Constructing feasible portfolios under tracking error, beta, alpha, utility and asset weight constraints

Abstract

Active portfolio managers are constrained by mandates which prevent them from taking on unnecessary absolute portfolio risk when pursuing returns in excess of the benchmark. By deviating away from index weightings, an element of active risk is introduced called the tracking error (TE) ? defined as the standard deviation of the difference between the returns of an investment and the prescribed benchmark. The returns and associated risk of a TE con-strained portfolio form a tilted ellipse in mean/variance space which has interesting proper-ties that may be exploited for investment purposes. Recently (2018), a new constraint has been proposed which isolates the portfolio with the highest risk-adjusted return, i.e. through maximisation of the Sharpe ratio for a given TE. Traditionally the TE constraint has been used in conjunction with other performance indicators based on the investment policy of the portfolio. This dissertation explores the severity of the restrictive practice of constructing efficient TE-constrained portfolios, while simultaneously imposing other constraints, such as ?, ? and utility. Additionally, the effects of long-only port-folio selection and asset weight allocation constraints are also investigated. The imposition of such limitations on TE-constrained portfolios has not been done before. This dissertation con-tributes by establishing the impossibility of satisfying more than two constraints simultaneously and explores the behaviour of these constraints on the maximum risk-adjusted return portfolio (defined arbitrarily here as the optimal portfolio). In doing so, this dissertation answers the first of two research questions. Active fund managers are responsible for driving capital gains while observing other restrictions (over and above the TE), most commonly, allocated asset weights. These boundaries are defined by upper or lower limits, acceptable ranges or ? for example ? long only limitations, depending on the active managers mandate. The locus of acceptable risk/return coordinates for active funds subject to these restrictions is also derived for the first time, thereby answering the second of two research questions.