1. Go to the spreadsheet that I attached called Solving for M and changing the risk-free rate 2015. You will see how I used matrix multiplication to solve for the weights in the M portfolio given a risk-free rate. First, solve for the weights in M* if the risk-free rate is changed by increments of 0.5% starting at 1% and going to 4%. How does that change your results? (Note I have included the Sharpe measure). Second, solve for the weights in the minimum variance portfolio as well as the expected return, variance and standard deviation of the MVP.

2. From that same spreadsheet (putting the risk-free rate back to 1%), consider adding a fifth risky asset to the portfolio with the following characteristics.

a. Cov(1,5) = -.03

b. Cov(2,5) = .02

c. Cov(3,5) = .01

d. Cov(4,5) = -.02

e. Var(5) = .50

f. Expected Return (5) = .09

First, solve for the weights in the new M portfolio as well as it's expected return and variance. Second, solve for the weights in the new minimum variance portfolio as well as the expected return, variance and standard deviation. Compare your answers from the 4 asset portfolio to the 5 asset portfolio.

3. From that same spreadsheet (assuming your M from #2 is the true market portfolio), how would you solve for the Z portfolio in the absence of a risk-free asset? Play around in Excel and see what you come up with. I am looking for a good attempt and not requiring that you get it exactly right.

4. Consider a three asset world with the following parameters:

Mean returns = 10% 0.30 0.02 -0.05

12%, Variance covariance matrix = 0.02 0.40 0.06

15% -0.05 0.06 0.60

Suppose you have two portfolios with the following portfolio weights:

Portfolio 1 = (0.33 0.33 0.33)

Portfolio 2 = (-0.15 -0.10 1.25)

First, calculate the mean and variance for each portfolio's returns and the covariance and correlation coefficient of the portfolio's returns. Second, create a graph of the means and variances of convex combinations of the two portfolios.

5. You believe that the Campbell company stock will be worth $50 in exactly one year. What should the stock be worth today if the risk-free rate is 1%, the expected return on the market portfolio is 6%, the covariance between the Campbell company returns and the market returns is -0.013, and the variance of the market is .0064. Solve for the price using the risk-adjusted rate of return valuation formula.

Attachment:- problem_set_3_2015.doc