Question

QUESTION 3

The next three questions involve stocks A and B which have the following characteristics:
   A                  B
Covariance of stock’s return with the market .03 .01
Standard deviation of the stock's returns .15 .30
Correlation between returns of A and B .25
Standard deviation of the market .18
Expected rate of return of the market 8%
Risk free rate of interest 1%
a) If you are a fully diversified investor, does buying A or B involve more risk?

b) What is the expected return of a portfolio of 70% of A and 30% of B. See stock characteristics above. Put you answer in decimal (not percentage) terms

Answer 1

1.
Beta=Covariance of stock with market/(Standard deviation of market)^2

Stock A=0.03/(0.18^2)=0.925925926

Stock B=0.01/(0.18^2)=0.308641975

For a well diversified investor relevant measure of risk is beta

Higher the beta higher is the risk

Hence, Stock A is more risky

2.
expected return=risk free rate+beta*(market return-risk free rate)

Stock A=1%+0.925925926*(8%-1%)=7.4815%

Stock B=1%+0.308641975*(8%-1%)=3.1605%

Portfolio returns=70%*7.4815%+30%*3.1605%=6.1852%