Question

Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:

Market Return		Aggressive Stock		Defensive Stock
7	%	3.7	%	5.5	%
20		30		14

a. What are the betas of the two stocks? (Round your answers to 2 decimal places.)

b. What is the expected rate of return on each stock if the market return is equally likely to be 7% or 20%? (Round your answers to 2 decimal places.)

c. If the T-bill rate is 8%, and the market return is equally likely to be 7% or 20%, what are the alphas of the two stocks? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

(a)

The Betas of two stocks:

Aggressive Stock = 30-3.7/20-7 = 2.02

Defensive Stock = 14-5.5/20-7 = 0.65

(b)

Expected returns of the two stocks:

Aggressive Stock = 0.5*3.7%+0.5*30% = 16.85%

Defensive Stock = 0.5*5.5%+0.5*14% = 9.75%

(c)

Expected return of market portfolio = 0.5*20%+0.5*7% = 13.5%

Therefore, market risk premium is 13.5% - 8% = 5.5%

Therefore, SML is, required return = 8% + β 5.5%

Rs = α + β Rm

For Aggressive Stock:

16.85 = α+2.02*13.5

α = -10.42%

For Defensive Stock:

9.75 = α+0.65*13.5

α= 0.975%