Covariance Crunch Revisited: One Year of Live Performance

SBV Research Working Paper, 2020

12 Pages Posted: 19 Nov 2020 Last revised: 7 Jan 2021

Date Written: October 30, 2020


A previous paper (“The Probability Frontier or, Covariance Crunch: A New Paradigm for Mean-Variance Optimization”) introduced the concept of a Directional Covariance matrix, which reduces market returns to pure directionality (+1 or -1), treating the magnitudes as noise. This is intended to produce better-diversified portfolios with more robust out-of-sample performance than traditional optimization. That paper showed the Directional Covariance matrix did indeed produce more diversified portfolios and better performance than a traditional optimizer in a 13-year back-test simulation for a seven-asset portfolio. We now revisit this test with one full year of new out-of-sample data, and compare its “live” performance against the hedge fund industry. While the traditional optimizer happened to do very well over the last year, the Directional Covariance technique produced a more diverse portfolio and outperformed the HFRI Fund-Weighted Composite index on an absolute basis and by nearly 2:1 on a risk-adjusted basis, with a beta of 0.53, an annual alpha of +2.6%, and R2 of 78%. Having a hedge fund-like risk profile and being fully liquid, this particular strategy is thus well-suited as a holding vehicle for committed (but uncalled) Private Equity capital, to avoid the dreaded “cash drag” effect. Don’t just shrink that covariance matrix; crush it!

Keywords: mean variance optimization, efficient frontier, covariance shrinkage, directional covariance

JEL Classification: C61, G11

Suggested Citation

Stock, Robert D., Covariance Crunch Revisited: One Year of Live Performance (October 30, 2020). SBV Research Working Paper, 2020, Available at SSRN: or

Robert D. Stock (Contact Author)

SBV Research ( email )

New Canaan, CT 06840
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics