Lesson 20 of 25 · 7 min

Cross-asset correlation, and the sign flip that surprises people

A 70/30 mix carried 11.48 percent volatility at one correlation and 12.99 percent at another, on identical holdings and weights.

Correlations between asset classes are not only unstable in size. They change sign, and the sign is the property most multi-asset portfolios are built around.

A broad equity holding with 17 percent annualised volatility at a weight of 0.70, and a long-duration government bond holding with 7.5 percent volatility at 0.30. The two squared terms are 0.49 times 0.0289 and 0.09 times 0.005625, summing to 0.01466725, and they do not move with the correlation. At minus 0.28 the cross term is minus 0.0014994, giving a variance of 0.01316785 and a volatility of 11.48 percent. At zero it is 12.11 percent. At plus 0.41 the cross term is plus 0.00219555 and the volatility is 12.99 percent.

A point and a half from a sign flip sounds modest, and the modesty is itself the finding. Against 17 percent for the equity holding alone, the bond allocation removed 5.52 points at minus 0.28 and 4.01 points at plus 0.41, so 73 percent of the benefit survived. Cross-asset diversification weathers a reversal far better than within-equity diversification weathers a correlation rise, and the reason is arithmetic: the second asset's volatility is 7.5 percent against 17, so most of what it contributes is quietness rather than offsetting movement.

The sign does flip, and the mechanism is not mysterious. When a rising policy rate is the dominant driver it lowers bond prices directly and equity valuations through the discount rate, so one factor moves both legs the same way. That is what happened across the 2022 rate cycle, and it is the general case: the negative correlation of the preceding decades was a property of a period in which growth shocks dominated rate shocks.

For a pledged portfolio the sign is embedded in the schedule rather than stated in it. Advance rates are assigned by asset type, and a schedule granting a higher blended rate to a mixed pool than to its parts is pricing an assumed offset. On a $3,460,000 pool, a blended 72 percent gives $2,491,200 of lending value and a blended 64 percent gives $2,214,400 — $276,800 turning on whether the two types are treated as offsetting.

Key terms

Cross-asset correlation: The correlation between two different asset classes rather than two holdings within one. Smaller in magnitude than within-class figures and more likely to change sign.
Sign flip: A correlation crossing zero, so that two holdings which used to offset each other begin to reinforce. The event a multi-asset construction is most exposed to.
Blended advance rate: One weighted-average advance rate applied to a mixed pool. Any credit it gives for holding different asset types is an embedded assumption about their correlation.

Worked example

A 70/30 mix at three correlations

A broad equity holding at 17% volatility, weight 0.70. A long-duration government bond holding at 7.5% volatility, weight 0.30. Illustrative annualised figures.

The two squared terms, at any correlation: 0.01466725
Volatility at r = -0.28: 11.48%
Volatility at r = 0: 12.11%
Volatility at r = +0.41: 12.99%
Share of the benefit surviving the flip: 73%
Lending value on a $3,460,000 pool, 72% against 64%: $2,491,200 against $2,214,400

The sign flip cost 1.51 volatility points and 27 percent of the benefit. Most of that benefit came from the second asset being quiet, not from it moving the other way.

Check yourself

A 60/40 mix holds a 19% volatility asset and a 6.5% volatility asset. What are the portfolio volatilities at correlations of -0.20 and +0.35?

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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.