Covariance Estimation and Performance of the GMV Portfolio Suppose you Wish to Construct a Characteristic Portfolio with Minimum Variance: Division of Banking and Finance Assignment, NTU, Singapore

Term Project

Covariance Estimation and Performance of the GMV Portfolio

Suppose you wish to construct a characteristic portfolio with minimum variance, i.e., the Global Minimum Variance (GMV) portfolio. This characteristic portfolio will consist of at least 10 stocks selected from the constituent stocks of the S&P 500 Index with one or two desirable characteristics. The desirable
characteristics may be a certain industry group, a group of green chip stocks1
, a specific level of beta, a similar category of dividend yield, etc2

Monthly Rebalance

To back test the performance of the portfolio, you estimate the covariance matrix based on traditional sample method, a constant correlation model, and the market model, then use these estimates in calculating the component weights (with and without short sales allowed) of the GMV portfolio. You will also impose monthly rebalancing of the portfolio weights.

The studied period is 10 years, from Jan-2011 to Dec-2020. Use the monthly returns from Jan-2011 to Dec2015 to estimate the COV matrix and construct the 1st GMV portfolio for the holding month of Jan-2016, then use the data from Feb-2011 to Jan-2016 to re-estimate the COV matrix and rebalance the GMV portfolio for the subsequent holding month, i.e., Feb-2016. Continue with this process until you exhaust the remaining data. For a certain method of covariance estimation, you will repeatedly compute the weights of the GMV
portfolio for 60 times. Note that the period of Jan-2016 to Dec-2020 is served as the out-of-sample test of the portfolio’s performance.

To find out which covariance estimation technique is superior, perform the paired-t tests on the GMV returns. Secondly test whether the best GMV portfolio beat the S&P500 portfolio or low volatility portfolios such as iShares MSCI USA Minimum Volatility Index Fund (USMV) and Russell 1,000 Low
Volatility ETF (LVOL).

Last analyze and discuss how the component weights and the rebalancing of the GMV portfolio behave for each method of covariance estimation. Organize the results into tables and figures and discuss them and their implications.

Note that the CRSP database on WRDS is a good source to retrieve the monthly returns for the project.

Quarterly Rebalance

Now you rebalance the GMV quarterly. Note that the portfolio becomes buy-and-hold for the months in a quarter. In the quarter, you need to determine the realized weights at the end of a month for calculating the return of the subsequent month. Compare and discuss the results to those found using the monthly data.