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Why VAR Fails: Long Memory and Extreme Events in Financial Markets

Listed author(s):
  • Cornelis A. Los

The Value-at-Risk (VAR) measure is based on only the second moment of a rates of return distribution. It is an insufficient risk performance measure, since it ignores both the higher moments of the pricing distributions, like skewness and kurtosis, and all the fractional moments resulting from the long - term dependencies (long memory) of dynamic market pricing. Not coincidentally, the VaR methodology also devotes insufficient attention to the truly extreme financial events, i.e., those events that are catastrophic and that are clustering because of this long memory. Since the usual stationarity and i.i.d. assumptions of classical asset returns theory are not satisfied in reality, more attention should be paid to the measurement of the degree of dependence to determine the true risks to which any investment portfolio is exposed: the return distributions are time-varying and skewness and kurtosis occur and change over time. Conventional mean-variance diversification does not apply when the tails of the return distributions ate too fat, i.e., when many more than normal extreme events occur. Regrettably, also, Extreme Value Theory is empirically not valid, because it is based on the uncorroborated i.i.d. assumption.

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Paper provided by EconWPA in its series Finance with number 0412014.

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Length: 26 pages
Date of creation: 08 Dec 2004
Handle: RePEc:wpa:wuwpfi:0412014
Note: Type of Document - pdf; pages: 26
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  1. Gregory P. Hopper, 1996. "Value at risk: a new methodology for measuring portfolio risk," Business Review, Federal Reserve Bank of Philadelphia, issue Jul, pages 19-31.
  2. Xiongwei Ju & Neil D. Pearson, 1998. "Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?," Finance 9810002, EconWPA.
  3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  4. Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 107-122, June.
  5. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
  6. Cornelis A. Los, 2004. "When to Put All Your Eggs in One Basket.....When Diversification Increases Portfolio Risk!," Finance 0411037, EconWPA.
  7. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
  8. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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