Fund rating model based on finite normal mixture distribution

This paper proposes a new method of fund rating based on the cross-sectional distribution of fund performance measured by alpha. This distribution-based fund rating model is more flexible and provides more interesting results than current commercial fund rating method used by Morningstar. Unlike Morningstar's rating, this method does not use preset percentiles to rate funds. It is the distribution of alpha that dictates the number of performance groups in a given fund category and time period. The framework is based on the crucial assumption that the expected fund performance may be different, and the difference of the expected fund performance arises from the segmented market information and/or the differentiated ability of mangers to acquire and analyze information. The multimodal shape and formal normality tests prompt us to model the distribution of alpha by finite normal mixture model. We introduce the parametric bootstrap procedure to determine the number of performance groups in the model. We then employ expectation and maximization (EM) algorithm to estimate the model. Based on the estimated posterior probabilities of the fund, we assign the rating to funds. Our empirical results show that the number of performance groups is not fixed and varies across time and fund categories. We observe a clear tendency of the merging of information sets, which implies that the fund market has become gradually more efficient over time as information was well transmitted and analyzed.