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3 Caveats
Unfortunately, VaR is not the panacea of risk measurement methodologies. A subtle technical problem is that VaR is not sub-additive. That is, it's possible to construct two portfolios, A and B, in such a way that VaR(A + B) > VaR(A) + VaR(B). This is unexpected because we expect portfolio diversification to reduce risk. See http://www.fenews.com/fen40/risk-reward/risk-reward.htm for more on this topic. Fortunately, Expected Value at Risk, or EVaR , modifies the VaR methodology slightly in a way that solves this difficulty.
4 Further Reading
- Crouhy M., D. Galai, and R. Mark, Risk Management, McGraw-Hill, 2001.
- Holton, Glyn A., Value-at-Risk: Theory and Practice, Academic Press, 2003.
- Hull, John C., Options, Futures, and Other Derivatives, 5th ed., Prentice Hall, 2002.
- Jorion, Philippe, Value at Risk: The New Benchmark for Managing Financial Risk, 2nd ed., McGraw-Hill Trade, 2001.
- A nice alternative overview of Value at Risk from investopedia.com. Part 1, Part 2
5 External links
financial mathematics
