Question

HW 10 Q7. The risk-free interest rate is 4% and the expected return on the market portfolio is 10%. Assume the return on the size factor is 3.5% and the return on the B/M factor is 5%. Scott’s portfolio has a market beta of 2/3, a β_SMB of 0.9, and a β_HML of -0.5. The average annual return on his portfolio is 9%.

Based on the FF3 factor model, what is the abnormal return (i.e. α) of Scott’s portfolio?

Answer 1

R(it) - R(ft) = α(it) + [β * (Expected Market Return - Risk-free Rate)] + [β_SMB * R_SMB] + [β_HML * R_HML]

9% - 4% = α(it) + [(2/3) * (10% - 4%)] + [0.9 * 3.5%] + [-0.5 * 5%]

5% = α(it) + 4% + 3.15% - 2.5%

5% = α(it) + 4.65%

α(it) = 5% - 4.65% = 0.35%