Robust Bayesian Portfolio Optimisation: Higher Moments and the Distorting Effects of Constraints

Wilson, Byron

Robust Bayesian Portfolio Optimisation: Higher Moments and the Distorting Effects of Constraints

Thesis / Dissertation

2012

Abstract

The aim of this thesis is to introduce the Bayesian approach to asset allocation. In particular, the Black-Litterman model is introduced as a powerful Bayesian asset allocation model that enables the incorporation of human decision making (in the form of views) within a portfolio optimisation framework. Several recommendations and adjustments are made within the Black-Litterman framework in order to improve its practical applicability. In particular, a major shortcoming of the Black-Litterman model is the normality of returns assumption. Robust estimates of higher moments and comoments (co-skewness and co-kurtosis) are introduced and implemented within the Black-Litterman framework, thereby enabling the investor to express preferences for skewness and kurtosis as well as avoiding the pitfall of large negative returns that typically occur with a greater frequency than what is suggested by the normal distribution. In addition, a suite of diagnostic tools aimed at analysing the individual contributions of the expressed views as well as constraints is developed. In particular, the diagnostic tools enable the investor to analyse the active weight and tracking error contributions of each view to the portfolio, therefore providing a transparent portfolio optimisation methodology whereby each particular driver of the asset allocations can be identified. More specifically, a novel approach is followed whereby the diagnostic tools are used to examine the severe distorting effects of the imposed constraints. Disturbing results are obtained whereby the imposed constraints effectively “drown out” the views expressed by the investor. For the particular example considered, the constraints account for over a third of the portfolio allocations and effectively change 32 out of the 40 expressed views. In order to mitigate the ill-effects of the imposed constraints, the long-only constraint is marginally relaxed. It was determined that a 123/23 portfolio resulted in a significant improvement in the expression of the investor views as well as a dramatic increase portfolio utility was observed. In summary, incorporating higher order moments and applying the suite of diagnostic tools to the Black-Litterman framework, a transparent portfolio optimisation methodology that effectively utilises the human decision making and investor preferences is obtained.

Keywords

Commerce

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