Abstract
The investment nous of active managers is judged on their ability to outperform specified benchmarks while complying with strict constraints on, for example, tracking errors, β and Value at Risk. Tracking error constraints give rise to a tracking error frontier – an ellipse in risk/return space which encloses theoretically possible (but not necessarily efficient) portfolios. The β frontier is a parabola in risk/return space and defines the threshold of portfolios subject to a specified β requirement. An α - TE frontier is similarly shaped: portfolios on this frontier have a specified TE for a maximum TE. Utility and associated risk aversion have also been explored for constrained portfolios. This paper contributes by establishing the impossibility of satisfying more than two constraints simultaneously and explores the behavior of these constraints on the maximum risk-adjusted return portfolio (defined arbitrarily here as the optimal portfolio).
Highlights
Active portfolio managers aim to outperform their benchmarks while adhering to constraints imposed by principals
We investigate the utility around the portfolio which lies on the constant tracking error (TE) frontier and has maximal risk-adjusted return, i.e. the maximum Sharpe ratio portfolio constrained to the constant TE frontier
As the TE constraint is in excess return space and relative to an investor or a somewhat arbitrarily defined benchmark, there is potential for greater inefficiency should fund managers naïvely pursue maximum excess returns as a sole investment objective
Summary
Active portfolio managers aim to outperform their benchmarks while adhering to constraints imposed by principals. Assume a fund manager is mandated to assemble (16) a portfolio P which minimizes the tracking error, generates an expected outperformance (or gain) G and maintains a specified β against the which describes an ellipse – a constant TE fron- benchmark portfolio b. This optimization probtier – in return/variance space
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have