Lesson 22 of 25 · 6 min

Correlation is not causation, and it is also not stability

One unchanged 0.62 sat above two covariances five times apart, and it is covariance the variance formula consumes.

Everyone knows correlation is not causation. Fewer notice the second failure: an unchanged correlation is not unchanged risk.

Dispose of the causation half first, because it matters less here than usual. A collateral calculation does not need to know why two holdings move together, only whether they do and by how much. Correlation's inadequacy as a causal statement is not an inadequacy for this purpose. Its inadequacy as a stability statement is, because stability is what it gets read as.

Two windows on the same pair, both measuring a correlation of exactly 0.62. In the first the volatilities are 18 and 15 percent, so by lesson 8's identity the covariance is 0.62 times 0.18 times 0.15 = 0.01674. In the second they are 41 and 33 percent, so the covariance is 0.62 times 0.41 times 0.33 = 0.083886. Five times larger, with the correlation identical to two decimals. An equally weighted pair of these holdings carries 14.86 percent volatility in the first window and 33.35 percent in the second.

So a report stating that correlations were unchanged is compatible with a portfolio whose variance rose by a factor of 5.03. Lesson 3's grid multiplies each correlation by two volatilities and two weights, and holding one of four inputs fixed constrains the product hardly at all.

The collateral version has two inputs moving on separate schedules. A haircut responds to volatility, as Track 1 lesson 4 set out, and a grouping rule responds to correlation. A window in which only volatility moved changes the lending value through the first channel while the second channel's inputs look reassuringly stable.

Correlation stability is a statement about shape; risk is a statement about shape and size. A portfolio can hold its shape while quintupling in size.

Key terms

Correlation stability: The property of a correlation not changing between windows. It constrains the shape of the relationship and says nothing about its scale.
Spurious correlation: A measured association with no causal link between the two series. Common, and largely beside the point when the question is how a pledged pool will behave.
Volatility regime: A stretch over which price movement is generally high or low. It can change while every correlation in the portfolio stays put.

Worked example

The same correlation, two volatility regimes

One pair of holdings, correlation measured at 0.62 in both windows. Only the volatility level differs. Illustrative annualised figures.

Window one: volatilities: 18% and 15%
Window one: covariance: 0.01674
Window two: volatilities: 41% and 33%
Window two: covariance: 0.083886
Equal-weight pair volatility, each window: 14.86% then 33.35%
Ratio of the two variances: 5.03

A correlation report on these two windows would show no change at all. The portfolio's variance changed by a factor of five.

Check yourself

A pair of holdings correlates 0.48 in two windows. In the first both volatilities are 20%; in the second both are 32%. What happens to the covariance?

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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.