This thesis provides an exhaustive and well-founded overview of risk measures, in particular of Value at Risk (VaR) and risk measures beyond VaR.
Corporations are exposed to different kinds of risks and therefore risk management has become a central task for a successful company. VaR is nowadays widely adapted internationally to measure market risk and is the most frequently used risk measure amongst practitioners due to the fact that the concept offers several advantages. However, VaR also has its drawbacks and hence there have been and still are endeavours to improve VaR and to find better risk measures.
In seeking alternative risk measures to try to overcome VaR’s disadvantages, while still keeping its advantages, risk measures beyond VaR were introduced. The most important alternative risk measures such as Tail Conditional Expectation, Worst Conditional Expectation, Expected Shortfall, Conditional VaR, and Expected Tail Loss are presented in detail in the thesis. It has been found that the listed risk measures are very similar concepts of overcoming the deficiencies of VaR and that there is no clear distinction between them in the literature – ‘confusion of tongues’ would be an appropriate expression. Two concepts have become widespread in the literature in recent years: Conditional VaR and Expected Shortfall, however there are situations where it can be seen that these are simply different terms for the same measure.
Additionally other concepts are touched upon (Conditional Drawdown at Risk, Expected Regret, Spectral Risk Measures, Distortion Risk Measures, and other risk measures) and modifications of VaR (Conditional Autoregressive VaR, Modified VaR, Stable modelling of VaR) are introduced.
Recapitulatory the basic findings of the thesis are that there are numerous sophisticated alternative measures and concepts readily available, that there prevails a ‘confusion of tongues’ with the alternative risk measures in the respective literature and that promising theories and models are on the verge of entering the mainstream financial risk management stage. At the end of the day however neither VaR nor any other introduced risk measure is perfect. There are certain limitations aligned with every method; no single method is the best risk measure.
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
4.3.1 VaR and Subadditivity
VaR is in general not a coherent risk measure in the sense of Artzner et al. VaR satisfies indeed the properties of translation invariance, positive homogeneity, and monotonicity but fails to satisfy the axiom of subadditivity. This is because the axiom requires that it should hold for all random variables Xn implicating that if there is one example where the property does not hold VaR cannot be considered being coherent. One example should be given here:
Two different bonds A and B with non-overlapping default probabilities should be considered (e.g. bonds issued by Nokia and Motorola – they will not default at the same time). It could be the case that a portfolio consisting of the two bonds has a VaR which is higher than the total of the two separate VaR’s. Assuming two bonds have different default states with recovery values of 70 and 90 and probabilities of 3 % and 2 % respectively. Normally they will redeem at 100.
The results in Table 4 illustrate that the VaR for the portfolio is higher than the sum of the VaR’s of A and B. This fact can lead to wrong decisions and in case of optimization the result would be a full investment in either A or B and therefore the investor would ignore diversification at all (as stated in chapter 4.1 – subadditivity). In companies, calculating a firm-wide VaR is often a very challenging task. Therefore calculations are often segmented by e.g. instruments or desks and separate VaR’s are then estimated. Here the problem of VaR’s lack of subadditivity arises because the global VaR could be larger than the added-up separate VaR’s. A solution to that problem is often found in the way that the separate VaR’s are added up and hence used as best practice if a firm-wide VaR calculation is not available and global risks have to be assessed.
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.
- Quote paper
- MMag. Bernhard Höfler (Author), 2007, Risk measures - value at risk and beyond, Munich, GRIN Verlag, https://www.grin.com/document/83867
