Portfolio Theory in Terms of Partial Covariance

19 Pages Posted: 14 May 2014 Last revised: 14 Jun 2016

Daniel Nadler

Kensho Technologies; Harvard University

Anatoly B. Schmidt

Kensho Technologies; Financial Engineering Program, Stevens Institute of Technology; Financial Risk and Engineering, NYU School of Engineering

Date Written: January 22, 2016

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

Suggested Citation

Nadler, Daniel and Schmidt, Anatoly B., Portfolio Theory in Terms of Partial Covariance (January 22, 2016). Available at SSRN: https://ssrn.com/abstract=2436478 or http://dx.doi.org/10.2139/ssrn.2436478

Daniel Nadler

Kensho Technologies ( email )

20 University Road
Cambridge, MA 02138
United States

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Anatoly B. Schmidt (Contact Author)

Kensho Technologies ( email )

World Trade Center, Suite 46J
NYC, NY 10007
United States

Financial Engineering Program, Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Financial Risk and Engineering, NYU School of Engineering

NY
United States

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