Portfolio Optimization
1. You have decided to invest in a portfolio that includes all companies in the Dow Jones Industrials Index. A list of the companies in the index can be found in Yahoo Finance (go to Market Data, then Stocks, select Dow Jones Industrial Average, and then look for "Index Components"). You should find 30 companies.
2. Compute monthly returns for the last five years for each of the companies in the portfolio. Use the data in Adj Close when you download monthly prices from Yahoo Finance. Your sample of historical returns should have 60 observations.
3. Compute the Mean and Standard Deviation of the Returns.
4. Estimate the variance-covariance matrix using both the covariance.s function in excel and matrix multiplication. Check that you get the same values using either approach.
5. Generate and plot the envelope curve using the following alternative approaches:
5A. Maximize the ratio E(rx - c)/σx for an arbitrary c (use solver)
5B. Minimize the portfolio variance for an arbitrary return (use solver). Assume the same portfolio return you obtained under approach 5A. Check that the portfolios are the same using both approaches.
6. Estimate the Minimum-Variance Portfolio.
7. Estimate the Optimal Portfolio. Use the current value of the 6 month T-bill as a proxy for the risk free rate. Find the expected return and variance for this portfolio.
8. Estimate the Optimal Portfolio assuming that no short sales are allowed. What is the expected return and variance of this portfolio?
9. Estimate the Optimal Portfolio assuming that no short sales are allowed and no more than 20% should be invested in a single stock. What is the expected return and variance of this portfolio?