Tail risk is everywhere

You can be forgiven for thinking that tail risk is especially prominent in banks. We can all remember that they nearly collapsed entirely, and in The Black Swan, Nassim Nicholas Taleb pointed out that banks were especially neglectful of tail risk.

However, by one measure at least, banks are no more prone to tail risk than most shares.

My table shows the point. It shows the number of weekly changes in sectors' prices of three standard deviations or more since January 1997. If returns were normally distributed, you'd expect to see just one rise and one fall of three standard deviations or more in this period. This is because a normal distribution implies that a three standard deviation fall is a 0.13 per cent probability and there have been 971 weeks since January 1997.

Number of three standard deviation weekly price changes since January 1997

However, for almost all sectors – tobacco being the only exception – falls of this magnitude are more common than this. Sectors' returns are better described by a cubic power law than a normal distribution; such a law predicts there should be 6.5 falls of three standard deviations or more in 971 weeks.

And here's the thing. Banks are not especially prone to big falls. They've seen three standard deviation losses in six weeks since 1997 – the same as retailers have seen, and fewer than some industrial sectors have suffered. Yes, you're more likely to lose a lot on banks than retailers – banks have seen 11 weekly losses of more than 10 per cent whilst general retailers have seen just four. But this is because bank shares are more volatile, not because they carry more tail risk.

Instead, the amount of tail risk is remarkably even across sectors. There are (at least) three reasons why this is.

One is simply that most sectors don't have the support that banks have (or have had) in the form of an implicit guarantee of state aid if they get into trouble. The "too big to fail" syndrome means banks have a put option which limits their tail risk. Other companies, with the misfortune to operate in the freer market, do not have this advantage, and so are exposed to tail risk - the possibility of being completely wiped out.

Secondly, shares tend to be highly correlated, especially in bad times. If the market falls a lot, most sectors will suffer badly. Many of the sectors' three standard deviation falls have come in the same bad weeks for the market: September 2001, October 2008 and August 2011.

Thirdly, this is not a story about sectors so much as about investors' behaviour. And this is much the same towards all shares. Investors are occasionally prone to herd and panic, and to try and sell the same shares at once.

But not just sell. My table shows that upside tail risk - three standard deviation rises - is about as common as downside risk. Herding works both ways; sometimes investors try to pile into the same stocks.

This fact, though, is not as comforting as it seems, because as the Nobel laureate Daniel Kahneman has pointed out, people tend to be loss averse; losses loom larger than gains. He's estimated that to compensate for the prospect of a £1000 loss, the average person needs a similar prospect of a £2000 gain.

But equities don't offer this; upside tail risk isn't that great. Instead, the reward for taking downside tail risk lies in getting a slight preponderance of small gains over small losses on average over the long-run.

For especially loss-averse investors, however, this might not be sufficient reward. In this sense, perhaps equity investing is not for everyone.