The Probability Frontier or, Covariance Crunch: A New Paradigm for Mean-Variance Optimization

11 Pages Posted: 22 Jan 2020

Date Written: October 30, 2019

Abstract

Three innovative concepts are combined here to create a new and unique framework for optimizing a portfolio of investments or bets. These inventions are:

1) The Probability Frontier, a generalization of the Markowitz Efficient Frontier;
2) The Positive Probability Estimate, which estimates the chance of a market to move up in the coming period, regardless of the magnitude of the move; and
3) The Directional Covariance, which measures the tendency of markets to move together, regardless of the size of the moves.

Looking at both market moves and their covariances in terms of pure directionality, treating their magnitudes as “noise” on the premise (demonstrated decisively in this paper) that direction is more robustly predictable, dramatically improves the optimized system performance. Indeed, if our estimates can’t even get market directions right, what’s the point of quibbling over tenths of a percentage point? Don’t 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., The Probability Frontier or, Covariance Crunch: A New Paradigm for Mean-Variance Optimization (October 30, 2019). Available at SSRN: https://ssrn.com/abstract=3516217 or http://dx.doi.org/10.2139/ssrn.3516217

Robert D. Stock (Contact Author)

SBV Research ( email )

New Canaan, CT 06840
United States

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