Dependence calibration and portfolio fit with factor-based subordinators

The paper explores the properties of a class of multivariate Lévy processes used for asset returns. We focus on describing both linear and non-linear dependence in an economic sensible and empirically appropriate way. The processes are subordinated Brownian motions. The subordinator has a common and an idiosyncratic component, to reflect the properties of trade, which it represents. A calibration to a portfolio of 10 US stock indices returns over the period 2009–2013 shows that the hyperbolic specification has a very good fit to marginal distributions, to the overall correlation matrix and to the return distribution of both long-only and long-short random portfolios, which also incorporate non-linear dependence. Their tail behaviour is also well captured by the variance gamma specification. The main message is not only the goodness of fit, but also the flexibility in capturing dependence and the ease of calibration on large sets of returns.     

Modelling soccer matches using bivariate discrete distributions with general dependence structure

In this paper copulas are used to generate bivariate discrete distributions. These distributions are fitted to soccer data from the English Premier League. An interesting aspect of these data is that the primary variable of interest, the discrete pair shots-for and shots-against, exhibits negative dependence; thus, in particular, we apply bivariate Poisson-related distributions that allow such dependence. The paper focuses on Archimedian copulas, for which the dependence structure is fully determined by a one-dimensional projection that is invariant under marginal transformations. Diagnostic plots for copula fit based on this projection are adapted to deal with discrete variables. Covariates relating to within-match contributions such as numbers of passes and tackles are introduced to explain variability in shot outcomes. The results of this analysis would appear to support the notion that playing the 'beautiful game' is an effective strategy—more passes and crosses contribute to more effective play and more shots on the goal.     

Saving under uncertainty: A bivariate non-expected utility approach

We adopt the multivariate non-expected utility approach proposed by Yaari [1986] to provide a characterization of the comparative statics effects of greater risk aversion and of mean-preserving increases in risk on saving and borrowing in the presence of income and interest rate risk.We show that in Yaari's model, it is possible to extend the applicability of the Diamond and Stiglitz [1974] and Kihlstrom and Mirman [1974] (DSKM) single-crossing property to establish a relationship between greater risk aversion and saving (or borrowing) on the basis of the individual's ordinal preferences as long as the two risks are independent. We also demonstrate that the comparative statics effects of a joint mean-preserving increase in random income and interest rate on saving and borrowing can be determined by an extension of the DSKM single-crossing property.     

The tactical and strategic value of hedge fund strategies: a cointegration approach

This paper analyzes long-term comovements between hedge fund strategies and traditional asset classes using multivariate cointegration methodology. Since cointegrated assets are tied together over the long run, a portfolio consisting of these assets will have lower long-term volatility. Thus, if the presence of cointegration lowers uncertainty, risk-averse investors should prefer assets that are cointegrated. Long-term (passive) investors can benefit from the knowledge of cointegrating relationships, while the built-in error correction mechanism allows active asset managers to anticipate short-run price movements. The empirical results indicate there is a long-run relationship between specific hedge fund strategies and traditional financial assets. Thus, the benefits of different hedge fund strategies are much less than suggested by correlation analysis and portfolio optimization. However, certain strategies combined with specific stock market segments offer portfolio managers adequate diversification potential, especially in the framework of tactical asset allocation.

Minimax character of the two-sample χ2-test

Abstract  We consider the problem of testing equality of the mean vectors of two multivariate normal populations when covariates are present and the covariance matrix is known. As an application of the H unt -S tein theorem it is shown that the χ²-^-test of level a maximizes, among all level a tests, the minimum power on each of the contours where the χ²-^-test has constant power. A corollary is that the χ²-^-test is most stringent level a .     

Multivariate statistics in industrial marketing management: A practitioner tool kit

Much published work over the years has pointed to the differences between business-to-consumer (B2C) and business-to-business (B2B) marketing. An undesirable by-product of this sometimes misdirected distinction is that managers working within B2B environments have generally not considered the use of what are seen as B2C techniques, such as multivariate statistical analysis. This article is structured in three parts. First, the argument for the similarities between B2B and B2C marketing is developed; second, three different multivariate statistical techniques are presented and combined to form a practical tool kit for use by B2B managers on strategic, operational, and tactical levels; and third, the results of an application of the techniques in the life science research chemicals industry is reported, demonstrating that the tool kit substantially enhanced managerial understanding of customer decision processes.     

The association between two random elements: A complete characterization and odds ratio models

For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint density is obtained as a limit of an iterative procedure of marginal fittings). Restricting only the odds ratio function but not the marginals leads to semi-parmetric association models for which statistical inference is available for samples drawn conditionally on either X or Y. Log-bilinear association models for random vectors X and Y are introduced which generalize standard (regression) models by removing restrictions on the marginals. In particular, the logistic regression model is recognized as a log-bilinear association model. And the joint distribution of X and Y is shown to be multivariate normal if and only if both marginals are normal and the association is log-bilinear.Acknowledgements The author thanks both referees for their helpful comments which improved the first draft of the paper.     

Multivariate risk aversion and uninsurable risks: Theory and applications

The objective of this paper is to develop conditions for global multivariate comparative risk aversion in the presence of uninsurable, or background, risks, and thus generalize Kihlstrom and Mirman [1974] and Karni [1979,1989]. We analyze von Neumann-Morgenstern (VNM) utility functionsas well as smooth preference functionals which are nonlinear in distribution but locally linear in probabilities. In each case we provide an economic application which illustrates how our theorems can be used. We analyze a risk sharing, a portfolio choice, and a labor supply problem for VNM utility functions, and the optimal allocation of effort to risky technologies in the presence of a random supply (or quality) of a public good for nonlinear preference functionals. We consider thecase where the random variables are mean-independent as well as the case where they are independent. In the labor supply application for VNM utility functions, we show that if the two risks are independent, the comparative statics effect of greater risk aversion on labor supply in the presence of a background non-wage income risk is determined by a monotonic relationship between labor supply and the wage rate under certainty. That is, we extend the applicability of the Diamond-Stiglitz [1974]-Kihlstrom-Mirman [1974]single-crossing property to the case where an independent background risk is present.     

Multivariate multiple regression modelling for technology analysis

Technology analysis is important for technology management areas such as research and development strategy and new product development. So many studies on technology analysis have been used across a diverse array of fields. Most of these were based on patent analysis, which analyses patent documents using text mining and statistics. The studies on conventional patent analyses constructed models consisting of various independent variables (technologies) and one dependent variable. But in reality, we have to consider a model that includes several dependent variables at the same time, because most technologies influence each other. In this paper, we propose a methodology for patent analysis that reflects the various response technologies simultaneously. We perform multivariate multiple regression modelling in order to efficiently conduct our technology analysis. To show how our modelling can be applied to realistic context, we carry out a case study using the patent documents related to three-dimensional printing technology.     

Relationship between oil price and exchange rate by FDA and copula

This article investigates the relationship between daily crude oil prices and exchange rates. Functional data analysis is used to show the clustering pattern of exchange rates and oil prices over the time period through high dimensional visualizations. We select exchange rates for important currencies related to crude oil prices by using the objective Bayesian variable selection method. The selected sample data exhibits non-normal distribution with fat tails and skewness. Under the non-normality of the return series, we use copula functions that do not require to assume the bivariate normality to consider marginal distribution. In particular, our study applies the popular and powerful statistical methods such as Gaussian copula partial correlations and Gaussian copula marginal regression. We find evidence of significant dependence for all considered pairs, except for the Mexican peso-Brent. Our empirical results also show that the rise in the West Texas Intermediate (WTI) oil price returns is associated with a depreciation of the US dollar.