Question

Suppose the average return on T-Bills was 2%. The average factor risk premiums were the following:

• market (MKT): 6%

• size (SMB): 2%

• value (HML): 3%

We have the following information about three fund managers:

Manager Average return % Market beta SMB beta HML beta

Nancy 15 1.1    0.2    -0.7

John 10 -0.5 1.3 0.3

David 11 0.9 0.1 -1.1

What are the realized Fama-French three factor alphas for these managers?

Answer 1

For Nancy:

Average Retrun - risk free rate = alpha + market beta * market return + SMB beta * size return + HML beta * value return

15 - 2 = alpha + 6% * 1.1 + .2 * 2% - .7* 3%

13% = alpha + 6.6% + .4% - 2.1%

alpha = 8.1%

For Jhon:

Average Retrun - risk free rate = alpha + market beta * market return + SMB beta * size return + HML beta * value return

10 - 2 = alpha - 6% * 0.5 + 1.3* 2% + .2* 3%

8% = alpha - 3% + 2.6% +.6%

alpha = 7.8%

For David:

Average Retrun - risk free rate = alpha + market beta * market return + SMB beta * size return + HML beta * value return

11 - 2 = alpha + 6% * 0.9 + .1* 2% - 1.1* 3%

9% = alpha + 5.4% + .2% -3.3%

alpha = 6.7%