Short Time Correction to Mean Variance Analysis in an Optimized Two-Stock Portfolio

Abstract

The effect of short time correlation in stock prices on a two-stock portfolio under the framework of Mean Variance Analysis is investigated. The theory of Markowitz on portfolio management, based on a long time scale analysis of return and variance, is first optimized over a selection of pair of stocks from the Hang Seng Index and then corrected by the return of short time scales of the stocks. Several choices of short time returns, from 1 to 5 days in the past, are studied. The cumulative return is highest when the returns of the two-stock portfolio in the past 2 days are included in the correction to the “modified Sharpe ratio”. The testing data cover the period between Jan 10, 2007 and July 21, 2009 for 24 blue chip stocks from the Hang Seng Index. The strategy is compared to the average return of these 24 stocks as well as to the Hang Seng Index in the same period. We conclude that our strategy has a positive return over most of the days of the testing period, including a very stable positive performance in the period of market crash. The variation of the cumulative return of our strategy is less than both the average returns of the chosen stocks or the Hang Seng Index, thereby providing a portfolio with a smaller risk but still attractive return. This strategy of time dependent mean variance analysis to include both the long and short time scale data appears to be a good investment scheme for conservative investors who prefer stable return even during market downturn.