Question

Problem 12-14 Expected Returns

Problem 12-14 Expected Returns (LO2) Consider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D. Rate of Return Aggressive Defensive Market Stock A Stock D -8% -115 -6% Scenario Bust -225 -6% Boom Required: a. Find the beta of each stock. b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock. c. If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks? d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)? Complete this question by entering your answers in the tabs below. Required A Required B Required Required D

Answer 1

Find the beta of each stock.

Beta of Aggressive Stock A

B – Aggressive Stock A = Cou(Ra, Rm)/Var(Rm)

Beta of Defensive Stock D

8 – Defensive StockD= Cou(Rd, Rm)/Var(Rm)

Covariance Formula =

Cou(X,Y)= (x – X)(Y - Y)/n - 1

Variance Formula =

I – u/z(x-x) =

Beta of Aggressive Stock A = 969/722 = 1.342

Beta of Defensive Stock D = 570/722 = 0.789

Covariance Calculation

Scenario	Market	X-Mean	Aggressive Stock A	A -Mean	Defensive Stock D	D - Mean	Market* Aggressive Stock A	Market * Defensive Stock D
Bust	-8	-19	-11	-25.5	-6	-15	484.5	285
Boom	30	19	40	25.5	24	15	484.5	285
Mean	11		14.5		9		969	570

Variance Calculation

Scenario	Market	X-Mean	(X-Mean)^2
Bust	-8	-19	361
Boom	30	19	361
Mean	11		722

Ans 2

If the each scenario is equally likely

Market will give 11% return

Aggressive A will give 14.5% returns

Defensive D will give 9% returns

Scenario	Market	Aggressive Stock A	Defensive Stock D	Each Scenario Equally Likely	Return from Market	Return from Aggressive A	Return from Defensive D
Bust	-8	-11	-6	0.5	-4	-5.5	-3
Boom	30	40	24	0.5	15	20	12
					11	14.5	9

Ans 3

As per CAPM = Assuming market returns as per each scenario is equally likely

Fair expected rate of return = risk-free return + Beta (benchmark return - risk-free return)

Stock A = 3+1.342*(11-3) = 13.736

Stock D = 3+0.789*(11-3) = 9.312

Ans 4 -

Stock A is better buy as this stock is giving higher returns.