Fama-French Benchmark





Kerry Back

Fama-French Factors

  • The Fama-French factors are
    • Mkt-RF
    • SMB = small minus big
    • HML = high book-to-market minus low book-to-market
    • CMA = conservative (low asset growth) minus aggressive (high asset growth)
    • RMW = robust (high profitability) minus weak (low profitability)

Fama-French Regression

  • We run the regression

\[r - r_f = \alpha + \beta_1 (r_m-r_f) + \beta_2 SMB + \beta_3 HML\]

\[ + \beta_4 CMA + \beta_5 RMW + \varepsilon\]

  • We can rearrange as

\[ r - \text{benchmark} = \alpha + \varepsilon\]

  • where the benchmark is

\[ \beta_1 r_m + (1-\beta_1)r_f + \beta_2 SMB\]

\[ + \beta_3 HML + \beta_4 CMA + \beta_5 RMW\]

Alpha and information ratio

  • The return in excess of the benchmark is again the active return.
  • The mean active return \(\alpha\) is the average return in excess of what we should expect to earn given market and other risk exposures.
  • The ratio \(\alpha /\text{stdev}(\varepsilon)\) is again an information ratio.

Compounding returns

  • To see visually how much the active return is adding to performance, compound
    • the market return \(\beta_1 r_m + (1-\beta_1)r_f\)
    • each of the other factor returns, e.g., \(\beta_2 SMB\)
    • and the total return \(r\).

Example