Why do correlations rise exactly when you need them low?

A correlation is one number for a whole distribution, and the part of the distribution a portfolio cares about is the tail. The table below measures the correlation between the S&P 500 fund and three things it is supposed to diversify — foreign shares, small shares, junk bonds — on ordinary days and on the days that mattered.

Measured, 2026-09-04

Daily returns on adjusted closes, 2 September 2016 to 3 September 2026:

Read across a row. In a calm year the foreign fund was 0.69 correlated with the S&P — a diversifier, on that measure. On the 151 large-move days of the decade it was 0.95, and in the six weeks of the pandemic crash 0.96. The diversification was real on the days it was not needed and absent on the days it was.

Why it happens

Two mechanisms, one statistical and one economic. The statistical one is that a correlation measured on large moves is a correlation between the parts of two distributions that are dominated by the common factor: on a −4% market day, almost everything that fell fell because of the market, and the share-specific noise that lowers correlation on ordinary days is swamped. The economic one is that crises are liquidations — the crowding lesson's mechanism — in which what is sold is what can be sold, regardless of what it is.

The portfolio-theory course's correlations-in-crisis lesson stated this; the table is its measurement.

What one number hides

A single correlation coefficient assumes the dependence is the same everywhere in the distribution — that the pair behaves the same on a +0.5% day and a −5% day. The table says it does not: dependence is stronger in the tails, and stronger in the left tail. The name for this is tail dependence, and the models that capture it — copulas, in the derivatives domain — exist because the correlation coefficient cannot.

The practical version needs no copula. Compute the correlation on the large-move days separately, as the third column does, and size diversification on that number rather than the full-period one. Assume the crisis correlation of anything risky with anything else risky is above 0.9, which is what every crisis in the record has delivered. Look for the assets whose crisis correlation is genuinely low or negative — the long Treasury fund in 2020, at −0.50, was one; in 2022 it was not — and treat those, not the merely different, as the diversifiers.

In the data

Four /eod/ pulls joined on date; the third column is the same correlation computed on the subset of dates where the SPY.US return exceeded 2% in either direction. The subset is what makes the number mean something, and the subset is what a full-period correlation averages away.

Try it now

1. The HYG.US row, split by the size of the day. Both series from /eod/ for the decade, joined on date, computed on 28 September 2026:

Half the decade's days are quiet ones, and on them the junk-bond fund is barely tied to the S&P. Say what a portfolio sized on the 0.30 would have assumed about the 151 days, and which of the three numbers belongs in a risk report. 2. The three "diversifiers" over the window, on the same range, where March 2020 is the same notch on every line:

3. A portfolio holds the S&P 500 fund, the foreign fund and the junk-bond fund at a third each, sized on the 2017 correlations. On 16 March 2020, what did it hold, effectively?