Problem 1 (15 points)
You are given the following information about Stocks A and B:

Rate of Return if State Occurs
State ofEconomy    Probability of
State of Economy    Stock A    Stock B
Boom    0.20    20%    25%
Normal    0.60    10%    12%
Recession    0.20    -5%    -6%

Stock A has a beta of 1.0, and Stock B has a beta of 1.4.  Assume that the CAPM holds, and that neither of these stocks is over or

undervalued.
a.    What is the market risk premium, risk-free rate, and expected return of the market portfolio? (Hint: Calculate the expected

returns of the two stocks first. Then use the CAPM.)

b.    What would be the beta of a portfolio consisting of 25% of Stock A and 75% of Stock B?

c.    What would be the expected return and standard deviation of the portfolio under b (25% of Stock A and 75% of Stock B)?

Problem 2 (8 points)
A portfolio consisting of Stocks 1 and 2 has an expected return of 13%.  What is the standard deviation of this portfolio given the

information about Stocks 1 and 2 in Table 3.1?

Table 3.1    Stock 1    Stock 2
Expected Return    10%    14%
Standard Deviation    12%    18%
Correlation (ρ1,2)    0.65

Problem 3 (7 points)
A portfolio consisting of Stocks 3 and 4 has zero variance.  What is the weight of Stock 3 in this portfolio given the information about

Stocks 3 and 4 in Table 3.2?
(Hint: set the portfolio variance to 0 and solve for the weights.)

Table 3.2    Stock 3    Stock 4
Standard Deviation    10%    15%
Correlation (ρ3,4)    -1