While traditional MPT suggests optimizing a portfolio on two statistics -- return and volatility, this "Improved" Modern Portfolio Theory suggests optimizing a portfolio on return and some measure of downside risk. Also, see the sections on Asset Allocation, Diversification, Risk Measures, and especially, Modern Portfolio Theory.

Vijay S. Bawa and Eric B. Lindenberg, "Capital Market Equilibrium in a Mean-Lower Partial Moment Framework," Journal of Financial Economics, November 1977, pp. 189-200. This paper derived a version of the Capital Asset Pricing Model which embraced Lower Partial Moment (a fancy term for downside risk) as the measure of risk. This model is a more generalized version of the more traditional CAPM.

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.

James C.T. Mao, "Survey of Capital Budgeting," Journal of Finance, May 1970, pp. 349-360. This paper is among the earliest to point out the superiority of a downside risk measure to the standard volatility measures of risk. This paper addresses the question from the perspective of an executive and notes that the concept of "risk" held by many financial decision makers is better described by downside risk measures than by volatility. "Variance is the generally accepted measure of investment risk in current capital budgeting theory. There are theoretical reasons for preferring semivariance and the evidence is more consistent with semi-variance than variance."

David N. Nawrocki, "Market Theory and the use of Downside Risk Measures," Working Paper, 1996. A good discussion of the issues.

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

David N. Nawrocki, "A Brief History of Downside Risk Measures," Journal of Investing, Fall 1999, pp. 9-25 (135kb). Also Here. Also Here. 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.

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 the idea of a "minimal acceptable return" as part of the measurement of risk-adjusted return. 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 numerator!

Tien Foo Sing and Seow Eng Ong, "Asset Allocation in a Downside Risk Framework," Journal of Real Estate Portfolio Management, July-September 2000, pp. 213-223. A good discussion of the issues.

Pete Swisher and Gregory W. Kasten, "Post-Modern Portfolio Theory," Journal of Financial Planning, September 2005, pp. 74-85. This outstanding article describes a clear improvement on traditional portfolio theory (a.k.a., Modern Portfolio Theory). The principle idea is changing the statistics being optimized. In traditional portfolio theory, the idea is to get the highest return (or perhaps highest return above a risk-free rate) for some given amount of volatility. This paper suggests instead trying to get the highest return (above some Minimal Acceptable Return) for some given amount of volatility, with the volatility calculated as the deviations below that Minimum Acceptable Return.

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.