Statistical Inference on Stochastic Dominance Efficiency. Do Omitted Risk Factors Explain the Size and Book-to-Market Effects?

This paper discusses statistical inference on the second-orderstochastic dominance (SSD) efficiency of a given portfolio relative toall portfolios formed from a set of assets. We derive the asymptoticsampling distribution of the Post test statistic for SSD efficiency.Unfortunately, a test procedure based on this distribution involveslow power in small samples. Bootstrapping is a more powerful approachto sampling error. We use the bootstrap to test if the Fama and Frenchvalue-weighted market portfolio is SSD efficient relative to benchmarkportfolios formed on market capitalization and book-tomarket equityratio. During the late 1970s and during the 1980s, the marketportfolio is significantly SSD inefficient, even if we use samples ofonly 60 monthly observations. This suggests that the size andbook-to-market effects cannot be explained by omitted risk factorslike higher-order central moments or lower partial moments.market efficiency;asset pricing;stochastic dominance;size and book-to-market effects;statistical inference

Testing for Third-Order Stochastic Dominance with Diversification Possibilities

We derive an empirical test for third-order stochastic dominance that allows fordiversification between choice alternatives. The test can be computed usingstraightforward linear programming. Bootstrapping techniques and asymptoticdistribution theory can approximate the sampling properties of the test results and allowfor statistical inference. Our approach is illustrated using real-life US stock market data.efficiency;stochastic dominance;portfolio selection;linear programming;portfolio evaluation

Testing for Stochastic Dominance with Diversification Possibilities

We derive empirical tests for stochastic dominance that allow for diversification betweenchoice alternatives. The tests can be computed using straightforward linearprogramming. Bootstrapping techniques and asymptotic distribution theory canapproximate the sampling properties of the test results and allow for statistical inference.Our results could provide a stimulus to the further proliferation of stochastic dominancefor the problem of portfolio selection and evaluation (as well as other choice problemsunder uncertainty that involve diversification possibilities). An empirical application forUS stock market data illustrates our approach.stochastic dominance;portfolio selection;linear programming;portfolio diversification;portfolio evaluation

Spanning and Intersection: a stochastic dominance approach

We propose linear programming tests for spanning and intersection based on stochasticdominance rather than mean-variance analysis. An empirical application investigates thediversification benefits to US investors from emerging equity markets.stochastic dominance;linear programming;emerging markets;intersection;spanning

A Stochastic Dominance Approach to Spanning

We develop a Stochastic Dominance methodology to analyze if new assets expand theinvestment possibilities for rational nonsatiable and risk-averse investors. This methodologyavoids the simplifying assumptions underlying the traditional mean-variance approach tospanning. The methodology is applied to analyze the stock market behavior of small firms in themonth of January. Our findings suggest that the previously observed January effect isremarkably robust with respect to simplifying assumptions regarding the return distribution.stochastic dominance;portfolio selection;linear programming;portfolio evaluation;spanning

LP Tests for MV Efficiency

We derive empirical tests for the mean-variance efficiency of a given portfolio. The testscan be computed using straightforward linear programming, and they give substantialflexibility in modeling the investment possibilities. Using this test, we can reject thehypothesis that the S&P 500 index is mean-variance efficient relative to the 25 Fama andFrench (1993) equity portfolios.linear programming;mean-variance analysis;portfolio selection and evaluation;quadratic programming

Asset prices and omitted moments; A stochastic dominance analysis of market efficiency

We analyze if the value-weighted stock market portfolio is second-order stochastic dominance (SSD) efficient relative to benchmark portfolios formed on market capitalization, book-to-market equity ratio and industry classification. During the period from the mid-1970s to the late 1980s, the market portfolio is significantly mean-variance inefficient. During this period, the market portfolio generally also is significantly SSD inefficient. This suggests that mean-variance inefficiency cannot be explained by omitted return moments like higher-order central moments or lower partial moments.market efficiency;asset pricing;stochastic dominance;size and book-to-market effects;statistical inference

Non-Parametric Tests for Firm Efficiency in Case of Errors-in-Variables

This paper develops a novel statistic for firm efficiency called efficiency depth thatallows for statistical inference in case of errors-in-variables. We derive statistical teststhat require minimal statistical assumptions; neither the sample distribution nor thenoise level is required. An empirical illustration for European banks illustrates that -despite the minimal assumptions- the tests can have substantial discriminating powerin practical applications.errors-in-variables;firm efficiency;nonparametric analysis

Does Risk Seeking Drive Asset Prices? A stochastic dominance analysis of aggregate investor preferences

We investigate whether risk seeking or non-concave utility functions can help to explainthe cross-sectional pattern of stock returns. For this purpose, we analyze the stochasticdominance efficiency classification of the value-weighted market portfolio relative tobenchmark portfolios based on market capitalization, book-to-market equity ratio andmomentum. We use various existing and novel stochastic dominance criteria that accountfor the possibility that investors exhibit local risk seeking behavior. Our results suggestthat Markowitz type utility functions, with risk aversion for losses and risk seeking forgains, can capture the cross-sectional pattern of stock returns. The low average yield onbig caps, growth stocks and past losers may reflect investors' twin desire for downsideprotection in bear markets and upside potential in bull markets.asset pricing;stochastic dominance;prospect theory;risk seeking;specification error

Nonparametric Efficiency Estimation in Stochastic Environments (II)

We consider the issues of noise-to-signal estimation, finite sample performance andhypothesis testing for the nonparametric efficiency estimation technique proposed inCherchye, L., T. Kuosmanen and G. T. Post (2001) 'Nonparametric efficiencyestimation in stochastic environments', forthcoming in Operations Research. Inaddition, we apply the technique for analyzing European banks.hypothesis testing;European banks;noise-to-signal estimation;nonparametric efficiency estimation;finite sample performance