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On tail risk

Investors must be on guard against tail risk – the small chance of extremely bad outcomes
January 29, 2019

The collapse of Patisserie Valerie reminds us of something that matters for all investors – tail risk.

This is the small chance of a disaster – that an apparently sound company can suddenly collapse because of fraud, bad management, an ill-judged takeover or being on the wrong side of technical change. Such risks are greater than you might think. Official figures show that 12.2 per cent of companies ceased trading in 2017. While the death rate for older and larger companies is much smaller than this, it is still significant, especially over the longer term – as investors in HMV or Carillion know.

Tail risk doesn't just affect individual equities but the whole market. A study of global stock markets in the 20th century by William Goetzmann and Philippe Jorion showed that "major disruptions" such as wars, revolution or financial crisis "afflicted nearly all the markets" that existed in the early 20th century. Less dramatically, big falls in prices are very possible. Since 1985 there have been six months in which the All-Share index has fallen more than 10 per cent. That’s twice as many as you’d expect if returns were normally distributed.

All of which raises the question. Does it pay to take tail risk?

Obviously it doesn’t if the risk materialises. But of course it often doesn’t: it is after all a small risk.

In fact, two things tell us that investors have actually been over-compensated on average for the danger.

One comes from a study of US corporate bonds by the London Business School’s Stephen Schaefer and colleagues. They’ve found that over the long run yields have been higher than justified by the number and scale of defaults, implying that investors have been well paid for taking this particular tail risk.

Another is the equity premium: since 1900 UK equities have out-performed gilts by an average of 3.7 percentage points per year. This is more than can be justified by ordinary volatility – hence the equity premium puzzle. And while some of it might be due to the risk of disaster, not all of it has been. Which again suggests investors have been over-compensated for taking tail risk.

Of course, tail risk isn’t just about bad things. There is also a slim chance of huge returns on some stocks. But we know that investors pay too much for this. New York University’s Robert Whitelaw has shown that US investors pay too much for lottery-type stocks. The fact that Aim shares have underperformed the All-Share index since the market’s inception in 1995 tells us the same is true in the UK. In fact, the same thing happens in sports betting: people pay too much for bets with long odds.

The pattern, then, seems clear: investors are over-compensated for negative tail risk but pay too much for positive tail risk. Sadly, however, this does not mean this will continue to be the case. People sometimes learn from their mistakes and so might have eliminated this mis-pricing: low spreads between lower- and higher-quality bonds suggest that this is more likely to be the case in bond than stock markets.

Tail risk, though, matters in another way. Changes in it cause prices to move more than they otherwise would.

The future is a probability distribution: we should think of it as an x per cent chance of one realisation, a y per cent chance of another, and so on. A share price today is the probability-weighted average of these different possible scenarios. This means that prices will change if tail risk does.

Let’s take a very simple example. Imagine there were just two scenarios for the FTSE 100 later this year – one in which it enjoys a moderate rise, taking it to 7300, and one in which tail risk materialises pushing it down to 5200. If there’s an 80 per cent chance of the former and 20 per cent chance of the latter, then the index today will be 6880 which is what it is as I write: (0.8 x 7300) + (0.2 x 5200) = 6880. If however the chance of a crisis were to fall to 10 per cent then the index would rise to almost 7100. This would happen even though moderate returns remain the most likely outcome and a crisis unlikely.

Granted, this is a simplified example. But it highlights an important point – that the market can rise, perhaps by a lot, not because the most likely scenario becomes better but because tail risk diminishes. This is why we often see big price rises after the end of bear markets, such as in 2009: it’s not that the economy looks much stronger, but that investors believe the chance of catastrophe has been averted.

Herein lies perhaps the best hope for the market this year. Yes, the economic outlook seems lacklustre: the US will slow and the eurozone and China grow only slowly even if they do recover. But above-average dividend yields and foreign selling of US shares both suggest that investors are worried a lot now about tail risk. If we avoid disaster these worries will diminish. And this will drive prices higher even if the global economy grows only moderately.