The last months of the financial market crisis and in particular the bankruptcy of the renowned investment bank Lehman Brothers, have taught us all that a financial institution, failing to identify and address its risks appropriately, may rapidly face problems it is not able to handle on its own. Avoiding such problems requires a rigorous risk management not only in bad times but also in times where business is going and growing well.
Today, the most popular tool to measure, control and manage financial risk within corporations and financial institutions is the Value at Risk (VaR) concept. However, since the computation of the traditional Value at Risk relies solely on market prices, one often criticized downside is its disregard of market liquidity risk, which is defined as the potential loss resulting from the time-varying cost of trading. Due to the neglect of liquidity risk, the calculated VaR measures are suspected to be generally underestimated.
This thesis aims at finding a method for calculating liquidity adjusted Value at Risk (lVaR) that is most accurate and at the same time implementable in practice. The first objective is to provide a comprehensive overview on existing liquidity adjusted risk measures, assess them critically and evaluate their practicability. Second, I propose a new method to measure liquidity adjusted Value at Risk that accounts for non-normality in price and liquidity cost data using a technique called Cornish-Fisher expansion. In a third step I conduct extensive backtests of all lVaR approaches that proved to be implementable in a large stock data set of daily data. After comparing the accuracy of the backtested models in detail, recommendations for practical applications are given. I find only a very small fraction of those models based on indirect liquidity measures to be implementable. Mainly due to their burdensome data requirement most of those approaches are empirically untraceable. In contrast, the models using direct liquidity measures appeal through their manageable data requirement which facilitates their practical implementation. The empirical part of the thesis reveals that the main drivers for obtaining precise risk forecasts are the appropriate consideration of distributional properties and the use of direct, order size dependent liquidity measures. The dominant performance of the new lVaR method applying the Cornish-Fisher expansion indicates the superiority of this type of risk parametrization.
Table of Contents
1 Introduction
2 Market liquidity and liquidity risk
2.1 Concept of liquidity
2.2 Liquidity costs
2.2.1 Indirect liquidity cost measures
2.2.2 Direct liquidity cost measures
2.3 Liquidity risk
3 Theory of existing liquidity adjusted Value at Risk (lVaR) approaches
3.1 Conventional market risk measurement with Value at Risk (VaR)
3.2 Models based on indirect liquidity cost measures
3.2.1 Trading volume approach by Cosandey (2001)
3.2.2 Stochastic supply curve approach by Jarrow & Protter (2005)
3.2.3 Adjusted market price approach by Berkowitz (2000)
3.2.4 Approach with stochastic execution lag and quantity discount by Jarrow & Subramanian (1997,2001)
3.2.5 Approach with permanent and temporary liquidity impact by Almgren & Chriss (2000)
3.3 Models based on direct liquidity cost measures
3.3.1 Add-on approach with bid-ask spread by Bangia et al. (1999)
3.3.2 Limit order approach by François-Heude & v. Wynendaele (2001)
3.3.3 Net return approach with weighted spread by Stange & Kaserer (2008) and Giot & Gramming (2005)
3.4 Synopsis
4 Liquidity adjusted Value at Risk accounting for non-normality
4.1 The Cornish-Fisher expansion
4.2 Modified lVaR approaches
4.2.1 Modified add-on approach with bid-ask spread
4.2.2 Modified add-on approach with weighted spread
4.2.3 Modified net return approach with bid-ask spread
4.2.4 Modified net return approach with weighted spread
4.2.5 Evaluation of the modified lVaR approaches
5 Empirical Analysis
5.1 Data
5.2 General implementation specifications
5.2.1 Situational assumptions
5.2.2 Choice of confidence level and liquidation horizon
5.2.3 Determination of liquidity impact
5.2.4 Forecasting return volatility with an exponentially weighted moving average model (EWMA)
5.3 Backtesting framework
5.4 Analysis of lVaR approaches based on indirect liquidity cost measures
5.4.1 Cosandey (2001)
5.4.2 Berkowitz (2000)
5.5 Analysis of lVaR approaches based on direct liquidity cost measures
5.5.1 Bangia (1999)
5.5.2 François-Heude & Wynendaele (2001)
5.5.3 Stange & Kaserer (2008)
5.5.4 Giot & Gramming (2005)
5.6 Analysis of modified lVaR approaches
5.6.1 Modified add-on approach with bid-ask spread
5.6.2 Modified add-on approach with weighted spread
5.6.3 Modified net return approach with bid-ask spread
5.6.4 Modified net return approach with weighted spread
5.7 Comparison of the implemented lVaR approaches
5.7.1 Overall ranking
5.7.2 Model performance differentiated by order size
5.7.3 Rate of over- and underestimations by order size
5.7.4 Model performance differentiated by indices
5.7.5 Synopsis
6 Conclusion and outlook
7 Appendix
7.1 Magnitude of lVaR exceedances
7.2 Higher moment estimates
Research Objectives and Thematic Focus
This master's thesis aims to identify a robust and practical method for calculating Liquidity adjusted Value at Risk (lVaR), specifically addressing the shortcomings of traditional risk models that often neglect market liquidity and the non-normal distribution of returns.
- Critical assessment of existing indirect and direct liquidity risk measurement approaches.
- Implementation and backtesting of various lVaR models using a large dataset of German stocks.
- Integration of the Cornish-Fisher expansion to account for skewness and kurtosis in return distributions.
- Comparative analysis of model accuracy and performance across different order sizes and market indices.
- Formulation of practical recommendations for the implementation of liquidity-adjusted risk models.
Excerpt from the Book
2.3 Liquidity risk
“Market liquidity risk is the risk that a firm cannot easily offset or eliminate a position without significantly affecting market price because of inadequate market depth or market disruption.” 29
Liquidity risk emerges due to the uncertainty about liquidity costs, i.e. the uncertainty with respect to its price impact PIt(x) and delay costs Dt(x).30 Concerning liquidity risk, it is necessary to differentiate between non-strategic transaction on the one hand and strategic transaction on the other hand.31
In case of a non-strategic transaction, liquidity risk Lt(x) in t* < t arises due to the uncertainty of liquidity cost which is solely determined by the insecurity of price impact. In absolute terms it can be expressed as the uncertain difference between the realized portfolio value RVt = q x Ptrans(q) and the fair value FVt = q x Pmid
Lt(x) := q x Ptrans(q) - q x Pmid (6)
Summary of Chapters
1 Introduction: Provides the motivation for the thesis, highlighting the financial crises and the need for liquidity risk integration into VaR frameworks.
2 Market liquidity and liquidity risk: Develops a foundational definition of market liquidity and defines the costs associated with it, distinguishing between direct and indirect measures.
3 Theory of existing liquidity adjusted Value at Risk (lVaR) approaches: Reviews current literature on liquidity-adjusted risk models, covering both indirect and direct cost-based methodologies.
4 Liquidity adjusted Value at Risk accounting for non-normality: Introduces the Cornish-Fisher expansion to address non-normal return distributions and proposes modifications to existing lVaR frameworks.
5 Empirical Analysis: Presents the data, implementation specifications, and extensive backtesting results for the various analyzed liquidity risk models.
6 Conclusion and outlook: Summarizes the findings, evaluates the practical applicability of the tested models, and suggests areas for future research.
7 Appendix: Contains detailed statistical tables regarding magnitude of exceedances and higher moment estimates for the empirical study.
Keywords
Liquidity Risk, Value at Risk, lVaR, Market Liquidity, Bid-Ask Spread, Cornish-Fisher Expansion, Empirical Analysis, Backtesting, Kupiec-statistic, Financial Risk Management, Trading Volume, Price Impact, Asset Returns, Non-normality, Xetra Liquidity Measure
Frequently Asked Questions
What is the primary focus of this master's thesis?
The thesis focuses on finding a reliable and practical approach to measure Value at Risk (VaR) that accounts for market liquidity, aiming to improve risk forecasting in financial institutions.
What are the core thematic areas addressed?
The work covers market liquidity definitions, liquidity cost measurement (direct and indirect), existing lVaR theoretical frameworks, and the integration of non-normality into these models.
What is the central research question?
The core objective is to identify a method for calculating liquidity-adjusted risk that is sufficiently accurate for academic standards while remaining implementable in practical financial scenarios.
Which scientific methodology is utilized?
The author performs an empirical analysis, including the application of the Cornish-Fisher expansion to handle skewness and kurtosis, followed by rigorous backtesting using the Kupiec-statistic on 160 German stocks.
What topics are discussed in the main body?
The main body examines various lVaR approaches, compares their performance across different order sizes and indices, and evaluates their relative accuracy through extensive empirical backtesting.
Which keywords summarize this work?
Key terms include Liquidity Risk, lVaR, Cornish-Fisher Expansion, Bid-Ask Spread, Empirical Analysis, Backtesting, Kupiec-statistic, and Market Liquidity.
How does the Cornish-Fisher expansion improve standard risk models?
It allows the models to adjust for the non-normality (skewness and kurtosis) typically found in financial return distributions, rather than assuming standard normal distributions which often lead to inaccurate risk estimates.
Why are indirect liquidity measures often criticized in this thesis?
The author argues that models relying on indirect liquidity measures often have burdensome data requirements or purely theoretical foundations, making them difficult to implement in real-world practice.
What specific role does the Xetra Liquidity Measure (XLM) play in this study?
XLM is utilized as an order-size dependent measure of liquidity costs, providing a practical, market-based input for models that adjust VaR for weighted spreads.
What is the conclusion regarding the most effective model?
The thesis concludes that models using order-size dependent weighted spread data generally outperform others, with the modified add-on approach often providing highly accurate results across different order sizes.
- Arbeit zitieren
- Cornelia Ernst (Autor:in), 2009, The most reliable approach to measure Value at Risk adjusted for market liquidity, München, GRIN Verlag, https://www.hausarbeiten.de/document/154859
