An intersection-union test for supporting the hypothesis that a given investment strategy is optimal among a set of alternatives is presented. It compares the Sharpe ratio of the benchmark with that of each other strategy. The intersection-union test takes serial dependence into account and does not presume that asset returns are multivariate normally distributed. An empirical study based on the G-7 countries demonstrates that it is hard to find significant results due to the lack of data, which confirms a general observation in empirical finance.Keywords: ergodicity; Gordin's condition; heteroscedasticity; intersection-union test; Jobson-Korkie test; performance measurement; Sharpe ratio JEL Classification: C12, G11
MotivationThis work builds upon Frahm et al. (2012), in which the authors argue why joint and multiple testing procedures should be applied in order to judge whether or not some investment strategy is optimal among a set of several alternatives. Frahm et al. (2012) can be understood as a complement to DeMiguel et al. (2009), who doubt that portfolio optimization on the basis of time-series information is worthwhile at all. Indeed, modern portfolio theory suffers from a serious drawback, namely that portfolio weights are very sensitive to estimation risk. It is well known that portfolio optimization fails on estimating expected asset returns. DeMiguel et al. (2009) show that well-established investment strategies are not significantly better than the naive strategy, i.e., the equally weighted portfolio. Of course, this does not mean that naive diversification is optimal, but we usually do not have enough observations in order to prove the opposite. They highlight a general problem of empirical finance, namely that hypothesis testing is difficult due to the lack of data. This is all the more true if there is more than one (single) null hypothesis. The results reported by DeMiguel et al. (2009) are convincing, but their statistical methodology does not take the undesirable effects of joint and multiple testing into account. The same holds true for similar studies (see, e.g., Fletcher 2011;Low et al. 2016). By contrast, the test presented in this work is designed to address those problems.The literature provides a wide range of different investment strategies (see, e.g., Burgess 2000;Conrad and Kaul 1998;DeMiguel et al. 2009; Menkhoff et al. 2012;Sawik 2012;Shen et al. 2007;Szakmary et al. 2010;Vrugt et al. 2004;Zagrodny 2003) and we are typically concerned with the question of whether a given investment strategy is optimal among a set of alternatives. 1 In order to validate our hypothesis, we usually compare the performance of our benchmark, e.g., its certainty 1 A different question is whether some asset universe allows the investor to achieve a higher performance compared to another asset universe (Hanke and Penev 2018).