Building And Testing a Minimum Variance Portfolio

Abstract

This paper investigates portfolio risk management using historical market data from six major U.S. companies operating across key sectors such as consumer goods, technology, and financial services. This paper applies the minimum variance portfolio (MV) model to a dataset covering 100 daily returns between March and July 2003. The training sample, consisting of the first 70 observations, is used to estimate the covariance matrix and derive optimal portfolio weights. The minimum variance portfolio assigns a large weight to Procter & Gamble. However, it gives negative weight to some assets, including Southwest Airlines and Cisco Systems. The study uses the remaining 30 observations for out-of-sample testing. It compares the cumulative returns of the minimum variance portfolio with those of the S&P 500 index. Results indicate that the S&P 500 outperforms the minimum variance portfolio during the test period. The index achieves a cumulative return of +0.74%, while the portfolio posts a loss of -0.32%.