Co-Occurrence: A New Perspective on Portfolio Diversification

Abstract

Investors typically measure an asset’s potential to diversify a portfolio by its correlations with the portfolio’s other assets, but correlation is useful only if it provides a good estimate of how an asset’s returns co-occur cumulatively with the other asset returns over the investor’s prospective horizon. And because correlation is an average of sub-period co-occurrences, it only serves as a good estimate of prospective co-occurrence if the assets’ returns are multi-variate normal, which requires them to be independent and identically distributed. The authors provide evidence that correlations differ depending on the return interval used to estimate them, which indicates they are not serially independent. Moreover, the authors show that asset co-movement differs between regimes of high and low interest rates and between turbulent and quiescent markets, and that they are asymmetric around return thresholds, which indicates that returns are not identically distributed. These departures from multi-variate normality cast serious doubt on the usefulness of full-sample correlations to measure an asset’s potential to diversify a portfolio. The authors propose an alternative technique for diversifying a portfolio that explicitly considers the empirical prevalence of co-occurrences and thus the non-normality of returns.

Keywords: Autocorrelation, Co-occurrence, Divergence, Full-scale Optimization, Informativeness, Lagged Cross Correlation, Mahalanobis Distance, Mean-variance Analysis, Multi-horizon Optimal Portfolio, Parametric Optimization, Pearson Correlation, Turbulence

JEL Classification: C00, C02, C10, C18, C40, C60, C61, G00, G11