Defining Activeness: Active Share, Risk Share & Factor Share

Abstract

This paper tackles a core question of portfolio management: How ‘active’ is an active portfolio? To answer this question holistically, we generalise the idea of Active Share by keeping the same calculation methodology but substituting in different types of portfolio and benchmark ‘weights’. In particular, we introduce the idea of Risk Share – based on asset risk contributions – and Factor Share – based on either factor style exposures or factor risk contributions. We describe these new metrics in a general multi-factor market framework and, using a set of simulated random portfolios of increasing activeness, explore some of the relationships between them and with other common fund performance measures. Finally, we conduct an empirical 'activeness' analysis on a set of South African equity funds. In both the simulated and empirical analyses, we find that the trio of Active Share, Risk Share and Factor Share provides one with a comprehensive, standardised means for easily assessing across multiple dimensions how a portfolio truly differs from its benchmark.

Keywords: active share, risk share, factor share, active management, risk decomposition, risk attribution, factor portfolios, returns based style analysis

JEL Classification: C01, C02, C21, C22, C31, C32, C51, C53, C58, C61