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%	-3%	4%
22	35	12

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

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 22%? (Do not round intermediate calculations. Round your answers to 1 decimal place.) 

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 4%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a) Beta = Change in Stock Returns / Change in Market Returns

Aggressive Beta = (35% + 3%) / (22% - 6%) = 2.375

Defensive Beta = (12% - 4%) / (22% - 6%) = 0.5

b) Expected Return = Average returns of both scenarios

Aggressive Stock Returns = (35% - 3%) / 2 = 16%

Defensive Stock Returns = (12% + 4%) / 2 = 8%

e) Market Returns = (22% + 6%) / 2 = 14%

Using CAPM, Required Return = Rf + beta x (Rm - Rf) = 4% + 2.375 x (14% - 4%) = 27.75%