Spanning Tests for Markowitz Stochastic Dominance

We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochastic dominance spanning, and develop an analytical representation of the spanning property. We construct a non-parametric test for spanning based on subsampling, and derive its asymptotic exactness and consistency. The spanning methodology determines whether introducing new securities or relaxing investment constraints improves the investment opportunity set of investors driven by Markowitz stochastic dominance. In an application to standard data sets of historical stock market returns, we reject market portfolio Markowitz efficiency as well as two-fund separation. Hence, we find evidence that equity management through base assets can outperform the market, for investors with Markowitz type preferences

Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach

We propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures, single-step methods such as continuously updated GMM yield numerically identical overidentifyng restrictions tests, so there is arguably a single spanning test. To prove these results, we extend optimal GMM inference to deal with singularities in the long run second moment matrix of the influence functions. Finally, we test for spanning using size and book-to-market sorted US stock portfolios.Asset Pricing, Continuously Updated GMM, Generalised Empirical Likelihood, Generalised Inverse, Representing Portfolios, Singular Covariance Matrix

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

Spanning with Zero-Price Investment Assets

Regression-based testing techniques has long been used to quantify whether the efficient frontier of a set of assets spans the frontier of a larger collection of investments. This work derives regression-based spanning tests for the case in which the investment possibilities set contains, or is constituted by, zero-investment assets. An empirical example illustrates that ignoring the zero-cost qualification of these assets might lead to wrong spanning propositions.mean-variance spanning; diversification benefits; portfolio choice; futures markets

Multimodel Response Assessment for Monthly Rainfall Distribution in Some Selected Indian Cities Using Best Fit Probability as a Tool

We carry out a study of the statistical distribution of rainfall precipitation data for 20 cites in India. We have determined the best-fit probability distribution for these cities from the monthly precipitation data spanning 100 years of observations from 1901 to 2002. To fit the observed data, we considered 10 different distributions. The efficacy of the fits for these distributions was evaluated using four empirical non-parametric goodness-of-fit tests namely Kolmogorov-Smirnov, Anderson-Darling, Chi-Square, Akaike information criterion, and Bayesian Information criterion. Finally, the best-fit distribution using each of these tests were reported, by combining the results from the model comparison tests. We then find that for most of the cities, Generalized Extreme-Value Distribution or Inverse Gaussian Distribution most adequately fits the observed data.Comment: 14 pages, 5 figure

New Statistical Results on the Angular Distribution of Gamma-Ray Bursts

We presented the results of several statistical tests of the randomness in the angular sky-distribution of gamma-ray bursts in BATSE Catalog. Thirteen different tests were presented based on Voronoi tesselation, Minimal spanning tree and Multifractal spectrum for five classes (short1, short2, intermediate, long1, long2) of gamma-ray bursts, separately. The long1 and long2 classes are distributed randomly. The intermediate subclass, in accordance with the earlier results of the authors, is distributed non-randomly. Concerning the short subclass earlier statistical tests also suggested some departure from the random distribution, but not on a high enough confidence level. The new tests presented in this article suggest also non-randomness here.Comment: in GAMMA-RAY BURSTS 2007: Proceedings of the Santa Fe Conferenc

Investment opportunities in Central and Eastern European equity markets: an econometric examination of the risk-return relationships for western investors

This study focuses on the diversification benefits of the most developed equity markets of Central and Eastern Europe (CEE). To evaluate these benefits of diversification we use so-called spanning tests based on a stochastic discount factor approach and estimated by General Methods of Moments (GMM). Spanning tests investigate whether the returns of test assets (in our case the returns of CEE equity markets) can be mimicked by the returns of some benchmark assets. If this is possible adding the test assets to the set of the benchmark assets does not improve the mean-variance efficient frontier. In recent studies as for example DeSantis (1994), Harvey (1995) or Bekaert/Urias (1996) spanning tests have been successfully applied to emerging equity markets but these studies do not cover the emerging equity markets of Central and Eastern Europe. In addition our study addresses the diversification benefits not only for U.S. investors, as is the usual case in these empirical studies, but extends the analysis on British and German investors, too. A third feature that distinguishes our investigation from most other studies on this topic is the analysis of the effects of currency hedging on diversification benefits. At a quick glance the CEE equity markets seem to offer significant and high diversification benefits. But this picture becomes cloudy after a thorough analysis. Only the equity markets of the Czech Republic, Slovakia and Slovenia contribute significantly to the diversification benefits. But a realisation of these benefits would imply to have not only long but also short positions in CEE equities. Taken into account transaction costs and limited access to futures and options markets it seems to be very doubtful that the theoretical diversification benefits can actually be realised. This result is in correspondence with recent studies on other emerging markets such as DeRoon/Nijman/Werker (2000). The results of the study also show that the home currency of the investor is of some importance for the results of the spanning tests. The outcomes for British, German and U.S. investors are similar but not identical. Therefore it seems to be useful to analyse benefits of diversification not only from the point of view of U.S. investors but to take explicitly into account the currency of the investor. Another interesting result is that currency hedging clearly improves the possible performance of an investment in CEE equity markets. What is now the consequence for investors that consider an investment in CEE equity markets? Our study comes to the result that a buy-and-hold investor could hardly benefit from such an investment. Only investors that have superior timing capabilities could profit from the remarkably strong swings in the levels of CEE equity indices in the past. --Spanning Test,Diversification,Emerging Markets,Central and Eastern Europe

Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

Heuristics based on greedy randomized adaptive search and variable neighbourhood search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-complete. A Greedy Randomized Adaptive Search Procedure (GRASP) and different versions of Variable Neighbourhood Search (VNS) are proposed. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

Asset Allocation in the Euro-Zone: Industry or Country Based?

We investigate the relative importance of country and industry factors as determinants of international equity returns in the Euro-zone over the period 1990 to 2003.We conduct our analysis from a portfolio performance perspective, using mean-variance spanning and efficiency tests as well as style analysis, and show how to adjust the tests for time varying market wide volatility.Although unconditional analysis over the full sample suggests that country-based or industry-based EMU-wide portfolios provide similar risk-return trade-offs, a rolling window analysis indicates a striking change in the structure of equity returns in the Euro-zone over the last decade.From 1992 to 1998 country-based strategies outperform industry-based strategies: country based strategies offer higher Sharpe ratios and higher diversification potential as indicated by both spanning tests and style analysis.In the preconvergence period, equity returns in the EMU-zone clearly had a country structure.In contrast, after the introduction of the Euro the country outperformance has disappeared, both in terms of mean-variance efficiency and in terms of mimicking abilities.Industry factors and country factors are now equally important.Our findings suggest that following the adoption of the single currency, Euro-zone sector-based strategies, while not dominating country-based strategies, offer similar risk return trade-offs and diversification benefits.International financial markets;Mean-variance efficiency;Style analysis;EMU