You are holding a stock that has a beta of 2.0 and is currently in equilibrium. The required return on the stock is 15%, and the return on an average stock is 10%. What would be the percentage change in the return on the stock, if the return on an average stock increased by 30% while the risk-free rate remained unchanged?

The percentage change in the return on the stock is 40%

Explanation:

Beta = 2

Required return = 15%

Return on average stock = 10%

Step 1:

Calculating the risk free rate on return, we use the formula;

Required Rate of Return = Rf + Beta (Rm - Rf)

Where;

Rf = risk free rate

Rm = return on average stock = 10%

Beta = 2

Substituting, we have

15% = Rf + 2 (10% - Rf)

0.15 = Rf + 2 (0.1 - Rf)

0.15 = Rf + 0.2 - 2Rf

0.15 = 0.2 - Rf

Rf = 0.2-0.15

= 0.05

Rf = 5%

Step 2: Calculating new market return, we have

Since the return on average stock increased by 30%,

Therefore Rm = 1.3 (10%) = 13%.

the new required return on stock becomes,

ks = 5% + 2 (13% - 5%)

= 5% + 2*8%

= 5% + 16%

= 21%.

Step 3: percentage change in the return on the stock;

The percentage change on return stock = (21 - 15) / 15

= 6, 6/15

= 40%