A moment-free nonparametric quantity-of-quality approach to optimal portfolio selection: A role for endogenous shortfall and windfall boundaries?

Abstract

This article proposes a Quantity-of-Quality (QoQ) approach to optimal portfolio selection, which builds on the intuition of the widely applied h-index and e-index from the bibliometric literature. While moment-free and nonparametric, the method embraces quantity-of-high-quality returns and upside potential while simultaneously avoiding quantity-of-low-quality returns and downside risk. A non-standard measure of central tendency is also present, which functions in a way similar to a portfolio mean or median. The method delivers attractive and intuitively appealing results, and appears to be less susceptible to overfitting issues than the stylized Sharpe Ratio portfolio. The method is demonstrated with an established data set, and out-of-sample performance is gauged using training-holdout analysis in two distinct data sets. Because the proposed method uses a fundamentally different portfolio selection objective function than standard moment-based methods, the QoQ approach extracts information about the data-generating process that is perhaps overlooked or deemphasized by traditional moment-based methods, and as such may serve as a capable complement to standard moment-based portfolio selection criteria.