Extreme Correlation of International Equity Markets
Source: Longin, F. & Solnik, B. (2001) · Journal of Finance 56(2), 649–676 · DOI: 10.1111/0022-1082.00340
TL;DR
Develops an extreme value theory (EVT) method to test whether international equity-market correlation rises in turbulent times, avoiding the spurious correlation-volatility relationship that plagued earlier conditional-correlation studies. The asymptotic distribution of conditional tail correlation is derived for a wide class of return distributions. Empirically, on five markets 1959–1996, multivariate normality is rejected in the negative (loss) tail but not the positive tail: correlation rises with the market trend (bear markets), not volatility per se — diversification fails when you need it most.
Problem it solves
Practitioners "know" correlations spike in volatile markets, but the standard test — comparing correlations estimated on subsamples conditioned on observed returns — is biased. Conditional correlation is a nonlinear function of the conditioning return even when the true correlation is constant: under bivariate normality with constant ρ=0.50, conditioning on large |returns| (above 0.674) gives conditional correlation 0.62 vs 0.21 for small returns, despite ρ being fixed. The same bias arises under GARCH. A valid test needs the distribution of conditional correlation under an explicit null.
The method
Model the marginal tails beyond a threshold u with the generalized Pareto / extreme value limit (Balkema–De Haan, Pickands): exceedance distributions converge to a known parametric form regardless of the parent distribution.
Model the joint tail dependence with a dependence function (the logistic/Gumbel form, indexed by parameter α; α=1, i.e. ρ=1−α²=0, is the asymptotic-independence / multivariate-normal limit case).
Derive the asymptotic correlation of extreme returns and its distribution; test whether it differs from zero (the normal benchmark). Estimate by maximum likelihood on tail exceedances.
Optimal threshold trades off bias (too low) vs variance (too high); ~20–30 tail observations (≈4–5% of the sample) are used per tail.
Assumptions & inputs
Data: MSCI monthly equity index returns for five markets — US, UK, France, Germany, Japan — Jan 1959–Dec 1996 (456 observations, 38 years).
Key result: under multivariate normality the correlation of extremes should → 0 as the threshold rises; even a normal with ρ=0.80 has zero asymptotic extreme correlation. EVT asymptotics hold for non-i.i.d. (incl. GARCH) processes.
The negative-tail extreme correlation does not converge to zero (rejecting normality); the positive tail is consistent with normality. Correlation increases in bear markets but not bull markets.
How to use it
Risk management / stress testing: use tail-dependence estimates rather than full-sample Pearson correlation when sizing international diversification and computing crash-scenario joint losses.
A template for copula and EVT-based dependence modeling in finance (Embrechts–McNeil–Straumann).
Limitations & pitfalls
EVT gives only asymptotic results; finite-sample tail estimation is data-hungry and sensitive to threshold choice.
The logistic dependence function is a parametric (somewhat arbitrary) choice imposed on the joint tail.
Documents the asymmetry more than its cause (contagion vs common fundamental shocks); monthly frequency limits the count of true extremes.
Key references
Ang, A. & Chen, J. (2002) — Asymmetric Correlations of Equity Portfolios — Journal of Financial Economics
Embrechts, P., McNeil, A. & Straumann, D. (2002) — Correlation and Dependence in Risk Management — (copulas)
Longin, F. & Solnik, B. (1995) — Is the Correlation in International Equity Returns Constant: 1960–1990? — Journal of International Money and Finance
Provenance: verified/generated from the paper's full text.
