FINA 6112
Excel Assignment 2

You are to act as an equity portfolio manager. Your client asks that you only consider allocating her portfolio across global industry sectors (available through low-cost ETF’s). You thus consider 10 indices for potential investment. The data spreadsheet contains monthly returns for 10 Dow Jones Global indices across major economic sectors for the 10-year period from September 2011 through August 2021. It also contains the current market weights of these industry sectors.

1. Using the historical data, estimate the means and covariance matrix for these 10 asset classes. Let’s keep everything in monthly terms.

2. You carefully question your client to ascertain her level of risk aversion (A). You find that she is indifferent between a risk-free return of 0.02, and a risky return with an expected return of 0.08 and standard deviation of 0.20. What is her risk aversion? (Note: these parameters are in annual terms.)

3. Using portfolio optimization, what are the weights for your recommended portfolio? Do you feel comfortable recommending this portfolio? Why or why not?

4. Suppose that you have many other clients also interested in an optimal allocation across these assets. Create a table that presents the optimal weights for a wide range of (A), along with each portfolio’s mean and standard deviation. Choose a reasonable range of A, based on your judgment. (I think 5 to 10 portfolios should be fine.)

5. Your client now informs you that she is not permitted to short any asset class.

What is your revised recommended portfolio? Why do you think this portfolio is recommended by the optimizer?

6. Now your client informs you that she faces the following constraint: her portfolio weight for each asset must be at least 5% and at most 25%. What is your revised recommended portfolio? Why do you think this portfolio is recommended by the optimizer?

7. Find the portfolio that produces the lowest possible variance (where we go back to the original case in which the only constraint is that the weights sum to one). What is the variance of this “minimum variance portfolio”? Compute its covariance with each of the 10 asset classes. Do you notice anything peculiar? (Purely optional, and tricky: could you prove this mathematically?)