Testing for Stochastic Dominance Efficiency

SSRN Electronic Journal

The paper extends the model of Kuosmanen (2004) and develops an operational approach to test for stochastic dominance efficiency of a given portfolio at orders higher than two. Applying this approach to equity indices representing seventeen developed and developing markets across the globe, we find that all of these indices are inefficient, nearly always at order three and very often at order two, implying that all of the prudent and most of the risk averse investors would be better off not investing in these market indices. The indices are often dominated by individual industry sub-indices, with consumer goods, services, and utilities performing especially well. A simple trading rule based on past stochastic dominance information improves the average out-of-sample return of a global portfolio by 2% per year while simultaneously reducing the return standard deviation by 3% per year. It substantially limits global portfolio losses during the financial crises of 2007-2008. Portfolios of low-beta and low-volatility stocks consistently stochastically dominate the market indices and seem to be more desirable alternatives for prudent and risk-averse investors.

The market portfolio efficiency remains controversial. This paper develops a new test of portfolio mean-variance efficiency relying on the realistic assumption that all assets are risky. The test is based on the vertical distance of a portfolio from the efficient frontier. Monte Carlo simulations show that our test outperforms the previous mean-variance efficiency tests for large samples since it produces smaller size distortions for comparable power. Our empirical application to the U.S. equity market highlights that the market portfolio is not mean-variance efficient, and so invalidates the zero-beta CAPM.

Journal of Banking & Finance, 2012

Stochastic dominance is a more general approach to expected utility maximization than the widely accepted mean-variance analysis. However, when applied to portfolios of assets, stochastic dominance rules become too complicated for meaningful empirical analysis, and, thus, its practical relevance has been difficult to establish. This paper develops a framework based on the concept of Marginal Conditional Stochastic Dominance (MCSD), introduced by Shalit and Yitzhaki (1994), to test for the first time the relationship between second order stochastic dominance (SSD) and stock returns. We find evidence that MCSD is a significant determinant of stock returns. Our results are robust with respect to the most popular pricing models.

2007

Extensions are presented to the results of Davidson and Duclos (2007), whereby the null hypothesis of restricted stochastic non dominance can be tested by both asymptotic and bootstrap tests, the latter having considerably better properties as regards both size and power. In this paper, the methodology is extended to tests of higherorder stochastic dominance. It is seen that, unlike the first-order case, a numerical nonlinear optimisation problem has to be solved in order to construct the bootstrap DGP. Conditions are provided for a solution to exist for this problem, and efficient numerical algorithms are laid out. The empirically important case in which the samples to be compared are correlated is also treated, both for first-order and for higher-order dominance. For all of these extensions, the bootstrap algorithm is presented. Simulation experiments show that the bootstrap tests perform considerably better than asymptotic tests, and yield reliable inference in moderately sized samples.

Computational Management Science, 2017

In the last decade, a few models of portfolio construction have been proposed which apply second order stochastic dominance (SSD) as a choice criterion. SSD approach requires the use of a reference distribution which acts as a benchmark. The return distribution of the computed portfolio dominates the benchmark by the SSD criterion. The benchmark distribution naturally plays an important role since different benchmarks lead to very different portfolio solutions. In this paper we describe a novel concept of reshaping the benchmark distribution with a view to obtaining portfolio solutions which have enhanced return distributions. The return distribution of the constructed portfolio is considered enhanced if the left tail is improved, the downside risk is reduced and the standard deviation remains within a specified range. We extend this approach from long only to long-short strategies which are used by many hedge fund and quant fund practitioners. We present computational results which illustrate (1) how this approach leads to superior portfolio performance (2) how significantly better performance is achieved for portfolios that include shorting of assets.

MPRA Paper No. 59418, 2013

In this paper we analyze the consistency of financial investment ordering based on mean-variance and stochastic dominance (SD) approaches in the context of an emerging financial market. We take 47 Chilean mutual funds and compute Sharpe index and the algorithms to verify first (FSD), second (SSD), and third degree (TSD) stochastic dominance relationships.We find evidence that both approaches generate similar sets of efficient investments. However, there are important dissimilarities between the rankings elaborated according to mean-variance and TSD criteria. TSD criterion presents itself as a complete method for evaluating the risk profile of an investment, as it takes into consideration risk-relevant characteristics of the return probability distribution that are not visible in mean-variance indicators.

recently revived the debate related to the market portfolio's efficiency, suggesting that it may be mean-variance efficient after all. This paper develops an alternative test of portfolio mean-variance efficiency based on the realistic assumption that all assets are risky. The test is based on the vertical distance of a portfolio from the efficient frontier. Monte Carlo simulations show that our test outperforms the previous mean-variance efficiency tests for large samples since it produces smaller size distortions for comparable power. Our empirical application to the U.S. equity market highlights that the market portfolio is not mean-variance efficient, and so invalidates the zerobeta CAPM.

Mathematical Finance, 1996

Stochastic dominance (SD) is a very useful tool in various areas of economics and finance. The purpose of this piper is to provide the results of SD relations developed in other areas such as applied probability which, we believe, are useful for many portfolio selection problems. In particular. the bivariate characterization of SD relations given by Shanthikumar and Yao (199 I) is a powerful tool for the demand and the shift effect problems in optitnal portliilios. The method enables one to extend many result< that hold for the case where the underlying assets are statistically independent to the dependent case directly.

Journal of Econometrics, 2018

We develop and apply a portfolio optimization method based on the Stochastic Dominance (SD) decision criterion and the Empirical Likelihood (EL) estimation method. SD and EL share a distribution-free assumption framework which allows for dynamic and non-Gaussian return distributions. The SD/EL method can be implemented using a two-stage procedure which first elicits implied probabilities using Convex Optimization and subsequently constructs the optimal portfolio using Linear Programming. We apply the method to a range of equity industry momentum strategies. Our moment conditions are based on stylized facts about common risk factors in the stock market. SD/EL yields important exante performance improvements relative to heuristic diversification, Mean-Variance optimization and a simple 'plug-in' approach. Relative to the CRSP all-share index, SD/EL improves average out-of-sample return by more than eight percentage points per annum, with less downside risk, semi-annual rebalancing and no short sales.

2001

We provide here a necessary and sufficient operational condition for determining whether a given portfolio is efficient in the sense of seconddegree stochastic Dominance (SSD). This condition also enables one to find a direction for improving on an inefficient portfolio, in the sense that all risk averse investors would weakly prefer that change in the portfolio composition. This condition can be applied among others to resolve questions that have long been posed in the literature, concerning on whether the portfolios that are promoted by portfolio managers are in fact efficient in the above sense.