Conditional Stochastic Dominance Research Articles

An improved criterion for almost marginal conditional stochastic dominance

An improved criterion for almost marginal conditional stochastic dominance

Revisiting almost marginal conditional stochastic dominance

In this paper, we propose a new notion of the almost marginal conditional stochastic dominance rule by confining the ratio of marginal utility to exclude decision makers with extreme preferences. We show that this new rule can be implemented by linear programming. Finally, we demonstrate the application of this new rule by constructing a set of efficient portfolios characterized by US 10-year Treasuries, the Dow Jones US index, the Dow Jones US Islamic index and the Dow Jones Emerging Markets Islamic index.

Some matheuristic algorithms for multistage stochastic optimization models with endogenous uncertainty and risk management

Two matheuristic decomposition algorithms are introduced. The first one is a Progressive Hedging type so-named Regularized scenario Cluster Progressive Algorithm. The second one is a Frank-Wolfe PH type so-named Regularized scenario Cluster Simplicial Decomposition Progressive Algorithm. An extension of endogenous Type III uncertainty is considered for representing the decision-dependent scenario probability and outlook. Its performance is tested in the time-consistent Expected Conditional Stochastic Dominance risk averse environment. As a result of the modeling, the typical risk neutral multistage mixed 0–1 linear stochastic problem under uncertainty is replaced with an enlarged model that is equivalent to the required mixed 0–1 bilinear model. Based on the special features of the problem, it is unrealistic to seek the optimal solution for large-scale instances. Feasible solutions and lower bounds on the solution value of the original model are provided. In total, 48 strategies are considered, each one consists of a combination of a regularization norm, a calibration type for the PH pseudo-gradient computation, and a set of value intervals of the influential variables on a representative endogenous uncertainty-based piecewise function in the scenarios. Computational results are reported for a large-scale extension of a well-known real-life pilot case for preparedness resource allocation planning aiming to natural disaster relief. The matheuristics outperform the plain use of a state-of-the-art solver.

Testing Stochastic Dominance with Many Conditioning Variables

We propose a test of the hypothesis of conditional stochastic dominance in the presence of many conditioning variables (whose dimension may grow to infinity as the sample size diverges). Our approach builds on a semiparametric location scale model in the sense that the conditional distribution of the outcome given the covariates is characterized by a nonparametric mean function and a nonparametric skedastic function with an independent innovation whose distribution is unknown. We propose to estimate the nonparametric mean and skedastic regression functions by the l₁-penalized nonparametric series estimation with thresholding. Under the sparsity assumption, where the number of truly relevant series terms are relatively small (but their identities are unknown), we develop the estimation error bounds for the regression functions and series coefficients estimates allowing for the time series dependence. We derive the asymptotic distribution of the test statistic, which is not pivotal asymptotically, and introduce the smooth stationary bootstrap to approximate its sample distribution. We investigate the finite sample performance of the bootstrap critical values by a set of Monte Carlo simulations. Finally, our method is illustrated by an application to stochastic dominance among portfolio returns given all the past information.

Downside Risk Sensitivity and Conditional Stochastic Dominance in Euro Area Stock Markets

This article compares portfolio selection based on the downside risk sensitivity with portfolio selection based on Sharpe or Treynor ratios. Downside risk sensitivity (DRS) is given by an asset pricing model in which the downside and upside market returns are separated variables relative to target return. While CAPM, Sharpe ratios and Treynor ratios are based on symmetric risk aversion in both sides of the expected return of the market portfolio, the assumption underlying downside risk sensitivity is that investors utility functions weight losses more heavily s than gains relative to the target return. The methodology used consists of making alternate estimations using a downside-upside risk model (DURM) and CAPM. Portfolios based on DRS, Sharpe ratios and Treynor ratios DRS were created and their composition is updated using the output of rolling estimations of the asset pricing models. The ex post returns of portfolios based on the three alternate methods of portfolio selection are evaluated comparatively by conditional Sharpe ratios which provide information about the conditional stochastic dominance between them. We found that portfolio selection based on downside risk sensitivity gives better protection against losses and better global performance than portfolios based on Sharpe ratios and Treynor ratios.

An application of almost marginal conditional stochastic dominance (AMCSD) on forming efficient portfolios

Investors always seek an efficient portfolio which is a portfolio that has a maximum return on specific risk or minimal risk on specific return. Almost marginal conditional stochastic dominance (AMCSD) criteria can be used to form the efficient portfolio. The aim of this research is to apply the AMCSD criteria to form an efficient portfolio of bank shares listed in the LQ-45. This criteria is used when there are areas that do not meet the criteria of marginal conditional stochastic dominance (MCSD). On the other words, this criteria can be derived from quotient of areas that violate the MCSD criteria with the area that violate and not violate the MCSD criteria. Based on the data bank stocks listed on LQ-45, it can be stated that there are 38 efficient portfolios of 420 portfolios where each portfolio comprises of 4 stocks and 315 efficient portfolios of 1710 portfolios with each of portfolio has 3 stocks.

Inference based on many conditional moment inequalities

We construct confidence sets for models defined by many conditional moment inequalities/equalities. The number of conditional moment restrictions can be up to infinitely many. To deal with the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify this condition in five examples from the recent partial identification literature.The confidence sets are shown to have correct uniform asymptotic size and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo experiments for a conditional stochastic dominance example and a random-coefficient binary-outcome example support the theoretical results.

Nonparametric tests of conditional treatment effects with an application to single-sex schooling on academic achievements

Summary We develop a general class of nonparametric tests for treatment effects conditional on covariates. We consider a wide spectrum of null hypotheses regarding conditional treatment effects, including the following: (a) the null hypothesis of the conditional stochastic dominance between treatment and control groups; (b) the null hypothesis that the conditional average treatment effect is nonpositive for each value of covariates; (c) the null hypothesis of no distributional (or average) treatment effect conditional on covariates. The test statistics are based on L1-type functionals of uniformly consistent nonparametric kernel estimators of conditional expectations that characterize the null hypotheses. We show that our tests using the standard normal critical values have asymptotically correct size. We also show that the proposed nonparametric tests are consistent against general fixed alternatives and have non-negligible powers against some n−1/2 local alternatives to the null hypothesis with inequality constraints and n−1/2h−d/4 local alternatives to the null hypothesis with equality constraints, where h is a bandwidth, n is the sample size and d is the dimension of continuous covariates. We illustrate the usefulness of our tests by applying them to the effect of single-sex schooling on academic achievements using Korean data.

Optimizing Marginal Conditional Stochastic Dominance Portfolios

Marginal Conditional Stochastic Dominance (MCSD) states the probabilistic conditions under which, given a specific portfolio, one risky asset is marginally preferred to another by all risk-averse investors. Furthermore, by increasing the share of dominating assets and reducing the share of dominated assets one can improve the portfolio performance for all these investors. We use this standard MCSD model sequentially to build optimal portfolios that are then compared to the optimal portfolios obtained from Chow’s MCSD statistical test model. These portfolios are furthermore compared to the portfolios obtained from the recently developed Almost Marginal Conditional Stochastic Dominance (AMCSD) model. The AMCSD model restricts the class of risk-averse investors by not including extreme case utility functions and reducing the incidence of unrealistic behavior under uncertainty. For each model, an algorithm is developed to manage the various dynamic portfolios traded on the New York, Frankfurt, London, and Tel Aviv stock exchanges during the years 2000-2012. The results show how the various MCSD optimal portfolios provide valid investment alternatives to stochastic dominance optimization. MCSD and AMCSD investment models dramatically improve the initial portfolios and accumulate higher returns while the strategy derived from Chow’s statistical test performed poorly and did not yield any positive return.

Income versus Consumption Inequality in Korea: Evaluating Stochastic Dominance Rankings by Various Household Attributes

Using four rounds (1999, 2002, 2005 and 2008) of the Korean Labor and Income Panel Study, the present paper examines determinants of household income and consumption levels and inequalities. Unconditional as well as conditional stochastic dominance tests are performed by year, by household heads’ characteristics (age, education, gender, health, marital status and occupation) and by household characteristics (household type, household size and degree of urbanization). Mean least squares regression techniques are used to predict conditional expectations. The residuals containing effects for each characteristic conditional on the remaining characteristics are then used for the stochastic dominance analysis employing extended Kolmogorov–Smirnov tests of first‐order and second‐order dominance in distribution of income and consumption. The results provide a detailed and up‐to‐date picture of inequality and poverty by subgroup in Korea, which helps in targeting particularly vulnerable groups. While inequality in disposable income is found to be substantial, consumption inequality is less substantial. Households headed by the elderly, the uneducated, the divorced, the widowed, females, and those with health problems are found to be the most vulnerable groups.

Conditional Sharpe Ratios

Facing investment choices, investors may care more about potentially excess losses in a downtrend market than excess gains in an upside market. Conditional Sharpe ratios (CSR) are statistical ordinates of conditional stochastic dominance (CSD) that measure lower partial risk-adjusted excess returns of an asset with respect to return distribution on the benchmark. A multiple comparison of serial CSR statistics thus provides an overall view of portfolio performance corresponding to different market scenarios. An example demonstrates that CSR is able to discriminate funds’ downside performance which the conventional Sharpe ratio generally fails to do. A large out-of-sample analysis of US mutual fund shows that CSR has predictability for portfolio future performance.

Conditional Sharpe Ratios

This article demonstrate the connection between Sharpe ratio and stochastic dominance. Conditional Sharpe ratios (CSR) are statistical ordinates of conditional stochastic dominance (CSD) that measure lower partial risk-adjusted excess returns of an asset with respect to return distribution on the benchmark. A multiple comparison of serial CSR statistics thus provides an overall view of portfolio performance corresponding to different market scenarios. An example demonstrates that CSR is able to discriminate funds' downside performance which the conventional Sharpe ratio generally fails to do. A large out-of-sample analysis of US mutual fund shows that CSR has predictability for portfolio future performance.

CONDITIONAL STOCHASTIC DOMINANCE TESTS IN DYNAMIC SETTINGS

This article proposes nonparametric consistent tests of conditional stochastic dominance of arbitrary order in a dynamic setting. The novelty of these tests lies in the nonparametric manner of incorporating the information set. The test allows for general forms of unknown serial and mutual dependence between random variables and has an asymptotic distribution that can be easily approximated by simulation. This method has good finite-sample performance. These tests are applied to determine investment efficiency between U.S. industry portfolios conditional on the dynamics of the market portfolio. The empirical analysis suggests that Telecommunications dominates the other sectoral portfolios under risk aversion.

Does it pay to be ethical? Evidence from the FTSE4Good

The empirical mean–variance evidence comparing the performance of Socially Responsible Investments (SRI) and conventional investments suggests that there is no significant difference between the two. This paper re-examines the problem in the context of Marginal Conditional Stochastic Dominance (MCSD), which can accommodate any return distribution or concave utility function. Our results provide strong evidence that there is a financial price to be paid for socially responsible investing. Indices composed of socially responsible firms are MCSD dominated by trademarked indices composed of conventional firms as well as by indices carefully matched by size and industry with the firms in the SRI indices. Zero cost portfolios created by shorting the SRI index and using the proceeds to invest in the conventional index generate higher average returns, lower variance and higher skewness than either of the two indices standing alone. They also MCSD dominate the SRI and conventional indices standing alone.

Almost marginal conditional stochastic dominance

Marginal Conditional Stochastic Dominance (MCSD) developed by Shalit and Yitzhaki (1994) gives the conditions under which all risk-averse individuals prefer to increase the share of one risky asset over another in a given portfolio. In this paper, we extend this concept to provide conditions under which most (and not all) risk-averse investors behave in this way. Instead of stochastic dominance rules, almost stochastic dominance is used to assess the superiority of one asset over another in a given portfolio. Switching from MCSD to Almost MCSD (AMCSD) helps to reconcile common practices in asset allocation and the decision rules supporting stochastic dominance relations. A financial application is further provided to demonstrate that using AMCSD can indeed improve investment efficiency.

Hmmm: AnRPackage for Hierarchical Multinomial Marginal Models

In this paper we show how complete hierarchical multinomial marginal (HMM) models for categorical variables can be defined, estimated and tested using the R package hmmm. Models involving equality and inequality constraints on marginal parameters are needed to define hypotheses of conditional independence, stochastic dominance or notions of positive dependence, or when the parameters are allowed to depend on covariates. The hmmm package also serves the need of estimating and testing HMM models under equality and inequality constraints on marginal interactions.

State‐owned Enterprises, Exporting and Productivity inChina: A Stochastic Dominance Approach

AbstractA popular explanation forChina's rapid economic growth in recent years has been the dramatic increase in the number of private domestic‐ and foreign‐owned firms and a decline in the state‐owned sector. However, recent evidence suggests thatChina's state‐owned enterprises (SOEs) are in fact stronger than ever. In this paper, we examine over 78,000 manufacturing firms between 2002 and 2006 to investigate the relationship between ownership structure and the degree of firm‐level exposure to export markets and firm‐level productivity. Using a conditional stochastic dominance approach, we reveal that although our results largely adhere to prior expectations, the performance ofSOEs differs markedly between those that export and those that supply the domestic market only. It appears thatChina's internationally focusedSOEs have become formidable global competitors.

Income vs. Consumption Inequality in South Korea: Evaluating Stochastic Dominance Rankings by Various Household Attributes

Using four rounds (1999, 2002, 2005, 2008) of the Korean Labor and Income Panel Study (KLIPS), this article examines determinants of household income and consumption levels and inequalities. Unconditional as well as conditional stochastic dominance (SD) tests are performed by year, by household heads' characteristics (age, education, gender, health, marital status and occupation) and by household characteristics (household type, household size, degree of urbanization). Mean least squares regression techniques are employed to predict conditional expectations. The residuals containing effects for each characteristic conditional on the remaining characteristics are then used for the SD analysis employing extended Kolmogorov-Smirnov tests of first- and second-order dominance in distribution of income and consumption. The results provide a detailed and up-to-date picture of inequality and poverty by subgroup in South Korea which helps targeting particularly vulnerable groups. Overall, while inequality in disposable income is found to be often substantial, strong savings preferences of richer households lead to relatively low consumption inequality. Households headed by elderly, uneducated, divorced or widowed, females and those with health problems are found to be the most vulnerable groups in Korea.

Conditional Stochastic Dominance Testing

This article proposes bootstrap-based stochastic dominance tests for nonparametric conditional distributions and their moments. We exploit the fact that a conditional distribution dominates the other if and only if the difference between the marginal joint distributions is monotonic in the explanatory variable at each value of the dependent variable. The proposed test statistic compares restricted and unrestricted estimators of the difference between the joint distributions, and it can be implemented under minimal smoothness requirements on the underlying nonparametric curves and without resorting to smooth estimation. The finite sample properties of the proposed test are examined by means of a Monte Carlo study. We illustrate the test by studying the impact on postintervention earnings of the National Supported Work Demonstration, a randomized labor training program carried out in the 1970s.

Forecasting the performance of hedge fund styles

This article predicts the relative performance of hedge fund investment styles using time-varying conditional stochastic dominance tests. These tests allow for the construction of dynamic trading strategies based on nonparametric density forecasts of hedge fund returns. During the recent financial turmoil, our tests predict a superior performance for the Global Macro investment style compared with the other strategies of ‘Directional Traders’. The Dedicated Short Bias investment style is stochastically dominated by the other directional styles. These results are confirmed by simple nonparametric tests constructed from realized excess returns. Further, by utilizing a cross-validation method for optimal bandwidth parameter selection, we discover the factors that have predictive power regarding the density of hedge fund returns. We observe that different factors have forecasting power for different regions of the returns distribution and, more importantly, that the Fung and Hsieh factors have power not only for describing the risk premium but also, if appropriately exploited, for density forecasting.