Risk measures - value at risk and beyond

Table of Contents

1 INTRODUCTION

2 INTRODUCTION TO RISK

2.1 DEFINITION OF “RISK”

2.2 TYPES OF RISK

2.3 MARKET RISK

2.4 MEASURING RISK

3 VALUE AT RISK (VAR)

3.1 HISTORY OF VAR, RISKMETRICS

3.2 WHAT IS VAR?

3.3 COMPUTING VAR

3.3.1 Analytic, Variance-Covariance or Parametric Approach

3.3.2 Historical Simulation Approach

3.3.3 Monte Carlo Simulation Approach

3.3.4 Choosing between methods

4 CRITICISM ON VALUE AT RISK

4.1 CONCEPT OF COHERENT RISK MEASURES

4.2 ADVANTAGES OF VAR

4.3 DRAWBACKS AND FLAWS OF VAR

4.3.1 VaR and Subadditivity

4.3.2 Further weaknesses of VaR

4.3.3 The Jorion-Taleb Debate

5 BEYOND VALUE AT RISK

5.1 TAIL CONDITIONAL EXPECTATION (TCE)

5.2 WORST CONDITIONAL EXPECTATION (WCE)

5.3 EXPECTED SHORTFALL (ES)

5.4 CONDITIONAL VALUE AT RISK (CVAR)

5.5 EXPECTED TAIL LOSS (ETL)

5.6 CONFUSION OF TONGUES

5.7 CONDITIONAL DRAWDOWN (CDD) AT RISK (CDAR)

5.8 EXPECTED REGRET (ER)

5.9 SPECTRAL RISK MEASURES

5.10 DISTORTION RISK MEASURES

5.11 OTHER RISK MEASURES

5.12 MODIFICATIONS OF VALUE AT RISK

5.12.1 Conditional Autoregressive Value at Risk (CAViaR)

5.12.2 Modified VaR

5.12.3 Stable modelling of VaR

5.13 OUTLOOK ON RESEARCH IN RISK MEASUREMENT

6 CONCLUSION

Objectives & Research Focus

This thesis examines the concept of Value at Risk (VaR) in financial risk management, specifically focusing on its limitations and the search for more robust alternative risk measures to address these shortcomings. The primary research goal is to provide a comprehensive literature overview of current risk measures, analyze the 'confusion of tongues' regarding alternative concepts, and evaluate whether these models can realistically replace VaR in mainstream financial practice.

• Review of the fundamental ideas, principles, and calculation methods of Value at Risk (VaR).
• In-depth analysis of the criticisms and theoretical limitations of VaR, including the lack of subadditivity and convexity.
• Comparison and classification of alternative risk measures like Expected Shortfall (ES), Conditional VaR (CVaR), and Expected Tail Loss (ETL).
• Investigation into the "confusion of tongues" regarding terminology in the literature of advanced risk management.

Excerpt from the Book

Summary of Chapters

1 INTRODUCTION: Introduces the importance of financial risk management and outlines the objectives of the thesis, which include reviewing VaR concepts, addressing its limitations, and providing a literature overview of alternatives.

2 INTRODUCTION TO RISK: Defines the term "risk" in finance, categorizes various types of risk such as market, credit, and operational risk, and explains the fundamentals of risk measurement.

3 VALUE AT RISK (VAR): Details the history, definition, and practical computation methods of VaR, including the analytic, historical simulation, and Monte Carlo approaches.

4 CRITICISM ON VALUE AT RISK: Analyzes the theoretical and practical flaws of VaR, focusing on its lack of subadditivity, lack of coherence, and the debate between proponents and critics like Nassim Taleb.

5 BEYOND VALUE AT RISK: Provides an extensive literature survey of alternative risk measures like Expected Shortfall, CVaR, and Spectral risk measures, while discussing the terminological confusion in the academic field.

6 CONCLUSION: Synthesizes the main findings, reiterating that while VaR is a successful industry standard, its limitations necessitate the transition to more sophisticated alternative risk management models.

Keywords

Value at Risk, VaR, Risk Management, Coherent Risk Measures, Subadditivity, Expected Shortfall, ES, Conditional Value at Risk, CVaR, Expected Tail Loss, ETL, Spectral Risk Measures, Financial Risk, Market Risk, Risk Measurement

Frequently Asked Questions

What is the core focus of this thesis?

The thesis focuses on the limitations of Value at Risk (VaR) as a tool for financial risk management and investigates the theoretical properties and practical advantages of alternative risk measures.

What are the primary themes discussed in the book?

The book covers the definition of risk, the history and computation of VaR, theoretical criticism regarding coherence axioms, and a review of modern alternatives like ES, CVaR, and spectral risk measures.

What is the main goal or research question of this thesis?

The primary goal is to address the criticisms of VaR and clarify the landscape of alternative risk measures, specifically exploring why "confusion of tongues" exists in the scientific terminology used for these measures.

Which scientific methodology is employed?

The thesis utilizes a literature review methodology, analyzing current financial theories, the axiomatic framework of coherent risk measures, and comparing empirical computation models.

What is covered in the main section of the document?

The main part of the document is divided into a technical overview of VaR, a critical analysis of its limitations (such as the subadditivity problem), and a detailed survey of "Beyond VaR" concepts.

Which keywords characterize this work?

Key terms include Value at Risk, Subadditivity, Expected Shortfall, Coherent Risk Measures, Market Risk, and Financial Engineering.

Why is the subadditivity of VaR so important?

Subadditivity is a fundamental requirement for risk measures because it ensures that diversifying a portfolio does not result in an increase in calculated risk, which is a key principle of portfolio theory.

What does the term "confusion of tongues" mean in this book?

It refers to the fact that researchers and authors use different terms (e.g., Expected Shortfall, CVaR, Expected Tail Loss) to describe essentially the same underlying mathematical concepts, causing confusion in the literature.

How does the book address the "Jorion-Taleb" debate?

The book details the 1997 academic dispute where Nassim Taleb criticized VaR as dangerous and intellectually flawed, while Philippe Jorion defended it as a practical, transparent tool for institutional risk management.