Steeper Yield Curves & The Limits Of Correlation

Authored by Simon White, Bloomberg macro strategist,

The US yield curve ought to proceed to steepen, with elevated Treasury-bill issuance seemingly one in all a number of supportive components. In displaying this, we’ll get to a deeper drawback in markets evaluation: the restrictions of correlation.

Finally, after one of many deepest inversions but seen, the yield curve seems like it’s on a sustainable steepening path. I count on that development to proceed, with one of many helps – as I argued in a current publish – the rise in invoice issuance. That prompted a riposte from Cameron Crise, arguing the correlation was low, and that anyway, correlation doesn’t indicate causation.

Both honest factors, however they provide up the chance to take a look at correlation extra intently, a device used freely, incessantly and sometimes misguidedly in market evaluation.

The chart that Cameron objected to is beneath. It reveals the yield curve versus T-bills excellent as a proportion of complete authorities debt excellent. As he identified, the correlation between the 2 collection, at ~25%, is sort of low.

But you will need to take the lead into consideration. Two traces on a chart with no lead could clarify, however they don’t predict. Two collection the place one leads the opposite, assuming no spurious correlation, can predict – which has appreciable extra utility for traders.

In the chart above the T-bills collection is pushed ahead by six months. Recalculating the correlation utilizing the collection appropriately offset reveals it rises to 36%.

This remains to be on the low facet, and doesn’t reveal causality. But we are able to higher see the connection by trying on the yield curve versus the common period of Treasury debt held by the general public. As the chart beneath reveals, the general public’s common period of debt held has accomplished an honest job of monitoring the yield curve – with a nine-month lead – since 2008 and the GFC.

The correlation of the annual modifications is -51%, with a t-stat of ~-5 within the linear regression. (As an necessary facet notice, we should always all the time do correlations on modifications not ranges to scale back the affect of drift co-linearity).

Cameron put ahead one other relationship between web new period (10y versus 2y issuance) and the yield curve, displaying they’re positively relatively than negatively associated, and having a still-on-the-low-side correlation of +44%.

Nonetheless, I desire the common period held by the general public as a yield-curve predictor, not solely as a result of larger correlation, however as: a) it offers info on web issuance throughout the entire curve; b) it negates Federal Reserve possession results; and c) the connection offers a lead relatively than being coincident.

But there are two additional necessary factors to make.

The first is causality. As Cameron reminded us, correlation doesn’t indicate causation. A -51% correlation just isn’t too dangerous, however even a 100% correlation wouldn’t indicate causality. In truth, no mathematical method can show causality.

The solely approach to point out causality is to have a causal concept. One supplied right here is that demand for shorter-term debt and payments is elastic, and when Treasury will increase its shorter-term issuance, the additional provide creates extra demand on the entrance of the curve relative to the again, and the curve steepens as common period falls – as is going on at this time.

Yet a fair greater difficulty right here issues the restrictions of the correlation measure itself which might be typically not appreciated. In markets, we’re most taken with turning factors. It is right here the place we get probably the most abrupt modifications, and it’s right here the place the consensus – which generally linearly extrapolates a development – is most flawed. It is subsequently at turning factors we are inclined to see the most important strikes in danger belongings.

But the usual manner of calculating correlation (the Pearson coefficient) seems at a mean of co-movements relative to every collection’ imply. Two collection could line up very properly at main turning factors, however that may simply get diluted by the remainder of the info factors within the set.

The de-emphasis of turning factors may be seen most instantly after we take into consideration regressions. The final purpose from an investor’s standpoint is to seek out relationships that lead. Regressions allow us to forecast values for knowledge collection. But the commonest sort used – linear regressions – are ailing suited to attempting to foretell all-important turning factors.

Take a a easy sine curve. A naive regression would return a straight line by the center. Not solely is that this unhelpful, it’s “peak wrong” whenever you want it most, i.e. on the turning factors.

Back to at this time and the yield curve. As talked about above, the common period of Treasury debt held by the general public is probably going one affect on the yield curve at turning factors. But you will need to not make assertions based mostly on just one indicator. In this case a steeper yield curve can be intimated by the rise in international extra liquidity (actual cash development minus financial development).

Here, regardless that we are able to visually see lots of the turns in extra liquidity lead the turns in modifications within the yield curve, the correlation is below 35%. Yet the indicator has been extra helpful in anticipating the turning factors than the low-ish correlation would infer.

Still, no relationships in finance and markets are mono-causal. There is reflexivity and there are suggestions loops, as we get in any complicated system. The purpose of market evaluation is to attempt to shine a lightweight on partial relationships that hopefully assist illuminate the larger image. As Niels Bohr, founding father of quantum mechanics, put it within the context of science:

“It’s wrong to think the task of physics is to find out how nature is. Physics concerns what we can say about nature”.

It seems just like the yield curve ought to proceed to steepen, based mostly on the above evaluation. The tacit caveat is that no relationship is ideal and there aren’t any crystal balls. After all, if anybody had the holy grail to earn money limitlessly, why would they share it?