Traditional Criticisms And Alternatives

Abstract Many authors have raised objections to mean-variance (MV) efficient as a framework for defining portfolio optimality. Most of the alternatives can be classified in one of five categories: (1) alternative risk measures; (2) utility function optimization; (3) multiperiod objectives; (4) Monte Carlo financial planning; and (5) linear programming. Analysis shows that the alternatives often have their own serious limitations and that MV efficient is far more robust than is commonly appreciated. Although they are symptomatic of an underlying unease with MV efficiency, none of the proposals address the basic limitations of MV optimization. In MV efficiency, the variance, or standard deviation, of return is the measure of security and portfolio risk. The variance measures variability above and below the mean. From an investor’s point of view, the variance of returns above the mean is often not viewed as “risk”. One obvious and intuitively appealing nonvariance measure of risk, discussed as early as Markowitz (1959), is the semivariance or semistandard deviation of return. In this risk measure, only returns below the mean are included in the estimate of variability. The semivariance is an example of a “downside” risk measure. In this case, “downside” risk is relative to the average or mean of return. There are many other ways to measure “downside” risk. A simple example is replacing average return with a specified level of return, such as zero or the risk-free rate.