Measuring financial interdependence in asset markets with an application to eurozone equities

https://doi.org/10.1016/j.jbankfin.2020.105985Get rights and content

Abstract

A general measure of asset market interdependence based on higher order comoments is developed and applied to studying weekly U.S. and eurozone equity returns from 1990 to 2017. A new test of independence is also developed. The empirical results show that interdependence peaks during the global financial crisis with the covariance and covolatility comoments being the dominant factors. Conditioning the interdependence measure on volatility does not change the overall qualitative results. Implications of the results for constructing diversified portfolios reveal economic benefits from portfolios based on higher order comoments than the usual assumption of bivariate normality, especially during the GFC. The empirical results also provide evidence that European Union membership led to higher interdependence than did the adoption of the common currency.

Introduction

Second-order comoments based on covariances and correlations are common measures of the degree of interdependence between asset markets in finance. Important applications include the capital asset pricing model (Sharpe, 1964), the intertemporal capital pricing model (Merton, 1973), arbitrage pricing theory (Ross, 1976), portfolio diversification and minimum variance portfolios (Markovitz, 1959), value at risk with multiple assets (Jorion, 1997), marginal expected shortfall (Brownless and Engle, 2017) and exchange options (Margrabe, 1978). A key assumption underlying many of these models is that the distribution of asset returns is multivariate normal with interdependence entirely encapsulated by the second-order comoment parameters.

Despite the widespread use of second-order comoments in finance, there is strong empirical evidence that higher-order comoments also affect asset returns (Christoffersen et al., 2012). Higher-order comoments capture linkages arising from co-risk tradeoffs between expected returns and volatility in different asset markets (coskewness), expected returns and skewness (cokurtosis), and cross-market volatilities (covolatility). The presence of higher-order comoments in asset returns has led to several extensions of existing models in finance: a third-order moment CAPM (Harvey and Siddique, 2000), portfolio selection with higher-order moments (Harvey et al., 2010), and pricing exchange options subject to coskewness (Fry-McKibbin et al., 2014).

The presence of higher-order comoments means there exist several potential channels linking asset markets, which contribute to the overall strength of the comovements between asset markets. No existing measure suffices to capture all of these linkages. The contribution of this paper is to develop an aggregate measure of interdependence by combining these individual measures. The approach involves using entropy theory to weight asset returns by their joint probability distribution. A flexible class of multivariate distributions based on the generalized exponential family (Lye, Martin, 1993, Fry, Martin, Tang, 2010) is adopted to model the joint probability distribution.1 This choice of distribution has several advantages. First, a number of important distributions are nested within this family, including the multivariate normal distribution. Second, the proposed class of distribution represents a natural theoretical choice as it yields maximum entropy given a set of higher-order comoments. Third, a general expression of asset market interdependence is derived which has a direct and explicit correspondence with the comoment measures commonly adopted in the literature, including the covariance as well as higher-order comoments of coskewness, cokurtosis and covolatility. Fourth, the proposed measure can be decomposed into its components, enabling the relative contributions of each channel linking asset markets to be quantified.

A further contribution of the paper is the development of a new omnibus test of independence, which nests existing higher-order comoment tests commonly used in empirical research. The test statistic is shown to have power in detecting changes in interdependence using a range of Monte Carlo experiments. An important implication from expanding the definition of interdependence to include higher-order comoments is that traditional measures solely based on covariances and correlations could be misleading. Under the assumption of bivariate normality, this relationship is parabolic with increases in (absolute) correlation representing monotonic increases in interdependence of the same magnitude. The inclusion of higher-order comoments can change this parabolic relationship to being asymmetric, or even bimodal.

The framework is applied to studying the relationship between the U.S. and eurozone equity markets using weekly equity returns from 1990 to 2017. The results provide evidence that European equities operate independently of the U.S. equity market before the adoption of the euro in 1999. However, the strength of the association becomes progressively stronger, peaking during the global financial crisis in 2008. The main contributing factors are the increased association between equity returns (covariance) and volatilities (covolatility), with partial offsetting effects from cokurtosis, whereas coskewness is found to have no significant effects.2 The economic benefits of higher-order comoments are investigated by simulating portfolios containing U.S. and European equities and comparing the value at risk of diversified and non-diversified portfolios. The empirical results provide strong evidence that diversified portfolios based on higher-order comoments generate benefits in excess of portfolios based on bivariate normality, especially during the GFC. The empirical results also provide some support for the view in the case of Austria and Finland, that European Union membership led to higher interdependence than did the adoption of the common currency (Bekaert et al., 2013).

The rest of the paper proceeds as follows. The framework for deriving the new measure of interdependence is presented in Section 2. An omnibus test of independence is developed in Section 3, including an investigation of the sampling properties of the test using simulated data generated from well-known models in finance. Section 4 provides the empirical results of the interdependence measure and its dynamics through time, with implications of these results discussed in Section 5. Concluding comments and suggestions for future research are given in Section 6, with theoretical derivations and additional empirical results presented in the Appendices.

Section snippets

Methodology

This Section provides the details of constructing a general measure of financial interdependence using entropy theory combining second- and higher-order comoments of asset returns. A feature of the approach is that it is possible to decompose the level of interdependence into its components, thereby enabling an assessment of the relative size and direction of the contributions of each comoment to the joint movements of asset markets.

Testing for independence

The measure in (9) is now used to construct an omnibus test of independence. To simplify the presentation of the test statistic, letz1t=r1tμ1σ1,z2t=r2tμ2σ2,represent the standardized returns where μiand σi2are respectively, the sample mean and sample variance of the ith asset return. The interdependence measure in (12)when expressed in terms of the standardized random variables becomesΨt=1+ht(Θ)η(Θ)1+log(2π),where the unknown parameters are now Θ={ρ,θ1,θ2,θ3,θ4,θ5},and whereht(Θ)=12(z1t2+z2t

Application to U.S. and eurozone equities

The framework developed in Section 2 is now applied to investigate the degree of interdependence between the U.S. and eurozone equity markets, and how these relationships changed over time as a result of the adoption of the euro and the effects of the GFC and the European debt crisis. The interrelationships between equity markets are also studied at both country and aggregate levels.

Economic benefits of portfolio diversification

The empirical results provide strong evidence of changes over time in the strength of interdependence between U.S. and European equity markets. The following portfolio diversification simulation experiment is performed to investigate the economic benefits of these changes. The approach involves simulating “weekly” returns from the bivariate generalized normal distribution where the parameters are evaluated at the maximum likelihood estimates based on (14). For each simulation, the return on the

Conclusions and extensions

There exists a range of measures to identify the degree of interdependence linking asset markets, ranging from traditional second-order comoments to higher-order comoments consisting of coskewness, cokurtosis, and covolatility. In general, all measures are important in capturing different aspects of a joint probability distribution of asset markets with no single measure providing a complete description of the overall strength of the relationships connecting asset markets. This paper has

CRediT authorship contribution statement

Renée Fry-McKibbin: Conceptualization, Validation, Writing - original draft, Writing - review & editing, Funding acquisition. Cody Yu-Ling Hsiao: Software, Validation, Data curation, Writing - original draft, Writing - review & editing. Vance L. Martin: Conceptualization, Software, Formal analysis, Writing - original draft, Writing - review & editing, Funding acquisition.

Acknowledgements

This work was supported by the Australian Research Council and the Macau SAR Government Higher Education Fund (HSS-MUST-2020-11) (Discovery Project grant numbers DP140102137, 2014 and DP120103443, 2012). We thank the editor and referees of the journal for very helpful comments and suggestions on previous versions of the paper. We also thank Joshua Chan, Thomas Flavin, Xun Lu, Esfandiar Maasoumi, James Morley, Pengfei Wang, Benjamin Wong, Sen Xue, Matthew Greenwood-Nimmo and Chrismin Tang for

References (30)

  • C. Brownlees et al.

    SRISK: A conditional capital shortfall measure of systemic risk

    Rev. Financ. Stud.

    (2017)
  • P. Christoffersen et al.

    Is the potential for international diversification disappearing? A dynamic copula approach

    Rev. Financ. Stud.

    (2012)
  • L. Cobb et al.

    Estimation and moment recursion relations for multimodal distributions of the exponential family

    J. Am. Stat. Assoc.

    (1983)
  • F.X. Diebold et al.

    Measuring financial asset return and volatilityspillovers, with application to global equity markets

    Econ. J.

    (2009)
  • M. Dungey et al.

    Transmission of Financial Crises and Contagion: A Latent Factor Approach

    (2010)
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