Abstract

In Markowitz’s (1952) portfolio theory, a reduction in volatility for a given level of expected return is implied as being equivalent to an increase in diversification. The recent development of risk-based portfolio construction methods, which emphasise diversification separately from volatility reduction, challenges this equivalence. Using a point-in-time database of liquid equities listed on the Johannesburg Stock Exchange between 1998 and 2016, a numerical simulation technique is employed to study the behaviour of a range of diversification measures as a portfolio-level attribute and assess and compare their usefulness in estimating out-of-sample portfolio volatility. The empirical performance of maximum diversification portfolios based on each measure is then investigated. It is found that a portfolio’s diversification level is a significant predictor of future portfolio risk beyond that of historic volatility, and that the empirical performance of maximum diversification portfolios, attractive in all cases, depends critically on the definition of diversification applied.