Question

Rate of return if state occurs

State of Economy	Probability of state	Stock A	Stock B
Bust	.30	-.13	-.11
Normal	.50	.08	.08
Boom	.20	.43	.23

A. Calculate the expected teturns on each stock.

Stock A Expected return in percent?

Stock B Expected return in percent?

B.

.	Assuming the capital asset pricing model holds and Stock A's beta is greater than Stock B's beta by .45, what is the expected market risk premium?

Answer 1

A. Expected Return = ?(probability of state*expected return on stock)

Stock A
State of Economy	Probability of state	Expected return	probability of state*expected return on stock
Bust	0.3	-0.13	-3.90%
Normal	0.5	0.08	4.00%
Boom	0.2	0.43	8.60%
Expected Return			8.70%

Stock B
State of Economy	Probability of state	Expected return	probability of state*expected return on stock
Bust	0.3	-0.11	-3.30%
Normal	0.5	0.08	4.00%
Boom	0.2	0.23	4.60%
Expected Return			5.30%

B)

If CAPM holds, Expected return on a stock = Rf+(Beta of the stock*Rp), where:

• Rf = risk free rate
• Rp = expected market risk premium

Stock A: 0.0870 = Rf+(Beta_A*Rp) ===> Rf = 0.0870-(Beta_A*Rp)

Stock B: 0.0530 = Rf+(Beta_B*Rp) ===> Rf = 0.0530-(Beta_B*Rp)

Given: Beta_A=Beta_B+0.45

Thus: 0.0870-((Beta_B+0.45)*Rp) = 0.0530-(Beta_B*Rp)

===> Rp = 7.56%

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