On Determination of Stochastic Dominance Optimal Sets

Applying Fishburn's [4] conditions for convex stochastic dominance, exact linear programming algorithms are proposed and implemented for assigning discrete return distributions into the first- and second-order stochastic dominance optimal sets. For third-order stochastic dominance, a superconvex stochastic dominance approach is defined which allows classification of choice elements into superdominated, mixed, and superoptimal sets. For a choice set of 896 security returns treated previously in the literature, 454, 25, and 13 distributions are in the first-, second-, and third-order convex stochastic dominance optimal sets, respectively. These optimal sets compare with admissible first-, second-, and third-order stochastic dominance sets of 682, 35, and 19 distributions, respectively. The applicability of superconvex stochastic dominance for continuous distributions defined over a bounded interval is then shown. The difficulties in identifying the elements of the superdominated set for distributions defined over the entire real line are demonstrated in the determination of the dominated choices for a set of normally distributed mutual fund returns previously examined by Meyer [9]. Specifically, we find that the dominated set determined by Meyer is too large.     

Spatial and Temporal Dependence in House Price Prediction

This paper incorporates spatial and temporal dependence among housing transactions in predicting future house prices. We employ the spatiotemporal autoregressive model and structure the spatial and temporal weighting matrices as in Pace et al. (1998). We control for the time variation of both the attribute prices and the spatial and temporal dependence parameters through performing the analysis on an annual basis. Spatial heterogeneity is accounted for using experience-based definition of submarkets by real estate professionals. Using a comprehensive housing transaction data set from the Dutch Randstad region, we show that integrating the spatial and temporal dependence within the hedonic modeling improves the prediction power as compared to traditional hedonic model that neglects these effects.     

Bootstrapping a distance test for stochastic dominance analysis

A major impediment to measuring portfolio performance under stochastic dominance has been the lack of test statistics for orders of stochastic dominance above first degree. In this article, the Bootstrap method, introduced by Efron (1979), is used to estimate critical values for distance statistics in order to test the null hypothesis of no dominance, under second- and third-degree stochastic dominance, for several samples of stock returns. These test statistics, suggested by Whitmore (1978), are analogous to the Kolmogorov-Smirnov distance statistics that can be used to test for first-degree stochastic dominance. Stochastic dominance is shown to accurately assess portfolio performance of sample distributions when the population distributions are controlled and Bootstrap statistics are employed in the analysis. In addition, second- and third-degree stochastic dominance analysis of the smallfirm January anomaly indicates that, over the 23-year time period 1964 to 1986, small firms statistically dominate a diversified market index in only one calendar year.     

Empirical Tests for Stochastic Dominance Efficiency

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.     

Predicting bear and bull stock markets with dynamic binary time series models

Despite the voluminous empirical research on the potential predictability of stock returns, much less attention has been paid to the predictability of bear and bull stock markets. In this study, the aim is to predict U.S. bear and bull stock markets with dynamic binary time series models. Based on the analysis of the monthly U.S. data set, bear and bull markets are predictable in and out of sample. In particular, substantial additional predictive power can be obtained by allowing for a dynamic structure in the binary response model. Probability forecasts of the state of the stock market can also be utilized to obtain optimal asset allocation decisions between stocks and bonds. It turns out that the dynamic probit models yield much higher portfolio returns than the buy-and-hold trading strategy in a small-scale market timing experiment.     

Ordering Uncertain Options under Inflation: A Note

Stochastic dominance rules (SD) have been extended to the case where investors are allowed to borrow and lend at the riskless interest rate. Stochastic dominance rules with a riskless asset (SDR) are much more effective than SD rules. However, it seems that this benefit is eliminated by an uncertain inflation, since riskless assets become risky once uncertain inflation is considered. We prove in this paper that SDR criteria are valid also in the face of uncertain (and independent) inflation. Moreover, while the mean-variance (MV) efficient set increases with uncertain inflation, the stochastic dominance efficient sets decrease.     

Reward–risk portfolio selection and stochastic dominance

The portfolio selection problem is traditionally modelled by two different approaches. The first one is based on an axiomatic model of risk-averse preferences, where decision makers are assumed to possess a utility function and the portfolio choice consists in maximizing the expected utility over the set of feasible portfolios. The second approach, first proposed by Markowitz is very intuitive and reduces the portfolio choice to a set of two criteria, reward and risk, with possible tradeoff analysis. Usually the reward–risk model is not consistent with the first approach, even when the decision is independent from the specific form of the risk-averse expected utility function, i.e. when one investment dominates another one by second-order stochastic dominance. In this paper we generalize the reward–risk model for portfolio selection. We define reward measures and risk measures by giving a set of properties these measures should satisfy. One of these properties will be the consistency with second-order stochastic dominance, to obtain a link with the expected utility portfolio selection. We characterize reward and risk measures and we discuss the implication for portfolio selection.     

Simple Monetary Rules under Fiscal Dominance

This paper asks whether interest rate rules that respond aggressively to inflation, following the Taylor principle, are feasible in countries that suffer from fiscal dominance. We find that if interest rates are allowed to also respond to government debt, they can produce unique equilibria. But such equilibria are associated with extremely volatile inflation. The resulting frequent violations of the zero lower bound make such rules infeasible. Even within the set of feasible rules the welfare optimizing response to inflation is highly negative. The welfare gain from responding to government debt is minimal compared to the gain from eliminating fiscal dominance.     

An empirical analysis of marginal conditional stochastic dominance

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.     

Stochastic Dominance Analysis of iShares

Abstract

Country indices as represented by iShares exhibit non-normal return distributions with both skewness and kurtosis. Earlier studies provide procedures for determining the statistical significance of stochastic dominance measures and the Sharpe Ratio. This present study uses these refinements to compare the performance of 18 country market indices. The iShares are indistinguishable when using the Sharpe Ratio as no significant differences are found. In contrast, stochastic dominance procedures identify dominant iShares. Although the results vary over time, stochastic dominance appears to be both more robust and discriminating than the CAPM in the ranking of the iShares.     

Stochastic dominance and portfolio analysis

The principle of stochastic dominance is used to characterize the optimal efficient sets when the distributions of the random prospects belong to a family. Most of the well-known distributions are considered. In each case, the optimal efficient sets are characterized by easily verifiable conditions on the parameters of the distributions. These optimal efficient sets are then compared with the corresponding mean-variance (MV) efficient set. It is often found that the optimal efficient sets are proper subsets of the MV efficient set. Thus, the MV criterion is a proper efficiency criterion, but the MV efficient set can be excessively large compared to the optimal efficient set.     

A relaxation algorithm for building undominated portfolios

Stochastic dominance methods which have been developed in recent years are generally more valid than mean-variance (EV) and higher moment methods for selecting a portfolio from a given finite set of possible portfolios. One of the limitations of these methods is the lack of procedures for building portfolios from a given set of securities and the probability distribution of their returns. Markowitz has developed an algorithm based on the restriction method in linear programming to build undominated portfolios. In this paper a more efficient method based on the relaxation method of linear programming is developed and tested for efficiency. Computational results justify its use as a practical tool for portfolio building.     

The Choice of Methodology for Computing Housing Price Indexes: Comparisons of Temporal Aggregation and Sample Definition

Housing transactions are executed and recorded daily, but are routinely pooled into longer time periods for the measurement and analysis of housing price trends. We utilize an unusually rich data set, covering essentially all arm's length housing sales in Sweden for a dozen years, in an attempt to understand the effect of temporal aggregation upon estimates of housing prices and their volatilities. This rich data set also provides a unique opportunity to compare the results using the conventional weighted repeat sales model (WRS) to those based on a research strategy which incorporates all available information on house sales. The results indicate the clear importance of temporal disaggregation in the estimation of housing prices and volatilities—regardless of the model employed.The appropriately disaggregated model is then used as a benchmark to compare estimates of the course of housing prices produced by the two models during the twelve year period 1981–1993. These results indicate that much of the difference between estimates of price movements can be attributed to the data limitations which are inherent in the repeat sales approach. The results, thus, suggest caution in the interpretation of government-produced price indices or those produced by private firms based on the repeated sales model.     

Cross-correlations and cross-bicorrelations in Sterling exchange rates

This paper proposes two new tests for linear and nonlinear lead/lag relationships between time series based on the concepts of cross-correlations and cross-bicorrelations, respectively. The tests are then applied to a set of Sterling-denominated exchange rates. Our analysis indicates that there existed periods during the post-Bretton Woods era where the temporal relationship between different exchange rates was strong, although these periods have become less frequent over the past 20 years. In particular, our results demonstrate the episodic nature of the nonlinearity, and have implications for the speed of flow of information between financial series. The method generalises recently proposed tests for nonlinearity to the multivariate context.     

Optimal rules for ordering uncertain prospects

In this paper, we obtain the optimal selection rule for ordering uncertain prospects for all individuals with decreasing absolute risk averse utility functions. The optimal selection rule minimizes the admissible set of alternatives by discarding, from among a given set of alternatives, those that are inferior (for each utility function in the restricted class) to a member of the given set. We show that the Third Order Stochastic Dominance (TSD) rule is the optimal rule when comparing uncertain prospects with equal means. We also show that in the general case of unequal means, no known selection rule uses both necessary and sufficient conditions for dominance, and the TSD rule may be used to obtain a reasonable approximation to the smallest admissible set. The TSD rule is complex and we provide an efficient algorithm to obtain the TSD admissible set. For certain restrictive classes of the probability distributions (of returns on uncertain prospects) which cover most commonly used distributions in finance and economics, we obtain the optimal rule and show that it reduces to a simple form. We also study the relationship of the optimal selection rule to others previously advocated in the literature, including the more popular mean-variance rule as well as the semi-variance rule.     

THE COUPON EFFECT ON TERM PREMIUMS

Monthly holding period returns for U.S. Treasury bills and notes of identical maturity indicate a significant coupon effect upon term premiums. Hotelling's T² test of the vectors of mean term premiums indicates that term premiums are not statistically significant for notes but are significant for bills. Mean-variance and stochastic dominance criteria indicate an investment preference for bills over notes on a pretax basis. Because the data set is Treasury bills and notes, which are identical except for coupon level, these results are evidence of a coupon effect on term premiums.     

Stochastic dominance as an approach to uncertainty in cost accounting

Presently textbook treatment of the topic of uncertainty in cost accounting never goes beyond the notions of mean and variance and the maximization of expected utilities. Because the application of these models requires artificial assumptions about either loss functions or utility functions, students are often left wondering how practical probabilistic models are afterall. This paper suggests that stochastic dominance be used to supplement the current textual material on uncertainty. Since these models are easy to implement in a cost accounting context, the class can devote more time to accounting issues in the context of uncertainty rather than get lost in decision theory. Three models of stochastic dominance are discussed here: the first order, the second order, and the third order stochastic dominance. All the necessary assumptions about each model are stated, and each model is accompanied by a numerical example.     

A new country risk index for emerging markets: A stochastic dominance approach

An optimal weighting scheme is proposed to construct economic, political and financial risk indices in emerging markets using an approach that relies on consistent tests for stochastic dominance efficiency. These tests are considered for a given risk index with respect to all possible indices constructed from a set of individual risk factors. The test statistics and the estimators are computed using mixed integer programming methods. We derive an economic, political and financial risk ranking of emerging countries. Finally, an overall risk index is constructed. One main result is that the financial risk is the leading contributor to sovereign risk in emerging markets followed by the economic and political risks.     

Consumer search and dynamic price dispersion: an application to gasoline markets

This article studies the role of imperfect information in explaining price dispersion. We use a new panel data set on the U.S. retail gasoline industry and propose a new test of temporal price dispersion to establish the importance of consumer search. We show that price rankings vary significantly over time; however, they are more stable among stations at the same street intersection. We establish the equilibrium relationships between price dispersion and key variables from consumer search models. Price dispersion increases with the number of firms in the market, decreases with the production cost, and increases with search costs.     

Refining the bootstrap method of stochastic dominance analysis: The case of the January effect

This study investigates the effect of sample size and population distribution on the bootstrap estimated sampling distributions for stochastic dominance (SD) test statistics. Bootstrap critical values for Whitmore's (1978) second- and third-degree stochastic dominance test statistics are found to vary with both data sample size and variance of the population distribution. The results indicate the parametric nature of the statistics and suggest that the bootstrap method should be used to estimate a sampling distribution each time a new data sample is drawn. As an application of the bootstrap method, the January small firm effect is examined. The results conflict with the SD results of others, and indicate that not all investors would prefer to hold just a portfolio of small capitalization firms in January.