We use various stochastic dominance criteria that account for (local) risk seeking to analyze market portfolio efficiency relative to benchmark portfolios formed on market capitalization, book-to-market equity ratio and price momentum. Our results suggest that reverse S-shaped utility functions with risk aversion for losses and risk seeking for gains can explain stock returns. The results are also consistent with a reverse S-shaped pattern of subjective probability transformation. The low average yield on big caps, growth stocks, and past losers may reflect investors' twin desire for downside protection in bear markets and upside potential in bull markets.

Abstract If a given risky prospect is compared with multiple choice alternatives, then a joint test for optimality is more appropriate than a series of pairwise Stochastic Dominance tests. We develop and implement a bootstrap empirical likelihood ratio test for this hypothesis. The test statistic and implied probabilities can be computed by searching over discrete distributions that obey a system of linear inequalities using quasi-Monte Carlo simulation and convex optimization methods. An extension of the Kroll–Levy simulation experiment shows favorable small-sample properties for data sets of realistic dimensions. In an application to Fama–French stock portfolios, pairwise tests classify a portfolio of small growth stocks as admissible, whereas our test classifies the portfolio as significantly non-optimal for every risk averter.

This study considers the issues of noise-to-signal estimation, finite sample performance and hypothesis testing for a new nonparametric and stochastic efficiency estimation technique. We apply the technique for analyzing the efficiency of European banks from various regions and with various specializations. The technique seems well suited for this application area because banking inputs and outputs generally are measured with error, the banking production technology is not well-defined and large banking data sets such as BankScope allow for a nonparametric approach.

Abstract We derive empirical tests for the stochastic dominance efficiency of a given portfolio with respect to all possible portfolios constructed from a set of assets. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the test results and allow for statistical inference. Our results could provide a stimulus to the further proliferation of stochastic dominance for the problem of portfolio selection and evaluation. Using our tests, the Fama and French market portfolio is significantly inefficient relative to benchmark portfolios formed on market capitalization and book‐to‐market equity ratio.

Abstract We develop empirical tests for stochastic dominance efficiency of a given investment portfolio relative to all possible portfolios formed from a given set of assets. Our tests use multivariate statistics, which result in superior statistical power properties compared to existing stochastic dominance efficiency tests and increase the comparability with existing mean-variance efficiency tests. Using our tests, we demonstrate that the mean-variance inefficiency of the CRSP all-share index relative to beta-sorted portfolios can be explained by tail risk not captured by variance.

Abstract Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

We analyze if the value-weighted stock market portfolio is stochastic dominance (SD) efficient relative to benchmark portfolios formed on size, value, and momentum. In the process, we also develop several methodological improvements to the existing tests for SD efficiency. Interestingly, the market portfolio seems third-order SD (TSD) efficient relative to all benchmark sets. By contrast, the market portfolio is inefficient if we replace the TSD criterion with the traditional mean–variance criterion. Combined these results suggest that the mean–variance inefficiency of the market portfolio is caused by the omission of return moments other than variance. Especially downside risk seems to be important for explaining the high average returns of small/value/winner stocks.

Abstract Existing approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance-based procedures promise a useful nonparametric alternative. However, these procedures have been limited to considering binary choices. In this paper we take a new approach that considers all diversified portfolios and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. Using our new test, we show that the U.S. stock market portfolio is significantly FSD nonoptimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no nonsatiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.

We use various stochastic dominance criteria that account for (local) risk seeking to analyze market portfolio efficiency relative to benchmark portfolios formed on market capitalization, book-to-market equity ratio and price momentum. Our results suggest that reverse S-shaped utility functions with risk aversion for losses and risk seeking for gains can explain stock returns. The results are also consistent with a reverse S-shaped pattern of subjective probability transformation. The low average yield on big caps, growth stocks, and past losers may reflect investors’ twin desire for downside protection in bear markets and upside potential in bull markets.

The effects of higher-order risk aversion on optimal cross-sectional portfolio choice are investigated using portfolio optimization with Stochastic Dominance constraints. Tractable sufficient conditions for higher-degree dominance are introduced that take the form of a system of linear inequalities. Existing studies of active equity industry rotation are extended from lower degrees to higher degrees of dominance. Fourth-degree dominance assumes that investors are ‘prudent’ and ‘temperate’ and therefore like skewness and dislike kurtosis. Using this dominance criterion leads to superior out-of-sample investment performance, by allowing for more concentration in recent winner industries which tend to show persistent positive abnormal returns and a favorable higher-order risk profile due to the industry-level price momentum effect.