Mean‐Variance Model for Portfolio Selection

Abstract

The theory of portfolio selection together with capital asset pricing theory provides the foundation and the building blocks for the management of portfolios. The goal of portfolio selec-tion is the construction of portfolios that maximize expected returns consistent with individually acceptable levels of risk. Using both historical data and investor expectations of future returns, portfolio selection uses modeling techniques to quantify expected portfolio returns and acceptable levels of portfolio risk and provides methods to select an optimal portfolio. The theory of portfolio selection presented in this entry, often referred to as mean-variance port-folio analysis or simply mean-variance analysis, is a normative theory. A normative theory is one that describes a standard or norm of behavior that investors should pursue in constructing a portfolio rather than a prediction concerning actual behavior. Asset pricing theory goes on to formalize the relationship that should exist between as-set returns and risk if investors behave in a hy-pothesized manner. In contrast to a normative theory, asset pricing theory is a positive theory—a theory that hypothesizes how in-vestors behave rather than how investors should behave. Based on that hypothesized be-havior of investors, a model that provides the expected return (a key input for constructing portfolios based on mean-variance analysis) is derived and is called an asset pricing model. Together, portfolio selection theory and asset pricing theory provide a framework to specify and measure investment risk and to develop re-lationships between expected asset return and