies such as Fama and French (1989), Pesaran and Timmermann (1995), Perez-Quiros and Timmermann, (PT) (2000; 2001), etc. The literature predominantly assumes a time-invariant relationship linking stock returns to a set of publicly known factors. However, as earlier discussed, some studies indicate that the conditional volatility of stock returns depends on the underlying state of the economy. For example, Schwert (1989) finds that the volatility of stock returns is higher during recessions than during expansions. The Schwert study analyses the relation of stock volatility with real and nominal macroeconomic volatility, economic activity, financial leverage (gearing), and stock trading activity using monthly data from 1857 to 1987. Schwert shows that while aggregate leverage is significantly correlated with volatility, it explains a relatively small part of the movements in stock volatility (See also Starica and Granger, 2005). McQueen and Roley report additional evidence on asymmetry in the conditional distribution of stock returns. Classifying three states according to the level of growth in industrial production, they find that announcement effects of macroeconomic news on daily stock prices critically depend on the state of the economy (PT, 2001:260).
PT (2001) investigate the time-series properties of higher order moments and of the full conditional density of stock returns when these are modeled as a two-state Markov mixture process with time-varying transition probabilities and state-dependent coefficients in the mean and volatility equation. Stock returns are reported to be heavily influenced by outliers and statistical models have been developed to account for these through time-varying volatility, error densities more general than the Gaussian or some combination of these. Nonlinearities in asset returns are also widely recognized but the empirical asset pricing literature almost exclusively models these within the context of single-state models. PT therefore present new statistical evidence suggesting that a two-state specification is necessary to capture nonlinearities and outliers in the conditional distribution of stock returns. In summary, the authors provide a comprehensive characterization of risk that goes beyond the mean and variance of returns via some econometric analyses (Refer also to Mikosch and Starica, 2004). Several mixture models with different specifications of the state transition are compared and they propose a new mixture of Gaussian and student-t distributions that captures outliers in returns. The models produce very similar expected returns and volatilities but imply very different time series for conditional skewness, kurtosis and predictive density. Consistent with economic theory, the gains in predictive accuracy from considering two-state mixture models rather than a single-state specification are higher for small firms than for large firms.
The Schwert study indicates greater volatility during recessions and that ‘operating leverage’ increases during recessions. There was weak evidence that macroeconomic volatility could help to predict stock volatility. The evidence is somewhat stronger that financial asset volatility helps to predict future macroeconomic volatility. Also, stock volatility increases with gearing. Further, there seems to be a relation between trading activity and stock volatility. The author shows that the number of trading days in the month is positively related to stock volatility. Also, share trading volume growth is positively related to stock volatility.
Irving Fisher noted that the nominal interest rate can be expressed as the sum of an expected real return and an expected inflation rate. The proposition that expected nominal returns contain market assessments of expected inflation rates can be applied to all assets. Thus, if the
market is an efficient or rational processor of the information available at time t-1, it will set the price of any asset j so that the expected nominal return on the asset from t-1 to t is the sum of the appropriate equilibrium expected real return and the best possible assessment of the expected inflation rate from t-1 to t. Formally,
Abbildung in dieser Leseprobe nicht enthalten
Where Rjt is the nominal return on asset j from t-1 to t. E [Abbildung in dieser Leseprobe nicht enthalten] is the appropriate equilibrium expected real return on the asset implied by the set of information Φt-1 available at t-1, E[Abbildung in dieser Leseprobe nicht enthalten] is the best possible assessment of the expected value of the inflation rate Δt that can be made on the basis of Φt-1.
The logic of (2.31) is that the market uses Φt-1 to correctly assess the expected inflation rate and to determine the appropriate equilibrium expected real return on asset j, including perhaps a risk adjustment which differentiates the expected return on asset j from that on other assets, term to maturity held constant. The market then sets the price of the asset so that its expected nominal return is the sum of the equilibrium expected real return and the correctly assessed expected inflation rate (Fama & Schwert, 1977).
As a quantity theorist, Fisher felt that the real and monetary sectors of the economy are largely independent. Thus, he hypothesized that the expected real return in (2.31) is determined by real factors, like the productivity of capital, investor time preferences, and tastes for risk and that the expected real return and the expected inflation rate are unrelated. This assumption is convenient for the purpose of studying asset return-inflation relationships without introducing a complete general equilibrium model (such as CAPM and APT) for expected real returns.
Given some way to measure the expected inflation rate, E(Δt/Φt-1), tests of the joint hypotheses that the market is efficient and that the expected real return and expected inflation rate vary independently can be obtained from estimates of the regression model,
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Since a regression estimates the conditional expected value of the dependent variable as a function of the independent variable, an estimate of the regression coefficient βj which is statistically indistinguishable from unity is consistent with the hypothesis that the expected nominal return on asset j varies in one-to-one correspondence with the expected inflation rate. Since the expected real return on the asset is its expected nominal return minus the expected inflation rate, an estimate of βj which is indistinguishable from unity is also consistent with the hypothesis that the expected real return on the asset and the expected inflation rate are unrelated.
Further, an issue of interest is the extent to which asset returns at t reflect the unanticipated component of the inflation rate between t-1 and t, Δt - E[Abbildung in dieser Leseprobe nicht enthalten]. To this end, (2.31) is expanded as follows:
Abbildung in dieser Leseprobe nicht enthalten
Estimates of (2.33) can be based on the regression model,
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An estimate of the regression coefficient γj, which is statistically indistinguishable from 1.0, is consistent with the hypothesis that on average the nominal return to asset j varies in one-to-one correspondence with the unexpected inflation rate.
Fisher’s model suggests that all assets should have a coefficient βj = 1.0 for the expected inflation rate in (2.34), but to obtain hypotheses about
the coefficient γ_{j} for the unexpected inflation rate, we must rely largely on intuition and intuition about γj is different for different assets. For instance, since the nominal value of a treasury bill, which matures at time t, is fixed at t-1, the return on the bill from t-1 to t cannot react to the unexpected rate of inflation from t-1 to t. On the other hand, there is a general belief that real estate and common stocks are hedges against inflation, unanticipated as well as anticipated, so that γj, for these asset should be positive. It is also widely believed that income from human capital adjusts to both anticipated and unanticipated inflation, although possibly with a lag. For longer-term bonds, whose cash payoffs are fixed in nominal terms, the signs and sizes of γj, in (2.33) and (2.34) depend on how the unanticipated inflation rate is related to changes in the market capitalization rate for bonds (Fama and Schwert, 1977:117).
Since the unexpected inflation rate is, by definition, uncorrelated with the expected rate of inflation, (2.34) produces tests of the Fisher hypothesis that βj = 1.0 which are identical to those that would be obtained from (2.32). When the tests suggest that βj = 1.0, we say that the asset is a complete hedge against expected inflation: The expected nominal return moves one -far-one with the expected inflation rate, and the expected real return on the asset is uncorrelated with the expected inflation rate. When γj = 1.0, the asset is a complete hedge against inflation: The nominal return on the asset varies in one-to-one correspondence with both the expected and unexpected components of the inflation rate, and the ex post real return on the asset is uncorrelated with the ex post inflation rate.
The fact that an asset is a complete hedge against expected and/or unexpected inflation does not imply that the real return on the asset has zero variance or even a small variance. Non-inflation factors can generate variation in nominal returns, which can be large or small relative to the variation in nominal returns associated with the expected and unexpected component of the inflation rate. In terms of (2.34), an asset might be a complete hedge against inflation, that is, both βj and γj equal to 1.0, but inflation might ‘explain ‘ a small fraction of the variation in the asset’s nominal return: that is, the variance of the disturbance term, njt, which in this case is the variance of the asset’s real return, might be large relative to the variance of the expected and unexpected components of the inflation rate.
Various arguments can be given for why common stocks might be helped or hurt by unanticipated inflation. For example, Kessel argues that unanticipated inflation is to the benefit of the stockholders of firms that are net debtors. In more general terms, it is argued that unanticipated inflation should benefit the common stocks of firms that have made more long-term commitments (such as accounts payable and long-term debts). The argument is that these firms should benefit from unanticipated inflation due to an unexpected decline in the real value of their nominal liabilities. Fama and Schwert (1977) note that the net debtor-creditor hypothesis is difficult to implement empirically in that a firm might have long-term contracts to purchase labour, raw materials, and capital, to sell its own products, and to borrow money to finance its operations. Nevertheless, this hypothesis and others (see, for example, Lintner’s (1975) discussion of tax effect of inflation) provide some theoretical possibilities for explaining the effects of unanticipated inflation on the returns to common stocks.
Using data from July 1959 to July 1971, Fama and Schwert (1977) present the following results on the inflation hedging capacity of some assets.
Table 2.6 Fama -Schwert Study on Sensitivities of Assets To Expected and Unexpected Inflation, 6-Month Holding Periods July 1959-July 1971.
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+Value - weighted average of all stocks listed on the New York stock Exchange (NYSE).
Source: Fama and Schwert (1977) pp. 130-1 (Table 6)
A popular rough estimate of expected rate of inflation is short term T.B interest rate. Unexpected inflation is calculated as the difference between actual inflation and expected inflation.
The results show that the U.S government bonds appear to have provided hedges against expected inflation on approximately a one-for- one basis, since their sensitivities to expected inflation are all in the vicinity of a value of one. However, since all these bonds had negative values of Yj, they all failed to serve as hedges against unexpected inflation. This fact was also confirmed is French, Ruback and Schwert (1983). Furthermore, the values of Yj were more negative when the life of the bond was longer. This is said to reflect the way investor’s revise expectations based on recent experience. A higher-than-expected inflation causes investors to obtain a lower-than-expected return and vice versa. Residential real estate provides a bright spot in an otherwise gloomy record of the relationship between security returns and in expected inflation. Thus, it has historically served as a complete hedge against inflation. The result of common stocks-inflation relation are puzzling given the conventional wisdom that common stocks, representing ownership of the income generated by real assets, should be a hedge against inflation. An attempt to explain the ‘anomalous’ stock return-inflation relations was made by Fama (1981).
Fama (1981) proposes a union of rational expectations models for the monetary and real sectors. The model of the monetary sector says that in setting prices for goods and services, goods markets make rational assessments of the current nominal money supply and future real activity. The economics of the monetary sector -- a combination of the money demand theory with an observation on the properties of the money supply process - then implies that the relations between inflation and future rates of growth of real activity are negative. Within the real sector, much of the task of a rational stock market also involves forecasting the values of the real variables that determine equity prices. However, the economics of the real sector implies that the resulting relations between stock returns and anticipated growth rates of real activity are positive. It is said therefore, that “the positive relations between stock returns and real activity that come of the real sector combine with the negative relations between inflation and real activity that come out of the monetary sector to induce spurious negative relations between stock returns and inflation.” (Fama 1981:546)
This chapter has presented some theories, evidence and applications of some corporate policies. The dominant issue has been the evaluation of the respective impacts of each of these policies on firm or common stock value when the objective of maximizing shareholders’ wealth is the normally accepted economic objective for decisions on allocation of resources.
The first section examines the fundamentalist approaches to valuation of common stocks. Generally, the choice of specific valuation technique should be influenced by the nature of the investor. The argument along this line has been put forth in Okafor (1983). Moreover, the literature documents that the cash flow valuation model is the preferred means of assessing common stock values in the capital market (Bansal, et.al, 2005). This technique is said to provide a convenient means of circumventing the complexities of accounting procedures and principles especially with respect to earnings recognition.
The second section presents the price-earnings ratio analysis and points in general that the P/E ratio is an indicator of the market’s optimism of a firm’s growth prospects. Under this analysis, the linkage between growth and retention ratio is the rate of return on investments available to a firm. Where the rate of return is higher than the required rate of return by providers of capital (cost of capital), then a higher retention ratio translates to a higher growth rate and by extension, the P/E ratio. Moreover, an inverse relation is said to exist between the riskiness of firms and their P/E ratios. Also, the business cycle is said to exert greater influence on earnings than on stock prices.
Next, the Nigerian stock market is introduced with discussion covering establishment, trading floors, securities listing and other stock market statistics. The impact of economic reforms, automation and globalization are also highlighted. The Nwokoma and Olofin study reveals positive signs of integration with other major stock markets. The Soyode studies reveal the impact of SAP on the Nigerian stock market.
Next, the capital structure relevance is presented. The major empirical concern is the impact of the capital structure on the value of the firm and on the weighted average cost of capital. MM (1958) posit that the value of a firm is independent of its capital structure, implying that a firm could theoretically estimate the required rate on a new investment just by looking at the stock market and observing the market’s valuation of equities whose distribution of earnings are proportional to those of the contemplated investment. However, studies indicate reasons why the valuation of a firm’s assets cannot be separated from its financial structure. Such theories that attempt to explain the financial structure relevance include the static theory of capital structure (also known as trade-off -theory), the pecking order theory and the cash flow theory. These theories emphasize taxes, asymmetric information and agency costs respectively. If the trade-off theory is right, there will be a positive and significant relationship between profitability and the degree of leverage. The pecking order theory presupposes the existence of inverse relation between profitability and the debt ratio. To the pecking order theorists, an announcement of a stock issue should depress the stock price. The free cash theory says that dangerously high debt levels will increase value when a firm’s operating cash flow significantly exceeds its profitable investment opportunities.
Further, the relationship between dividend policy and the value of a firm is presented. There are several competing theories. However, the dominant argument seems to be that the value of an all-equity firm (unlevered firm) depends on the expected returns from current and future investment and not on the form in which returns are paid out. MM(1961) argues that if investment is held constant, it makes no difference whether the firm pays out high or low dividends. On the other hand, a firm’s announcement of increase in dividend payout may be interpreted as a signal by shareholders that the firm anticipates permanently higher levels of return from investment, and of course, higher returns on investment will result in higher share prices. Empirical evidence along this line provides support for the ‘information content of dividends’ hypothesis or signaling theory.
In addition, we present some empirical studies on tests of the CAPM. Most studies indicate (a) that the intercept term is higher than the CAPM would predict, (b) a flatter slope indicating that low beta securities earn more than the CAPM prediction, (c) dominance of beta as a risk measure,
(d) capacity of certain factors in explaining security returns not captured by beta. The CAPM debate is also presented together with Roll’s critique on the problem of measurement of the ‘true’ market portfolio.
Some theoretical issues on the impact of systematic factors on common stock performance are also presented.
Further, comparison of the CAPM and the APT is presented. The Chen study shows that the APT could explain a statistically significant portion of the CAPM residual variance, but the CAPM could not explain the APT residuals. However, empirical studies do not indicate that the APT is error-proof. For instance, Wei’s study demonstrates that, in finite economy, the pricing error bound of the Ross APT in a correlatedresiduals factor structure is an increasing function of the absolute value of market-residual beta.
Also, the theory of hedging capacity of assets against inflation is presented. Empirical studies by Fama and others indicate contradiction of the conventional wisdom on common stock inflation hedging capacity. However, an attempt by Fama to explain this anomalous result is the hypothesis that negative relations between stock returns and inflation are proxying for positive relations between stock returns and real variables, which are more fundamental determinants of equity values. Fama explains that negative stock return-inflation relations induce negative relations between inflation and real activity. Accordingly, the proxy effect hypothesis predicts the disappearance of the anomalous relations when both real variables and measures of expected and unexpected inflation are used to explain stock returns.
It is important to emphasize that most of the empirical evidence on these theories are predominantly based on developed markets. The inspiration for this research therefore, is the awareness that these theories, however logically sound and valid the points they make, may not all be applicable at the same time in all environments. In similar vein, the researcher, here, attempts an empirical investigation of some of the stated theories in the Nigerian economy using figures derived from the Nigerian Stock Exchange (NSE) and some major macro-economic indicators in Nigeria. The related data and methodological issues of this study are discussed in the next chapter.
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Xu, Y. and B.G. Malkiel (2003) “Investigating the Behaviour of Idiosyncratic Volatility,” Journal of Business, Vol. 76, No. 4, pp. 613-644.
Yoon, G. (2005) “Stochastic Unit Roots in the Capital Asset Pricing Model?” Bulletin of Economic Research, Vol. 57, No. 4, pp. 369-389.
Zwiebel, J. (1996) “Dynamic Capital Structure Under Managerial Entrenchment,” American Economic Review, Vol. 86, No.5 (December), Pp. 1197-1215.
Having presented the theories and empirical evidence on the cogent issues of this research, an attempt would be made to present the technique of collecting data and analyzing the same in order to contribute to the existing line of thinking on these subjects. This is the purpose of this chapter. To this end, the research design, data and methodological issues are discussed; the models for testing the hypotheses are presented cum bases for evaluation of estimates. The chapter concludes with the limitations of methodology with implications for further research.
This study is structured into six main parts on the issues underscored by our theoretical hypotheses. The EfficientMarket Hypothesis which underscores this study has been tested and, with very few exceptions, found consistent with the data in a wide variety of markets: Stock Exchanges, Commodity Future Markets, the Over-the -Counter Markets, the Corporate and Government Bond Markets, the Option Market and the Market for seats on some Stock Exchanges. In similar manner with empirical studies, the data for this research, obtained mainly from the NSE, were analysed using some of the best empirical methods. The study rests on the comparative stochastic dynamics of optimal corporate growth using the criterion of maximum present value of the common stocks where the latter in turn is equal to the present value of the certainty equivalents of the prospective cash flow (dividend) stream.
Every listed stock during the study period (1990-2004) has an equal chance of being picked. The first set of data relates more to the theory of firm behaviour while the rest of the data relate either to investor behaviour or investor reaction to managerial decisions. For hypotheses three, five and six, aggregate data for the respective periods were used and by this, we implicitly assume that the relationship between the variables involved is homogeneous across firms.
Results are evaluated first on the basis of the theoretical rationales behind the variables involved. Thereafter, statistical and econometric techniques are applied to establish reliability of results.
The data used for this study are secondary and time-series. They were obtained from various issues of the NSE Annual Reports and Statement of Accounts and FACT BOOKS, and from various issues of the CBN Statistical Bulletin and Annual Reports and Statement of Accounts. In addition, data were sourced from the International Finance Corporation (IFC) Emerging Markets Fact-books. The researcher employed annual data in respect of all the specified hypotheses. The choice of variables is influenced by apriori knowledge from related studies as were reviewed in the previous chapter.
The population of this study is the entire list of common stocks that are listed on the Nigerian Stock Exchange. There are six broad categories of quoted companies on the NSE namely Agriculture, Financial, Manufacturing, Commercials, Services and the Foreign Listings. These classifications all reflect the nature of economic activities constituting respective lines of business.
On the choice of sample, the researcher picked a random sample of fourteen (14) stocks across four broad sectors of Financial, Manufacturing, Commercials and Services. Specifically, four stocks - Afribank, First Bank (FBN), UBA and Union Bank (UBN) - were chosen from the banking sub-sector of Financial; two stocks - Nestle and Cadbury - were picked from the Food, Beverages and Tobacco sub-sector of Manufacturing; two stocks from Conglomerate (CFAO and John Holt) and four common stocks from Petroleum (Mobil, Texaco, Total and Unipetrol/Oando) sub-sectors of Commercials and last, two stocks from Construction (ROADS and Julius Berger) sub-sector of Services. The choice is influenced by parameters such as the relative strengths of capitalization, length of quotation, and most important, possession of requisite data for the study’s objectives.
The methods of analyses, using time-series data, would be statistical and econometric approaches.
A. Hypothesis 1 - Regression Analysis.
The weighted average cost of capital (WACC) would be regressed on the debt ratio in order to determine the influence of leverage on firm value. A negative and significant coefficient of debt ratio would indicate gain from leverage and by extension increase in firm value, which accrues to common stockholders.
In addition, the degree of correlation between the average Earnings Per Share (EPS) and the degree of leverage would indicate which of two common theories of optimal capital structure (the pecking order theory or the trade- off theory) dominates in Nigeria.
Abbildung in dieser Leseprobe nicht enthalten
Where d = debt ratio (a measure of financial leverage)
Abbildung in dieser Leseprobe nicht enthalten
B. Hypothesis 2 Regression Analysis:
Aims at testing for the relation between dividends and share price reaction on the NSE.
The model should be of the form:
Abbildung in dieser Leseprobe nicht enthalten
Where
Abbildung in dieser Leseprobe nicht enthalten
It is in the opinion of the researcher that this specification accords directly with the objective of determining the signaling effect of dividend payout policy. This specification does not assume that the riskiness of the firm is uncorrelated with dividend payout and firm is uncorrelated with dividend payout and price-earnings ratios. Rather, the usual argument against this line of specification is overcome by relating average market price per share against averages of dividend per share and retained earnings per share thereby comparing ‘like with like.’ Besides, Friend and Puckett’s argument of possible depression of the retained argument of possible depression of the retained earnings coefficient is overcome by the condition of non-negativity (i.e RPS ≥ O). Market information is employed in generating these data sets and as such the measurement error argument associated with accounting principles does not hold.
C. Hypothesis 3. - Multiple Regression and Correlation Analysis Multiple regression analysis is intended whereby the NSE all - share index would be regressed on certain macroeconomic variables such as industrial production index, changes in expected inflation (as measured by changes in short-term Treasury bill interest rates), unanticipated inflation (measured by changes between actual inflation and expected inflation), unexpected changes in default risk premiums (measured by the difference between returns on corporate bonds and long-term government bonds), unanticipated changes in term premium (measured by the difference between the returns on long- and short term government securities) and the volume of money supply (M1).
In addition, the degree of inter-correlation amongst the chosen cues would be examined to determine their joint impacts on common stock returns.
With the existence of cointegration in the multiple regression, it is implied that the long-run movements in the variables are related. (See De Jong, 2001 and Nwokoma, 2002). The equation would be of the form:
Abbildung in dieser Leseprobe nicht enthalten
ε_{it} is a random variable believed to represent a Gaussian white noise.
Alternatively, the return on market index as documented in the IFC’s Emerging Market Factbook could be regressed on the explanatory variables as listed above.
Recently, Longstaff, et al, (2005) find evidence in support of our UR measure.
Suffice to note that the variables were selected in the spirit of Chen, Roll and Ross (1986) study.
D. Hypothesis 4. - Simply Linear Regression
The equation of the ex post CAPM is of the form.
Abbildung in dieser Leseprobe nicht enthalten
The predictions should meet the specified criteria in chapter two i.e
Abbildung in dieser Leseprobe nicht enthalten
The alternative test to the CAPM assumes that the market model is true and has been recommended on the ground that the risk-free interest rate does not appear. The problem with the risk-free interest rate is its nonstationarity (Markellos and Mills, 2001; Yoon, 2005).
Consistent with Gibbon’s submission, the two-factor CAPM implies earlier stated constraint on the intercept of the market model (as in 2.29). If that restriction holds, then the CAPM is valid.
E. Hypothesis 5 - Multiple Regression Analysis.
P/E ratio would be regressed on the growth rate in earnings per share (in percentage) and the average dividend payout ratio (in decimal). This is in line with the much quoted Whitbeck and Kisor Jr. argument as documented in Fuller and Farrell (1987).
The equation should be of the form:
Abbildung in dieser Leseprobe nicht enthalten
A statistically significant δ1 would indicate the strong relation between the P/E ratio and growth prospects.
F. Hypothesis 6 - Multiple Regression Analysis.
The system of equation on common stock return - inflation relation should be of the form.
Abbildung in dieser Leseprobe nicht enthalten
Where R_{it} = average return on common stocks
Abbildung in dieser Leseprobe nicht enthalten
Following the Fisher hypothesis, when the tests suggest that
βj = 1.0, we say that common stock is a complete hedge against expected inflation. When Yj = 1.0, common stock is a complete hedge against inflation.
It is important to emphasize that estimates would be evaluated first on the basis of their conformity with the theoretical expectations as to the signs and magnitudes of the parameters. The explanatory power of the variables selected under each of the specified hypotheses would be indicated by the coefficient of determination (R^{2} ), which is the statistical measure of explained variation. The higher the coefficient of determination, the lower the possibility of omission of variables and vice versa. Furthermore, econometric tests of serial dependence of random disturbances would be evaluated using the ‘Durbin- Watson d statistic.’ (see Koutsoyiannis, 1977; Heckman, 2001; Hendry, 2001; Phillips, 2001; Tauchen, 2001; Clark and McCracken, 2001; Hotchkiss and Strickland, 2003; Ferson, et. al 2003, etc).
This study is limited in the following respects.
1. Annual data are employed whereas in certain studies monthly or quarterly data are utilized.
2. Parametric studies (e.g Pastor and Veronesi, 2003) that utilize regression analysis seek to transform the variables into logarithmic forms in order to circumvent the linearity problem associated with certain relationships. The methodology of this study does not conform to this log transformation. In the opinion of the researcher the basic specification accords well to the research objective and constitute the most basic issues of attention to the target audience.
3. The test of the first hypothesis presupposes the existence of a single variable (debt ratio) in explanation of the average cost of capital. However, studies such as Titman and Wessels (1988) and Allayannis, et. al, (2003) indicate other variables such as firm size, growth rate of EPS, relative use of local currency versus foreign currency debt, etc.
4. The chosen samples could have been broader covering all the major sectors of the economy in Nigeria.
5. Further, in analyzing certain hypotheses, individual security returns (rather than portfolio returns) might be needed to obtain more statistically powerful results. This study however strongly relies on (statistical) averages in the analyses of collected data.
Allayannis, G., G. Brown And L.F. Klapper (2003) “Capital Structure And Financial Risk: Evidence From Foreign Debt Use In East Asia,” Journal of Finance, Vol. 58, No. 6, pp.2667-2709.
Clark, T.E. And M.W. McCracken (2001) “Tests of Equal Forecast Accuracy And Encompassing For Nested Models,” Annals Journal of Econometrics, Vol. 105, No.1, pp. 85-110.
De Jong, R.M. (2001) “Nonlinear Estimation Using Estimated Cointegrating Relations,” Journal of Econometrics, Vol.101, No.1, (March), pp.109-122.
Ferson, W.E., S. Sarkissian, And T.Simin (2003) “Spurious Regressions In Financial Economics?” Journal of Finance, Vol.58, No.4, (August), pp. 1393-1413.
Fuller, R.J. And J.L. Farrell (1987) Modern Investments And Security Analysis, 1st Edition, New York: McGraw-Hill Inc.
Heckman, J.J. (2001) “Econometrics And Empirical Economics,” Journal of Econometrics, Vol. 100, No.1 (Jan), pp. 3-5. Hendry, D.F. (2001) “Achievement And Challenges In Econometric Methodology,” Journal of Econometrics, Vol.100, No.1 (Jan) , pp. 7-10.
Hotchkiss, E.S. And D. Strickland (2003) “Does Shareholders Composition Matter? Evidence From The Market Reaction To Corporate Earnings Announcements,” Journal of Finance, Vol. 58, No.4, pp.1469-1498.
Koutsoyiannis, A. (1977) Theory Of Econometrics, 2nd Edition, Basingstoke: Palgrave.
Longstaff, F. A., S. Mithal and E. Neis (2005) “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market,” Journal of Finance, Vol. 60, No. 5, pp.2213-2253.
Markellos, R.N. and T.C. Mills (2001) “Unit Roots in the CAPM?” Applied Economics Letters, Vol. 8, pp. 499-502.
Pastor, L., And P. Veronesi (2003) “Stock Valuation And Learning About Profitability,” Journal of Finance, Vol. 58, No. 5, (October), pp. 1749-1789.
Phillips, P.C.B (2001) “Trending Time Series And Macroeconomic Activity: Some Present And Future Challenges,” Journal Of Econometrics, Vol.100, No 1 (Jan), pp. 21-27.
Tauchen, G. (2001) “Notes on Financial Econometrics,” Journal of Econometrics, Vol. 100, No. 1 (Jan), Pp. 57-64.
Titman S. And R. Wessels (1988) “The Determinants of Capital Structure Choice,” Journal of Finance, Vol. 43, No.1, pp. 1-19. Yoon, G. (2005) “Stochastic Unit Roots in The Capital Asset Pricing
Model?” Bulletin of Economic Research, Vol. 57, No. 4, pp.369- 389.
In this chapter, an attempt to present our empirical findings is made from the results of our data analyses. The chapter is organized as follows:
i. Results on Capital Structure Relevance.
ii. Results on Information Content of Dividends.
iii. Common Stock Performance and Systematic Factors.
iv. Applicability of the CAPM.
v. P/E Ratio- Growth Relation.
vi. Inflation- Hedging Capacity of Common Stocks.
The results obtained provide answers to our research questions. The main results are as follows:
i. The MM theorem holds well in Nigerian corporate environment. The financial structure of firms do not affect the cost of capital of firms and by extension, does not determine common stock valuation. However, the relation between return on common stocks and debt-equity ratio (proxy for financial risk) is not significant.
ii. The analyses confirm the empirical validity of the static trade-off and pecking order theories of optimal capital structure. This evidence does not necessarily overthrow the MM theorem but provides basis for its modification to move closer to reality. The pecking order theory is consistent with financial signaling.
iii. Dividend policy of firms in Nigeria communicates crucial message to market participants. The information content of dividends’ hypothesis holds well in Nigeria.
iv. Systematic factors do not jointly impact on stock returns. The only exception is the strong co-movement between the level of money supply and the proxy for output. This has some implications for multifactor asset pricing models. Researchers should construct portfolios that are highly correlated with these factors and estimate the related premiums from average returns.
v. The CAPM does not conform to common stock pricing on the NSE.
vi. The P/E ratio is not significantly related to growth but to the payout ratio.
vii. Common stocks are fairly effective inflation hedgers.
The reader would recall that the first hypothesis is about the independence of gearing on common stock valuation, which could be put equivalently that the cost of capital is completely independent of capital structure following MM proposition 1.
The regression specification, as indicated in the previous chapter is of this form:
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.1a: REGRESSION RESULTS ON CAPITAL STRUCTURE IMPACT
Abbildung in dieser Leseprobe nicht enthalten
The figures in parentheses represent t-values.
When V= degrees of freedom = 15-2 =13, the critical value of the t- distribution at 5% level of significance is 2.16. For majority of the chosen companies, the coefficient of the debt ratio is insignificant, indicating the independence of the cost of capital to the financial structure. In particular, after analyzing average data, the results indicate that, on the overall, the debt ratio coefficient, though negative, is statistically insignificant thereby supporting the MM capital structure theorem especially the proposition 1.
As long as these results hold, we cannot reject the (null) hypothesis that the degree of financial leverage (gearing) is independent of common stock values. Therefore, the financial structure of firms in Nigeria is not the critical factor that determines the payoffs attributable to common stockholders.
Note:
Abbildung in dieser Leseprobe nicht enthalten
The implication of low coefficient of determination- 19%- is that there are other factors, outside gearing, that might help to explain variation in the cost of capital of firms.
The difficulties here are concerned with the isolation of the leverage effect (if any) from all the other factors, which might be expected to have an effect on the overall cost of capital and its components.
TABLE 4.1b: REGRESSION EQUATIONS USING 4 BANK STOCKS
Abbildung in dieser Leseprobe nicht enthalten
Degrees of freedom for each of the regression equations equal thirteen (13).
Except for Afribank’s stock, the regression equations of the three (other) banks indicate the existence of favourable financial leverage because the statistically significant negative coefficients indicate that the respective costs of capital decline with increase in gearing. This is, of course, a contradiction to the MM hypothesis but the special nature of the financial sector (or in particular, the banking industry) may not permit us to generalize. Of course the nature of banks’ liabilities determines the investment strategy they pursue, as they are primarily spread businesses. Moreover, the banking industry is a highly leveraged environment.
However, the results obtained using average data are consistent with MM theorem.
TABLE 4.1c: DEBT RATIOS OF FOUR BANKS (1990-2004)
Abbildung in dieser Leseprobe nicht enthalten
Source: Computed from NSE Factbooks (Various Years)
TABLE 4.1d: RETURN ON BANK CAPITAL EMPLOYED (%) FOR 1990-2004
Abbildung in dieser Leseprobe nicht enthalten
Source: Computed from NSE Factbooks (Various Years)
A contentious issue relating to our first research question is whether the market would revise its valuation of a company because of a change in the financing mix. Assuming book returns approximate market returns and that financial markets are efficient, our empirical results do not support an instant revision of the market’s view of a company’s worth following a (slight) change in capital proportions.
It is also important to note that the MM theorem is crucially dependent on the willingness and ability of some market participants to engage in “arbitrage” operations by which means the equilibrium of the market will be maintained over time. Temporary disequilibrium in the market means, specifically, any disparity (abstracting from differences in scale) among the total market values of companies in the same “risk class” or “equivalent return” set.
In addition, MM derived from their proposition 1, another proposition concerning the equity capitalization rate in levered firms. Accordingly, they proposed that the expected rate of return, or yield, on the stock of any company is a linear function of leverage. In mathematical terms;
Abbildung in dieser Leseprobe nicht enthalten
D/E = debt-equity ratio
The second term of equation (4.1) is the premium related to financial risk.
The results of the regression equations, using ten (10) firms, that test the relationship between return on equity and the debt-equity ratio are tabulated in table 4.1e with t-values indicated in brackets. [Abbildung in dieser Leseprobe nicht enthalten]
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.1e: THE COST OF EQUITY AND DEBT-EQUITY (D/E) RATIO.
Abbildung in dieser Leseprobe nicht enthalten
* Significant @ 5 percent
** Significant @ 10 percent
***Significant @ 20 percent
At the various significance levels (viz 0.05, 0.10 and 0.20) six (out of ten) stocks indicate a linear relationship between the return on equity and the debt-equity ratio. This is consistent with the MM proposition II without taxes.
However, with taxes and on average, there is no significant relation between the cost of equity and the debt-equity ratio. Thus, shareholders of levered firms do not earn (or expect to earn) any after-tax premium for financial risk. These results might have implication on investors’ attitudes toward risk.
In addition, two theories of optimal capital structure viz- pecking order theory and the static trade-off theory- posit contrary relationships regarding profitability and leverage. According to the static trade-off theory, high profitability would signify high debt capacity and thereby stimulate high levels of gearing. In statistical terms, the static trade-off theory hypothesizes a positive correlation coefficient between profitability and leverage.
However, the pecking order theory posits that most profitable firms will borrow less because internal equity is at the top of the financing choice- not because they have low target debt ratios but because they don’t need don’t need outside money. In the pecking-order theory, the attraction of interest tax shields is assumed to be a second-order effect. Highly profitable firms with limited investment opportunities work down to low debt ratios and vice versa. In statistical terms, the theory explains the inverse relationship between profitability and financial leverage. Alternatively, an increase in gearing would exert a positive price reaction.
Again, the interested reader is referred to the related articles (e.g Fama and French, 2002; Baker and Wurgler 2002; Welch, 2004; Leary and Roberts, 2005; Miao, 2005 and the references cited in these papers).
Using earnings per share (EPS) as a proxy for profitability and debt-equity ratio as a measure of leverage. The following regression results are obtained.
Abbildung in dieser Leseprobe nicht enthalten
Where Et represent earnings per share Gt represents debt-equity ratio
TABLE 4.1f: EARNINGS PER SHARE (EPS) AND D/E RATIO
Abbildung in dieser Leseprobe nicht enthalten
On the basis of the correlation coefficients, it can be said that there is a moderate relationship between profitability and leverage and hence the static trade-off theory applies in Nigerian corporate environment.
The regression equation for the test of the Pecking Order Theory is as follows:
Abbildung in dieser Leseprobe nicht enthalten
The correlation coefficient of 48 percent also indicates moderate relationship and implies the empirical validity of the Pecking Order Theory. This result is also consistent with financial signaling under asymmetric information.
However, we cannot conclude as to which one, between the two theories (static trade-off or pecking order), dominates in Nigeria.
Recall that the related regression equation is of the form:
Abbildung in dieser Leseprobe nicht enthalten
The hypothesis tested here is statistically expressed thus:
Abbildung in dieser Leseprobe nicht enthalten
Where the average market price per share of ten selected stocks is regressed on average dividend per share as well as the average retained earnings per share, the summary statistics are tabulated as follows.
TABLE 4.2a: DESCRIPTIVE STATISTICS (HYPOTHESIS TWO)
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.2b: INTERCORRELATION MATRIX OF PRICES,
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.2c: MODEL SUMMARY -- PRICES, DIVIDENDS AND
Abbildung in dieser Leseprobe nicht enthalten
Dependent Variable: Prices
R^{2} = 0.60 Adjusted R^{2} = 0.53
Durbin-Watson d statistic = 1.05
The above results indicate a significant dividend coefficient at 1% significance level.
The implication of the results is that information content of dividends hypothesis holds well in Nigeria.
It is also important to note that a positive correlation between changes in market prices and dividend changes is consistent with the information-signaling effect of dividends. Using data sets generated on four (4) bank stocks, the Pearson Product Moment Correlation Coefficient (PPMCC) indicates a strong association between dividends and stock prices. In fact, the degree of relationship (r) is approximately 89 percent.
Here, the study period is extended to 20 years (from 1985 to 2004) in a bid to enhance the reliability of our estimates.
Analyses of two alternative models are presented viz the regression of NSE all-share index on systematic variables and the regression of the total return index on systematic variables. In mathematical form, the equations are:
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.3a: DESCRIPTIVE STATISTICS (HYPOTHESIS THREE)
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.3b: CORRELATIONS OF ALL-SHARE INDEX WITH
Abbildung in dieser Leseprobe nicht enthalten
Table 4.3b indicates strong association between:
i. The NSE all-share index and the proxy for output (i.e index of industrial production). This is consistent with the conjecture that any growth in output should generally affect the future cash flows of firms in the same direction alongside stock prices.
ii. The NSE all-share index and index of expected inflation. This result might be consistent with hedging capacity of common stocks against expected inflation.
iii. NSE all-share index and level of money supply as narrowly defined. This runs counter to the Fama’s (1981) submission that there is a positive relationship between monetary growth and inflation rate, implying that monetary growth would adversely affect stock prices. Rather, the relationship between money stock and stock prices is positive.
iv. Output and money supply. This might imply that monetary growth brings about increase cash flows for firms and by extension, their productive capacity. Also, it might be that the growth in money supply transmits to output growth in the economy’s real sector via interest rate reduction.
v. Expected inflation and money stock. This is consistent with economic theory that postulates a direct relationship between the level of money supply and the general price level (or people’s perception of future price level ).
However, there exists moderate relationship between:
i. Output level and unanticipated changes in term premium
ii. Stock index and unanticipated changes in term premium
iii. Output level and expected inflation
iv. Output level and unanticipated changes in default risk premiums
v. Expected inflation and unanticipated changes in default risk
vi. Expected inflation and unanticipated changes in term premium
vii. Unanticipated changes in term premium and the volume of money supply.
In addition, our results might indicate that an upward-sloping term structure of interest rates is driven primarily by expected inflation. This result might generate implication for future research on term structure of interest rates in Nigeria.
TABLE 4.3c: COEFFICIENTS DERIVED FROM NSE ALL-SHARE
Abbildung in dieser Leseprobe nicht enthalten
Dependent Variable: NSE All-share Index R^{2} = 0.98, Adjusted R^{2} =0.97
Standard Error of Estimate = 1146.73
Now, turning to the research question on the joint impact of systematic factors on common stock returns. Tables 4.3d, 4.3e and 43f give our summary results.
TABLE 4.3d: DESCRIPTIVE STATISTICS
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.3e: CORRELATIONS OF RETURN INDEX WITH
Abbildung in dieser Leseprobe nicht enthalten
Index of total return on stocks responds most significantly to the level of money supply (as narrowly defined). From the table, M1 accounts for about 94 percent of the total variation in the total return index (RMT). Next, return responds to output level (Y) and then unanticipated changes in term premium (UT).
The association between NSE Index (Z) and the level of money supply (M1) on one hand and the association between total return index (RMT) and level of money stock (M1) on the other, are indications of the possible linkage of the monetary sector and the capital market. Specifically, changes in monetary policy could exert significant impact on equity prices and returns. A recent justification of this conjecture is provided in Bernanke and Kuttner (2005).
Now regarding whether there exists co-movement of systematic variables in the explanation of stock returns, table 4.3e shows that systematic factors do not jointly impact on common stock returns. The only exception in shown by the strong correlation between the proxy for output (Y) and the level of money supply. The implication of this is that sophisticated investors could, after factor analysis, require compensation in form of premium for each of the systematic variables. This is the logic of multifactor asset pricing models. Besides, the presence of low (or negative correlation) between pairs of systematic variables helps to distinguish the separate impacts of the variables on ex post stock returns. Hence, the problem of multicollinearity of explanatory variables in the cross-section of equity returns does not hold. The implication of the exception to portfolio investments is that only one of the two factors (i.e either output or money supply) will command a premium in analysis or evaluation of investment in the capital market.
The regression results of total return index (RMT) are summarized in table 4.3f.
TABLE 4.3f: COEFFICIENTS FROM TOTAL RETURN REGRESSION
Abbildung in dieser Leseprobe nicht enthalten
a. Predictors: (constant), M1,DEI, UT, UI, UR, Y
b. Dependent Variable RMT
R^{2} = 0.973 Adjusted R^{2} =0.960
Standard Error of estimate = 39.4610 Durbin- Watson Statistic = 2.028
The Durbin- Watson d statistic also indicates that there is no problem of autocorrelation of the random (error) variable.
In sum, on the basis of the t-values, the order of significance starting with the most significant variable is:
i. the level of money supply;
ii. changes in expected inflation;
iii. unanticipated changes in term premium;
iv. unanticipated inflation;
v. unexpected changes in default risk premiums;
vi. the index of industrial production.
There are two alternative tests.
1. Utilizing the regression described in chapters two and three. The results from running the regression using data obtained from NSE publications for the period 1990-2004 are as follows:
Abbildung in dieser Leseprobe nicht enthalten
Standard error of estimate = 0.5789
In summary, these results indicate that:
i. The intercept (Yo) is significantly different from zero which runs contrary to CAPM prediction.
ii. Beta lacks explanatory power. This is indicated by the coefficient of determination which is approximately nil. The theoretical expectation of the linear relation between return and beta lacks empirical support.
iii. The coefficient of beta is negative (though insignificant) whereas the CAPM predicts a positive coefficient.
However, certain studies have long recognized that the above methodology is fraught with limitations (see Markellos and Mills, 2001; Yoon, 2005 and Ross, Westerfield and Jaffe, 1996: 289-290, for a summary of issues involved).
A major problem arises, however, from the non-stationarity of the risk-free interest rate. Because the market model does not require the risk-free interest rate in its application, Markellos and Mills recommend using it.
2. Using the market model which is of the form:
Abbildung in dieser Leseprobe nicht enthalten
Where Rit = return on a security or portfolio at time t.
R_{mt} = return on market portfolio or general market index εit = random variable
a_{i} and β_{i} = parameters of the model.
The condition imposed on the intercept term (ai) by Gibbons must hold for the CAPM to be accepted.
Abbildung in dieser Leseprobe nicht enthalten
Where E(Rf) = expected return on Treasury Certificates as a proxy for return on a minimum variance portfolio in the market (computed as 18% for the study period).
The null hypothesis that CAPM applies could be specified thus:
Abbildung in dieser Leseprobe nicht enthalten
The alternative hypothesis:
Abbildung in dieser Leseprobe nicht enthalten
The results are presented hereunder:
TABLE 4.4: MARKET MODEL TEST OF CAPM
Abbildung in dieser Leseprobe nicht enthalten
NOTE. Average Data I refers to results from average data sets on the non bank stocks (10) chosen for this study.
Average data II refers to results obtained from average data sets on the four (4) bank stocks.
COMMENT
The CAPM lacks strong empirical support as shown in the market model test of CAPM. Therefore factors other than beta might contribute to explaining the cross-section of stock returns consistent with FamaFrench (1992 and 1993) studies. Besides the relevance of factors such as size, market to book ratios, price earnings (P\E) ratio, dividend yield, etc, single factor multi-index models might exhibit some reliable goodness of fit in the cross section of equity returns.
Further, recent survey by some scholars indicates that idiosyncratic risk (an unsystematic risk) matters in explaining stock market returns. In particular Goyal and Santa-Clara (2003) find a positive relation between average stock variance (largely idiosyncratic) and the return on the market. Bali, et al (2005) obtain results which contradict Goyal and Santa-Clara’s study. Bali, et al (2005) show that the earlier result by Goyal and Santa-Clara is driven by small stocks traded on the Nasdaq, and is in part due to a liquidity premium. The investigation of these results is beyond the scope of this study.
Following the required regression model specified in chapter three, the P/E ratio points to a stock’s growth potential if the growth coefficient is positive and significantly different from zero. Statistically, this hypothesis is tested.
Abbildung in dieser Leseprobe nicht enthalten
The results are presented hereunder:
TABLE 4.5a: DESCRIPTIVE STATISTICS (HYPOTHESIS FIVE)
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TABLE 4.5b: INTERCORRELATION MATRIX OF P/E,
Abbildung in dieser Leseprobe nicht enthalten
4.5c: MODEL SUMMARY - P/E, PAYOUT AND GROWTH,
Abbildung in dieser Leseprobe nicht enthalten
R^{2} = 0.24 Adjusted R^{2} = 0.10
Standard Error of estimate = 7.03 Durbin-Watson d statistic = 0.996.
The above results indicate that the P/E Ratio responds more to the payout ratio than to the growth in earnings per share. Besides, the coefficient of the growth variable is not significantly different from zero at the 5 percent level of significance. It is highly improbable that the true growth coefficient is positive. Therefore, the P/E ratio is independent of growth percentage.
In interpreting these results, one can infer that a high P/E ratio does not indicate a low risk firm or a low capitalization rate. There is no reliable association between a stock’s P/E ratio and the capitalization rate. The ratio of EPS to price (Po) measures the capitalization rate only if the present value of growth opportunities is nil and only if reported EPS is the average future earnings the firm could generate under a no-growth policy (see Brealey and Myers, 2003:75).
The results are presented hereunder (Recall equation
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TABLE 4.6a: DESCRIPTIVE STATISTICS (HYPOTHESIS 6)
Abbildung in dieser Leseprobe nicht enthalten
It is important to note that the return defined here refers to average return on all common stocks that are listed on the NSE. The total return index data is derived from the IFC Emerging Market Factbooks.
The Ho hypothesis is tested.
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TABLE 4.6b: CORRELATIONS OF RETURN INDEX WITH EXPECTED INFLATION AND UNANTICIPATED INFLATION
Abbildung in dieser Leseprobe nicht enthalten
TABLE 4.6c: MODEL SUMMARY -- RETURN INDEX AND INFLATION COMPONENTS
Abbildung in dieser Leseprobe nicht enthalten
R^{2} = 0.90 Adjusted R^{2} = 0.88
Standard Error of estimate = 69.55 Durbin-Watson d statistic = 1.366
On the bases of the standardized slope coefficients and t values, the above results indicate that common stocks are fairly effective in inflation hedging in Nigeria. We reject the null hypothesis that common stocks are not effective inflation hedgers at 10 percent significance level.
Thus, investors can preserve their wealth from the negative impact of changing price levels by investing in common stocks. In addition, shareholders of firms with long-term commitments would benefit from Unanticipated Inflation (UI) due to an unexpected decline in the real value of their nominal liabilities. This is to say that investors should invest wisely. Investors should consider the peculiarities of each stock to determine its response to performance drivers as identified in this study.
Baker. M. and J. Wurgler (2002) “Market Timing and Capital Structure,” Journal of Finance, Vol. 57, pp. 1-32.
Bali, T.G., N. Cakici, X. Yan and Z. Zhang (2005) “Does Idiosyncratic Risk Really Matter?” Journal of Finance, Vol. 60, No. 2, pp. 905- 929.
Bernanke, B.S. and K.N. Kuttner (2005) “What Explains the Stock Market’s Reaction to Federal Reserve Policy?” Journal of Finance, Vol. 60, No. 3, pp. 1221-1257.
Brealey, R. and S. Myers (2003) Principles of Corporate Finance, 7th Edition, Boston: McGraw-Hill, p. 75.
Fama, E.F. and K.R. French (2002) “Testing Trade-off and Pecking Order Predictions About Dividends and Debt,” Review of Financial Studies, Vol. 15, pp. 1-33.
Goyal, A. and P. Santa-Clara (2003) “Idiosyncratic Risk Matters!” Journal of Finance, Vol. 58, No. 3 pp. 975-1008.
Leary, M.T., and M.R. Roberts (2005) “Do firms Rebalance their Capital Structures?” Journal of Finance, Vol. 60, No. 6, pp. 2575-2619.
Markellos, R.N. and T.C. Mills (2001) “Unit Roots in the CAPM?” Applied Economics Letters, Vol. 8, pp. 499-502.
Miao, J. (2005) “Optimal Capital Structure and Industry Dynamics,” Journal of Finance, Vol. 60, No. 6, pp. 2621-2659.
Welch, .I. (2004) “Capital Structure and Stock Returns,” Journal of Political Economy, Vol. 112, pp. 106-131.
Yoon, G. (2005) “Stochastic Unit Roots in the Capital Asset Pricing Model?” Bulletin of Economic Research, Vol. 57, No. 4, pp. 369-389.
This completes our efforts at investigating the investment performance of common stocks in Nigeria with the aim of ascertaining some financial theories that are applicable in the Nigeria investment environment. Hence, this chapter provides the summary of our findings, conclusions based on findings and then recommendations.
The major findings of this study are itemized as follows:
i. The valuation of firms is independent of their financial structure. Or equivalently, the average cost of capital to any firm is completely independent of its financial structure. This is a confirmation of the MM theorem under mean assumptions. However, the relation between return on common stocks and debt-equity ratio (proxy for financial risk) is not significant. A recent support of this is also provided in Low (2004).
ii. The study confirms the empirical validity of two theories of optimal capital structure viz: static trade-off theory and the pecking order theory. The pecking order theory is consistent with financial signaling that changes in firms’ financial structure communicate crucial information to the market especially as insiders have information that investors do not have. The credibility of such signal stems from asymmetric information.
iii. Changes in corporate dividend policy communicate an important message to investors in the market. To some extent, the payout policy of firms determines why some stocks are priced above others on the Nigerian Stock Exchange (NSE). This is referred to as the information- signaling effect of dividends or information content of dividends’. The researcher also observed that firms smooth their dividends.
iv. Systematic factors do not jointly affect equity returns in Nigeria. The only exception is the strong comovement of the level of money stock and the proxy for output.
v. The order of significance of systematic variables on stock returns, starting with the most significant, are:
a. The level of money supply,
b. Changes in expected inflation,
c. Unanticipated changes in term premium,
d. Unanticipated inflation
e. Unexpected changes in default risk premiums,
f. The index of industrial production.
vi. The CAPM does not apply to pricing on the Nigerian Stock Exchange (NSE). Our analyses confirm the poor explanatory power of beta.
vii. The P/E ratio-growth relation is weak. The theoretical expectation is that the price-earnings (P/E) ratio points to a firm’s growth potential. Our analysis indicates, however, an insignificant growth coefficient, where growth is defined as
percentage increases in the earnings per share (EPS) Rather, P/E ratio responds better to the payout ratio, a finding consistent with the result of our second hypothesis. viii. Investment in common stocks could be an effective inflation- hedging strategy. Specifically, common stocks, on average, are greater hedging vehicles against expected inflation relative to unanticipated inflation.
Here, an attempt is made to discuss the findings along the specified questions and hypotheses and from insights gained from literature review.
The mix of all sources of funds to a firm is referred to as the financial structure. The idea that one mix of financing sources would reduce the cost of capital, which in turn might permit the acceptance of more worthwhile investments and thus increase the value of the company, whereas another mix might have the opposite effect, does not hold. The choice of capital structure is a marketing problem. Our results imply that attempts to maximize value by mere capital structure changes are not worthwhile. The really important decisions concern the company’s earning capacity as shown in its assets base. Thus, the capital structure is irrelevant as long as the firm’s investment decisions are taken as given. It implies that a company can adopt any value- maximizing capital budgeting procedure without worrying about where the money for capital expenditures comes from.
MM’s hypothesis, as its creators expected, caused something of a commotion in academic and business cycles, because it challenged the generally accepted views about the effects of leverage on the overall cost of capital to a company. The commotion produced two related results: first, it prompted empirical research to support or refute their hypothesis; second, it focused those who hold a different view of leverage to be much more precise and explicit about the exact nature of those views. Although the traditional position had been in existence before the MM hypothesis appeared, it acquired greater clarity and substance as a direct result of the MM hypothesis, a process which may be observed by reading the relevant articles.
On the face of it, one capital structure might be better than another because of certain market imperfections. Some of these imperfections explain a traditional view in corporate finance that firms strive to maintain an optimal capital structure that balances the costs and benefits associated with varying degrees of leverage. These imperfections, such as taxes, costs of bankruptcy, costs of writing and enforcing complicated debt contracts, asymmetric information, agency costs, incentive effects and capital rebalancing or adjustment costs, could make a good case for the existence of optimal capital structure which could vary systematically across firms depending on industrial peculiarities. Also, the interrelationships between investment and financing decisions might result in the variation of the cost of capital, because of the impact of the investment on the business risk of the company.
However, we do not throw away MM theory by admitting that financial policy matters. Rather, we seek a theory that unifies MM’s insights plus the effects of taxes, costs of financial distress, asymmetric information, agency costs and various other complications.
Dividend policy could be regarded as the trade-off between retaining earnings on the one hand and paying out cash and issuing new shares on the other. The Dividend controversy mainly considers how corporate dividend policy affects value. Specifically, the MM Dividend Invariance Proposition states that in the presence of perfect capital markets and given firms investment decisions, dividend policy does not matter. There are, however, various complications relating to dividend policy of firms. In particular, firms try to smooth dividends and that’s why we have behavioural models of dividend policy along the lines of Lintner’s observations. Further, firms decisions about dividends are often mixed up with other financing and investment decisions. Some firms adopt low payout policy because of managements’ optimism of the firms’ future and therefore wish to retain for onward expansion. Here, dividend is related to capital budgeting decision. If we suppose, however, that future opportunities evaporate and a dividend increase is announced which leads to a fall in stock price, how do we separate the impact of the dividend increase from the impact of the investors’ disappointment at the lost growth opportunities? Another firm might finance capital expenditures by borrowing and this provides cash for dividends. In this case, a firm’s dividend is a by-product of the borrowing decision.
Similar to the capital structure theorem, the presence of market imperfections and some of the complications discussed above has led to the evolution of theories that provide the bases for optimal dividend policy (though the empirical evidence is still inconclusive) by balancing the benefits as well as the costs of dividend payout. This study has adopted a rather noble approach by focusing essentially on the informativeness of dividend payout. By relating market prices of common stocks to dividend per share and retentions in a regression model, our results confirm that the information signaling effect of dividends is quite strong both for the non-financial corporations and banks in Nigeria. Several related approaches abound in the finance literature and some were reviewed in the second chapter of this study. A different approach, which also has a good deal of intuitive appeal is provided by Grullon, et al (2002).
In particular our results suggest that dividend increases convey good news while dividend decreases convey bad news. This is consistent with asymmetric information and resolution of uncertainty, among other arguments.
Further, the pecking order hypothesis, as it relates to dividend policy, predicts a negative long-run stock return reaction following secondary equity offerings. This provides an interesting linkage between asymmetric information and agency cost, sometimes explained by the windows of opportunity hypothesis. Other possible hypotheses relating to the dividend controversy include: the leverage tax shield hypothesis; the dividend tax avoidance hypothesis; the bondholder expropriation hypothesis; wealth transfers and microstructure arguments.
The finance literature provides evidence that there are volatilities and asymmetries in stock returns, some of which are driven by systematic factors. This fact provides basis for the asset pricing models in corporate finance (i.e CAPM and its variants). The investigation of the relation between common stock returns and systematic factors is motivated by the Chen, Roll and Ross (1986) and Nwokoma (2002) studies. In particular, we find that our chosen systematic variables do not vary jointly to impact on stock returns. The only exception is the co- variation between the proxy for output and the level of money supply as narrowly defined. The implication is that investors would be concerned with securities or portfolios that provide premiums in respect of the identified factors.
On the significance order of systematic variables on stock returns, the most significant is the level of money supply, followed by changes in expected inflation, unanticipated changes in term premium, unanticipated inflation, unexpected changes in default risk premiums and the index of industrial production (our proxy for output). In particular, the NSE all-share index is strongly related to three variables namely: the level of money supply, the index of expected inflation, and the level of industrial production.
In line with the postulates of economic theory, our study confirms a strong relation between the level of money supply and index of expected inflation. However, the argument that increases in money supply should translate to increase in inflation does not hold. This is because the Nigerian economy, like any other economy with slacks in its productive capacity, could generate sufficient increase in output that would more than offset the inflationary impact of a rise in the level of money supply.
Further, we find a strong relation between output level and money supply. Also, this is consistent with theory. The output response to a change in money stock is consistent with a negative interest rate reaction following a change in the volume of money supply. For instance, when interest rates decline following increase in volume of money supply, productive activities in the real sector are stimulated as a result of the low cost of investment.
Another interesting finding are the varying (through moderate) degrees of relationship that exist between the unanticipated changes in term premium and four factor viz: index of expected inflation, the level of money supply, index of industrial production and the stock index. In particular, our results indicate that unanticipated changes in term premium might largely be driven by the index of expected inflation. This should provide basis for the shape of the yield curve in explanation of the term structure of the interest rates.
If capital market deepening is a prime government economic objective, then monetary policy should be co-ordinated with other related policies (such as fiscal, income and exchange rate policies) to ensure that the expansion of money and credit will be adequate for the long-run needs of the growing economy at stable prices.
Our results refute the theoretical expectation regarding the expected return-beta relationship. In particular, we find that beta lacks explanatory power. Using both the return-beta regression model and the
market model, there are no bases to support the empirical conformity of the CAPM on pricing on the Nigerian Stock Exchange (NSE). The implication of this is that there are other factors that might help to explain the cross section of equity returns. For instance, size and book-to-market equity might be related to systematic patterns in relative profitability and growth that could well be the source of common risk factors in returns. Other helpful factors would relate to maturity and default risks in the bond market. This is in line with the discussion in the preceding sub-section (i.e 5.2.3).
Our results refute the conventional belief of a strong P/E ratio- growth relation. High price-earnings multiples do not necessarily indicate that all those firms that have high P/Es do have good growth opportunities, or that their earnings are relatively safe or both. firms can have high P/E ratios not because price is high but because earnings are low. A firm which earns nothing (EPS=0) in a particular period will have an infinite P/E as long as its shares retain any value at all.
However, relative P/Es are sometimes helpful in evaluating stocks. Suppose an individual holds stock in a corporation whose shares are not actively traded or if the individual holds stock in a private firm, P/E ratios could serve as the closest approximation to the stock’s worth. A decent estimate is possible if such individual can find traded firms that have roughly the same profitability, risks and growth opportunities.
Our empirical results indicate that on the overall, common stocks are fairly effective in inflation hedging. Specifically, they are more effective hedges against expected inflation. This finding is consistent with the conventional doctrine in financial theory.
Shareholders of companies that have made long-term commitments such as accounts payable and long-term debts can benefit more from unanticipated inflation. This is consistent with the wealth redistribution effect during inflationary periods or in inflationary environments. It is important to state here that investors would require precision as to which stocks to hold in order to preserve their wealth over their lifetime. Not all stocks are effective inflation hedgers. More specifically, stocks whose earnings respond well to the business cycles would be good vehicles for inflation hedging.
The study conclusions are as follows:
i. On the face of it, the MM hypothesis simplifies the finance
manager’s task with regard to managing the capital structure. Their theory appears to suggest that the finance manager can legitimately use debt or equity to finance new investment or switch from one to the other, in the knowledge that his decision would have no impact on firm valuation. The tax-deductibility of debt interest will apparently mean that he should maximize the amount of debt in the capital structure so as to minimize the overall cost of capital. Such a simplistic view of his role would be misleading for several related reasons: First, the finance manager may prefer the relative freedom of action afforded by equity finance. Debt holders may wish to constrain his authority to raise new debt finance or to take on high-risk investments, in order to safeguard their own wealth. As a result, the company’s investment plans may be aborted thus diminishing the quality and quantity of its expected operating earnings, lowering its total market value and increasing its overall cost of finance. Second, the MM theorem deals in long- term equilibrium positions on the capital market. This does not, however, mean that there are no opportunities for short adjustments to the financing mix, to take advantage of the continual adjustments which will be occurring in the market. Arbitrageurs seek to do just that; and finance managers might, for example, take an opportunity to issue debt, rather than equity if the debt market fails to revise its rates in line with expected inflation (Wurgler and Zhuravskaya, 2002 and Attari, et al, 2005). Third, it appears that corporate failures will be more likely as high levels of gearing are reached. The associated costs would offset the current estimates of debt’s tax benefits. Again, see a recent survey in Molina (2005). Other factors that should make managers worry about capital structure decisions include conflicts of interest, information and incentive problems. A view that incorporates all these, moves away from MM’s basic assumptions.
There is no universal theory of the debt-equity choice and no reason to expect one. The logic of the MM theorem is widely accepted though financing clearly can matter. The conditions under which the MM theorem holds should be fully understood by managers as the bases to grasping the kinds of market imperfections to look for.
There may be deeper, less conditional theories of optimal capital structure, but they will require careful modeling of the financial objectives of the managers of the firm. (Each of the theories reviewed and tested here implies, but does not derive, a particular objective for managers). However, these deeper models will not follow just from writing down the utility function of a Chief Executive Officer (CEO) or the parameters of his or her employment contract. These firms act as organizations, not individuals. They presumably act in the interest of some group or coalition of the managers or employees who make, or are affected by, the financial decisions of the firm. Myers (2000) suggests that the firm acts to maximize the value of current and future benefits to “insiders”. The benefits come in various forms: cash; over and above opportunity wages; stock or options in the firm; and private benefits, such as perquisites (Myers, 2001: 99-100). ii. Similar to the capital structure theorem, the dividend decision requires a balancing of the MM invariance proposition with specific market imperfections and other complications that run counter to MM assumptions. Specifically, in the Nigerian investment environment that is pervaded with a host of uncertainties, a stable dividend payout policy would be favoured by investors. This is without prejudice to withholding taxes on dividends. A high payout policy, that is consistently followed, provides resolution for uncertainties. Also, the presence of institutional investors such as pension funds, investment companies, insurance companies, unit trusts, etc provides incentives for corporations to be liberal in their distribution policy.
iii. Investors would seek securities or portfolios that are highly correlated with the systematic variables employed in this study. A multi-factor asset pricing model, such as the Arbitrage Pricing Theory (APT) could therefore be presented thus:
Abbildung in dieser Leseprobe nicht enthalten
Where E(Ri) = the expected rate of return on a security or portfolio. bi’s = the sensitivities of the ith asset’s returns to the k factors. The items in brackets represent risk premiums for each factor. Stocks with positive sensitivity to output, for instance, will tend to have higher returns when output increases. Also, investors would seem to prefer stocks that protect them against inflation. They might even be willing to accept lower expected returns from such stocks.
In addition, this study might underlie the need for government (through the CBN) to balance target economic growth rates with monetary policy variables such as money supply and interest rates. A great deal of financial programming would be required.
iv. Multi-factor asset pricing models would help to explain the cross section of equity returns unlike the single factor CAPM. In addition, the industry costs of stocks might conform to factors that influence the stock market such as the overall market factor and factors related to firm size and book- to-market equity in line with some Fama-French studies. However, we do not reject the CAPM (totally).
v. Private firms’ stock’s worth could sometimes be derived by examining some fundamentals of certain listed firms with similar earnings capacity, risks and growth opportunities. To derive this, the private firm’s earnings per share (EPS) should be multiplied by the P/E of the counterpart firms. A strong reason why P/E multiples are hard to interpret is that the figure for earnings depends on the accounting procedures for calculating revenues and expenses. The potential biases in accounting earnings are discussed in Brealey and Myers (2003:326-334).
vi. Investors can judiciously preserve their wealth stock from inflation risk through active investment strategies as against passive portfolio management.
Our recommendations are as follows:
i. Managers should adjust their capital structures to an optimal range depending on their specific objectives. For instance, managers of highly profitable firms with good growth potentials might lever up to constrain themselves and pursue efficiency. This is even more relevant in an environment where the market for corporate control is active. The imperfections that concern an environment should provide bases for the modification of the underlying MM theorem. It is important to stress the need for the pursuit of value-maximizing strategies by managers. A firm’s capital budgeting decision is crucial to its long-term solvency and stability.
ii. Managers should continue (or follow) a stable dividend policy.
iii. Managers should commit themselves to the following strategies, among others, to enhance value: revenue enhancement, cost reduction, asset utilization and cost of capital reduction. The firm can increase its revenue by improving its market share and/or increasing the product’s price. The requisite strategies for this include patents, product differentiation, monopoly power, etc. Also the firm can become a cost leader by lowering its costs beneath that of its competitors through economies of scale, vertical integration or captive sources of material.
Further, the firm can improve its profitability by reducing its capital intensity through improved utilization of its assets.
In addition, the firm can design debt and equity securities that appeal to special niche of capital market and thereby attract cheaper funds (refer to Pandey, 1999:1189).
iv. Capital market regulators and supervisors should recognize that they are moderators and facilitators of capital market development. They should enforce fairness, transparency and professionalism in the securities business. Further, they should recognize that the capital market performs better under liberalization or deregulation. This is indicated by the NSE performance since around 1995 as a result of removal of government restrictions on investment that year. As long as regulation does not impede an otherwise worthwhile transaction, outflow of funds from the economy would be limited. We should borrow a leaf from Britain’s (and other nations’) deregulation of its stock market - the ‘Big Bang’ - which was, in part, a response to competition from foreign exchanges and trading opportunities. In particular, SEC and NSE should be cautious with innovations/regulations that increase transaction costs beyond the level average investors can bear.
v. Investors should invest in portfolios that compensate them for the factor risks identified in this study. More specifically, they should look out for stocks that preserve their wealth from unanticipated shifts in general price level.
vi. Financial analysts should be cautious in their interpretation of P/E ratios. Averages of industrial price -earnings multiples for a period of five years or so might, however, help to resolve the confusion about what P/Es really signify and thereby give realistic directions.
vii. There are many possible directions for future research, which could be more obvious by following keenly, the discussion of findings. For instance, the alternative test for the information signaling theory provided in Grullon, et al (2002) is the investigation of the relation between dividend changes and subsequent changes in profitability (earnings growth rates or return on assets). The pecking order theory of dividends could also be examined following the framework provided by Fama and French (2002) and several other scholars. The debt capacity or tax benefits of debts of corporations could be empirically investigated by researchers, following Graham (2000) Molina (2005), etc. This study has not shown whether managers exploit “windows of opportunity” by issuing over valued shares or whether there are different market reactions to different equity offerings viz: primary versus secondary offerings (refer to Clarke, et al, 2004, and Heron and Lie, 2004).
Further, we do not know in quantifiable terms, the impact of these qualitative factors, such as automation and more recently mergers, and acquisitions, and demutualization of the NSE, strict enforcement of corporate governance, on equity values (Jain, 2005; Martijn Cremers and Nair, 2005; Zhou and Swan, 2003).
It seems safe to say that this study has presented some voluminous evidence on the investment performance of common stocks in Nigeria. In business and economic research, however, one can never claim to have established a hypothesis beyond question. Additional or alternative tests to issues raised in this study, which would either confirm the validity of the empirical evidence or contradict the obtained results, are suggested.
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Utility theory establishes the basis of rational decision making in the face of risky alternatives. It focuses on the question: “how do people make choices?” The objects of choice are described by asset pricing theories. When we combine the theory of choice with the objects of choice, we are able to determine how risky alternatives are valued.
Risk aversion is related to the concavity of the utility function. The concepts of risk aversion (i.e risk neutrality, risk loving behaviour and risk-averse behaviour) were developed by Arrow and Pratt. Suppose an investor had initial wealth Wo, which he can invest in a portfolio divided between a safe asset and a risky asset. The safe asset has a fixed gross rate of return of s, and the risky asset has stochastic gross rate of return of Y (Y= 1+r), with its distribution function denoted by Prob (Y < g) = F (g). Letting x be the share of wealth invested in the risky asset, final wealth W is given for Y = g by
Abbildung in dieser Leseprobe nicht enthalten
The utility of wealth is such that U(W) = 0, U^{1} (W) > 0 for all W. The sign of U^{11} (W) captures the investor’s attitude toward risk: U^{11} > O for a risk lover and U^{11} < O for a risk averter. In the intermediate case, U^{11} = O, the investor is risk neutral. Strictly speaking, this is a local characteristic. The same investor may switch from one category to another at different values of W. Expected utility of wealth is
Abbildung in dieser Leseprobe nicht enthalten
which is a function of x and Wo, given the probability distribution of g. Risk -averse behaviour.
The first-order condition for an interior solution in a graphical utility function is found by differentiating Eq. (A.2) wrt x and setting to zero.
Abbildung in dieser Leseprobe nicht enthalten
This is a maximum if the second order condition ∂^{2} EU/∂x^{2} < O is met:
Abbildung in dieser Leseprobe nicht enthalten
A sufficient condition for (A.3) to define a maximum is that U^{11} (W) < 0 for all W, that is, risk aversion. A necessary condition is that U^{11} W) < O for some W. Consider now how the share of the portfolio held in the risky asset varies with initial wealth. The question is the sign and size of the derivative ∂x/∂Wo. Eq. (A.3) can be interpreted as making x implicitly a function of Wo, given s. Let this implicit function be H (Wo, X;S) = O, where H is ∂EU (W)/∂x as evaluated in Eq. (A.3). Differentiating H=O with respect to Wo gives:
Abbildung in dieser Leseprobe nicht enthalten
of which the first term is zero.
Consequently,
Abbildung in dieser Leseprobe nicht enthalten
which may be positive or negative or zero.
Relative risk aversion is defined as ψ (W) =
Abbildung in dieser Leseprobe nicht enthalten
Now if ψ(W) is constant at ψ, the right - hand side of Eq. (A.8) is ψH=O, by the first - order condition Eq. (A.3). Thus, constant relative risk aversion implies that ∂x/∂Wo = O, that is, the share of risky assets in the portfolio is independent of the level of initial wealth.
If ψ (W) is monotonically declining in W, the right-hand side of Eq. (A.8) is positive because the integral is negative and because low values of g, hence negative values of g-s, are associated with low wealth and thus high ψ(W). That is, the negative
values for g-s are more heavily weighted in the integral than the positive outcomes. Similarly, if ψ^{1} (W) > O, the right-hand side is negative. Summarizing.
-^{1} (W) Negative implies [Abbildung in dieser Leseprobe nicht enthalten]
-^{1} (W) Positive implies [Abbildung in dieser Leseprobe nicht enthalten]
-^{1} (W) Zero implies [Abbildung in dieser Leseprobe nicht enthalten]
it can also be observed that constant relative risk aversion restricts the form of the utility function: [Abbildung in dieser Leseprobe nicht enthalten] which implies the following:
Abbildung in dieser Leseprobe nicht enthalten
if U (O) = O then β = O
Absolute risk aversion is defined as O (W)
[Abbildung in dieser Leseprobe nicht enthalten] This is not a pure number like relative risk aversion. Its
dimension is (change in marginal utility) per (unit of marginal utility). Using the
definition of O (W), Eg. (A.7) can be rewritten as:
Abbildung in dieser Leseprobe nicht enthalten
If O (W) is constant at O, then Eq. (A.11) is zero by Eq. (A.6) again, and ∂(xWo)/ ∂Wo is zero. That is, the absolute size of the holding of the risky asset is constant, and all incremental initial wealth is invested in the safe asset. Similarly, diminishing absolute risk aversion implies that some fraction of marginal wealth is invested in the risky asst, whereas increasing absolute risk aversion implies that the amount invested in the risky asset actually decreases as wealth increases.
Constant absolute risk aversion restricts utility to a negative exponential function, as follows. U^{11} = - O U^{1} implies U^{1} = βeOW, which implies U = C - (β/O) e-OW.
APPENDIX B: MARKET CLEARING AND THE CAPM
The capital asset pricing model is derived by combining the separation theorem with the assumption that the markets for assets clear. The market-clearing condition is that the outstanding supply ZK of any asset K, measured in physically units or shares of replacement cost, is equal to the sum of the individual demands for shares, Zik,
Abbildung in dieser Leseprobe nicht enthalten
To express Eq. (B.1) in value rather than physical terms, let qk be the market-clearing price of asset k. Measured at market prices, individual i's wealth Wi, the aggregate market value of all assets MV, and wik, wmk can then be defined as the shares of asset k in the individual and market portfolios respectively:
Abbildung in dieser Leseprobe nicht enthalten
Multiplying both sides of Eq. (B.2a) by qk and substituting in Eqs. (B.2c) and (B.2d), we can express the market clearing condition for asset k,
Abbildung in dieser Leseprobe nicht enthalten
and in vector format, for all assets
Abbildung in dieser Leseprobe nicht enthalten
Asset demand functions can be expressed in matrix form as follows:
Abbildung in dieser Leseprobe nicht enthalten
Where wi is the vector of portfolio weights, μ is the vector of expected returns on the risky assets, 1 is a vector of ones, Ω-^{1} is the inverse of the variance-covariance matrix of returns on the risky assets, and Ti = - ui1/2ui2 is a measure of investor i's risk tolerance. Under the assumption that all investors face the same probability distribution of returns, only Ti is specific to investor i (For details, refer to Tobin, 1998: 166-169 and Bajeux- Besnainou, et al, 2003).
Substituting Eq. (B.4) into Eq. (B. 3b) yields, after rearranging,
Abbildung in dieser Leseprobe nicht enthalten
Where Tm = Σi (TiWi/MV), Eq. (B.5) can be rewritten as
Abbildung in dieser Leseprobe nicht enthalten
Pre-multiplying by wm yields:
Abbildung in dieser Leseprobe nicht enthalten
Where μm and s refer to returns on market portfolio and safe asset respectively.
Using Eq. (B.7) to eliminate Tm in Eq. (B.6), and pre-multiplying Eq. (B.6) by any chosen portfolio p consisting of weights wj yields the CAPM relationship:
Abbildung in dieser Leseprobe nicht enthalten
Alternatively, interpreting the portfolio as a single asset j, the CAPM states.
Abbildung in dieser Leseprobe nicht enthalten
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