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52
Extreme Correlation of International Equity Markets
 Journal of Finance
, 2001
"... Testing the hypothesis that international equity market correlation increases in volatile times is a difficult exercise and misleading results have often been reported in the past because of a spurious relationship between correlation and volatility. This paper focuses on extreme correlation, that i ..."
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Cited by 177 (0 self)
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Testing the hypothesis that international equity market correlation increases in volatile times is a difficult exercise and misleading results have often been reported in the past because of a spurious relationship between correlation and volatility. This paper focuses on extreme correlation, that is to say the correlation between returns in either the negative or positive tail of the multivariate distribution. Using “extreme value theory ” to model the multivariate distribution tails, we derive the distribution of extreme correlation for a wide class of return distributions. Using monthly data on the five largest stock markets from 1958 to 1996, we reject the null hypothesis of multivariate normality for the negative tail, but not for the positive tail. We also find that correlation is not related to market volatility per se but to the market trend. Correlation increases in bear markets, but not in bull markets.
Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
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Cited by 149 (2 self)
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
2001. “Correlation Structure of International Equity Markets During Extremely Volatile Periods
 Journal of Finance
"... Recent studies in international finance have shown that correlation of international equity returns increases during volatile periods. However, correlation should be used with great care. For example, assuming a multivariate normal distribution with constant correlation, conditional correlation duri ..."
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Cited by 37 (1 self)
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Recent studies in international finance have shown that correlation of international equity returns increases during volatile periods. However, correlation should be used with great care. For example, assuming a multivariate normal distribution with constant correlation, conditional correlation during volatile periods (large absolute returns) is higher than conditional correlation during tranquil periods (small absolute returns) even though the correlation of all returns remains constant over time. In order to test whether correlation increases during volatile periods, the distribution of the conditional correlation under the null hypothesis must then be clearly specified. In this paper we focus on the correlation conditional on large returns and study the dependence structure of international equity markets during extremely volatile bear and bull periods. We use “extreme value theory ” to model the multivariate distribution of large returns. This theory allows one to specify the distribution of correlation conditional on large negative or positive returns under the null hypothesis of multivariate normality with constant correlation. Empirically, using monthly data from January 1959 to December 1996 for the five largest stock markets, we find that the correlation of large positive returns is not inconsistent with multivariate normality, while the correlation of large negative returns is much greater than expected.
Beyond Correlation: Extreme Comovements Between Financial Assets
, 2002
"... This paper inv estigates the potential for extreme comov ements between financial assets by directly testing the underlying dependence structure. In particular, a tdependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three ..."
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Cited by 34 (5 self)
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This paper inv estigates the potential for extreme comov ements between financial assets by directly testing the underlying dependence structure. In particular, a tdependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three di#erent markets (equities, currencies, and commodities) indicate that extreme comov ements are statistically significant. Moreov er, the "correlationbased" Gaussian dependence structure, underlying the multiv ariate Normal distribution, is rejected with negligible error probability when tested against the tdependencealternativ e. The economic significance of these results is illustratedv ia three examples: comov ements across the G5 equity markets; portfoliov alueatrisk calculations; and, pricing creditderiv ativ es. JEL Classification: C12, C15, C52, G11. Keywords: asset returns, extreme comov ements, copulas, dependence modeling, hypothesis testing, pseudolikelihood, portfolio models, risk management. # The authorsw ould like to thankAndrew Ang, Mark Broadie, Loran Chollete, and Paul Glasserman for their helpful comments on an earlier version of this manuscript. Both authors arewS; the Columbia Graduate School of Business, email: {rm586,assaf.zeevi}@columbia.edu, current version available at www.columbia.edu\# rm586 1 Introducti7 Specification and identification of dependencies between financial assets is a key ingredient in almost all financial applications: portfolio management, risk assessment, pricing, and hedging, to name but a few. The seminal work of Markowitz (1959) and the early introduction of the Gaussian modeling paradigm, in particular dynamic Brownianbased models, hav e both contributed greatly to making the concept of co rrelatio almost synony...
2008a, International Asset Allocation under Regime Switching, Skew and Kurtosis Preferences
 Review of Financial Studies
"... This paper investigates the international asset allocation effects of timevariations in higher order moments of stock returns such as skew and kurtosis. In the context of a fourmoment international CAPM specification that relates stock returns in five regions to returns on a global market portfoli ..."
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Cited by 21 (4 self)
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This paper investigates the international asset allocation effects of timevariations in higher order moments of stock returns such as skew and kurtosis. In the context of a fourmoment international CAPM specification that relates stock returns in five regions to returns on a global market portfolio and allows for timevarying prices of covariance, coskewness and cokurtosis risk, we find evidence of distinct bull and bear regimes. Ignoring such regimes, an unhedged US investor’s optimal portfolio is strongly diversified internationally. The presence of regimes in the return distribution leads to a substantial increase in the investor’s optimal holdings of US stocks as does the introduction of skew and kurtosis preferences. We relate these findings to the US market portfolio’s relatively attractive coskewness and cokurtosis properties with respect to the global market portfolio and
Beyond the Sample: Extreme Quantile and Probability Estimation
, 1997
"... Economic problems such as large claims analysis in insurance and valueatrisk in finance, require assessment of the probability P of extreme realizations Q: This paper provides a semiparametric method for estimation of extreme #P;Q# combinations for data with heavy tails. We solve the long standin ..."
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Cited by 15 (0 self)
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Economic problems such as large claims analysis in insurance and valueatrisk in finance, require assessment of the probability P of extreme realizations Q: This paper provides a semiparametric method for estimation of extreme #P;Q# combinations for data with heavy tails. We solve the long standing problem of estimating the sample threshold of where the tail of the distribution starts. This is accomplished by the combination of a control variate type device and a subsample bootstrap technique. The subsample bootstrap attains convergence in probability, whereas the full sample bootstrap would only provide convergence in distribution. This permits a complete and comprehensive treatment of extreme #P;Q# estimation. Keywords: Extreme value theory, tail estimation, risk analysis # Corresponding author: C. G. de Vries, Tinbergen Institute, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, email cdevries@few.eur.nl. Danielsson's email is jond@hi.is. This and related papers can be downl...
The Virtues and Vices of Equilibrium and the future of financial economics
, 2009
"... The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we p ..."
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Cited by 13 (1 self)
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The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, and should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out,i.e.,where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models.We sketch some alternative approaches and discuss why they should play an important role in
Taming large events: Optimal portfolio theory for strongly fluctuating assets
 International Journal of Theoretical and Applied Finance
, 1995
"... We propose a method of optimization of asset allocation in the case where the stock price variations are supposed to have “fat ” tails represented by power laws. Generalizing over previous works using stable Lévy distributions, we distinguish three distinct components of risk described by three diff ..."
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Cited by 12 (8 self)
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We propose a method of optimization of asset allocation in the case where the stock price variations are supposed to have “fat ” tails represented by power laws. Generalizing over previous works using stable Lévy distributions, we distinguish three distinct components of risk described by three different parts of the distributions of price variations: unexpected gains (to be kept), harmless noise inherent to financial activity, and unpleasant losses, which is the only component one would like to minimize. The independent treatment of the tails of distributions for positive and negative variations and the generalization to large events of the notion of covariance of two random variables provide explicit formulae for the optimal portfolio. The use of the probability of loss (or equivalently the ValueatRisk), as the key quantity to study and minimize, provides a simple solution to the problem of optimization of asset allocations in the general case where the characteristic exponents are different for each asset.
An Application of Extreme Value Theory for Measuring Financial Risk
, 2006
"... Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. Extreme value theory provides the solid fundamentals needed for the statistical modelling of such events and the computation of extreme risk measures. The focus of the paper is ..."
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Cited by 12 (0 self)
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Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. Extreme value theory provides the solid fundamentals needed for the statistical modelling of such events and the computation of extreme risk measures. The focus of the paper is on the use of extreme value theory to compute tail risk measures and the related confidence intervals, applying it to several major stock market indices.
Overnight Borrowing, Interest Rates and Extreme Value Theory
, 2001
"... We examine the dynamics of extreme values of overnight borrowing rates in an interbank money market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of t ..."
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Cited by 11 (4 self)
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We examine the dynamics of extreme values of overnight borrowing rates in an interbank money market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of the interest rate distribution. We also provide predictions of extreme overnight borrowing rates before the crisis. The examination of tails (extreme values) provides answers to such issues as what are the extreme movements expected in financial markets; have we already seen the largest moves; is there a possibility for even larger movements and, are there theoretical processes that can model the type of fat tails in the observed data? The answers to such questions are essential for proper management of financial exposures and laying ground for regulations.