Correlations Rise Exactly When You Need Them Low
Will portfolio diversification survive a sharp rise in cross-asset correlations?
Estimate correlations separately in ordinary and stressed observations, with the stress rule fixed in advance, then recompute portfolio loss under both estimates. A shift in correlation does not by itself quantify lost diversification; sample size and estimation error matter.
A change in estimated stress correlations does not by itself quantify the exact diversification loss.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | The body of evidence that dependence between assets can increase in falling markets, so that the diversification measured on an average correlation is not the diversification available in a crisis. |
| Key result / formula | Longin and Solnik model the joint extremes of international equity markets with extreme value theory, which avoids assuming a joint distribution, and find that the correlation of large negative returns is substantially higher than the correlation of large positive ones, and that the increase in the lower tail is not what a multivariate normal would produce. |
| Why it matters for backtesting | This is the single most important correction to make to any diversification claim an agent produces. |
What it is
Three papers establish it with different methods and agree.
Key result / formula
Ang and Chen measure the asymmetry in the cross-section of United States equities, confirming that portfolios move together more in downside markets than in upside ones, and quantify the departure from the symmetric benchmark. Chua, Kritzman and Page put the consequence in portfolio terms, showing that conditional on large joint moves, the diversification an allocation appears to provide largely disappears, so that a portfolio built on full-sample correlations is more concentrated in bad states than its owner expects. The common structure of the finding is that dependence is asymmetric, and correlation, being a single symmetric number, cannot express it.
Why it matters for backtesting
This conditional measurement can be performed from the user's own data: compute correlations conditional on the market or on the portfolio being in its lowest-return decile, and compare with the unconditional value. A gap between the two is the amount of diversification that will not be there when it is needed. The practical consequences follow: size a portfolio on the conditional correlation rather than the average, expect the effective number of bets to collapse in stress, and treat a low full-sample correlation between two strategies as insufficient evidence that they diversify (see [Correlation & Diversification: Count the Correlation of the Legs]). One caveat belongs with the measurement, and the next note supplies it.
Source
Longin & Solnik, "Extreme Correlation of International Equity Markets", Journal of Finance 56(2), 2001, 649-676; Ang & Chen, "Asymmetric correlations of equity portfolios", Journal of Financial Economics 63(3), 2002, 443-494; Chua, Kritzman & Page, "The Myth of Diversification", Journal of Portfolio Management 36(1), 2009, 26-35. Primary source