Near the end of the semester, I will be using class time for competitions based on Modern Portfolio Theory. In these competitions, you will be given the last five years of monthly returns on ten mutual funds (possibly together with some other data) and asked to choose a portfolio that best achieves some objective, like minimizing variance or maximizing Sharpe ratios. You will use MPT, possibly with some variations of your own choosing, to select portfolio weights for the ten funds. The performance of that portfolio will then be evaluated based on the subsequent 12 months of returns on the same funds.

To prepare for the contest, I have posted "practice data" that look just like the data that you will be given in the contests. To get that practice data, go to jones.marshall.usc.edu and click the "investment simulation" link. There is a lot on this page that I won't explain until later - all you need to do for now is to click the "Data" button and then follow the "Get practice data" link. Download the 1_retdata_practice.xls file, which is the first of the 250 files available.

When you open the spreadsheet, go to the "returns" sheet. The past excess returns on the ten funds you will be analyzing are in columns F to O. You may ignore the other data in the spreadsheet for now.

Note: Excess returns are just regular returns minus the riskless rate. Work with them just the way you would normally work with regular returns, but treat the riskless rate as though it is zero since it has already been subtracted from the returns.

Using this data, answer the following questions:

What long-only portfolio has the lowest variance?

What long-only portfolio has the highest Sharpe ratio?

What happens when the long-only requirement is eliminated?

If possible, you should strive to answer these questions using a spreadsheet in which it is easy to change the returns data that underlie your calculations. You will then be able to use your spreadsheet, or at least a modified version of it, in the competitions we will hold, which will require you to compute optimal portfolio weights quickly.

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To find the answers to your questions youll need to follow these steps 1 Calculate the covariance ma... View the full answer