Modern Portfolio Theory: Foundations, Analysis, and New Developments, + Website

Chapter 4

Single-Period Utility Analysis

A person can derive utility from food, an automobile, a diversified portfolio, and from many other things. Utility measures the relative magnitude of satisfaction someone derives from something; it is a subjective index of preference. If a person is faced with a decision, the alternative with the highest utility is the preferred choice. Thus, if the utility from a candy bar is less than the utility from an apple, the apple is preferred to the candy bar. Symbolically, this preference may be written: U(candy bar) < U(apple). In this monograph, utility theory is used to analyze investment decisions.

In a world of certainty, utility theory says a person should assign a numerical value to each alternative and then choose the alternative with the largest numerical value. The investor's utility function is used to determine the numerical values for each alternative investment. The application of utility theory to portfolio selection is complicated by uncertainty. In a world of certainty the rates of return to be earned from alternative portfolios are known and the investor can simply choose the portfolio with the highest return. Under uncertainty the rates of return on alternative portfolios are stochastic variables—that is, random variables. In such a situation, how should the investor proceed? Utility theory states that the investor should act so as to maximize expected utility, where expected utility is a numerical value assigned to a portfolio's ...