Question

Consider the following table, which gives a security analyst’s expected return on two stocks in two particular scenarios for the rate of return on the market:

Market Return		Aggressive Stock		Defensive Stock
6	%	–4	%	3	%
21		34		9

a. What are the betas of the two stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Beta
Aggressive stock
Defensive stock

b. What is the expected rate of return on each stock if the two scenarios for the market return are equally likely to be 6% or 21%? (Do not round intermediate calculations. Round your answers to 1 decimal place.)

	Expect rate of return
Aggressive stock	%
Defensive stock	%

e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm’s stock if the two scenarios for the market return are equally likely? Also, assume a T-Bill rate of 3%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Hurdle rate__________%

Answer 1

Ans:- (a) Beta for the stock, in this case, will be given by

= Change in the return of the stock / Change in the return of the market.

Beta for Aggressive stock = (-0.04 - 0.34) / ( 0.06 - 0.21) = 2.53

Beta for Defensive stock = ( 0.03 -0.09) / (0.06 - 0.21) = 0.40

(b) If the two scenarios are equally likely then the weights will be 0.5 for each case

Expected rate of return for the stock if the two scenarios for the market return are equally likely will be given by

= weights 1 * Return 1 + weights 2 * Return 2

Aggresive stocks expected return  = 0.5 * -0.04 + 0.05 * 0.34 = 0.15 = 15%

Defensive stocks expected return = 0.5 * 0.03 + 0.5 * 0.09 = 0.06 = 6%

(e) By CAPM hurdle rate will be given by Risk-free rate + ( Market Return - Risk-free rate)

Market return if both scenarios are equally likely will be 0.5 * 0.06 + 0.5 * 0.21 = 0.1350 = 13.50%.

Beta will be 0.40 because risk characteristics is of the defensive stock. Risk-free rate is 3%,then hurdle rate will be

= 3% + 0.40 * (13.5% - 3%) = 7.20%