A Bootstrap Test of Portfolio Performance Tailored to Individual Preferences

This paper presents a novel performance test for investment portfolios by constructing bootstrap confidence intervals around the distance to the efficient frontier of risky assets. Using a general input-output framework, with outputs like return and skewness, and inputs such as variance and kurtosis, our distance measure quantifies efficiency loss relative to a personalized efficient benchmark aligned with each investor’s risk preferences. We estimate the efficient frontier accounting for random asset return variations and apply subsampling to derive confidence intervals for the distances. In our empirical illustration, we evaluate ‘decarbonized’ portfolios that exclude the most polluting firms from the S&P 500, considering four distinct investor types: those aiming to maximize return, minimize variance, maximize skewness, or balance these objectives. Results show that investors prioritizing return, skewness, or balanced criteria can decarbonize without significant efficiency loss. In contrast, those focused on minimizing variance face larger performance declines. Moreover, the portfolio closest to the efficient frontier varies according to investor preferences, highlighting the importance of personalizing performance metrics to individual investment goals.