Project - Covariance Estimation and Performance of the GMV Portfolio

Suppose you wish to construct a benchmark portfolio with minimum variance, i.e., the Global Minimum Variance (GMV) portfolio. You plan to choose at least 10 stocks listed on the US exchanges with a desirable characteristic. The desirable characteristic may be a certain industry group, a particular geographical region, a specific level of beta, a similar category of dividend yield, etc'.

Monthly Analysis - Compulsory

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-2008 to Dec-2017. You use the monthly returns from Jan-2008 to Dec-2012 to estimate the COV matrix and construct the 1st GMV portfolio for the holding month of Jan-2013, then use the data from Feb-2008 to Jan-2013 to re-estimate the COV matrix and rebalance the GMV portfolio for the subsequent holding month, i.e., Feb-2013. Continue with this process until you exhaust the available data. In total you will repeatedly compute the weights of the GMV portfolio for 60 times, for a given method of covariance estimation. Note that the period of Jan-2013 to Dec-2017 is served as the out¬of-sample test of the portfolio's performance.

To find out which covariance estimation technique is superior, perform the student-t test on the paired-difference of 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. Ouarterly Analysis - Optional

Convert the monthly data to quarterly data and redo the analysis. That is to use the quarterly returns from Q1-2008 to Q4-2012 to estimate the COV matrix and construct the In GMV portfolio for the investment holding quarter of Q1-2013, then use the data from Q2-2008 to Q1-2013 to re-estimate the COV matrix and rebalance the GMV portfolio for the subsequent holding quarter. Compare the results to those found with using the monthly data.