• Mortgage
• Credit Cards
• Auto

# Fama-French Three Factor Model

By: Frank Armstrong

The Fama-French Three Factor Model provides a highly useful tool for understanding portfolio performance, measuring the impact of active management, portfolio construction and estimating future returns. The Three Factor Model has replaced Capital Asset Pricing Model (CAP-M) as the most widely accepted explanation of stock prices in the aggregate and investor returns.

CAP-M: A First Cut at the Problem

To review, and greatly oversimplify, CAP-M established the relationship between risk and reward. The market would set stock prices, and investors achieve returns directly related to risk. Said another way, investors would drive down the price of stocks until the expected return for owning them compensated them for the risk that the stock exhibited.

CAP-M explains stock performance, or investor returns as the sum of:

The zero risk returnThe market premiumA return for individual security risk proportional to its volatility relative to the market (Beta)The impact of management (Alpha)Random Error

So, stocks with higher volatility relative to the market would command lower prices and achieve higher expected returns. As an example, suppose we had a stock (or a portfolio of stocks) that was 20% more volatile than the market, and that the treasury bill yielded 3% and the S&P 500 return was 11%. Market premium was then the difference between the T-bill and market or 8%. Beta is 0.2 times the market premium or 1.6%

3.00 The zero risk return

8.00 The market premium

1.60 Beta (0.2 X 8.0)

Alpha

Random Error

12.60 Expected Total Return

The market will adjust the price of the stock to the point where an investor can expect a 12.20% average return.

Had the stock (or a portfolio with a Beta of 1.2) returned, for instance, 13.20% then the unexplained difference (Alpha) would have been presumed to be due to management impact. In that case, Alpha would be presumed to be 0.60%. (Let's be real here. A portfolio manager that happened to have a higher than expected return is hardly going to attribute it to random error! Of course not. He is going to claim that the result was due to his superior skill and cunning.)