Lesson 13 of 25 · 7 min

Why correlations converge in a drawdown

Fifty ordinary months measured 0.29, ten drawdown months measured 0.76, and the sixty containing both measured 0.60.

Track 4 lesson 15 stated that correlations rise toward one in stressed markets. This lesson measures it on a specific history, and the measurement contains a third figure that neither of the first two prepares you for.

Take an illustrative sixty-month history of six holdings, ten of those months belonging to a severe drawdown. Averaged across the fifteen distinct pairs, the correlation in the fifty ordinary months is 0.2938. In the ten drawdown months it is 0.7599. Over all sixty together it is 0.6029, which is neither — a pooled figure inflated by the regime shift, for exactly the reason lesson 11 computed. A reported full-sample correlation of 0.60 here would be a correct calculation describing no regime the portfolio ever occupied.

The convergence is not a few pairs moving. In the ordinary months all fifteen pairwise entries sit between 0.20 and 0.35; in the drawdown months they sit between 0.57 and 0.91. The whole matrix moved together.

Comparing the portfolio with its holdings is the cleanest way to see that correlation did the work. Average single-name monthly volatility rose from 6.11 percent in the ordinary months to 10.65 percent in the drawdown, a factor of 1.74. The equally weighted portfolio's monthly volatility rose from 3.91 percent to 9.55 percent, a factor of 2.44. The holdings got 74 percent more volatile and the portfolio got 144 percent more volatile, and the difference between those multiples is the correlation.

In a drawdown a portfolio does not simply inherit its holdings' extra volatility. It inherits that, plus the loss of the offsetting that used to sit between them.

Key terms

Correlation convergence: The movement of every pairwise correlation in a portfolio toward one at the same time, rather than a few pairs shifting.
Full-sample correlation: A correlation computed over a history containing more than one regime. It describes a blend and may match no regime the portfolio was ever in.
Drawdown window: The stretch of months making up a severe decline. Short by construction, which is why the correlations measured in it are the least precisely known and the most consequential.

Worked example

One history, three windows

An illustrative sixty-month return history for six equally weighted holdings, ten of those months belonging to a severe drawdown. Fifteen distinct pairwise correlations, averaged.

Average pairwise correlation, 50 ordinary months: 0.2938
Average pairwise correlation, 10 drawdown months: 0.7599
Average pairwise correlation, all 60 months: 0.6029
Range of the fifteen entries, ordinary then drawdown: 0.20 to 0.35, then 0.57 to 0.91
Average single-name monthly volatility: 6.11% then 10.65%
Equal-weight portfolio monthly volatility: 3.91% then 9.55%

Single-name volatility rose 74 percent and portfolio volatility rose 144 percent. The extra 70 points came from the correlations, and the effective bets fell from 2.43 to 1.25.

Check yourself

In a drawdown window, the average holding's volatility rose by 74% while the equally weighted portfolio's volatility rose by 144%. Where did the difference come from?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.