Co-Occurrence: A New Perspective on Portfolio Diversification

Investors seek to diversify a portfolio by combining assets that have low correlations with each other, but a correlation coefficient is a useful guide to diversification only under special conditions that rarely hold in practice. If returns are not serially independent and if they do not conform to a stable multivariate normal distribution, correlation will not provide a reliable guide to the asset co-occurrences that a portfolio is likely to experience. The authors provide evidence that assets frequently violate these assumptions of serial independence, stationarity, and normality. These empirical realities cast serious doubt on the usefulness of full-sample correlations to measure an asset’s potential to diversify a portfolio. The authors introduce a measure of co-occurrence as a fundamental building block of diversification. An informativeness weighted average of co-occurrence across a full sample equals correlation, but co-occurrence offers an intuitive and flexible way to assess complexities of co-movement that lie beyond the grasp of any summary statistic. The authors present an alternative technique for diversifying a portfolio that explicitly considers the empirical prevalence of co-occurrences and thus the nonnormality of returns.