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.
Inhaltsverzeichnis (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 (IVaR) 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 Alm-gren & 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 VaR 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 1VaR 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 IVaR approaches based on indirect liquidity cost measures
- 5.4.1 Cosandey (2001)
- 5.4.2 Berkowitz (2000)
- 5.5 Analysis of IVaR 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 VaR 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 VaR 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
- 6 Conclusion and outlook
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This Master's thesis investigates the most reliable approach to measure Value at Risk (VaR) adjusted for market liquidity. It aims to explore and evaluate various methodologies for incorporating liquidity risk into VaR calculations, focusing on both indirect and direct liquidity cost measures.
- Understanding the concept of market liquidity and liquidity risk.
- Analyzing existing liquidity adjusted VaR (IVaR) approaches based on indirect and direct liquidity cost measures.
- Developing and evaluating modified VaR approaches that account for non-normality in liquidity cost distributions.
- Conducting an empirical analysis to compare the performance of different IVaR approaches.
- Identifying the most reliable approach to measure VaR adjusted for market liquidity.
Zusammenfassung der Kapitel (Chapter Summaries)
The thesis begins with an introduction to the concept of market liquidity and liquidity risk. It then delves into the theory of existing liquidity adjusted VaR approaches, categorizing them based on their use of indirect or direct liquidity cost measures. The chapter explores various models, including the trading volume approach by Cosandey (2001), the stochastic supply curve approach by Jarrow & Protter (2005), the adjusted market price approach by Berkowitz (2000), and the approach with stochastic execution lag and quantity discount by Jarrow & Subramanian (1997,2001). It also examines models based on direct liquidity cost measures, such as the add-on approach with bid-ask spread by Bangia et al. (1999) and the limit order approach by François-Heude & v. Wynendaele (2001).
Chapter 4 focuses on the Cornish-Fisher expansion and its application to address non-normality in liquidity cost distributions. It explores various modified VaR approaches that incorporate bid-ask spreads and weighted spreads. Chapter 5 presents an empirical analysis, outlining data selection, implementation specifications, and a backtesting framework. It analyzes the performance of different IVaR approaches, examining both indirect and direct liquidity cost measures. The chapter provides a comprehensive comparison of the implemented VaR approaches, considering factors like overall ranking, performance differentiated by order size, and model performance differentiated by indices.
Schlüsselwörter (Keywords)
The key themes and concepts explored in this thesis include: market liquidity, liquidity risk, Value at Risk (VaR), liquidity adjusted VaR (IVaR), indirect liquidity cost measures, direct liquidity cost measures, non-normality, Cornish-Fisher expansion, empirical analysis, backtesting framework, model performance, order size, and indices. This thesis provides a comprehensive exploration of the most reliable approach to measure VaR adjusted for market liquidity, offering valuable insights into risk management practices in financial markets.
- 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.grin.com/document/154859
