Question

Two investment advisers are comparing performance. Adviser A averaged a 20% return with a portfolio beta of 1.5, and adviser B averaged a 15% return with a portfolio beta of 1.2. If the T-bill rate was 5% and the market return during the period was 13%, which adviser was the better stock picker?
A. Advisor A was better because he generated a larger alpha.
B. Advisor B was better because she generated a larger alpha.
C. Advisor A was better because he generated a higher return.
D. Advisor B was better because she achieved a good return with a lower beta.

Answer 1

Answer:

Option A is the correct answer.

A. Advisor A was better because he generated a larger alpha.

Explanation:

To determine which adviser would be the better stock selector, we will calculate the required rate of return of each adviser and the return actually averaged. The adviser with the greater abnormal return, which is return in excess of required rate, will be the better stock selector.

Using the CAPM, we can calculate the required rate of return on a stock. This is the minimum return required by the investors to invest in a stock based on its systematic risk, the market's risk premium and the risk free rate.

The formula for required rate of return under CAPM is,

r = rRF + Beta * (rM - rRF)

Where,

• rRF is the risk free rate

• rM is the market return

r of Adviser A = 0.05 + 1.5 * (0.13 - 0.05)

r of Adviser A = 0.17 or 17%

Abnormal or excess return of Adviser A = 20% - 17% = 3%

r of Adviser B = 0.05 + 1.2 * (0.13 - 0.05)

r of Adviser B = 0.146 or 14.6%

Abnormal or excess return of Adviser B = 15% - 14.6% = 0.4%

Adviser A performed better as the excessive return or alpha of Adviser A was 3% while that of Adviser B was 0.4%