On Tails

Tail events, in probability speak, are extreme events with the potential for a very large impact but which have a very low likelihood of occurring. Many people (I think accurately) view the most recent financial crisis as the occurrence of a tail event: it was highly unlikely that the system would experience such a drastic collapse, but it happened. We might consider the change of nuclear war or alien invasion as a tail risk. In N. Nassim Taleb’s The Black Swan, Taleb discusses the dangers of such risks with an analogy: even if you have encountered thousands of swans in your lifetime, and have never seen a black swan, you cannot entirely be sure you won’t someday come across a black one. There is still a very small likelihood this rare event can occur.

Now, seeing a black swan doesn’t have to turn your world upside down, but if major financial or political decisions are based on assuming that highly improbable events are impossible, there can be catastrophic consequences if one such event actually comes true. We might be able to say the probability of alien invasion of Earth is 0.00000001, but we can’t say that the probability of alien invasion of Earth is 0. And this is a big difference.

But one oft-ignored side of the equation is that tail events don’t always have to be on the downside. In fact, Taleb suggests there can be a big payoff if an unlikely but extremely lucrative event occurs. Chris Dillow describes:

A tweet from Lily Allen raises some interesting economic issues:

About 5 years ago someone asked me to stream a gig live on second life for hundreds of thousands of bitcoins, ‘as if’ I said. #idiot #idiot.

This reminds us that tail risk – the small chance of extreme outcomes – isn’t just on the downside. It’s also on the upside. Which raises the question: is it wise to chase such upside risk, as Nassim Nicholas Taleb advises in The Black Swan?

I think Chris is on the right track when he then suggests we often focus on our regret in such situations. At the time, the offer presented to Ms. Allen likely seemed crazy, and how can we distinguish between the perhaps hundreds of crazy offers, schemes, and opportunities out there? How do we appear when we are willing to entertain a potentially crazy idea in the hopes of cashing in on the tail?

Now, after the fact, we lament the missed opportunity and are tempted to call it a failure in judgment. But in reality, we will miss countless opportunities in our lives to have become billionaires, and we barely think about it. Dillow:

Every choice we make (or don’t) closes off some opportunities; all choice carries an opportunity cost. We could therefore spend our lives regretting the countless shares we might have bought when they were dirt cheap, the horses we didn’t back, the job offers we might have accepted, the partners we might have met had we bothered to go to that party, and so on. But if we did this, we’d just be crippled with remorse.

There’s a good reason and a bad reason why we’re not. The bad reason lies in a variant of the availability heuristic. Often, we don’t see where the road not taken would lead, so its costs and benefits aren’t available to us – and out of sight is out of mind. This heuristic, I suspect, explains why Ms Allen should single out rejecting that gig; its costs are now salient, which is unusual for a rejected option.

We should remember that tails matter on both the downside (being aware that even alien invasions and financial crises are possible) and the upside (maybe this silly “Bitcoin” thing will catch on).

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