Proper Conditioning for Coherent VaR in Portfolio Management
Value at risk (VaR) is a central concept in risk management. As stressed by Artzner et al. (1999, Coherent measures of risk, Math. Finance 9(3) 203-228), VaR may not possess the subadditivity property required to be a coherent measure of risk. The key idea of this paper is that, when tail thickness is responsible for violation of subadditivity, eliciting proper conditioning information may restore VaR rationale for decentralized risk management. The argument is threefold. First, since individual traders are hired because they possess a richer information on their specific market segment than senior management, they just have to follow consistently the prudential targets set by senior management to ensure that decentralized VaR control will work in a coherent way. The intuition is that if one could build a fictitious conditioning information set merging all individual pieces of information, it would be rich enough to restore VaR subadditivity. Second, in this decentralization context, we show that if senior management has access ex post to the portfolio shares of the individual traders, it amounts to recovering some of their private information. These shares can be used to improve backtesting to check that the prudential targets have been enforced by the traders. Finally, we stress that tail thickness required to violate subadditivity, even for small probabilities, remains an extreme situation because it corresponds to such poor conditioning information that expected loss appears to be infinite. We then conclude that lack of coherence of decentralized VaR management, that is VaR nonsubadditivity at the richest level of information, should be an exception rather than a rule.
Volume (Year): 53 (2007)
Issue (Month): 3 (March)
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- Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.
- Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
- Enrique Sentana & Enrique Sentana, 1999.
"Least Squares Predictions and Mean-Variance Analysis,"
FMG Discussion Papers
dp312, Financial Markets Group.
- Enrique Sentana, 2005. "Least Squares Predictions and Mean-Variance Analysis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(1), pages 56-78.
- Sentana, E., 1997. "Least Squares Predictions and Mean-Variance Analysis," Papers 9711, Centro de Estudios Monetarios Y Financieros-.
- Sentana, Enrique, 1999. "Least Squares Predictions and Mean-Variance Analysis," CEPR Discussion Papers 2088, C.E.P.R. Discussion Papers.
- Merton, Robert C, 1987.
" A Simple Model of Capital Market Equilibrium with Incomplete Information,"
Journal of Finance,
American Finance Association, vol. 42(3), pages 483-510, July.
- Merton, Robert C., 1987. "A simple model of capital market equilibrium with incomplete information," Working papers 1869-87., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Basak, Suleyman & Shapiro, Alexander, 2001.
"Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices,"
Review of Financial Studies,
Society for Financial Studies, vol. 14(2), pages 371-405.
- Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-.
- Suleyman Basak & Alex Shapiro, . "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 6-99, Wharton School Rodney L. White Center for Financial Research.
- Suleyman Basak & Alex Shapiro, . "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 06-99, Wharton School Rodney L. White Center for Financial Research.
- repec:nys:sunysb:93-02 is not listed on IDEAS
- Robert Engle & Simone Manganelli, 2000.
"CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,"
Econometric Society World Congress 2000 Contributed Papers
0841, Econometric Society.
- Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
- Jon Danielsson & Hyun Song Shin & Jean-Pierre Zigrand, 2004.
"The impact of risk regulation on price dynamics,"
LSE Research Online Documents on Economics
16628, London School of Economics and Political Science, LSE Library.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
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