Of Mountain Lions And Market Tail Risks

Over the years, I have used the probability of mountain lion attacks as an example of a tail risk that I, as a trail runner in California, face every time I go out for a run in the wilderness. I know the statistics, that mountain lion attacks on humans are incredibly rare, so rare that in the last century only a couple dozen of humans have been attacked fatally in the state. But this does not cause me to relax when I am out on a long trail run, because my own actions can create an increased risk. In mathematical terms, the conditional probability of an attack goes up as I put myself in an environment that is more likely to contain a bold – and hungry — mountain lion.

Over the last few months, the semi-rural community in which we have some livestock has experienced the real risk of thinking purely statistically. A mountain lion (or maybe a group of them), has begun to attack livestock. Instead of hunting the very agile deer and coyotes, the lion(s) have been lurking on the outskirts of the community, and have opportunistically entered the community, day and night, to stake out small animals. Goats, dogs and sheep have gone missing. In response, the terrified community, which also has many small children, religiously followed the guidelines of the fish and wildlife commission and has begun to lock up livestock (not yet little children!) from dusk to dawn.

The lions have adapted to this, and being the predators they are, found ways around to get their prey. One of them jumped a metal fence, entered an enclosed space over three horse stalls, sauntered across the aisle of a horse barn, jumped another wall and dive bombed into the stall of two of our sheep and killed them last week, which was all recorded on motion sensitive video on our “sheep cam”. The lion then returned later to eat its kill numerous times, including later that evening, again recorded on live video. Fortunately no human was around at the same time in the same location.

The law in California (proposition 117) makes it illegal for mountain lions to be killed without a “depredation permit” (requiring three “strikes” against livestock), and only if the lion threatens human life, which has been critical in keeping the lion population from becoming extinct. But as in all things with many well-intended but poorly thought-out laws, there are unintended consequences and philosophical conundrums.

The conundrum is that while the law permits killing a lion that threatens a human, if it is bold enough to threaten human life, it might be too late to save that human life, especially if the life is that of a small child, which would appear no different than a hairless lamb to the lion. This is a very tough conundrum, since killing a mountain lion has many assorted costs, including the possible extinction of an amazing species, but not killing a rogue predator also has costs, including the possible loss of human life and almost certain loss of livestock and pets.


We see similar conundrums in the market today. If we think of an impending, debilitating market crash as a similar rare event, we really have two choices. We can either remove the risk (“depredation”), by exiting risky positions or purchasing insurance against market crashes. Or we can wait and see if the crash is ready to happen, and then hope to exit the market right before the crash. This latter, “just-in-time” approach to risk management is used by participants when the cost of hedging is considered to be too high. I have had the opportunity to present to many investment committees and boards over three decades, and the decision almost always boils down to this: should we (hedge) or shouldn’t we? In other words, it’s a decision between paying for managing the risk today against deferring the decision until the bad event seems imminent. The worst response is to blame one-self in hindsight with the statement: “I should have known better and done something different”.

The calculus of catastrophic risk mitigation fundamentally depends on the probability of the event in question, since we can agree that the severity in either case is quite extreme and destructive. So the question becomes one of forecasting the likelihood of an extreme market crash (or lethal human mountain lion attack). The question becomes harder to answer because very intelligent people (experts), including well-funded researchers and organizations, are on both sides of the question, effectively cancelling out each other. 

In the case of the mountain lion controversy, the anguish of the community was somewhat managed by a presentation by the leader of a mountain lion protection group, who eloquently argued that eliminating one lion was not only unlikely to solve the problem of livestock attack, but could actually increase the likelihood and long run risk because other, competing lions could move into the territory and go for the easy pickings rather than hunt deer. In the case of markets, the issue is no less confusing. Very sophisticated researchers, most with storied credentials and institutional backing, argue eloquently that hedging market risk will not help, since the cost of hedging will outweigh the benefits over the long run, and that avoidance or diversification is the better approach.

Faced with this confusing set of inputs, what is an investor (or rancher) supposed to do? First, it goes without saying that in either case, severity or exposure should be minimized. For instance, leaving animals unprotected or running massively levered portfolios is just asking for trouble. So reducing the potential severity, of course, is the first step. But having done that, what is our next step?

If the expected loss in either case arises from the product of the severity and the probability, then minimizing the probability of the severe event is the only other course. Unfortunately, in both cases the probability of the loss can be reduced, but not eliminated. Unless we have a crystal ball or some tool that allows us to forecast the probability of a very rare event, we are out of luck if we just wait to make the right decision in the nick of time. To my knowledge, and after three decades in the investment business, there are very few mathematical tools that can accurately forecast rare events and market crashes. Yes, we can start to anticipate rare events as somewhat more likely, but even then the quantitative probabilities of these events are likely to be off by many orders of magnitude. I have not been able to forecast market crashes with any accuracy, or a mountain lion attack for that matter, but there are indeed times when I feel queasy in both cases. If it’s any reassurance, most of the time when I feel queasy, nothing happens.

So we are faced with only main one decision: should we incur the cost today or not. This question is much easier to answer even without knowing the probabilities. All we need to answer is the counterfactual question: how severe will the consequences be if we do nothing and the rare event happens?

It is very easy to get emotional when faced with the picture of mountain lions killed by ranchers to protect their livestock, or by the video of a mountain lion attacking lambs (or suburban poodles). Scientists on both sides of the aisle can pick the data that best supports their thesis (and life’s work and funding sources) to move opinion in their direction. I know this, because my own training is in the hard sciences, and even in the hard sciences, selective reasoning occurs very frequently, especially when research funds are tied to it.

Killing mountain lions willy-nilly is illegal as well as cruel, regardless of the experience, emotions and opinions of folks affected by them, and surely there are good logical arguments on both sides. Fortunately for market participants the choice to hedge risk is neither illegal nor cruel. Given the levels of volatility and the massive buildup in leverage and asset prices, this question can be answered by each investor faced with the simple alternative: how bad will I feel if the market crashes and if I have done nothing to protect my investments?

We see that implied volatilities in the options markets have collapsed as the markets have rallied to record highs. While COVID and its impact on markets was unforecastable, it was still hedge-able, and those who did so were able to come out of 2020 very well. We are in a similar situation today. We have no idea what’s on the horizon, but by all metrics, even these unknown risks are yet again quite hedge-able.

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