# Arbitrage Pricing Theory

Topics: Capital asset pricing model, Risk, Arbitrage pricing theory Pages: 2 (607 words) Published: June 24, 2013
Summary of the Arbitrage Pricing Theory (APT)

The APT model was developed as an alternative to the CAPM. Like the CAPM, this model provides implications for the relationship between expected returns and risk on securities. However, the model differs from CAPM in its assumptions, its implications, and in the way that equilibrium prices are reached. • Assumptions: The CAPM model assumes that all investors are risk-averse utility maximizers. In other words, all investors solve the investment problem in the way we described in portfolio theory (Lecture 3). The APT model makes a less restrictive assumption about the way investors behave. Here we just assume that there are at least some investors out there who would like to take extremely large positions in any risk-free arbitrage opportunities that arise. So, if securities are priced correctly in equilibrium, there cannot be any remaining risk-free arbitrage opportunities. Equilibrium: Both the APT model and the CAPM describe what expected returns should look like in equilibrium. However, equilibrium is reached in different ways. In the CAPM, all investors solve the portfolio theory problem we described in Lecture 3 using mean-variance optimization and maximizing their utility. This leads to an equilibrium where all investors hold the same optimal risky portfolio (the “market” portfolio) and also results in the expected return – beta equation that we typically refer to as the CAPM equation. In the APT model, any mispriced securities will create arbitrage opportunities that will immediately be traded on by investors. Equilibrium results when the trades of these investors push prices back to their correct values. Implications: Both the CAPM and the APT lead to equations for expected returns. These equations are shown below. The equations are very similar, but have several important differences. First, the CAPM has only one risk factor (market risk), while the APT model can have multiple sources of risk. Second, the...