Optimal Portfolio Control
1. Introduction
So far in the course, we have not established any benchmarks to compare securities or portfolios other than expected returns. It is impossible to judge the quality of an investment be simply looking at its expected returns. For example, consider an advertisement from Wall Street Journal.
The Franklin Income Fund 516% Dow Jones Industrial Average 384% Salomon's High Grade Bond Index 273% Cost of Living 169%
These are average returns over the past 15 years than the Dow Jones Industrial Average and Salomon's High Grade Bonds. Does this mean that we can beat the market by investing in Franklin now? The answer is no. The advertisement tells us nothing about the risk of the Franklin Fund. We will always want to consider risk as well as return. The Franklin Fund stocks may be very risky and the only way people will hold the component stocks is to have a high expected return. So we have go beyond returns and develop a model of risk that allows us to compare stocks and portfolios. [By the way, this ad last appeared in September 1987.]
There are many models of risk and return. Two popular models are: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). We will spend most of our time examining the Capital Asset Pricing Model. The CAPM was the first of the pricing models [William Sharpe (1964)] and the most commonly used by practitioners. The APT is examined in considerable detail in the elective courses. I will briefly introduce these models after we have finished with the CAPM.
2. The Planning Problem
The Capital Asset Pricing Model is an equilibrium model. The pri ...