Portfolio optimisation under the tracking error constraint

Abstract

Active portfolio managers are judged on their ability to outperform agent's benchmarks, hence optimising fund returns is critically important. Maximising fund outperformance is, however, non-trivial because active portfolios are subject to tracking error (TE) (and other) constraints. Portfolios constrained by a TE are fenced by an elliptical frontier in mean/variance space and may not be efficient. The ellipse's flat shape suggests an additional constraint which improves the performance of the active portfolio. Some at-tempts have been made to identify optimal portfolios subject to the restrictions imposed by TEs, i.e. to locate these on the frontier. Although subsequent work isolated and explored different portfolios subject to these constraints, absolute portfolio risk has been consistently ignored. First a different restriction ? maximisation of the traditional Sharpe ratio on the constant tracking error frontier in absolute risk/return space ? is added to the existing constraint set, and a method to generate this portfolio is explained. The resultant portfolio has a lower volatility and higher return than the benchmark, it satisfies the tracking error constraint and the ratio of excess absolute return to risk is maximised (i.e. maximum Sharpe ratio in absolute space). Second, we review these portfolio assemblies and introduce more possibilities using the previously derived method: portfolios which are maximally diversified, exhibit risk parity, have minimal intra-correlation, and minimum risk. Such portfolios behave differently to those which are part of the efficient set, i.e. populate the efficient frontier and are TE-unconstrained, giving managers constrained by TEs portfolio selection options based on risk preferences and/or investment strategies.