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Return Attribution Using The Fama-French Three-Factor Model
The analysis employed tested to see if the characteristics of the small-cap indices can be explained in the traditional Fama-French Three Factor model framework (1993). In the model, portfolio returns are explained using their exposures to three factors: sensitivity to the market (beta), size of the stocks in the portfolio (size) and average weighted book-to-market (value).
The risk premium for each factor is defined as follows:
1. Equity Risk Premium – As represented by (RM – RF), which is the return on a market value-weighted equity index minus the return on one-month T-Bill. It measures the systematic risk.
2. Size Premium – As represented by SMB (Small Minus Big), which measures the additional return from investing in small stocks. The SMB factor is computed as the average return on three small-cap portfolios minus the average return on three large-cap portfolios.
3. Value Premium – As represented by HML (High Minus Low), which measures additional return from investing in value stocks, as measured by high book-to-market ratios. It is calculated as the average return on two high book-to-market portfolios minus the average return on two low book-to-market portfolios.
The FFM estimate of the required return on an asset is:
The coefficient for each factor, β, measures the sensitivity of the asset’s return to the factor.
Given the framework above, the historical monthly returns from 1994-2008 of the Russell 2000 and the S&P SmallCap 600 are then regressed against the historical values of (1) the excess return on the market (RM- RF), (2) the performance of small stocks relative to large stocks (SMB), and (3) the performance of value stocks relative to growth stocks (HML).[1]
Results from the FF Three Factor model are summarized in the Exhibit 8.
Exhibit 8: Return Attribution using the Fama-French Three-Factor Model
Source: Standard & Poor’s. Data from 1994-2008.
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