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Risk Measures

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Robert D. Arnott, "What Risk Matters?  A Call for Papers," Financial Analysts Journal, MayJune 2003, pp. 6-8 (655kb).  A good discussion of the nature of risk.

Andrew W. Lo, "The Three P's of Total Risk Management," Financial Analysts Journal, JanuaryFebruary 1999, pp. 13-26 (197kb).  A good discussion of the nature of risk.

David N. Nawrocki, "A Brief History of Downside Risk Measures," Journal of Investing, Fall 1999, pp. 9-25 (135kb).  Also HereHere is a related piece by the same author. A comprehensive discussion of downside risk measures.  Downside risk turns out to be a superior risk measure (i.e., better than standard deviation) in circumstances where the return distribution is not symmetrical andor a "Minimal Acceptable Return" can be defined.

David N. Nawrocki, "The Case for Relevancy of Downside Risk Measures," Working Paper, 1999.  Also here.  "We need downside risk measures because they are a closer match to how investors actually behave in investment situations."

Brian M. Rom, "Using Downside Risk to Improve Performance Measurement," Presentation, Investment Technologies. A good summary of issues surrounding use of downside risk measures.

A.D. Roy, "Safety First and the Holding of Assets," Econometrica, July 1952, pp. 431-450.  This may have been the first paper to suggest a downside risk measure.  Roy suggested maximizing the ratio "(m-d)σ", where m is expected gross return, d is some "disaster level" (a.k.a., minimum acceptable return) and σ is standard deviation of returns.  This ratio is just the Sharpe Ratio, only using minimum acceptable return instead of risk-free return in the denominator!

Frank A. Sortino and Robert van der Meer, "Downside Risk," Journal of Portfolio Management, Summer 1991, pp. 27.31. Concludes that Downside Variance is a superior measure of risk.

Larry Swedroe, "Risk: What Exactly is it?," Indexfunds.com, August 8 2003. A great article on the topic.

W. Van Harlow, "Asset Allocation in a Downside-Risk Framework," Financial Analysts Journal, SeptemberOctober 1992, pp. 28-40. An outstanding article on use of downside risk measures (e.g., downside variance or downside deviation).  Downside risk turns out to be a superior risk measure (i.e., better than standard deviation) in circumstances where the return distribution is not symmetrical andor a "Minimal Acceptable Return" can be defined.

Susan Wheelock, "Risky Business," Plan Sponsor, September 1995. An excellent, very readable description of downside risk.  All of the performance measures discussed in the Performance Evaluation section are risk-adjusted measures.  The Sortino Ratio and the Upside Potential Ratio use downside risk as their risk measure.

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