Title: Risk seeking and measures of portfolio performance

Authors: C.J. Adcock

Addresses: Management School, The University of Sheffield, 9, Mappin Street, Sheffield, S1 4DT, UK

Abstract: This paper considers the case when asset returns follow a multivariate elliptically symmetric distribution. A multivariate extension of the Sharpe ratio is the measure of portfolio performance for all expected utility maximisers. Performance measures in common use arise formally in the multi-asset case using utility functions based on lower and upper partial moments. This utility function allows risk-seeking for some values of portfolio return and permit choice of the preferred degree of loss aversion. Performance measures which have expected excess return in their numerator are equivalent to the multivariate Sharpe ratio. The Farinelli-Tibiletti ratio also arises in the multi-asset setting. General portfolio selection is considered. The paper presents two results which give conditions for a utility function based on partial moments to lead to a portfolio on the efficient frontier. The paper contains an example based on the weekly returns of a number of FTSE indices.

Keywords: elliptically symmetric distributions; loss aversion; portfolio performance measures; risk seeking; Sharpe ratio; portfolio selection.

DOI: 10.1504/IJPAM.2012.049200

International Journal of Portfolio Analysis and Management, 2012 Vol.1 No.2, pp.161 - 178

Received: 12 Mar 2012
Accepted: 13 Mar 2012
Published online: 23 Aug 2014 *

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