The Cost of a Free Lunch: Dabbling in Diversification

Abstract

It’s 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 don’t fully know what we mean when we’re talking about diversification. While the qualitative purpose of diversification is well-known, a satisfactory quantitative definition of portfolio diversification is not. In this report, we summarise a wide range of diversification measures, focussing our efforts on those most commonly used in practice. We categorise each measure based on which portfolio aspect it focusses 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 to fund managers in this space. Finally, we introduce the idea of diversification profiles. These regime-dependent 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.