An Introduction to the Fama French Three Factor Model

The Fama-French three factor model is adapted from the Capital Asset Pricing Model (CAPM). The CAPM attempts to measure a "good" price for a security based on the risk of the security, but the Fama-French model accounts for high performance among value and small-cap stocks. These two categories of securities tend to outperform the market, and this means the value of the asset may be affected if it falls into one of these two categories.

Capital Asset Pricing Model

To understand the Fama-French model, it is important to first understand the CAPM. The CAPM formula is this:  

Asset price = risk free rate + beta * (expected market return - risk free rate)

The risk-free rate is a theoretical rate of return that represents how much a stock would return if it posed zero risk. Of course, no stock actually poses zero risk, so this remains a theoretical figure. The beta of any security is a measure of its volatility. The stock market as a whole has a beta of 1.0. Therefore, the CAPM is entirely based on risk factors. Gene Fama and Ken French saw a flaw in this model since it did not account for the high performance of certain classes of securities. They added two more factors to account for these phenomena. Their new formula is this:

Asset price = beta * (expected market return - risk free rate + b(s) * SMB + b(v) * HML + alpha

Effect of a Value Stock--HML

Value stocks are considered to be "undervalued" on the market. They are undervalued because they trade at a price lower than the sum of their parts. These parts include dividends, earnings, sales and other terms used to analyze stock price. When investors can properly identify a value stock, they may be able to outperform the market as a whole. In the Fama-French model, High Minus Low (HML) accounts for a value stock. HML is a measure of the difference in returns between value and growth stocks using the ratio of book/price. B(v) is a quantitative expression of a stock's value based on a factor of 1. A value stock will have a b(v) closer to 0 than 1, and it will have a lower book/price ratio when compared to the market as a whole. 

Effect of a Small-Cap Stock--SMB

A small-cap stock is any that meets the definition of low capitalization. Each broker sets this definition differently, but most use a range under $2 billion in market capitalization. Securities from low-cap companies tend to outperform the market, when successful, so Fama and French measure this with Small Minus Big (SMB), which accounts for the spread in returns between small- and large-capitalization firms. B(s) is a quantitative expression of a stock's capitalization based on a factor of 1. A small cap security will have a b(s) closer to 0 than to 1, and it will have a capitalization below the small cap breakpoint as defined by a given broker. 

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