Eugene Fama and Kenneth French's work popularized the value and size effects, the puzzlingly high returns that value and small-cap stocks have earned in almost every market studied. Their research has resonated with indexers, many who overweight value and small-cap stocks in their portfolios. Despite style tilting's popularity, the popular discussion is short on specific numbers. Some tilters point out that small-value stocks as defined by Fama and French have earned 14.2% annualized from 1928 to 2010, 4 percentage points above the U.S. market's return. But that doesn't mean any value index, small-cap or large-cap, will earn a similar value premium--some indexes are more size- or value-laden than others. The style map is a beautiful way to represent value and size tilts, but it doesn't quantify value and size tilts as readily observable numbers. For that, we have to go back to the size and value premiums' academic roots, to the Fama-French model.

Models and Models

In simple terms, the Fama-French model estimates how sensitive a stock strategy's returns are to three risk factors: the total stock market's returns, value stocks' returns, and small-cap stocks' returns. Value is defined as low price/book; the other factors are self-explanatory. However, since value stocks have both market and size risk mixed into their returns, Fama and French isolate the value-return factor with a strategy that owns a portfolio of low price/book stocks and short-sells a dollar-equivalent portfolio of high price/book stocks, earning the spread between value and growth stocks. The size factor is isolated in a similar manner. An extended version of the Fama-French model, called the Carhart model, adds a momentum factor, which captures the return of a strategy that every month buys the best-performing stocks and short-sells the worst-performing stocks. We'll wield this model from now on.