Subadditivity Re–Examined: the Case for Value-at-Risk

This paper explores the potential for violations of VaR subadditivity both theoretically and by simulations, and finds that for most practical applications VaR is subadditive. Hence, there is no reason to choose a more complicated risk measure than VaR, solely for reasons of coherence.

[1]  S. Resnick.  Extreme Values, Regular Variation, and Point Processes , 1987 .

[2]  Claudio Nordio,et al.  Expected Shortfall as a Tool for Financial Risk Management , 2001 .

[3]  Sidney I. Resnick,et al.  Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes , 1989 .

[4]  Dennis W. Jansen,et al.  On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective , 1989 .

[5]  Jón Dańıelsson,et al.  Tail Index and Quantile Estimation with Very High Frequency Data , 1997 .

[6]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[7]  M. Hall.  The amendment to the capital accord to incorporate market risk , 1996 .

[8]  E. Fama,et al.  The Theory of Finance , 1974 .

[9]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[10]  B. Mandlebrot.  The Variation of Certain Speculative Prices , 1963 .

[11]  Jan Dhaene,et al.  Economic Capital Allocation Derived from Risk Measures , 2002 .

[12]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[13]  Adrian Pagan,et al.  The econometrics of financial markets , 1996 .

[14]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[15]  Namwon Hyung,et al.  Portfolio diversification effects and regular variation in financial data , 2001 .

[16]  M. Meerschaert.  Regular Variation in R k , 1988 .

[17]  Éric Renault,et al.  Proper Conditioning for Coherent VaR in Portfolio Management , 2007, Manag. Sci..

[18]  Jon Danielsson,et al.  Value-at-Risk and Extreme Returns , 2000 .

[19]  R. Engle,et al.  Multivariate Simultaneous Generalized ARCH , 1995, Econometric Theory.

[20]  D. Tasche,et al.  Expected Shortfall: a natural coherent alternative to Value at Risk , 2001, cond-mat/0105191.

[21]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[22]  Yasuhiro Yamai,et al.  Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization , 2002 .

[23]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[24]  Sidney I. Resnick.  Point processes, regular variation and weak convergence , 1986 .

[25]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.