Question

Suppose you observe the following situation:

  

				Rate of Return If State Occurs
State of	Probability of
Economy	State			Stock A			Stock B
Bust		.30			−.10			−.08
Normal		.50			.11			.11
Boom		.20			.46			.26

  

a.	Calculate the expected return on each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	Expected return
Stock A	%
Stock B	%

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? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected market risk premium

%

Answer 1

Stock A

State	Probability (P)	Return(%)	P*Return
Bust	0.3	-10	(3.00)
Normal	0.5	11	5.50
Boom	0.2	46	9.20

Expected return = -3+5.5+9.2

= 11.70%

Stock B

State	Probability (P)	Return(%)	P*Return
Bust	0.3	-8	(2.40)
Normal	0.5	11	5.50
Boom	0.2	26	5.20

Expected return = -2.4+5.5+5.2

= 8.30%

using Capital Asset Pricing Model

Expected return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return

b – Beta

Rm – Expected return on market portfolio

Rm-Rf - Market risk premium

Expected return of stock A = 11.70 = Rf+((beta of b+.45)*(Rm-Rf))

Expected return of stock B = 8.30= Rf+(beta of b*(Rm-Rf))

Subtracting the above 2 equations

3.4 = .45*(Rm-Rf)

Rm-Rf = 3.4/.45

= 7.56%