You keep using that word. I do not think it means what you think it means.

By Felix Salmon
January 28, 2013

This year’s Davos was all about tail risk — or, more to the point, the absence thereof. The ECB’s Mario Draghi said — more than once — that he had “removed the tail risk from the euro”. His colleague Ignazio Visco went almost as far, saying that only a few tail risks remain. The EU’s Olli Rehn talked about how there’s “no tail risk” any more. The IMF’s Zhu Min said that “In Europe, the tail risk has been moved off the table”, which was exactly the same language also used by Ray Dalio. Bank of America CEO Brian Moynihan said that “euro tail risk is now sorted”. The FT editorialized about the best policy response when “the tail risk of renewed financial chaos is reduced”. Even Nouriel Roubini declared that tail risks have declined in the past six months, although they haven’t gone away. And that was just the on-the-record comments: off the record, many more people, including at least one official US representative, were saying the same thing.

It was enough for both incoming Bank of England chief Mark Carney and UBS’s Alex Weber to start cracking jokes about how tail risks had been reduced on Wednesday and downright eliminated by Friday. As Stephanie Flanders says, Davos wouldn’t be Davos if people weren’t constantly talking about the need to avoid complacency — but for once, this year, “there seemed a genuine risk of it breaking out”.

There’s a worrying trend here, and it’s not complacency. Rather, it’s the use of the term “tail risk” to mean “priced-in and foreseeable euro crisis”. Last year, everybody was worried that Greece could end up leaving the euro, and those worries were reflected in European markets. This year, those worries have abated somewhat. But please, let’s not use the term “tail risk” to refer to such things.

We live in a fat-tailed world: everybody at Davos would probably agree on that. But here’s what none of them seem to understand: tail risks, by definition, can’t be measured. If you can look at a certain risk and determine that it has gone down, then it’s not a tail risk: it’s something else. Let’s say that last year there was a 25% chance that Greece would leave the euro: if something has a 25% chance of happening, it’s not a tail risk any more, it’s just a risk. If you’re planning a trip to the Grand Canyon, you might think about buying travel insurance to cover yourself in the event you are seriously injured. But when you’re right up at the edge of the canyon and the ground starts slipping beneath your feet, at that point you have to actually do something to avoid injury or death. The risk has gone from being theoretical to being real — and at that point it’s not a tail risk any more, it’s a real possibility with a scarily high probability.

The World Economic Forum spends many millions of dollars every year looking at risks both imminent and remote. It’s a useful exercise, and helps to remind us how complex the world is: with so many moving parts, it’s impossible for anybody to have much success as a predictor of the future. What’s not a useful exercise is to try to quantify the world’s risks, and to make determinations as to whether the tails are getting thinner.

And it’s certainly not a useful exercise, when markets have calmed down a little, to turn around and say that something as momentous as a fully-fledged euro crisis was only ever a “tail risk” to begin with. It wasn’t: it was much more imminent than that, and in order to avert it the EU had to venture far into the realm of policy actions which only a few months earlier would have been unthinkable. (Including effectively writing off a large amount of the money Greece owes the official sector.)

Tails are the realm of unknown unknowns. They can be positive, like the discovery of antibiotics, or they can be negative, like the uncovering of Bernie Madoff. In markets, they’re not even real-world events at all: they’re just any large move of say three standard deviations or more. Such moves happen almost every week, in some market somewhere, and they happen pretty much randomly. Measuring risks is good; seeing those risks diminish is pleasurable. But let’s not refer to measurable risks as “tail risks”. Because tail risks are always hidden, and unexpected.

11 comments

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Welcome to the world of having a perfectly good industry term being abused by everybody Felix. See also :
http://www.catb.org/~esr/faqs/hacker-how to.html

Posted by dandraka | Report as abusive

Tail risk has different meanings in different contexts. In the medical community, it refers to the risk of litigation after you have stopped practicing, or have switched jobs – times where your normal malpractice insurance would have changed.

I think Draghi is using tail risk to refer to risks that arose that were unforeseen. In that case, the problems in Greece, Spain and Ireland should not be viewed as tail risk, but the cost of the monetary union. Hoocoudanode?

If he is merely taking about an asset price moving more than 3 standard deviations from its mean, he is using the term correctly. He can keep Greece’s bond prices within 3 std-dev’s from their mean, especially now since their volatility has dramatically increased their sigma. However, there are problems in addition to merely Greece’s bond prices.

Normal distributions are ridiculous in some situations. First, most asset price movements are bounded by 0. That stock you bought can go to zero, but not below. However, it could go from 10 to 10,000. You will have a hard time capturing that behavior in a normal distribution. Yes, law of large numbers, blah, the risk being measured is the price of a single asset.

Bond prices are also somewhat limited on the high end. Who would pay $10,000 for a bond with $10 par value (and not a collector’s item). You could think of interest rate movements that could generate that, but you’d have to start out at a very high rate. However, a lot of complicated math has been built upon the foundation of the Gaussian distribution. Undoing the use in instances where the Gaussian does not tether to real events would be a positive.

Posted by winstongator | Report as abusive

I don’t think it means what you think it does either, Felix.

Tail Risks and Fat Tails do not have to be “unknown unknowns”, they are just outcomes that indicate a severely non-normal distribution of outcomes, so that people who are used to stability or are caught unprepared. Something that is widely discussed, like Greece leaving the euro, is a legitimate tail risk as a result of its low generally assumed probability, even if its fallout cannot be precisely calibrated, which is what makes it a “known unknown”. Martian invasion is also a tail risk, one that cannot seriously be contemplated in any kind of scenario planning.

To illustrate: let’s play a card game where you pay $1 per draw, but if you get dealt the ace of spades you win $52. The expected value of a single draw is zero, but you almost always lose; the standard deviation is $7.2 which makes drawing the ace of spades a 7-standard-deviation event. It is the tail risk.

Now, if we modify the game so that you don’t shuffle after every draw, and after playing a while there are two cards left, one of which is the ace of spades, I’d agree that it is no longer a tail risk event. But even while a few people thought a Grexit was likely, it was never the markets’ view that the outcome had a high likelihood, except perhaps for a few weeks in mid-2012.

Posted by TheUberDave | Report as abusive

Oddly enough, Donald Rumsfeld made the best quote regarding tail risk:
“As we know, there are known knowns: There are things we know we know.
We also know there are known unknowns: That is to say we know there are some things we do not know.
But there are also unknown unknowns: The ones we don’t know we don’t know.”

At the time, it just seemed nonsensical on the surface, but like a Mickey Mantle quote, it quite simply tells you exactly what you need to know.

It is impossible to price in risk that you’re not aware of.

Posted by GRRR | Report as abusive

“tail risks, by definition, can’t be measured”

I don’t know whose definition you are using but there is a whole branch of statistical literature (Extreme Value Theory) devoted to measuring tail risks. It originated in the study of (I think) floods, and is routinely used in insurance, finance etc.

Posted by Th.M | Report as abusive

I will not type “tail risk was eliminated from the EU when DSK was replaced by Christine Lagarde.”

A year ago, a Grexit went from being tail risk to being mainstreamed. Now, Cyprus and Portugal have joined Greece, while Draghi pretends that countries with 20%+ unemployment (Eire, Latvia) are “recovered.”

The “tail risk” right now is that people will realise that the combination of risks that have been mainstreamed means that German banks are insolvent. Fortunately, no one will ever realise that.

Posted by klhoughton | Report as abusive

I was going to echo what Th.M was going to say, but I think there is an issue of phrasing. For instance, I can take S&P500 returns and fit a t or stable distribution and obtain Conditional Value at Risk (CVaR) to measure tail risk. However, what these policy makers are talking about isn’t tail risk in the sense of measured CVaR. They are basically talking about black swans or Knightian uncertainty. They know that the probability of a Greek default scenario has declined, even if they cannot formulate the distribution of securities prices in the event that it would occur.

Posted by jmh530 | Report as abusive

A bit of both, maybe. There is no precedent for exiting the Euro, but there are some for sovereign default, and “tail risk” might refer to the last one.

Posted by Th.M | Report as abusive

Taking definitions from Investopedia and Wikipedia, tail risk is:

“A form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution”

and

“Tail risk is sometimes defined less strictly, as merely the risk (or probability) of rare events”

So, expanding on the points from Th.M and jmh, I would say that tail risks encompass far more than unknown unknowns. Those are a component of tail risk, but it also encompasses events that could be foreseen but are viewed as extremely low probability (3 standard deviations is a 0.03% probability of occurring). Call them “knowns viewed as more improbable than they actually are.”

I agree that by the time people are thinking about an event as having a 25% chance of happening, it is no longer a tail risk.

Posted by realist50 | Report as abusive

I think I saw a porn flick called Euro Tail Risk?

Posted by Woltmann | Report as abusive

Great article and great comments.

Posted by M.C.McBride | Report as abusive