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Contagion or Interdependence: the Bias That Inflates Crisis Correlations

Was a crisis correlation spike contagion, or dependence already present before the crisis?

Forbes and Rigobon found that higher volatility can inflate measured cross-market correlation even when underlying dependence is unchanged. Their correction reduces apparent contagion in the episodes they studied, without settling every crisis or portfolio.

The result concerns the crisis episodes and markets studied; it cannot classify every future correlation spike.

Recorded strategy returns are aligned around several named crisis windows.
Recorded strategy returns are aligned around several named crisis windows.

Evidence map

AspectFinding
What it isA correction to test whether correlations rose in the crisis episodes studied by Forbes and Rigobon.
Key result / formulaThe argument is a statistical identity. If two series are linked by a fixed relationship and one of them becomes more volatile, the measured correlation between them rises even though the relationship has not changed, because the common component grows relative to the idiosyncratic noise.
Why it matters for backtestingThis is the note that keeps an agent accurate when it reports that a user's strategies became correlated in a drawdown.

What it is

In their setting, correlation measured during high volatility can be biased upward for mechanical reasons; after their correction much of the apparent increase in those episodes disappears.

Key result / formula

The crisis periods in their study have high volatility, so comparing a crisis-period correlation with a calm-period one compares two different measurement conditions rather than two different market states. The authors derive the adjustment that removes the heteroskedasticity bias and apply it to several well-known episodes of apparent contagion. Corrected, the increase in correlation largely vanishes: markets were already highly interdependent, and what looked like contagion was mostly that interdependence being measured through a noisier lens. This result is about the markets and episodes they studied; it does not establish that every crisis correlation rise is an artefact.

Why it matters for backtesting

That increase could reflect changed dependence, the measurement bias, or both; the possibilities require different responses. The practical procedure is to apply a suitable volatility adjustment, or more simply to compare correlations across periods of similar volatility before drawing a conclusion, since a calm-versus-crisis comparison mixes the two conditions. The deeper lesson generalises beyond correlation: any statistic computed on a conditionally selected subsample is measured under different conditions than the full sample, and the difference is not automatically a change in the world (see [A sub-period difference detects a change; it does not measure its size]).

Source

Forbes & Rigobon, "No Contagion, Only Interdependence: Measuring Stock Market Comovements", Journal of Finance 57(5), 2002, 2223-2261. Primary source

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