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An Objective Analysis of Alternative Risk-to-Reward Ratios

Gerken, JL; (2015) An Objective Analysis of Alternative Risk-to-Reward Ratios. Doctoral thesis , UCL (University College London). Green open access

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This thesis is devoted to the task of investigating the merits of employing a generalised reward-to-risk ratio for the dual purpose of ranking assets and forming optimal portfolios. In quantitative portfolio optimisation and risk management, the optimal allocation of assets often relies on traditional and well-established measures including the Sharpe ratio. Despite their frequently-documented drawbacks, these quantitative tools continue to be relied on. This is partly due to familiarity and ease of use. Another reason stems from the empirical evidence that alternative and more complex measures often produce results highly correlated with those based on their standard counterparts. This thesis presents an objective analysis of various risk-to-reward measures, for the purpose of portfolio optimisation, which are flexible enough to represent asymmetry in risk and return preferences. In particular, we regard the one-sided variability ratio (Farinelli and Tibiletti (2002)), ϕ(b; p; q), as an intuitive tool to be used in an optimal allocation model on account of its flexibility and ability to account for any distributional model. Focusing on two parameterisations of ϕ(b; p; q) (Omega = ϕ(b; 1; 1) and Sortino ratio = ϕ(b; 1; 2)), we show how these ratios can be analytically reduced to functions of the Sharpe ratio based on Student t returns. This sheds unfavourable light on such alternative and supposedly superior measures and verifies what practitioners commonly observe: that several theoretically advocated ratios replicate the same, or near identical, outcomes as the Sharpe ratio. Analogously, Eling and Schuhmacher (2012) provide further support for this hypothesis, conditional on the location-scale property being satisfied. Relaxing this distributional assumption, however, we cannot claim that ratios including Omega and Sortino do not produce substantially different results to the Sharpe ratio. In an empirical setting, it is questionable to suppose that return distributions satisfy the location-scale property. We consider anisotropic bivariate distributions proposed by Shaw and Lee (2008) to facilitate the simulation of situations where alternative measures produce different results in terms of asset rankings and dissimilar optimal asset weights. In light of this, we argue that it is critical to take an objective approach to constructing a portfolio optimisation model from modelling the underlying data to selecting the relevant risk and performance measures.

Type: Thesis (Doctoral)
Title: An Objective Analysis of Alternative Risk-to-Reward Ratios
Event: University College london
Open access status: An open access version is available from UCL Discovery
Language: English
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1472261
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