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19 March, 22:47

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?

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  1. 20 March, 02:28
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    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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