A fund has loadings of 1.0 on the market, -0.3 on size and 0.6 on value. The premia are 6%, 2% and 3%, cash is 2%, and the fund returned 11%. What is its three factor alpha, and how does it compare with the single factor number?

A fund has loadings of 1.0 on the market, -0.3 on size and 0.6 on value. The premia are 6%, 2% and 3%, cash is 2%, and the fund returned 11%. What is its three factor alpha, and how does it compare with the single factor number?

Approach: Price the fund off all three premia at its stated loadings, then repeat with the market alone and attribute the difference to the two extra loadings.

1.8%. The Fama-French three factor expected return is 2 + 1.0*6 + (-0.3)*2 + 0.6*3 = 9.2%, so the alpha is 11 - 9.2 = 1.8 points. The single factor alpha is 11 - (2 + 6) = 3.0 points, so the value loading of 0.6 earning a 3% risk premium explains 1.8 points of it while the negative size loading gives 0.6 points back. A loading is the slope of the fund's return on the factor return, so 0.6 on value says the book moves like 60% of a long cheap short expensive portfolio, which describes the positions and passes no judgement on them. Alpha exists only relative to the factors in the regression, so adding momentum and quality can take 1.8% to zero without a single position changing.

Follow-up: The same fund shows a 0.4 loading on momentum in the second half of the sample and zero in the first. What does that do to the alpha estimate?

Key concepts: fama-french, factor loading, alpha, risk premium.