Fund Ratings: The Method Reconsidered

Abstract

This paper compares the performance of a quadratic utility function and discusses how to change its characteristic parameter, ARA, so that rating is consistent with return and risk measurements. In particular, this parameter is modified in such a way that a positive return Fund has always a rating higher than one with a negative yield. This modification confirms the possibility of building a new ranking procedure which is more coherent with the actual behaviour of investors.

The paper moreover demonstrates that the CRRA utility function has not such behaviour, it is possible therefore a ranking in which a Fund with negative return has a rank greater than a Fund with positive return. This seems counterintuitive with respect to the expectations of investors. The CRRA utility function also shows a very slight link with the standard deviation and, consequently, the induced ranking depends mainly on the returns.

The CRRA utility function here considered is that one used by Morningstar.

Keywords: Quadratic Utility Function, Positive and Negative Returns, Absolute Risk Aversion, Morningstar Rating, Truncated Normal Distribution, Incomplete Gamma Function, Italian Pension Fund

JEL Classification: G11, G14, G24