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.)

Expected 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

a)What are the betas of the two stocks?

ANSWER =

Beta is the sensitivity of the stock’s return to the market return, i.e., the change in the stock return per unit change in the market return

_A = (-0.04 - 0.34 )/ (0.06 - 0.21) = 0.39

_D = (0.03 - 0.09 )/ (0.06 - 0.21) = 0.4

B) What is the expected rate of return on each stock if the market return is equally likely to be 6% or 21%?

Answer =

E(rA) = 0.5 x (-0.04 + 0.34) = 0.15 = 15%

E(rD) = 0.5 x (0.03 + 0.09) = 0.06 = 6%

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?

The hurdle rate is determined by the project beta (0.39), not the firm’s beta. The correct discount rate is 7.09%, the required return for stock A.

The SML is determined by the market expected return of [0.5 x (0.06 + 0.21)] = 13.5%, with βM= 1, and rf= 3% (which has β = 0).The equation for the security market line is: E(r) = 0.03 + β x (0.135 − 0.03)

The aggressive stock has a required return of:

E(rA) = 0.03 + 0.39 x (0.135 − 0.03) = 0.07095 = 7.09

αA= actual expected return − required return (given risk)

= 15% − 7.09% = 7.91%

Similarly, the required return for the defensive stock is:

E(rD) = 0.03 + 0.4 x (0.135 − 0.03) = 7.2%

The stock’s alpha is:

αD= actual expected return − required return (given risk)

= 0.06 − 0.072 = - 1.2%