Question

1. Expected return on two stocks for two particular market returns: Market Return Aggressive Stock Defensive Stock 2% -5% 3% 22% 35% 15% 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 2% or 22%? c. If the T-bill rate is 3% and the market return is equally likely to be 2% or 22%, draw the SML for this economy. d. Between aggressive and defensive stocks, which one is undervalued, which is overvalued, and why?

Answer 1

Market Return Aggressive Stock Defensive Stock
2% -5% 3%
22% 35% 15%

1.
Aggressive=(-5%-35%)/(2%-22%)=2.00000000

Defensive=(3%-15%)/(2%-22%)=0.60000000

2.
Aggressive=(-5%+35%)/2=15.0000%

Defensive=(3%+15%)/2=9.0000%

3.
market return=(2%+22%)/2=12.0000%

Equation for SML:
required return=risk free rate+beta*(market return-risk free rate)
=3%+beta*(12.0000%-3%)
=3%+beta*9.0000%

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%+2.00*9%=21.0000%

required return for Defensive stock=3%+0.60*9%=8.4000%

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