Stock markets and coronavirus – an endogenous perspective

Markets collapse when they’re in a vulnerable state. Coronavirus might be the straw that broke the camel’s back – this time – but there’s no clear pandemic to stock price causality.

The predominant explanation for this week’s steep decline in the stock market is coronavirus. I take this as evidence that the pandemic of open-loop, event-based thinking is as strong as ever.

First, let’s look at some data. Here’s interest in coronavirus:

It was already pretty high at the end of January. Why didn’t the market collapse then? (In fact, it rose a little over February). Is there a magic threshold of disease, beyond which markets collapse?

How about other pandemics? Interest in pandemics was apparently higher in 2009, with the H1N1 outbreak:

Did the market collapse then? No. In fact, that was the start of the long climb out of the 2007 financial crisis. The same was true for SARS, in spring 2003, in the aftermath of the dotcom bust.

There are also lots of examples of market crashes, like 1987, that aren’t associated with pandemic fears at all. Corrections of this magnitude are actually fairly common (especially if you consider the percentage drop, not the inflated absolute drop):

Wilshire Associates, Wilshire 5000 Full Cap Price Index [WILL5000PRFC], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/WILL5000PRFC, February 28, 2020.
So clearly a pandemic is neither necessary nor sufficient for a market correction to occur.

I submit that the current attribution of the decline to coronavirus is primarily superstitious, and that the market is doing what it always does.

It’s hard to do it justice briefly, but the stock market is basically an overlay of a complicated allocation mechanism on top of the real economy. In the real economy (green positive loop) capital and technology accumulation increase output (thinking strictly of on-market effects). Growth in that loop proceeds steadily in the long run, but with bumps from business cycles. The stock market is sending signals to the real economy about how to invest, but that’s complicated, hence the dashed line.

In the stock market, prices reflect expectations about the future flow of dividends from the economy (blue negative loop). If that were the whole story, coronavirus (orange) would have to have induced fears of a drop in the NPV of future profits of about 10%. Hopefully that’s way outside any plausible scenario. So why the big drop? It’s due to the other half of the story. Expectations are formed partly on fundamentals, and partly on the expectation that the market will go up, because it’s been going up (red positive loop).

There are actually a number of mechanisms behind this: naive extrapolation, sophisticated exploitation of the greater fool, redirection of media attention to prognosticators of growth when they’re right, and so on. The specifics aren’t important; what matters is that they create a destabilizing reinforcing feedback loop that inflates bubbles. Then, when some shock sufficient to overcome the expectations of appreciation arrives, the red loop runs the other way, as a vicious cycle. Diminished expected returns spark selling, lowering prices, and further diminishing expectations of appreciation. If things get bad enough, liquidity problems and feedback to the real economy accentuate the problem, as in 1929.

Importantly, this structure makes the response of the market to bad news nonlinear and state-dependent. When SARS and H1N1 arrived, the market was already bottomed out. At such a point, the red loop is weak, because there’s not much speculative activity or enthusiasm. The fact that this pandemic is having a large impact, even while it’s still hypothetical, suggests that market expectations were already in a fragile state. If SARS-Cov-2 hadn’t come along to pop the bubble, some other sharp object would have done it soon: a bank bust, a crop failure, or maybe just a bad hot dog for an influential trader.

Coronavirus may indeed be the proximate cause of this week’s decline, in the same sense as the straw that broke the camel’s back. However, the magnitude of the decline is indicative of the fragility of the market state when the shock came along, and not necessarily of the magnitude of the shock itself. The root cause of the decline is that the structure of markets is prone to abrupt losses.

For a nice exploration of these dynamics, from the complexity/nonlinear dynamics thread of systems science, see Didier Sornette’s Why Stock Markets Crash: Critical Events in Complex Financial Systems.

Coronavirus Roundup

I’ve been looking at early model-based projections for the coronavirus outbreak (SARS-CoV-2, COVID-19). The following post collects some things I’ve found informative. I’m eager to hear of new links in the comments.

This article has a nice summary, and some

Disease modelers gaze into their computers to see the future of Covid-19, and it isn’t good

The original SIR epidemic model, by Kermack and McKendrick. Very interesting to see how they thought about it in the pre-computer era, and how durable their analysis has been:

A data dashboard at Johns Hopkins:

A Lancet article that may give some hope for lower mortality:

The CDC’s flu forecasting activity:

Some literature, mostly “gray” preprints from MedRxiv, all open access:

A podcast with some background on transmission from Richard Larson, MIT (intestine alert – not for the squeamish!):

This blog post by Josh at Cassandra Capital collects quite a bit more interesting literature, and fits a simple SIR model to the data. I can’t vouch for the analysis because I haven’t looked into it in detail, but the links are definitely useful. One thing I note is that his fatality rate (12%) is much higher than in other sources I’ve seen (.5-3%) so hopefully things are less dire than shown here.

I had high hopes that social media might provide early links to breaking literature, but unfortunately the signal is swamped by rumors and conspiracy theories. The problem is made more difficult by naming – coronavirus, COVID19, SARS-CoV-2, etc. If you don’t include “mathematical model” or similar terms in your search, it’s really hopeless.

If your interested in exploring this yourself, the samples in the standard Ventity distribution include a family of infection models. I plan to update some of these and report back.

S-shaped Functions

A question about sigmoid functions prompted me to collect a lot of small models that I’ve used over the years.

A sigmoid function is just a function with a characteristic S shape. (OK, you have to use your imagination a bit to get the S.) These tend to arise in two different ways:

  • As a nonlinear response, where increasing the input initially has little effect, then considerable effect, then saturates with little effect. Neurons, and transfer functions in neural networks, behave this way. Advertising is also thought to work like this: too little, and people don’t notice. Too much, and they become immune. Somewhere in the middle, they’re responsive.
  • Dynamically, as the behavior over time of a system with shifting dominance from growth to saturation. Examples include populations approaching carrying capacity and the Bass diffusion model.

Correspondingly, there are (at least) two modeling situations that commonly require the use of some kind of sigmoid function:

  • You want to represent the kind of saturating nonlinear effect described above, with some parameters to control the minimum and maximum values, the slope around the central point, and maybe symmetry features.
  • You want to create a simple scenario generator for some driver of your model that has logistic behavior, but you don’t want to bother with an explicit dynamic structure.

The examples in this model address both needs. They include:

I’m sure there are still a lot of alternatives I omitted. Cubic splines and Bezier curves come to mind. I’d be interested to hear of any others of interest, or just alternative parameterizations of things already here.

The model:

Vensim: sigmoids 1.mdl (works in PLE, Pro, DSS)

Ventity: Sigmoids 1.zip

 

Assessing the predictability of nonlinear dynamics

An interesting exploration of the limits of data-driven predictions in nonlinear dynamic problems:

Assessing the predictability of nonlinear dynamics under smooth parameter changes
Simone Cenci, Lucas P. Medeiros, George Sugihara and Serguei Saavedra
https://doi.org/10.1098/rsif.2019.0627

Short-term forecasts of nonlinear dynamics are important for risk-assessment studies and to inform sustainable decision-making for physical, biological and financial problems, among others. Generally, the accuracy of short-term forecasts depends upon two main factors: the capacity of learning algorithms to generalize well on unseen data and the intrinsic predictability of the dynamics. While generalization skills of learning algorithms can be assessed with well-established methods, estimating the predictability of the underlying nonlinear generating process from empirical time series remains a big challenge. Here, we show that, in changing environments, the predictability of nonlinear dynamics can be associated with the time-varying stability of the system with respect to smooth changes in model parameters, i.e. its local structural stability. Using synthetic data, we demonstrate that forecasts from locally structurally unstable states in smoothly changing environments can produce significantly large prediction errors, and we provide a systematic methodology to identify these states from data. Finally, we illustrate the practical applicability of our results using an empirical dataset. Overall, this study provides a framework to associate an uncertainty level with short-term forecasts made in smoothly changing environments.

Eroding Environmental Goals

In System Dynamics we typically refer to this as the eroding goals archetype, or the boiled frog syndrome:

Shifting baseline syndrome: causes, consequences, and implications

With ongoing environmental degradation at local, regional, and global scales, people’s accepted thresholds for environmental conditions are continually being lowered. In the absence of past information or experience with historical conditions, members of each new generation accept the situation in which they were raised as being normal. This psychological and sociological phenomenon is termed shifting baseline syndrome (SBS), which is increasingly recognized as one of the fundamental obstacles to addressing a wide range of today’s global environmental issues. Yet our understanding of this phenomenon remains incomplete. We provide an overview of the nature and extent of SBS and propose a conceptual framework for understanding its causes, consequences, and implications. We suggest that there are several self‐reinforcing feedback loops that allow the consequences of SBS to further accelerate SBS through progressive environmental degradation. Such negative implications highlight the urgent need to dedicate considerable effort to preventing and ultimately reversing SBS.

CAFE and Policy Resistance

In 2011, the White House announced big increases in CAFE fuel economy standards.

The result has been counterintuitive. But before looking at the outcome, let me correct a misconception. The chart above refers to the “fleetwide average” – but this is the new vehicle fleetwide average, not the average of vehicles on the road. Of course it is the latter that matters for CO2 emissions and other outcomes. The on-the-road average lags the standards by a long time, because the fleet turns over slowly, due to the long lifetime of vehicles. It’s worse than that, because actual performance lags the standards due to loopholes and measurement issues. The EPA puts the 2017 model year here:

But wait … it’s still worse than that. Notice that the future fleetwide average is closer to the car standard than to the truck standard:

That implies that the market share of cars is more than 50%. But look what’s been happening:

The market share of cars is collapsing. (If you look at longer series, it looks like the continuation of a long slide.) Presumably this is because, faced with consumer appetites guided by cheap gas and a standards gap between cars and trucks, automakers are doing the rational thing: they’re dumping their cars fleets and switching to trucks and SUVs. In other words, they’re moving from the upper curve to the less-constrained lower curve:

It’s actually worse than that, because within each vehicle class, EPA uses a footprint methodology that essentially assigns greater emissions property rights to larger vehicles.

So, while the CAFE standards seemingly require higher performance, they simultaneously incentivize behavioral responses that offset much of the improvement. The NRC actually wondered if this would happen when it evaluated CAFE about 5 years ago.

Three outcomes related to the size of vehicles in the fleet are possible due to the regulations: Manufacturers could change the size of individual vehicles, they could change the mix of vehicle sizes in their portfolio (i.e., more large cars relative to small cars), or they could change the mix of cars and light trucks.

I think it’s safe to say that yes, we’re seeing exactly these effects in the US fleet. That makes aggregate progress on emissions rather glacial. Transportation emissions are currently rising, interrupted only by the financial crisis. That’s because we’re not working all the needed leverage points in the system. We have one rule (CAFE) and technology (EVs) but we’re not doing anything about prices (carbon tax) or preferences (e.g., walkable cities). We need a more comprehensive approach if we’re going to beat the unintended consequences.

Rise of the Watt Guzzler

Overconsumption isn’t green.

Tesla’s strategy of building electric cars that are simply better than conventional cars has worked brilliantly. They harnessed lust for raw power in service of greener tech (with the help of public subsidies – the other kind of green involved).

That was great, but now it’s time to grow up. Not directly emitting CO2 just isn’t good enough. If personal vehicle transport continues to grow exponentially, it will just run into other limits, especially because renewable electricity is not entirely benign.

The trucks on the horizon are perfect examples. The Cybertruck consumes nearly twice the energy per mile of a Model 3 (and presumably still more if heavily loaded, which is kind of the point of a truck). That power is cheap, so anyone who can afford the capital cost can afford the juice, but if it’s to be renewable, it’s consuming scarce power that could be put to greener purposes than stroking drivers’ egos. It’s also consuming more parking and road space and putting more rubber into waters.

When you consider in addition the effects of driving automation on demand, you get a perfect storm of increased depletion, pollution, congestion and other side effects.

The EV transition isn’t all bad – it’s a big climate mitigation enabler. But I think we could find wiser ways to apply technology and public money that don’t simply move the externalities to other areas.