The maximum-return-and-minimum-volatility effect: evidence from choosing risky and riskless assets to form a portfolio

The healthcare sector has the highest mean and a low correlation with the business cycle, while Treasury Bills (T-Bills) have the lowest variance in our study. In this paper, we examine the conjecture of whether investors should choose an asset with the highest expected return and an asset with the smallest variance even when the mean–variance rule says “NO”. We examine the conjecture by comparing the performance of portfolios with and without healthcare and 6-M T-bills in the US market. Our findings support the conjecture that investors prefer to invest in portfolios with both healthcare and 6-M T-bills. In addition, we find an arbitrage opportunity in the markets and our findings reject market efficiency. Based on our findings, academics could incorporate both maximum-return and minimum-volatility assets to construct a maximum-return-and-minimum-volatility aggressive-and-yet-defensive trading approach that stochastically dominates most of other assets/portfolios. Thus, our findings can be called the maximum-return-and-minimum-volatility anomaly or the maximum-return-and-minimum-volatility puzzle, or the maximum-return-and-minimum-volatility paradox.