Defining and measuring portfolio diversification

It is often said that diversification is the only ‘free lunch’ available to investors; meaning that a properly diversified portfolio reduces total risk without necessarily sacrificing expected return. However, achieving true diversification is easier said than done, especially when we do not fully know what we mean when we are talking about diversification. While the qualitative purpose of diversification is well known, a satisfactory quantitative definition of portfolio diversification remains elusive. In this research, we summarise a wide range of diversification measures, focusing our efforts on those most commonly used in practice. We categorise each measure based on which portfolio aspect it focuses on: cardinality, weights, returns, risk or higher moments. We then apply these measures to a range of South African equity indices, thus giving a diagnostic review of historical local equity diversification and, perhaps more importantly, providing a description of the investable opportunity set available tofund managers in this space. Finally, we introduce the idea of diversification profiles. These regimedependent profiles give a much richer  description of portfolio diversification than their single-value counterparts and also allow one to manage diversification proactively based on one’s view of future market conditions. Keywords: Portfolio diversification; index concentration; weight-based diversification; risk-based diversification; correlation; covariance; market regimes