Risk Measures and Portfolio Selection

Abstract

The standard assumption in financial models is that the distribution for the return on financial assets follows a normal (or Gaussian) distribution and therefore the standard deviation (or variance) is an appropriate measure of risk in the portfolio selection process. This is the risk measure that is used in the well-known Markowitz portfolio selection model (that is, mean-variance model) which is the foundation for modern portfolio theory. With mounting evidence since the early 1960s that return distributions do not follow a normal distribution, researchers have proposed alternative risk measures for portfolio selection. These risk measures fall into two disjointed categories: dispersion measures and safety-first measures. In addition, there has been considerable theoretical work in defining the features of a desirable risk measure. Keywords: relativity of risk; multidimensionality of risk; asymmetry of risk; propagation effect; mean-variance analysis; semivariance; dispersion measures; safety-first risk measures; mean standard deviation; mean absolute deviation (MAD); mean absolute moment; index of dissimilarity; Gini measure; mean entropy; mean colog; classical safety first; value at risk (VaR); conditional value at risk (CVaR); expected tail loss; MiniMax; lower partial moment; downside risk; probability-weighted function of deviations below a specified target return; power conditional value at risk