Active Investment Strategies under Tracking Error Constraints

Abstract

Active portfolio managers are judged on their ability to outperform agent’s benchmarks, so optimising fund returns is important. Maximising fund outperformance is, however, non-trivial because active portfolios are subject to tracking error (TE) and other constraints. Feasible portfolios constrained by TE are bounded by an elliptical frontier in mean/variance space and may not be efficient. Also, ‘optimal’ can involve different objectives for different investors. Previous attempts to isolate optimal portfolios on the constant TE frontier have been limited to the maximum return, minimum risk and benchmark risk portfolios. More recently, the maximum risk-adjusted return portfolio on this frontier was identified. Using a highly stylised portfolio comprising only three assets for clarity and ease of explanation, we review for the first time existing optimal portfolio assemblies and introduce other possibilities: TE-constrained portfolios which are maximally diversified, exhibit risk parity, and have minimal intra-correlation between constituents. The methodology to generate optimal risk weights for these portfolios is explained and the way risk/return profiles change as TE changes is characterised. The way portfolios move in risk/return space in a changing TE milieu could initiate novel investment strategies for active fund managers.