Question

Problem 1. Consider the following table, which gives a security analysts expected return on two stocks for two particular market returns:

States	Market Return	Aggressive Stock	Defensive Stock
Bad Good	5% 25%	-2% 38%	6% 12%

a) What are the betas of the two stocks?

b) What is the expected rate of return on each stock if the market return is equally likely to be 5% or 25%?

c) If the T-bill rate is 6% and the market return is equally likely to be 5% or 25%, draw the SML for this economy.

d) Plot the two securities on the SML graph. What are the alphas of each?

Problem 2. Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16%.

a) A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year?

b) A stock has an expected rate of return of 4%. What is its beta?

Answer 1

You have asked two unrelated questions in the same post. Further, your first question has multiple sub parts. Hence, I have addressed all the sub parts of the first question. Please post the second question separately.

a) What are the betas of the two stocks?

Aggressive stock = Difference in return / difference in market return = (38% - (-2%)) /(25% - 5%) = 2.00

Defensive stock = (12% - 6%) / (25% - 5%) = 0.30

b) What is the expected rate of return on each stock if the market return is equally likely to be 5% or 25%?

Aggressive stock return = 50% x 38% + 50% x (-2%) = 18%

Defensive stock return = 50% x 12% + 50% x 6% = 9%

c) If the T-bill rate is 6% and the market return is equally likely to be 5% or 25%, draw the SML for this economy.

Expected market return = 50% x 5% + 50% x 25% = 15%

So, when beta = 0, return = risk free return = 6%

and when beta = 1, return = expected market return = 15%

Hence, SML will be:

d) Plot the two securities on the SML graph. What are the alphas of each?

Return predicted by CAPM = Risk free rate + Beta x (Expected market return - risk free rte) = 6% + Beta x (15% - 6%)

Alpha of agressive stock = return in excess of that predicted by CAPM

= 18% - [(6% + 2 x (15% - 6%)] = 18% - 24% = - 6.00%

Alpha of defensive stock = return in excess of that predicted by CAPM

= 9% - [(6% + 0.3 x (15% - 6%)] = 9% - 8.7% = 0.30%