Question

Suppose you observe the following situation:

State of Economy	Probability of State	Return if State Occurs
		Stock A	Stock B
Bust	.15	−.08	−.10
Normal	.60	.11	.09
Boom	.25	.30	.27

a.	Calculate the expected return on each stock. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	Assuming the capital asset pricing model holds and Stock A’s beta is greater than Stock B’s beta by .30, what is the expected market risk premium? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

State of Economy	Probability	Stock A return	Stock B return
Bust	0.15	-0.08	-0.1
Normal	0.6	0.11	0.09
Boom	0.25	0.3	0.27

Part a

Expected Return is calculated using the formula:

E[R] = p₁*R₁ + p₂*R₂ + p₃*R₃

where p_i is the probability of a state of economy and R_i is the return during that particular state of the economy

Stock A

Expected return on A = E[R_A] = 0.15*(-0.08) + 0.6*0.11 + 0.25*0.3 = 0.129 = 12.9%

Stock B

Expected return on stock B = E[R_B] = 0.15*(-0.1) + 0.6*0.09 + 0.25*0.27 = 0.1065 = 10.65%

Answer a

Expected return on stock A = 12.90%

Expected return on stock B = 10.65%

Part b

It is given that CAPM holds and beta of stock A is greater that beta of stock B by 0.30

Beta of stock A = β_A, Beta of stock B = β_B

β_A = β_B + 0.3

According to CAPM, expected return on a stock is given by:

E[R] = R_F + β*MRP

where R_F = Risk-free rate, β = beta of the stock, MRP = Expected market risk premium

Applying CAPM for stock A

E[R_A] = R_F + β_A*MRP

12.9% = R_F + β_A*MRP

Using, β_A = β_B + 0.3

12.9% = R_F + (β_B+0.3)*MRP

12.9% = R_F + β_B*MRP + 0.3*MRP

Applying CAPM for stock B

E[R_B] = R_F + β_B*MRP

10.65% = R_F + β_B*MRP

Now, we have these two equations

10.65% = R_F + β_B*MRP (From Stock B CAPM)

12.9% = R_F + β_B*MRP + 0.3*MRP (from stock A CAPM equation)

Now, since R_F + β_B*MRP = 10.65%

12.9% = 10.65% + 0.3*MRP

0.3*MRP = 12.9% - 10.65% = 2.25%

0.3*MRP = 2.25%

MRP = 2.25%/0.3 = 7.5%

Answer b

Expected Market risk premium = 7.5%