Question

Expected return on two stocks for two particular market returns:

Market Return            Aggressive Stock        Defensive Stock

5%                               2%                               8%

20%                             25%                             20%

1. What are the betas of the two stocks?
2. What is the expected rate of return on each stock if the market return is equally likely to be 5% or 20%?
3. If the T-bill rate is 4% and the market return is equally likely to be 5% or 20%, draw the SML for this economy.
4. Between aggressive and defensive stocks, which one is undervalued, which is overvalued, and why?

Answer 1

a).

Beta of a stock is calculated as change in the stock compared to change in market.

So, Beta of Agressive stock= 25%-(2%)/(20%-5%)

= 23%/15%= 1.53

Beta of Defensive stock= (20%-8%)/(20%-5%)

= 12%/15%

= 0.8

b).

Given that both the scenarios are equally likely. So, probabilities are 0.5 and 0.5

So, Expected return on Agressive stock = (0.5*2%)+(0.5*25%)= 13.5%

Expected return on Defensive stock= (0.5*8%)+(0.5*20%)= 14%

c).

Given that risk free rate is 4% and market return is equally likely of 5% and 20%, expected return on market= (0.5*5%)+(0.5*20%)= 12.5%. So, SML can drawn as below.

d).

From the graph, we can see Defensive stock is lying above SML line and Agressive stock is lying below SML.

So, Defensive stock is undervalued and Agressive stock is overvalued.