Encyclopedia of Financial Models III

Risk Measures and Portfolio Selection

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair-Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

CHRISTIAN MENN, Dr Rer Pol

Managing Partner, RIVACON

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

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.

Most of the concepts in theoretical and empirical finance that have been developed over the last 50 years rest upon the assumption that the return or price distribution for financial assets follow a normal distribution. Yet, with rare exception, studies that have investigated the validity of ...