Risk Measures for the 21st Century

By: Giorgio Szegö

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Product code: 21043
ISBN: 0470861541
512 pages
Format: Hb
Published by: John Wiley & Sons, 2004, 1st edition

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Risk Measures for the 21st Century - front page cover image

Description of Risk Measures for the 21st Century

The last five years have witnessed a great momentum in the research into measures of financial risk. After many years of ad-hoc and non-consistent measures, now the problem is finally well formulated and some useful and very user-friendly solutions have been proposed. These new measures of risk should be of great interest for investors, financial institutions as well as for regulators.

Under the editorship of Professor Giorgio Szego of the University of Rome "La Sapienza", this book is a collection of the revised and updated papers from prestigious international specialists who are leaders in their field, amongst whom is Robert Engle, a newly-announced Nobel prize-winner in finance. These authors bring a broad perspective across a wide selection of topics, ranging from the critique of some currently used methods, like Value at Risk, to the presentation of some correct risk measures and of some advanced application.

The book provides a detailed and up-to-date reference for researchers within academia, and risk managers or financial engineers.

Risk Measures for the 21st Century - Chapter headings

About the Contributors

1. On the (Non)Acceptance of Innovations (Giorgio Szegö)
1.1 Introduction
1.2 The path towards acceptance of previous innovations
1.3 How to answer
1.4 Conclusions
References

PART I: RISK MEASURES AND REGULATION

2. The Emperor has no Clothes: Limits to Risk Modelling (Jón Daníelsson)
2.1 Introduction
2.2 Risk modelling and endogenous response
2.3 Empirical properties of risk models
2.3.1 Background
2.3.2 Robustness of risk forecasts
2.3.3 Risk volatility
2.3.4 Model estimation horizon
2.3.5 Holding periods and loss horizons
2.3.6 Non-linear dependence
2.4 The concept of (regulatory) risk
2.4.1 Volatility
2.4.2 Value-at-risk
2.4.3 Coherent risk measures
2.4.4 Moral hazard - massaging VaR numbers
2.4.5 The regulatory 99% risk level
2.5 Implications for regulatory design
2.6 Conclusion
Acknowledgements
Appendix A: Empirical study
References

3. Upgrading Value-at-Risk from Diagnostic Metric to Decision Variable: A Wise Thing to Do? (Henk Grootveld and Winfried G. Hallerbach)
3.1 Introduction
3.2 Preliminaries
3.2.1 VaR and downside risk
3.2.2 Downside risk portfolio selection
3.2.3 Incomplete risk meaure
3.2.4 Computational issues
3.3 The mean-value-at-risk portfolio selection model
3.3.1 Deriving the mean-VaR portfolio selection model
3.3.2 Distinctive properties of the mean-VaR portfolio selection model
3.3.3 Solving the mean-VaR portfolio selection problem
3.4 The mean-value-at-risk portfolio selection model in practice
3.4.1 Data
3.4.2 Methodology
3.4.3 Results
3.5 Conclusions
Acknowledgements
References

4. Concave Risk Measures in International Capital Regulation (Imre Kondor, András Szepessy and Tünde Ujvárosi)
4.1 Introduction
4.2 Risk measures implied by the trading book regulation
4.2.1 Specific risk of bonds
4.2.2 Foreign exchange
4.2.3 Equity risk
4.2.4 The general risk of bonds
4.3 Conclusion
Acknowledgements
References

5. Value-at-Risk, Expected Shortfall and Marginal Risk Contribution (Hans Rau-Bredow)
5.1 Introduction
5.2 Value-at-risk as a problematic risk measure
5.3 Derivatives of value-at-risk and expected shortfall
5.3.1 Preliminary remarks
5.3.2 First and second derivative of value-at-risk
5.3.3 First and second derivative of expected shortfall
5.4 Outlook
Appendix
References

6. Risk Measures for Asset Allocation Models (Rosella Giacometti and Sergio Ortobelli Lozza)
6.1 Introduction
6.2 Portfolio risk measures
6.2.1 Safety risk measures
6.2.2 Dispersion measures
6.3 Portfolio choice comparison based on historical data
6.4 Portfolio choice comparison based on simulated returns
6.4.1 Portfolio choice comparison with jointly Gaussian returns
6.4.2 Portfolio choice comparison with jointly stable non-Gaussian returns
6.5 Conclusions
Acknowledgements
References

7. Regulation and Incentives for Risk Management in Incomplete Markets (J´on Daníelsson, Bjørn N. Jorgensen and Casper G. de Vries)
7.1 Introduction
7.1.1 Complete and incomplete markets
7.2 Moral hazard regarding project choice
7.2.1 Deposit insurance and moral hazard
7.2.2 Threat of an alternative project choice
7.3 Moral hazard regarding risk management
7.3.1 The basic principal-agent model
7.3.2 Supervision
7.4 Risk monitoring and risk management
7.4.1 Coarser risk monitoring without regulation
7.4.2 Indirect risk monitoring with regulation
7.4.3 Finer risk monitoring: no regulation
7.4.4 Direct risk monitoring with regulation
7.4.5 Evaluation
7.5 Conclusion
References

8. Granularity Adjustment in Portfolio Credit Risk Measurement (Michael B. Gordy)
8.1 Introduction
8.2 Granularity adjustment of VaR for homogeneous portfolios
8.3 Granularity adjustment of ES for homogeneous portfolios
8.4 Application to heterogeneous portfolios
Appendix: Wilde’s formula for ?
Acknowledgements
References

9. A Comparison of Value-at-Risk Models in Finance (Simone Manganelli and Robert F. Engle)
9.1 Introduction
9.2 Value-at-risk methodologies
9.2.1 Parametric models
9.2.2 Nonparametric models
9.2.3 Semiparametric models
9.3 Expected shortfall
9.4 Monte Carlo simulation
9.4.1 Simulation study of the threshold choice for EVT
9.4.2 Comparison of quantile methods performance
9.5 Conclusion
References
Appendix: Tables

PART II: NEW RISK MEASURES

10. Coherent Representations of Subjective Risk-Aversion (Carlo Acerbi)
10.1 Forewords and motivations
10.1.1 In defense of axiomatics
10.1.2 Scope and objectives
10.1.3 Outline of the work
10.2 Building a risk measure: the expected shortfall
10.2.1 A close look into VaR’s definition
10.2.2 A natural remedy to probe the tail: the expected shortfall
10.2.3 Coherency of ES
10.2.4 Estimation of ES
10.3 Spectral measures of risk
10.3.1 Estimation of spectral measures of risk
10.3.2 Characterization of spectral measures via additional conditions
10.3.3 Spectral measures and capital adequacy
10.4 Optimization of spectral measures of risk
10.4.1 Coherent measures and convex risk surfaces
10.4.2 Minimization of expected shortfall
10.4.3 Minimization of general spectral measures
10.4.4 Risk–reward optimization
10.5 Statistical errors of spectral measures of risk
10.5.1 Variance of the estimator
10.5.2 Some meaningful examples
Acknowledgements
References

11. Spectral Risk Measures for Credit Portfolios (Claudio Albanese and Stephan Lawi)
11.1 Introduction
11.2 Test-portfolios with market risk and entity-specific risk
11.3 Properties of risk measures
11.4 Discussion of test-portfolios
11.5 Concluding remarks
Acknowledgements
References
Appendix: Tables

12. Dynamic Convex Risk Measures (Marco Frittelli and Emanuela Rosazza Gianin)
12.1 Introduction
12.1.1 Notation
12.1.2 Axioms
12.1.3 Coherent risk measures
12.2 Convex risk measures
12.2.1 Representation of convex risk measures
12.2.2 Law-invariant convex risk measures
12.3 Indifferent prices and risk measures
12.4 Dynamic risk measures
12.5 Appendix
References

13. A Risk Measure for Income Processes (Georg Ch. Pflug and Andrzej Ruszczyński)
13.1 Introduction
13.2 The one-period case
13.3 Risk of multi-period income streams
13.4 Finite filtrations
13.5 Properties of the risk measure
13.6 Mean-risk models
13.7 Examples
13.8 A comparison with the ADEHK approach
13.9 The discounted martingale property for final processes
References

PART III: COPULA FUNCTIONS FOR THE ANALYSIS OF DEPENDENCE STRUCTURES

14. Financial Applications of Copula Functions (Jean-Frédéric Jouanin, Gaëulet and Thierry Roncalli)
14.1 Introduction
14.2 Copula functions
14.3 Market risk management
14.3.1 Non-Gaussian value-at-risk
14.3.2 Stress testing
14.3.3 Monitoring the risk of the dependence in basket derivatives
14.4 Credit risk management
14.4.1 Measuring the risk of a credit portfolio
14.4.2 Modelling basket credit derivatives
14.5 Operational risk management
14.5.1 The loss distribution approach
14.5.2 The diversification effect
References

15. Hedge Funds: A Copula Approach for Risk Management (Hélyette Geman and Cécile Kharoubi)
15.1 Introduction
15.2 Hedge funds industry, strategies and data
15.2.1 Hedge funds industry: definitions and description
15.2.2 The different strategies
15.2.3 Biases in hedge funds data
15.2.4 Hedge funds indices: descriptive statistics
15.3 Copulas and hedge funds
15.4 Value-at-risk with copulas
15.4.1 Monte Carlo simulation
15.4.2 Value-at-risk computation
15.5 Conclusion
Acknowledgements
References

16. Change-point Analysis for Dependence Structures in Finance and Insurance (Alexandra Dias and Paul Embrechts)
16.1 Introduction
16.2 Statistical change-point analysis
16.2.1 The test statistic
16.2.2 An example: the Gumbel case
16.2.3 The power of the test
16.2.4 The time of the change and corresponding confidence intervals
16.2.5 Multiple changes
16.3 A comment on pricing
16.4 An example with insurance data
16.5 Conclusion
Acknowledgements
References

PART IV: ADVANCED APPLICATIONS

17. Derivative Portfolio Hedging Based on CVaR (Siddharth Alexander, Thomas F. Coleman and Yuying Li)
17.1 Introduction
17.2 Minimizing VaR and CVaR for derivative portfolios
17.2.1 How well is the minimum risk derivative portfolio defined?
17.2.2 Difficulties due to ill-posedness
17.3 Regularizing the derivative CVaR optimization
17.3.1 Example 1: Hedging a short maturity at-the-money call
17.3.2 Example 2: Hedging a portfolio of binary options
17.4 Minimizing CVaR efficiently
17.4.1 Efficiency for CVaR minimization using an LP approach
17.4.2 A smoothing technique for CVaR minimization
17.5 Concluding remarks
Acknowledgements
References

18. Estimation of Tail Risk and Portfolio Optimisation with Respect to Extreme Measures (Giorgio Consigli)
18.1 Introduction
18.2 From risk measurement to risk control: the setup
18.2.1 VaR control with non-normal return distributions
18.3 Beyond VaR: From non coherent to coherent measures
18.3.1 Risk measures in the tails: methods accuracy
18.3.2 A case study. Application 1: Risk measurement
18.3.3 Multidimensional Poisson-Gaussian model
18.4 Risk control based on portfolio optimization
18.4.1 Risk–return and trade-off optimisation: QP and LP solvability
18.4.2 Optimal portfolios during periods of market instability
18.5 Conclusions and future research
Acknowledgements
References

19. Risk Return Management Approach for the Bank Portfolio (Ursula A. Theiler)
19.1 Introduction
19.2 Step 1 of the RRM approach: optimization model for the bank portfolio
19.2.1 Survey
19.2.2 Modeling the internal risk constraint
19.2.3 Integration of the regulatory risk constraint into the optimization model
19.2.4 Summary of the optimization model of step 1 of the RRM Approach
19.3 Step 2 of the RRM Approach: risk return keys for the optimum portfolio
19.3.1 Survey
19.3.2 Derivation of risk return keys on the asset level
19.3.3 Aggregation of risk return keys on the profit center level
19.3.4 Summary of the risk return ratios generated by the RRM Approach
19.4 Application example
19.4.1 Situation and problem statement
19.4.2 Results
19.5 Conclusion
References

PART V: LAST, BUT NOT LEAST

20. Capital Allocation, Portfolio Enhancement and Performance Measurement: A Unified Approach (Winfried G. Hallerbach)
20.1 Introduction
20.2 Preliminaries
20.3 Portfolio optimization, RAROC and RAPM
20.3.1 Portfolio optimization without risk-free rate
20.3.2 Portfolio optimization allowing for risk-free activities
20.4 Conclusions
Appendix
Acknowledgements
References

21. Pricing in Incomplete Markets: From Absence of Good Deals to Acceptable Risk (H´elyette Geman and Dilip B. Madan)
21.1 Introduction
21.2 No-good-deal pricing in incomplete markets
21.2.1 Good-deal asset price bounds (Cochrane and Saá, 2000)
21.2.2 Gain, loss and asset pricing (Bernardo and Ledoit, 2000)
21.2.3 The theory of good-deal pricing (Cerny and Hodges, 2001)
21.3 Pricing with acceptable risk
21.3.1 The economic model
21.3.2 The first fundamental theorem
21.3.3 The second fundamental theorem
21.3.4 Pricing under acceptable incompleteness
21.4 Conclusion
References

Index

Authobiography of Giorgio Szegö

GIORGIO SZEGO graduated in Physics at the University of Pavia. After postgraduate studies at the Technische Hochschule Darmstadt, he held teaching and research positions (Research Institute of Advanced Studies) in the USA. From 1964 to 1970 he had an appointment at the Faculty of Sciences of the University of Milan, and held visiting poisitions in various US universities.

He was then granted a chair in Mathematics for Economics at the University of Venice and in 1977 he co-founded and became Managing Director of the Journal of Banking and Finance. Giorgio Szego holds a chair in "Economics of Financial Markets" at the University of Rome and in January 2000 the University of Bergamo awarded him an honorary degree in Economics. His current line of research is on Risk Measures and their regulatory impact. He is the author of more than 200 research papers and books on many subjects ranging from the theory of dynamical systems, to optimisation and portfolio theory.