Suppose the market portfolio is equally likely to increase by 35% or decrease by

Question

Suppose the market portfolio is equally likely to increase by 35% or decrease by 5%. Also suppose that the risk-free interest rate is 5%.

a. Use the beta of a firm that goes up on average by 50% when the market goes up and goes down by 10% when the market goes down to estimate the expected return of its stock. How does this compare with the stock's actual expected return?

b. Use the beta of a firm that goes up on average by 17% when the market goes down and goes down by 24% when the market goes up to estimate the expected return of its stock. How does this compare with the stock's actual expected return?

Explanation / Answer

Expected market return=1/2*35%+1/2*-5%=15%

Expected return=risk free+beta*(market-riskfree)

Beta=Change in stock/Change in market

a)Beta=(50-(-10))/(35-(-5))=1.5

Expected return=5+1.5*(15-5)=20%

Actual expected return=(35-(-5)/2=20%

b)Beta=(17-(-24))/(35-(-5))=1.025

Expected return=5+1.025*(15-5)=15.25%

Actual expected return=(17-(-24))/2=20.5

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