Low Volatility Optimal Portfolio Selection: Financial Experiments with Mixture Designs

Abstract

This article assesses the performance of various stock market portfolios using a space-filling mixture design and a model for the logratios in the portfolio allocation. Traditional portfolio analysis relies on historical correlations between various returns and adopts various optimization models. However, these methods rely excessively on the assumptions made and often tend to ignore the statistical variability in their optimization procedures. As a result, they may not perform well when implemented on independent future data. Additionally, the constraints and bounds imposed play a crucial role in determining the feasible region and hence the optimal value therein. By integrating a systematic simplex design approach for exploring component mixtures in our portfolio and applying a logratio transformation, we offer a robust framework for analyzing the portfolios and exploring how various portfolios perform relative to each other. An advantage of our method is that we are able to estimate the standard error for each portfolio, and this allows us to incorporate the consideration of volatilities into our decision making. Using publicly available stock market data, we demonstrate the effectiveness of our approach.