In search of the optimal number of fund subgroups

The idea of determining the number of fund subgroups is of central importance in the currently popular academic field of Risk Parity Portfolio Theory, and especially for practitioners’ direct use of Funds-of-Funds (FoF) managers. Can the Gaussian Mixture Distributions plug- in approach via traditional procedures select the right number of fund subgroups? Probably not. According to our in-sample/out-of-sample likelihood score analysis, the actual locations of subgroups in real data (of both U.S. mutual funds and hedge funds) are too close to each other. The information loss incurred by parameter uncertainty outweigh those incurred by mis-specification, and can only be slightly alleviated using the nonparametric density estimators. An arbitrary choice of two subgroups only causes affordable information loss relative to more fund subgroups. These findings challenge the reliability of the Gaussian Mixture Distributions plug-in approach via traditional procedures (e.g., BIC, Likelihood Ratio and Chi-square statistics) in selecting the correct number of subgroups.