Question

Consider the following table, which gives a security analyst’s expected return on two stocks in two particular scenarios for the rate of return on the market. Assume that both scenarios are equally likely to happen (i.e., probability of scenario 1 = probability of scenario 2=0.5).

	Scenarios				Market Return		Aggressive Stock		Defensive Stock
	1				5%		−2%		6%
	2				25 %		38%		12%

1. What are the betas of the two stocks? 

2. Plot the two securities on the SML graph. Assume that T-bill rate is 6%. 

3. What are the alphas of each? 

Answer 1

Q3)

a)

beta = change in security return / change in market return

Aggressive stock:

Beta = (38% - (-2%)) / (25% - 5%) = 2

Defensive stock:

Beta = (12% - 6%) / (25% - 5%) = 0.3

b)

Expected return on market = (0.5*5%) + (0.5*25%) = 15%

given risk free rate = 6%

As per CAPM requird return = Rf + beta*(Rm - Rf)

Rf = risk free rate

Rm = market return

SML return of aggressive stock = 6% + 2*(15% - 6%) = 24%

SML return of Defensive stock = 6% + 0.3*(15% - 6%) = 8.7%

Graph:

c)

Expecetd return on aggressive stock = (0.5*(-2%)) + (0.5*38%) = 18%

Expected return on defesive stock = (0.5*6%) + (0.5*12%) = 9%

Alpha = expected return - SML return

Alpha Aggressive = 18% - 24% = -6%

Alpha Defensive = 9% - 8.7% = 0.3%