Question

Assume that the economy has three types of people. 20% are fad followers, 75% are passive investors, and 5% are informed traders. The portfolio consisting of all informed traders has a beta of1.4 and an expected return of 16%. The market has an expected return of 10% and the risk-free rate is 4%. The alpha for the informed investors is closet to:

A. -2.4%

B.0.0%

C.3.6%

D.-0.9%

Answer 1

We have following formulas for alpha calculation -

Alpha of the stock = expected return from the stock – [risk free rate + beta of the Stock * (expected market return – risk free rate)]

Now we can apply that for the informed investors in following manner –

Alpha for the informed investors = expected return for the informed investors – [risk free rate + beta of for the informed investors * (expected market return – risk free rate)]

Where,

Expected return for the informed investors = 16%

Risk free rate = 4%

Beta of for the informed investors = 1.4

Expected market return = 10%

Therefore,

Alpha for the informed investors = 16% - [4% + 1.4 * (10% -4%)]

= 16% - 12.4%

= 3.6%

Therefore correct answer is option C.3.6%