Portfolio optimization efficiency test considering data snooping bias

Background: In the portfolio optimization area, most of the research is focused on insample portfolio optimization. One may ask a rational question of what the efficiency of the portfolio optimization strategy is and how to measure it. Objectives: The objective of the paper is to propose the approach to measuring the efficiency of the portfolio strategy based on the hypothesis inference methodology and considering a possible data snooping bias. The proposed approach is demonstrated on the Markowitz minimum variance model and the fuzzy probabilities minimum variance model. Methods/Approach: The proposed approach is based on a statistical test. The null hypothesis is that the analysed portfolio optimization strategy creates a portfolio randomly, while the alternative hypothesis is that an optimized portfolio is created in such a way that the risk of the portfolio is lowered. Results: It is found out that the analysed strategies indeed lower the risk of the portfolio during the market's decline in the global financial crisis and in 94% of the time in the 2009-2019 period. Conclusions: The analysed strategies lower the risk of the portfolio in the out-of-sample period.