Question

Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta for the first adviser was 1.5, while that of the second was 1.
Required:
a. If the T-bill rate was 6% and the market return during the period was 14%, which adviser would be the superior stock selector.
b. Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)?
c. What if the T-bill rate were 3% and the market return 15%?

Answer 1

Answer: Adviser B is the superior stock selector.

Explanation:

For the comparision between the two investment advisers, the Jenson's Alpha will be utilized.

Jenson's Alpha:

= Portfolio Actual Return - CAPM(Benchmark Portfolio Return)

T Bill Rate(Risk free rate) = 6%

Market return(E(Em) = 14%

Beta of Investment Adviser A = 1.5

Beta of Investment Adviser B = 1

For Adviser A:

CAPM = Risk free return + Beta ( E(Rm) - Risk free return)

CAPM(Benchmark Portfolio) = 6 + 1.5 (14-6)

= 6 + 12

= 18%

Actual Return = 19%

Jenson's Alpha = 19% - 18% = 1%

For Adviser B:

CAPM = Risk free return + Beta ( E(Rm) - Risk free return)

CAPM(Benchmark Portfolio) = 6 + 1(14-6) = 6 + 1(8) = 14%

Actual Return = 16%

Jenson's Alpha = 16% - 14% = 2%

Adviser B is a better selector because he has a larger alpha of 2% compared to Adviser A who has 1%.

T Bill Rate(Risk free rate) = 3%

Market return(E(Rm) = 15%

Beta of Investment Adviser A = 1.5

Beta of Investment Adviser B = 1

For Adviser A:

CAPM = Risk free return + Beta ( E(Rm) - Risk free return)

CAPM(Benchmark Portfolio) = 3 + 1.5 (15-3)

= 3 + 18

= 21%

Actual Return = 19%

Jenson's Alpha = 19% - 21% = -2%

For Adviser B:

CAPM = Risk free return + Beta ( E(Rm) - Risk free return)

CAPM(Benchmark Portfolio) = 3 + 1(15-3) = 3 + 1(12) = 15%

Actual Return = 16%

Jenson's Alpha = 16% - 15% = 1%

Given the changes, Adviser B is still the better selector because he has a larger alpha of 1% compared to Adviser A who has -2%.