Kaplanski, Guy and Kroll, Yoram
(2002):
*VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey.*
Published in: Journal of Risk
, Vol. 4, No. 3
(2002): pp. 1-27.

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## Abstract

The article presents an analysis and survey regarding the validity of VaR risk measures in comparison to traditional risk measures. Individuals are assumed to either maximize their expected utility or possess a lexicographic utility function. The analysis is carried out for generally distributed functions and for the normal and lognormal distributions. The main conclusion is that although VaR is an inadequate measure within the expected utility framework, it is at least as good as other traditional risk measures. Moreover, it can be improved by modified versions such as the Accumulated-VaR (Mean-Shortfall) Assuming a lexicographic expected utility strengthens the argument for using AVaR as a legitimate risk measure especially in the case of a regulated firm.

Item Type: | MPRA Paper |
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Original Title: | VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey |

Language: | English |

Keywords: | Value-at-Risk, Risk management, Risk measures, Mean-Shortfall |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other |

Item ID: | 80070 |

Depositing User: | Dr. Guy Kaplanski |

Date Deposited: | 17 Jul 2017 16:39 |

Last Modified: | 26 Sep 2019 18:42 |

References: | Ahn, D.H., Boudoukh, J., Richardson, M., and R.F., Whitelaw, "Optimal Risk Management Using Options", J. of Finance, 54(1), February 1999, 359-375. Alexander, J.G., and A.M., Baptista, "Economic Imlications of Using a Mean-VaR Model for Portfolio Selection: A Comparison with Mean-Variance Analysis", Working paper, University of Minnesota, 2000. Artzner, P., Delbaen, F., Eber, J.M., and D., Heath, "Thinking Coherent", Risk, 11, November 1997, 68-72. Artzner, P., Delbaen, F., Eber, J.M., and D., Heath, "Coherent Measures of Risk", Mathematical Finance, 9, 1999, 203-228. Arzac, E., "Utility Analysis of Chance-Constrained Portfolio Section", J. of Financial and Quantitative Analysis, 8, 1974, 993-1007. Arzac, E., and V., Bawa, "Portfolio Choice and Equilibrium in Capital Markets with Safety-First Investors", J. of Financial Economics, 4, 1977, 277-288. Atkinson, A.B., "On the Measurement of Inequality", J. of Economic Theory, 2, 1970, 244-263. Basak, S., and A., Shapiro, "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices", Review of Financial Studies, 14(2), 2001, 371-405. Basel Committee on Banking Supervision, Amendment to the Capital Accord to Incorporate Market Risks, January 1996. Baumol, W.J., "An Expected Gain Confidence Limit Criterion for Portfolio Selection", Management Science, 10, 1963, 174-182. Bawa, V.S., "Optimal Rules for Ordering Uncertain Prospects", J. of Financial Economics, 2, 1975, 95-121. Bawa, V.S., "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice, J. of Financial and Quantitative Analysis, 13, June 1978, 255-271. Beder, T.S., "VaR: Seductive but Dangerous", Financial Analyst Journal, Sep-Oct 1995, 12-24. Bey, R.P., "Estimating the Optimal Stochastic Dominance Efficient Set with Mean Semi-Variance Algorithms", J. of Financial and Quantitative Analysis, 14, 1979, 1059-1070. Boudoukh, J., Richardson, M., and R., Whitelaw., "Expect the Worst", Risk, September 1995, 100-101. Chipman, J.S., "The Foundation of Utility", Econometrica, 28, April 1960, 193-224. Crouhy, M., Galai, D., and R., Mark, "Comparative Analysis of Current Credit Risk Models", Journal of Banking and Finance, 24, January 2000, 59-117. Crouhy, M., Galai, D., and R., Mark, Risk Management, (Eds.), McGrow-Hill, 2001. Domar, E., and R.A., Musgrave, "Proportional Income Taxation and Risk Taking", Quarterly J. of Economics, 57, May 1944, 388-422. Duffie, D., and J., Pan, "An Overview of Value at Risk", Journal of Derivatives, 4, Spring 1997, 7-49. Duffie, D., and J., Pan, "Analytical Value-at-Risk with Jumps and Credit Risk", Finance and Stochastic, 5, 2000, 155-180. Embrechts, P., Klueppelberg, C., and T., Mikosch, "External Events in Finance and Insurance, 1997, Springer. Fishburn, P.C., Decision and Value Theory, Wiley, New York, 1964. Fishburn, P.C., "A Study of Lexicographic Expected Utility", Management Science, 17, 1971, 672-678. Fishburn, P.C., "Mean-Risk Analysis with Risk Associated with Below-Target Returns", American Economic Review, 67, March 1977, 116-126. Hadar, J. and W. Russell, "Rules for Ordering Uncertain Prospects", Ameran Economic Review, 59, 1969, 25-34. Hallerbach, W.G., "Decomposing Portfolio Value-at-Risk: A General Analysis", Working Paper, Erasmus University Rotterdam, 1999. Halpern, P., and Y. Kahane, "A Pedagogical Note on Baumol's Gain-Confidence Limit Criterion for Portfolio Selection and the Probability of Ruin", J. of Banking and Finance, 4, 1980, 191-195. Hanoch, G. and H. Levy, "The efficiency Analysis of Choices Involving Risk", Review of Economic Studies, 36, 1969, 335-346. Hausner, M., "Multidimensional Utilities", in: Decisions Processes, Thrall, R.M., Croombs, C. H., and R.L. Davis, (Eds.), Wiley, New York, 1954, 167-180. Ho, Thomas, S.Y., Chen, Michael, Z.H., and H.T., Eng, Fred, "VAR Analytics: Portfolio Structure, Key Rate Convexities, and VAR Betas, J. of Portfolio Management, 23(1), Fall 1996, 89-98. Johansson, F., Seiler, M.J. and M., Tjarnberg, "Measuring Downside Portfolio Risk", J. of Portfolio Management, Fall 1999, 96-107. Jorion, P., "Risk Management Lessons from Long-Term Capital Management.", European Financial Management, 6, September 2000a. Jorion, P., Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, December 2000b. Jorion, P., "Portfolio Optimization with Constraint on Tracking Error", Working paper, University of California at Irvine, 2001. JP Morgan, RiskMetriskTM--technical document. 4 ed, 1996. Konno, H., and H., Yamazaki, "Mean Absolute Deviation Portfolio Optimization Model and its Application to Tokyo Stock Market", Management Science, 37, 1991, 519-531. Kaplanski, G., and Y., Kroll, "Efficient VaR Portfolios", Working paper, Hebrew University, 2001. Levy, H., "Stochastic Dominance Among Log-Normal Prospects", Internat. Economic Review, 14, 1973, 601-614. Levy, H., "The Mean-Coefficient of Variation Rule: The Lognormal Case", Management Science, June 1991, 745-747. Levy, H., and Y., Kroll, "Ordering Uncertain Options with Borrowing and Lending", J. of Finance, 33(2), May 1978, 552-573. Linsmeier, T., and N., Pearson, "Risk Measurement: An introduction to Value at Risk", Working paper, University of Illinois, 1996. Longin, M.F., "Beyond the VaR", Journal of Derivatives, Summer 2001, 36-48. Lucas, A., and P., Klaassen, "Extreme Returns, Downside Risk, and Optimal Asset Allocation", J. of Portfolio Management, Fall 1998, 71-79. Mandelbrot, B., "The variation of Certain Speculative Prices", J. of Business, 36, 1963, 394-419. Mao, J.C.T., "Models of Capital Budgeting, E-V vs. E-S ", J. of Finance and Quantitative Analysis, 4, January 1970a, 657-675. Mao, J.C.T., "Survey of Capital Budgeting: Theory and Practice", J. of Finance, 25, May 1970b, 349-360. Markowitz, H.M., Portfolio Selection, John Wiley & Sons, New York, 1959. Merton, R.C., "Optimum Consumption and Portfolio Rules in a Continuous-Time Model", J. of Economic Theory, 3, 1971, 373-413. Merton, R. C., "An Inter-temporal Capital Asset Pricing Model", Econometrica, 41(5), September 1973, 867-887. Pratt, J.W., "Risk Aversion in the Small and in the Large", Econometrica, 32, 1964, 122-136. Quirk, J.P., and R., Saposnik, "Admissibility and Measurable Utility Function", Review of Economic Studies, 29, 1962, 140-146. Rothschild, M., and J.E., Stiglitz, "Increasing Risk. I: A Definition", J. of Economic Theory, 2, 1970, 225-243. Roy, A.D., "Safety First and the Holding of Assets", Econometrica, 20, July 1952, 431-449. Tesler, L., "Safety First and Hedging", Review of Economic Studies, 23, 1955, 1-16. Uryasev, S., "Conditional Value-at-Risk: Optimization Algorithms and Applications", Financial Engineering News, February 2000, 1-5. Uryasev, S., and R.T., Rockafellar, "Optimization of Conditional Value-at-Risk", Research Report 99-4, ISE Dept., University of Florida. Whitmore, G.A., "Third Degree Stochastic Dominance", American Economic Review, 60, 1970, 457-459. Yitzhaki, S., "Stochastic Dominance, Mean-Variance and Gini's Mean Difference", American Economic Review, 72, March 1982, 178-185. Yitzhaki, S., "On An Extension of the Gini Inequality Index", International Economic Review, 24, 1983, 617-628. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/80070 |