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%

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