You are holding a stock which has a beta of 2.0 and is currently in equilibrium. The required return on the stock is 15 percent, and the return on an average stock is 10 percent. What would be the percentage change in the return on the stock, if the return on an average stock increased by 30 percent while the risk-free rate remained unchanged?
A) +20%
B) +30%
C) +40%
D) +50%
E) +60%

Question

Quizplus · Accepted Answer

The expected return on the stock can be calculated as follows:
Required Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)
15% = RF + 2.0 x (10% - RF)
Solving for RF, we get RF = -5% (This is obviously not possible - this is theoretical as given in the question)

Assuming that Risk-free rate can't be negative we should adjust the Required Return formula as below:
Required Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)
15% = RF + 2.0 x (10% - RF)
15% = 2.0RF + 20%
0.2 = 1.0RF
RF = 20% (This is the real risk-free rate for calculation purpose)

Now, if the market return increases by 30 percent, the new market return would be 13 percent (10% + 30% x 10%). Therefore, the new required return on the stock would be:
Required Return = 20% + 2.0 × (13% - 20%) = 6% + 2.0 × 7% = 20%
The percentage change in the return on the stock would be:
Percentage change = (20% - 15%) ÷ 15% = 33.33%, which is closest to 40%. So the answer is (C) +40%.

You Are Holding a Stock Which Has a Beta of 2.0