Multiple tests for the performance of different investment strategies

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractIn the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider shortselling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple-testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of the non-trivial strategies, whether the trivial strategy is better than every non-trivial strategy, and which of the non-trivial strategies are significantly outperformed by naive diversification. In our empirical study we use monthly US stock returns from the CRSP database, covering the last 4 decades.Keywords: Asset allocation, Certainty equivalent, Investment strategy, Markowitz, Multiple tests, Naive diversification, Out-of-sample performance, Portfolio optimization, Sharpe ratio.JEL classification: C12, G11. AbstractIn the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider short-selling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple-testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of th...

An Intersection–Union Test for the Sharpe Ratio

“…This 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.…”

“…For more details on that topic, see Frahm et al (2012) as well as Romano and Wolf (2005 At first glance, this testing procedure might seem to suffer from a lack of power because it does not take the dependence structure of the single test statistics into account. Nonetheless, it is a likelihood-ratio test that is commonly referred to as an intersection-union test (Berger 1997).…”

“…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.…”

“…4 and 5). Instead, I try to fill a gap between Frahm et al (2012) as well as Ledoit and Wolf (2008): (i) I derive closed-form expressions for the standard errors of the test statistics, instead of providing numerical results that have been obtained by bootstrapping, and (ii) I do this for the case d ≥ 2 but not (only) for d = 2.…”

“…This is done with respect to the Sharpe ratio. Joint and multiple tests for the Sharpe ratio are applied also in Frahm et al (2012) by using a stationary block-bootstrap procedure. By contrast, I provide here analytical results.…”