Should Investors Choose Both the Highest-Return and Small-Variance Assets When the Mean-Variance Rule Says No? A Study of Health Care and T-Bill in the Investment

Abstract

The high-speed growth of the health care sector has given this sector an increasingly important role in the stock market. This sector however has the highest mean in our study and a low correlation with the business cycle. On the other hand, T-Bill is also an important asset in investment because of its positive return and low variance. In this paper, we examine the conjecture of whether investors should choose both the highest-return and small-variance assets even when the mean-variance rule says “NO”. This conjecture is explored by making a comparison of the performance of portfolios with and without health care and 6-M T-bill in the U.S. market using portfolio optimization, mean-variance and stochastic dominance approaches. Our findings imply that all risk averters prefer to invest in portfolios with both health care and 6-M T-bill, regardless of whether they buy long or sell short in the market. Our findings do not support the existence of any arbitrage opportunity in the markets we studied but do support market efficiency. We also show that risk averters as well as investors with components of both risk aversion and risk seeking will choose both the highest-return and small-variance assets even when the mean-variance rule says NO.