Portfolio Theory in Terms of Partial Covariance

Abstract

It is found that partial correlations between 12 major US equity sector ETFs conditioned on the state of economy (mimicked here by the S&P 500 index) are significantly lower than the Pearson’s correlations. The Markowitz mean-variance portfolio theory is modified in terms of partial covariance. The maximum Sharpe portfolios formed by 12 equity sector ETFs in 2007 – 2015 are examined. With the exclusion of the bear market of 2008, the partial correlation based portfolios (PaCP) are much more diversified than the Pearson’s correlation based portfolios (PeCP). Out-of-sample performance of the maximum Sharpe PeCP and PaCP, and the equal-weight portfolio (EWP) are compared. The results are very sensitive to the model parameters (portfolio calibration window and frequency of portfolio rebalancing). While the PeCP weights change significantly from month to month, the PaCP weights outside the bear market effects are almost constant. PaCP outperforms both EWP and PeCP when the 36-month calibration window and one-month rebalancing frequency are used. We conclude that partial covariance is a promising concept for constructing optimal portfolios.

Keywords: portfolio theory, portfolio performance, partial correlations