Question

Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1.

a. Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)?

b. If the T-bill rate were 6% and the market return during the period were 14%, which adviser would be the superior stock selector?

c. What if the T-bill rate were 3% and the market return 15%?

Short answer

The correct answer would be:

a. No

b. Second advisor

c. Second advisor

Step-by-step solution

Given Information

r₁ = 19%;

r₂ = 16%;

β₁ = 1.5;

β₂ = 1.0

Solution for ‘a’

No. Without information about the risk-free rate and the market rate of return, we cannot determine which investment adviser is the better selector of individual stocks.

Solution for ‘b’ Calculation of alpha of investment suggested

If r_f = 6% and r_M = 14%, then (using alpha for the abnormal return):

σ₁ = Average return – Expected return₁

σ₁ = Average return -[ r_f +β₁ (r_M – r_f)]

σ₁ = 19% – [6% + 1.5(14% – 6%)] = 19% – 18% = 1%

Similarly,

σ₂ = 16% – [6% + 1.0(14% – 6%)] = 16% – 14% = 2%

From the above scenario, it appears that the second advisor has the larger abnormal returns hence he appears to be a better selector of individual stocks.

Solution for ‘c’ Calculation of alpha of investment suggested

If r_f = 3% and r_M = 15%, then (using alpha for the abnormal return):

σ₁ = Average return – Expected return₁

σ₁ = Average return -[ r_f +β₁ (r_M – r_f)]

σ₁ = 19% – [3% + 1.5(15% – 3%)] = 19% – 21% = -2%

Similarly,

σ₂ = 16% – [3% + 1.0(15% – 3%)] = 16% – 15% = 1%

From the above scenario, it appears that the second advisor has the larger abnormal returns hence he appears to be a better selector of individual stocks. On the other side, the selections of the first advisor appear valueless.