Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 10. Risk Measures and Portfolio Selection

SVETLOZAR T. RACHEV, PhD, DrSci

Chair-Professor, Chair of Econometrics, Statistics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and Department of Statistics and Applied Probability, University of California, Santa Barbara

CHRISTIAN MENN, Dr. rer. pol.

Associate, Sal. Oppenheim Jr. & Cie, Frankfurt, Germany

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

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, ...