Question

1. Expected return on two stocks for two particular market returns: Please show all work.

                        Market Return            Aggressive Stock        Defensive Stock

                        5%                               1%                               8%

   20%                             25%                             18%

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 3% 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

1.
Aggressive=(1%-25%)/(5%-20%)=1.60

Defensive=(8%-18%)/(5%-20%)=0.67

2.
Aggressive=(1%+25%)/2=13.0000%

Defensive=(8%+18%)/2=13.0000%

3.
market return=(5%+20%)/2=12.5000%

Equation for SML:
required return=risk free rate+beta*(market return-risk free rate)
=3%+beta*(12.5000%-3%)
=3%+beta*9.5000%

The SML can be drawn using above equation
with return on y axis and beta on x axis

4.
required return for Aggressive stock=3%+1.60*9.5000%=18.2000%

required return for Defensive stock=3%+0.67*9.5000%=9.3650%

Aggressive stock is overvalued as expected return is more than required return