The most reliable approach to measure Value at Risk adjusted for market liquidity

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

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.