What is the deal with all these risk indicators?

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If you liked the financial conditions index and the trade policy uncertainty index, then you’ll probably love the ECB’s new risk appetite index. If you don’t, then you might find yourself asking: What’s the purpose of all these things? Why are central bank economists so keen on taking the complexity of the world and reducing it to a single number?

Because that’s the basic project here. The new ECB index takes 10 daily financial markets series (equity prices, volatility futures, bond spreads and FX rates), then finds the first principal component (the combination of the series which explains the greatest proportion of their aggregate variance). The idea is that since all of the series are affected by the general “risk-on/risk-off” environment, but they otherwise have quite different macroeconomic drivers, the common component is likely to correspond to some measure of risk tolerance in the markets as a whole.

And it works, kind of sort of. Since risk on/off is an important driver of returns across asset classes, more-or-less any statistical technique that looks for common factors is going to find one which goes up and down at more-or-less the right moments. 

The ECB demonstrates on a chart that they’re not just fitting noise to noise:

But unfortunately, in demonstrating that there is a common risk appetite factor, they inadvertently also demonstrate the problems with the whole approach. 

The ECB’s methodology was taken from a 2023 article by Michael Bauer, Ben Bernanke, and Eric Milstein in which a similar chart appears:

The second chart is a bit easier to read, as it’s a standardised and cumulative time series rather than a forest plot of daily returns, but that doesn’t really change the location of the key events. And although the Bernanke paper is put together from a slightly different set of financial time series, this shouldn’t matter too much; risk appetite ought to be a relatively global phenomenon, and the ECB paper shows that in most cases the time series line up, albeit with regional differences in emphasis. 

The problem is in the words, not the numbers.

As can be seen, the two exercises agree pretty well on the dates of the key risk events. But Bauer et al. think that “Euro crisis II” in 2011 was actually the “US Credit downgrade”, while the “Brexit referendum” was the “2015-16 mini-recession”. The September 11 attacks might have just been the dotcom bust, while the euro rescue package might just have been a particularly strong day in the normalisation after the Lehman Brothers collapse.

Which is the fundamental problem — statistical methodology will pick up a common component in a bunch of time series, but it won’t tell you anything about the world. (A mathematician once told me: “You can do principal component analysis of a plate of spaghetti; all you’ll get is orthogonalized spaghetti, but you can do it.”) It neither predicts nor explains; it just substitutes one chart for ten, with a loss of information in doing so.

For some reason, central bankers find it comforting to do this; they think it’s more rigorous and objective to have a single indicator than to try to make specific statements about what they think is driving risk appetite. But in creating the standardised cumulative weighted average, the exact thing which you’re losing is the diversity of perspective. 

If equity markets are telling a different story from bond spreads, or if VIX futures don’t seem to be moving in line with USD, then that’s important — it’s something to be understood, not averaged out. The reluctance to get involved in institutional detail, and the preference for dealing with a version of reality mediated through statistics, is a terrible blind spot of policymakers that often has bad consequences.  

Because, although the ECB argues persuasively that changes in risk appetite are both partly driven by monetary policy expectations and partly contributory to the effectiveness of monetary policy, this doesn’t mean that there is a sensible or straightforward answer to the question: “Risk appetite just fell by 20 per cent — so what?” You can only actually incorporate a risk-on/off move into your policy framework if you have at least some understanding of what’s driving it. And in order to get that, you need to go back to the underlying information which the indicator was trying to summarise. 

Unfortunately, the lesson of several decades’ effort on creating indicators is that there’s really no substitute for knowing what you’re talking about, and there isn’t a statistical substitute either.