Hedges or safe havens—revisit the role of gold and USD against stock: a multivariate extended skew-t copula approach

Our paper concerns the question of whether there exist hedge assets during extreme market conditions, which has become increasingly important since the recent financial crisis. This paper develops a novel extended skew-t copula model to examine the effectiveness of gold and US dollar (USD) as hedge or safe haven asset against stock prices for seven developed markets over the 2000–2013 period. Our results indicate the existence of skewness and heavy/thin tails in the distributions of all three types of assets in most of the developed markets, lending support to the employment of flexible distributions to evaluate the tail dependences among assets. We find that USD is preferred to gold as a hedge asset during normal market conditions, while both assets can serve as safe haven assets for most countries when stock markets crash. Our simultaneous analysis of the three assets advises against a joint hedge strategy of gold and USD due to the high tail dependence between them during extreme market conditions. This result highlights the importance of simultaneous modelling of multiple assets in financial risk analysis.     

Measuring large comovements in financial markets

A general, copula-based framework for measuring the dependence among financial time series is presented. Particular emphasis is placed on multivariate conditional Spearman's rho (MCS), a new measure of multivariate conditional dependence that describes the association between large or extreme negative returns—so-called tail dependence. We demonstrate that MCS has a number of advantages over conventional measures of tail dependence, both in theory and in practical applications. In the analysis of univariate financial series, data are filtered to remove temporal dependence as a matter of routine. We show that standard filtering procedures may strongly influence the conclusions drawn concerning tail dependence. We give empirical applications to two large data sets of high-frequency asset returns. Our results have immediate implications for portfolio risk management, derivative pricing and portfolio selection. In this context we address portfolio tail diversification and tail hedging. Amongst other aspects, it is shown that the proposed modeling framework improves the estimation of portfolio risk measures such as the value at risk.     

Tail dependence between Bitcoin and financial assets: Evidence from a quantile cross-spectral approach

Using daily price data for Bitcoin and 10 representative financial assets from the stock, commodity, gold, foreign exchange and bond markets from 2011 to 2019, we study the tail dependence between returns for Bitcoin and these other financial assets using the novel “quantile cross-spectral dependence” approach of Baruník and Kley (2019). We find evidence of right-tail dependence between Bitcoin returns and the S&P 500 in the long term and weaker normal return dependence between Bitcoin and the US Dollar (USD)–Euro (EUR) foreign exchange rate in the monthly term. In addition, we note that the dependence between Bitcoin and commodity as well as oil, and silver decrease the most within their respective medium return quantiles over the short term. Furthermore, we document a one-way causality running from each of the financial assets considered to Bitcoin in different quantiles of the return distribution. In sum, our findings support the notion that Bitcoin can provide financial diversification in certain return quantiles (i.e., bear, normal, or bull asset conditions) and time frequencies (i.e., short, medium, or long term investment horizon).     

The t copula with multiple parameters of degrees of freedom: bivariate characteristics and application to risk management

The t copula is often used in risk management as it allows for modeling the tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, the grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a generalized grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on the finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula is significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall.     

Multivariate dependence of implied volatilities from equity options as measure of systemic risk

This paper presents a methodology to examine the multivariate tail dependence of the implied volatility of equity options as an early warning indicator of systemic risk within the financial sector. Using non-parametric methods of estimating changes in the dependence structure in response to common shocks affecting individual risk profiles, possible linkages during periods of stress are quantifiable while recognizing that large shocks are transmitted across financial markets differently than small shocks. Before and during the initial phase of the financial crisis, we find that systemic risk increased globally as early as February 2007 — months before the unraveling of the U.S. subprime mortgage crisis and long before the collapse of Lehman Brothers. The average (multivariate) dependence among a global sample of banks and insurance companies increased by almost 30% while joint tail risk declined by about the same order of magnitude, indicating that co-movements of large changes in equity volatility were more likely to occur and responses to extreme shocks became more differentiated as distress escalated. The key policy consideration flowing from our analysis is that complementary measures of joint tail risk at high data frequency are essential to the robust measurement of systemic risk, which could enhance market-based early warning mechanisms as part of macroprudential surveillance.     

Financial stress relationships among Euro area countries: an R-vine copula approach

One of the biggest challenges of keeping Euro area financial stability is the negative co-movement between the vulnerability of public finance, the financial sector, security markets stresses as well as economic growth, especially in peripheral economies. This paper utilizes a ARMA-GARCH based R-vine copula method to explore tail dependance between the Financial Stress Indices of 11 euro area countries with an aim of understanding how financial stress are interacting with each other. We find larger economies in the Euro area tend to have closer upper tail dependence in terms of positive shocks, while smaller economies tend to have closer lower tail dependence with respect to negative shocks. The R-vine copula results underline the complex dynamics of financial stress relations existing between Euro Area economies. The estimated R-vine shows Spain, Italy, France and Belgium are the most inter-connected nodes which underlying they might be more efficient targets to treat in order to achieve a quicker stabilizing. Our results relate to the fact that Eurozone is not a unified policy making area, therefore, it needs to follow divergent policies for taming the effects of financial instability to different regions or groups of economies that are more interconnected.     

COVID-19 and stock returns: Evidence from the Markov switching dependence approach

This paper aims to investigate the regime-switching and time-varying dependence between the COVID-19 pandemic and the US stock markets using a Markov-switching framework. It makes two contributions to the empirical literature by showing that: (a) the variations of the daily reported COVID-19 cases and cumulative COVID-19 deaths induced asymmetric lower (left) and upper (right) tail dependence with the stock markets, and its left and right tail dependence exhibited significant time-varying trends; and (b) the left and right tail dependence between the stock markets and the pandemic exhibited significant regime-switching behaviours, with its switching probabilities in the higher tail dependence stage all being greater than in the lower tail dependence stage after 1 December 2019. Moreover, given that there is concurrent but significant financial market reaction to any unexpected emergence of a transmittable respirational disease or a natural calamity, the outcomes have some vital implications to market players and policymakers.     

Stock–bond dependence and flight to/from quality

This paper investigates the stock–bond dependence structure using a dependence-switching copula model. The model allows stock–bond dependence to switch between positive dependence regimes (contagions or crashes of the two markets during downturns or booms in both markets during upturns) and negative dependence regimes (flight-to-quality from stock markets to bond markets or flight-from-quality from bond markets to stock markets). Using data from four developed markets including the US, Canada, Germany, and France for the period between January 1985 and August 2022, we find that the within-country stock–bond (extreme) dependence could be both positive and negative. In the positive dependence regimes, the stock–bond dependence is asymmetric with stronger left tail dependence than the right tail dependence, giving evidence of a higher likelihood of joint stock–bond market crashes or contagions during market downturns than the collective stock–bond market booms. Under the negative dependence regimes, we find both flight-from-quality and flight-to-quality, with flight-to-quality being more dominant in the North American markets while flight-from-quality is more prominent in the European markets. Further, the dependence switches between positive and negative regimes over time. Moreover, the dependence is mainly in the positive regimes before 2000 while mostly in the negative regimes after that, indicating contagions mostly before 2000 and flights afterwards. Further, the dependence switches between positive and negative regimes around financial crises and the COVID-19 pandemic. These results greatly enrich the findings in the existing literature on the co-movements of stock–bond markets and are important for risk management and asset pricing.     

Risk management under extreme events

This article presents two applications of extreme value theory (EVT) to financial markets: computation of value at risk (VaR) and cross-section dependence of extreme returns (i.e., tail dependence). We use a sample comprised of the United States, Europe, Asia, and Latin America. Our main findings are the following. First, on average, EVT gives the most accurate estimate of VaR. Second, tail dependence of paired returns decreases substantially when both heteroscedasticity and serial correlation are filtered out by a multivariate GARCH model. Both findings are in agreement with previous research in this area for other financial markets.     

Time-Varying Dependency and Structural Changes in Currency Markets

This study employs Patton's (2006) conditional copula framework to model dynamic conditional joint distribution with currency data for Taiwan and its trading counterparties. Empirical findings suggest that the exchange rate of Taiwan tends to display high tail dependence with those of Asian countries during currency depreciations. Because financial events during the sample period may be the source of structural changes for dependence structure, this study applies Bai and Perron's (1998, 2003) approach to detect the internal structural breaks. Empirical results reveal significant structural changes in the persistence of dependence, especially during the financial crisis of 2008.     

The Dynamic Extreme Co-Movement between Chinese Stock Market and Global Stock Markets

ABSTRACT

We use time-varying Symmetrized Joe-Clayton Copula model to study the extreme co-movement (boom or crash together) between the Chinese stock market and major stock markets in the world from 2007 to 2017, including developed markets and stock markets on “Belt and Road Initiative” (hereafter B.R.I.). We find that the extreme co-movement probability between Chinese market and “Belt and Road Initiative” markets is higher than developed markets at both tails. Then we study important “real” and “non-fundamental” factors affecting the excess co-movement probability, including bilateral trade openness, financial integration, and economic policy uncertainty. The results of panel regression analysis show that: the bilateral financial integration has significant effects over the lower tail dependence between Chinese and developed markets, but does not affect the extreme co-movement between Chinese and B.R.I. markets. And the bilateral trade openness is an important factor for the extreme co-movement at both tail between Chinese and global markets. The economic policy uncertainty index, especially China’s economic policy uncertainty, plays a key role in the extreme co-movement between Chinese and developed markets at both tails. However, it has sizable effects only at the upper tail co-movement between Chinese and B.R.I. markets.     

A semi-parametric approach to risk management

Abstract

The benchmark theory of mathematical finance is the Black–Scholes–Merton (BSM) theory, based on Brownian motion as the driving noise process for stock prices. Here the distributions of financial returns of the stocks in a portfolio are multivariate normal. Risk management based on BSM underestimates tails. Hence estimation of tail behaviour is often based on extreme value theory (EVT). Here we discuss a semi-parametric replacement for the multivariate normal involving normal variance–mean mixtures. This allows a more accurate modelling of tails, together with various degrees of tail dependence, while (unlike EVT) the whole return distribution can be modelled. We use a parametric component, incorporating the mean vector μ and covariance matrix Σ, and a non-parametric component, which we can think of as a density on [0,∞), modelling the shape (in particular the tail decay) of the distribution. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We discuss efficient methods to estimate the parametric and non-parametric components of our model and provide an algorithm for simulating from such a model. We fit our model to several financial data series. Finally, we calculate value at risk (VaR) quantities for several portfolios and compare these VaRs to those obtained from simple multivariate normal and parametric mixture models.     

Testing the Gaussian copula hypothesis for financial assets dependences

Abstract

Using one of the key properties of copulas that they remain invariant under an arbitrary monotonic change of variable, we investigate the null hypothesis that the dependence between financial assets can be modelled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student copula, cannot be rejected if it has sufficiently many ‘degrees of freedom’. As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the coefficient of correlation between the pairs of assets is too high, such that the tail dependence neglected by the Gaussian copula can became large, leading to the ignoring of extreme events which may occur in unison.     

ESG,risk, and (tail) dependence

While environmental, social, and governance (ESG) trading activity has been a distinctive feature of financial markets, the debate if ESG scores can also convey information regarding a company’s riskiness remains open. Regulatory authorities, such as the European Banking Authority (EBA), have acknowledged that ESG factors can contribute to risk. Therefore, it is important to model such risk dependencies and quantify what part of a company’s riskiness can be attributed to the ESG scores. This paper aims to question whether ESG scores can be used to provide information on (tail) riskiness. By analyzing the (tail) dependence structure of companies with a range of ESG scores, that is within an ESG rating class, using high-dimensional vine copula modeling, we are able to show that risk can also depend on and be directly associated with a specific ESG rating class. Empirical findings on real-world data show positive not negligible ESG risks determined by ESG scores, especially during the 2008 crisis.     

A multivariate jump-driven financial asset model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that—opposite to other, non-jointly Gaussian settings—its risk-neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.     

The shifting dependence dynamics between the G7 stock markets

The growing interdependence between financial markets has attracted special attention from academic researchers and finance practitioners for the purpose of optimal portfolio design and contagion analysis. This article develops a tractable regime-switching version of the copula functions to model the intermarkets linkages during turmoil and normal periods, while taking into account structural changes. More precisely, Markov regime-switching C-vine and D-vine decompositions of the Student’s t copula are proposed and applied to returns on diversified portfolios of stocks, represented by the G7 stock market indices. The empirical results show evidence of regime shifts in the dependence structure with high contagion risk during crisis periods. Moreover, both the C- and D-vines highly outperform the multivariate Student’s t copula, which suggests that the shock transmission path is as important as the dependence itself, and is better detected with a vine copula decomposition.     

Economic evaluation of asymmetric and price range information in gold and general financial markets

Gold is widely perceived as a good diversification or safe haven tool for general financial markets, especially in market turmoil. To fully understand the potential, this study constructs an asymmetric multivariate range-based volatility model to investigate the dependence and volatility structures of gold, stock, and bond markets and further to compare the difference between the financial crisis and post-financial crisis periods. We find a striking explanatory ability to volatility structures provided by the price range information and significant evidence of asymmetric dependence across gold, stock, and bond markets. We implement an asset-allocation strategy incorporating asymmetric dependence and price range information to explore their economic importance. The out-of-sample results show that between 35 and 517 basis points and between 90 and 1111 basis points are earned annually when acknowledging asymmetric dependence and price range information, respectively. These economic benefits are inversely related to the level of investors’ risk aversion and are particularly significant in the period of the global financial crisis.     

Commodity market financialization,herding and signals: An asymmetric GARCH R-vine copula approach

Institutional investors have significantly increased their exposure to commodity futures after 2004 in the process of commodity market financialization, raising questions about the risk-sharing and price-discovery functions of the market. We identify some symptoms of financialization through examining S&P500, JPM bond index, and 18 S&P GSCI excess return indices, employing ARMA-GARCH R-vine copula approach that can flexibly model high-dimensional multivariate asymmetric tail dependence. We discover three trends: an increased resemblance between the news impact curve of stocks and those of commodities; an increased bi-variate stock-commodity tail dependence; and an increased multivariate tail-dependence across all commodities. We also explore the market structural change underlying these symptoms using an augmented news impact curve. We suggest and provide evidence that herding, in addiction to leverage effect, explains the observed symptoms. The findings have profound implications for commercial hedgers and financial traders, and for regulators who are concerned about the functionalities of commodity futures market.     

Modelling systemic price cojumps with Hawkes factor models

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating portfolios of highly liquid stocks, we find that there are a large number of high-frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one-factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets.     

Evolution of multivariate copulas in continuous and discrete processes

There has been much interest in copulas, which are known to provide a flexible tool for analyzing the dependence structure among random variables. Dependence relations must be dynamic rather than static in nature. However, copulas are useful mainly for static matters. Thus we introduce evolving multivariate copulas, which transform through time autonomously governed by the multivariate heat equation. Our aims are to prove their existences and solutions to analyze their transitions. Moreover, we construct discrete type to apply empirical data analysis and investigate their properties, and prove that they converge to their original continuous type.