Multi-Moment and Multi-Time Nonparametric Frontier-Based Mutual Fund Rating: A Buy-and-Hold Backtesting Strategy with Robust Moment Statistics and a Baseline Comparison

This contribution introduces a comprehensive multi-moment and multi-time nonparametric frontier framework for mutual fund rating and selection. Without limiting ourselves to traditional central moments, we systematically integrate central moments, L-moments, and truncated Lmoments into the multi-moment and multi-time frontier rating models. To validate out-ofsample performance of the proposed models, we design a novel baseline approach within a buy-and-hold backtesting framework ensuring that any outperformance stems from the rating capability rather than pure luck. Applying this framework to a large database of 713 European equity mutual funds yields three key findings. First, the robust L-moments provides a better balance between total returns and maximum drawdown compared to the central moments and truncated L-moments. Second, incorporating higher-order moments improves both total returns and maximum drawdown. Finally, the nonconvex rating models demonstrate the strongest statistical significance in providing superior maximum drawdown, whereas convex rating models tend to favour aggressive, higher-risk mutual funds.