Do Androids Dream of Systemic Risk?

“Fiery the Angels fell; Deep thunder rolled around their shores; burning with the fires of Orc.”

— Roy Batty

Last year, forest fires turned my enchanting San Francisco into a scene out of Blade Runner. As I walked around the city, doing the world’s worst Rick Deckard cosplay, I had so many questions. Why was this set of fires so bad? Could we better detect and prepare for these fires? Is global warming at all to blame? And…how can I force this as an analogy to talk about systemic risk in financial markets?

I would argue that financial markets are a bit like forest fires. Corrections (small fires) happen more or less all the time. Some market is always in tumult. But every so often one of these ordinary bouts of volatility turns into a systemic crisis. Many assets fall violently in unison. A narrative forms. Past events now seem to lead inexorably to eventual catastrophe. But, and I cannot emphasize this point enough, it is hard to know in real-time if you’re experiencing ordinary volatility or a systemic crisis. Is this an ordinary fire or a fire that will turn the sky dark at noon? I think a helpful tool in this situation is a metric called the Absorption Ratio.

Absorption Ratio

Analogy

In the context of our analogy about forest fires, the absorption ratio measures the fuel mosaic — the amount of fuel on the ground, the dryness, etc. These conditions are necessary but not sufficient for a super fire. The arboreal equivalent of gasoline-soaked rags can be cleared out before catching alight. But it’s not hard to see how such conditions can turn a small fire into a much, much larger one.

Technical definition

The absorption ratio measures the fraction of total variance of returns explained by a fixed set of eigenvectors. A higher AR implies more systemic risk because it implies that sources of risk are more integrated. If I can normally explain 60% of asset returns with three independent factors, then it should be concerning when I can start explaining 90% of asset returns with those same factors. The implication is that, under such conditions, a shock to any of these factors would spread more rapidly and broadly. Hence the absorption ratio has a link, in theory, to systemic risk in financial markets.

Mathematical definition

Standardizing the Ratio

The raw absorption ratio is not in a format that is diagnostically useful. For example, is a spike from 50% to 60% big? What about 80% to 90%? You can address such questions by standardizing the ratio. First, compute the moving average of the absorption ratio over the trailing 21 days and subtract it from the moving average of the absorption ratio of one year. Then to standardize the differences, divide them by the trailing one year standard deviation.

Below, I plot the standardized absorption ratio of 49 US industry indices from Ken French’s data library versus the rolling drawdown of the Russell 2000. Visually we can see that the standardized absorption ratio tends to move above 1 standard deviation preceding large drawdowns.

Let’s put some numbers around this idea. The table below shows the percent of drawdowns preceded by a 1 sigma spike in the absorption ratio. You can see that the percentages look especially compelling for the 1% worst drawdowns — the super fires.

Why is this useful?

In short, the absorption ratio is useful because it has a decent link to systemic risk and the crises therein. Contrast this with the conventional approach. Every day articulate, well-credentialed people go out into the media and pitch their vision of doom and collapse. They have compelling theses and often even data to support them. But, in my opinion, this usually amounts to little more than screaming into the ether about high valuations. (I don’t think the people who do this are naive. I think valuations are easily digestible and often coincide with investors visceral memories of crises past.) But valuations are not terribly useful when it comes to gauging systemic risk. In the context of our analogy it’s like screaming about a super fire happening because it’s summer. I’m not saying that high valuations do not reflect some level of fragility in the financial system. What I am claiming is that they are not useful in terms of gauging or acting on systemic risk. Vague notions of regression to the mean are all that can be offered up in support but that can take a long time. To take my riff on the well-worn finance joke: what do you call something trading at 100 times fair value? Something that was trading at 50 times and doubled. As trite as that sounds, there’s truth in it. The absorption ratio gets at least within statistical spitting distance of being necessary for a systemic crisis. So save yourself the grief and stop staring at charts showing extreme valuations or debt levels wondering if you should do something. Instead search out more actionable and useful metrics like the absorption ratio.

Applications

The absorption ratio has many potential applications. First, you can feed it into an ML model as a feature. Second, you can use it in tactical asset allocation. You could extend it to not just be a signal into or out of assets but also different models for different regimes. This is akin to playing blackjack tighter or looser depending on the count. Finally, you could use the absorption ratio to selectively engage in paying for tail insurance. The bleed on puts is costly and it could prove effective to add extra tail insurance during periods where the absorption ratio is high. For more on applications of the absorption ratio I recommend reading Mark Kritzman’s work. He and his collegues came up with the Absorption Ratio. Your humble author did not.

PostScript: Scouting Markets

What I aim to do with these posts, for now, is to layout and utilize different tools to scout capital markets. You can call them lenses, tools, frameworks etc. The goal is to have a ready set of means of assessing what is happening and hopefully catch a glimpse about what might happen. I like the term scouting. There’s a lack of objective implied in that term. I’m not trying to write yet another article using a neural net to predict price performance. I’m not trying to demonstrate that any of these methods result in greater profits. I leave that to others. I’m simply trying to share my explorations with others in the hopes that you might learn of a new tool to incorporate into your own ventures. To that end, I plan to make these more interactive going forward so you can play with these artifacts yourself.