Consider the following Table, which gives a security analyst’s expected returns on two stocks and the market portfolio for two possible economic states:
Market Portfolio, Aggressive Stock , Defensive Stock
State 1 3% 6% 9%
State 2 9% 24% 18%
a) What are the market betas of the two stocks?
b) What is the expected rate of return on each stock if the economy is equally likely to be in the two economic states?
c) If the T-bill rate is 1% and the economy is equally likely to be in the two economic states. Derive the SML. What is the alpha of each stock?
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Answer:
a)
Beta of aggressive stock is computed as
= change in security return/change in market return
=24-6/9-3
= 18/6
=3
Beta of Defensive stock
= change in security return/ change in market return
= 18-9/9-3
=9/6
= 1.50
b)
Expected return of Aggressive stock
= 6*.50+24*.50
= 3+12
= 15℅
Expected return of Defensive stock
= 9*.50+18*.50
= 4.50+ 9
= 13.50℅
c)
SML
Expected Market return of portfolio= 3*.50+9*.50
= 6℅
= Risk free+ Beta( Market return- Risk free)
= 1+Beta(6-1)
= 1℅+ Beta 5℅
Alpha of aggressive stock
= Return of security- Beta*market return
= 15-3*6
= -3℅
Alpha of Defensive stock
= Return of security- beta*market return
= 13.50-1.50*6
=4.50%
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