4. Suppose that you’re given the following information of rates of return for the stock market as assessed by your financial analyst in mutual fund. Answer the following questions:
a)What are the means, standard deviations for each fund? Why do you need to specify the means and the standard deviations?
b)What are the co-variances for these funds? Are these funds mutually “diversifiable”? Why or why not? (Hint: apply correlation coefficients to tell)
c)Explain the assumption(s) and reason(s) why the expected rate of return of investor can be represented by the expected value of the rate of return.
d)Suppose that Fund A represents the Market Index Portfolio. What are the “beta’s” for Fund B and Fund C? What is the difference in concept between standard deviation and beta for Fund B and Fund C?
e)Suppose the risk-free rate is 2% and Fund A represents the Market Index Portfolio. What are the expected rates for Fund B and Fund C now according to CAPM? Are they different from the “means” you calculated in a)? Why?
States of the worldProbability Fund A Fund B Fund C
Boom 1/416% 12% 8%
Recovery 1/224% 36% 8%
Recession 1/4 -32% -20% 4%