Part 2: Markowitz Model and Optimal Portfolios

For this part of the assignment, use the data in hw2data.xls.

1. Generating some summary statistics:

(a) Report the mean and standard deviation of monthly returns for each of the six stocks.

(b) Report the covariance matrix of returns (6 by 6). Are the covariances between returns on these stocks generally positive or negative? Are the signs of the co-variances surprising?

2. Solving the Markowitz Problem: Take the means above as the expected returns and the estimated covariance matrix above as your best estimate of the covariance between

the returns of the six stocks.

(a) Suppose that the target return is 0.8%. What are the portfolio weights for a portfolio with this return and the minimum possible variance?

(b) Repeat for target returns of 0.9%, 1%, 1.1%, all the way to 1.8%. Report a table of portfolio weights, expected returns, and volatilities. Plot a graph of the expected return (y-axis) versus the volatility (x-axis) of the optimal portfolios.

(c) Would an investor who likes higher expected returns and dislikes volatility ever invest in the portfolio constructed in (a)? Why or why not?

3. Now suppose that the risk-free rate is 0.4167%.

(a) What is the optimal risky portfolio?

(b) What is the expected return if we invest 50% in the optimal risky portfolio and 50% in the risk-free asset? What about 150% in the optimal risky portfolio and -50% in the risk-free asset?

(c) For an investor with a utility function and a coecient of risk aversion of 4, what is the optimal asset allocation?