State of Economy | Probability of state | Stock A return | Stock B return |
Boom | 0.15 | -0.08 | -0.05 |
Normal | 0.70 | 0.13 | 0.14 |
Bust | 0.15 | 0.48 | 0.29 |
Part a
Expected Return is calculated using the formula:
E[R] = p1*R1 + p2*R2 + p3*R3
where pi is the probability of a state of economy and Ri is the return during that particular state of the economy
Stock A
Expected return on A = E[RA] = 0.15*(-0.08) + 0.7*0.13 + 0.15*0.48 = 0.151 = 15.1%
Stock B
Expected return on stock B = E[RB] = 0.15*(-0.05) + 0.7*0.14 + 0.15*0.29 = 0.134 = 13.4%
Expected return on stock A = 15.1%
Expected return on stock B = 13.4%
Part b
It is given that CAPM holds and beta of stock A is greater that beta of stock B by 0.25
Beta of stock A = βA, Beta of stock B = βB
βA = βB + 0.25
According to CAPM, expected return on a stock is given by:
E[R] = RF + β*MRP
where RF = Risk-free rate, β = beta of the stock, MRP = Expected market risk premium
Applying CAPM for stock A
E[RA] = RF + βA*MRP
15.1% = RF + βA*MRP
Using, βA = βB + 0.25
15.1% = RF + (βB+0.25)*MRP
15.1% = RF + βB*MRP + 0.25*MRP
Applying CAPM for stock B
E[RB] = RF + βB*MRP
13.4% = RF + βB*MRP
Now, we have these two equations
13.4% = RF + βB*MRP (From Stock B CAPM)
15.1% = RF + βB*MRP + 0.25*MRP (from stock A CAPM equation)
Now, since RF + βB*MRP = 13.4%
15.1% = 13.4% + 0.25*MRP
0.25*MRP = 15.1% - 13.4% = 1.7%
0.25*MRP = 1.7%
MRP = 1.7%/0.25 = 6.8%
Expected Market risk premium = 6.8%
Answers:
a | Stock A | 15.1 | % |
Stock B | 13.4 | % | |
b | Market Risk premium | 6.8 | % |
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