Abstract
Morey and Morey [1] have developed an approach for gauging portfolio efficiencies in the context of the Markowitz model. Following some recent contributions [2,3], this paper analyzes the axiomatic properties of distance functions extending an earlier approach proposed by Morey and Morey. The paper also focusses on the hyperbolic measure and the McFadden gauge function [4]. Among other things, overall, allocative and portfolio improvements possibilities (in term of return expansion or/and risk contraction) based upon the indirect mean-variance utility function are analyzed. Along this line, duality results are established in each case. This enables us to calculate the degree of risk aversion maximizing the investor indirect mean-variance utility function in either return expansion or risk contraction. An empirical illustration is provided and reveal ranking of preferred risks aversion for some “CAC40” assets.
Highlights
Distance functions, have been introduced by Shephard to measure by Shephard [5] for efficiency measurement either in input or output orientation
The purpose of this paper is to provide a general taxonomy of ratio-based performance indicator for risk management. This contribution extends the analysis proposed by Morey and Morey [1] and provides a new look at some more recent contributions
Among other things we propose a procedure to compute the distance functions introduced by Morey and Morey in the case where short sales are allowed
Summary
Distance functions, have been introduced by Shephard to measure by Shephard [5] for efficiency measurement either in input or output orientation. Markowitz [6,7] has formulated the mean-variance model, a mathematical approach for determining the optimal riskreturn trade-off for portfolio selection. The purpose of this paper is to provide a general taxonomy of ratio-based performance indicator for risk management This contribution extends the analysis proposed by Morey and Morey [1] and provides a new look at some more recent contributions. Transposed in a portfolio optimization context, this function looks for possible simultaneous improvement of return and reduction of risk in the direction of a vector g Though this approach generalizes that of Morey and Morey in the mean-variance space, the choice of a direction remains much arbitrary.
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