The Fat-Tailed Straw Man

I started my Time article about the quant meltdown of August, 2007 with “Looks like Wall Street’s mad scientists have blown up the lab again.” Articles on Wall Street’s mad scientist blowing up the lab seem to come out every month in one major publication or another. The New York Times has a story along these lines today and had a similar story in January.

There is a constant theme in these articles, invariably including a quote from Nassim Taleb, that quants generally, and quantitative risk managers specifically, missed the boat by thinking, despite all evidence to the contrary, that security returns can be modeled by a Normal distribution.

This is a straw man argument. It is an attack on something that no one believes.

Is there is anyone well trained in quantitative methods working on Wall Street who does not know that security returns have fat tails? It is discussed in most every investment text book. Fat tails are apparent – even if we ignore periods of crisis – in daily return series. And historically, every year there is some market or other that has suffered a ten standard deviation move.

Is there any risk manager who does not understand that VaR will not capture the risk of market crises and regime changes? The conventional VaR methods are based on historical data, and so will only be an accurate view of risk if tomorrow is drawn from the same population as the sample it uses. VaR is not perfect, it cannot do everything. But if we understand its flaws – and every professional risk manager does – then it is a useful guide for day-to-day market risk. If you want to add fat tails, fine. But as I will explain below, that is not the solution.

So, then, why is there so much currency given to a criticism of something that no one believes in the first place?

It is because quant methods sometimes fail. We can quibble with whether ‘sometimes’ should be replaced with ‘often’ or ‘frequently’ or ‘every now and again’, but we all know they are not perfect. We are not, after all, talking about physics, about timeless and universal laws of the universe when we deal with securities. And the place where the imperfection is most telling is in risk management.

When the risk manager misses the equivalent of a force five hurricane, we start to ask what is wrong with his methods. By definition, what he missed was a ten or twenty standard deviation event, so we tell him he ignored fat tails. There you have it, you failed because you did not incorporate fat tails. This is tautological. If I miss a large risk – which will occur on occasion even if I am fully competent; that is why they are called risks – I will have failed to account for a fat tailed event. I can tell you that ahead of time. I can tell you now – as can everyone in risk management – that I will miss something. If after the fact you want to castigate me for not incorporating sufficiently fat tailed events, let the flogging begin.

I remember a cartoon that showed a man sitting behind a desk with a name plate that read ‘risk manager’. The man sitting in front of the desk said, “Be careful? That’s all you can tell me, is to be careful?” Observing that extreme events can occur in the markets is about as useful as saying “be careful”. We all know they will occur. And once they have occurred, we will all kick ourselves, and our risk managers and our models, and ask “how could we have missed that?”

The flaw comes in the way we answer that question, a question that can be stated more analytically as “what are the dynamics of the market that we failed to incorporate.” If we answer by throwing our hands into the air and saying, “well, who knows, I guess that was one of them there ten standard deviation events”, or “what do you expect; that’s fat tails for you”, we will be in the same place when the next crisis arrives. If instead we build our models with fatter and fatter tailed distributions, so that after the event we can say, “see, what did I tell you, there was one of those fat tailed events that I postulated in my model”, or “see, I told you to be careful”, does that count for progress?

So, to recap, we all know that there are fat tails; it doesn’t do any good to state the mantra over and over again that securities do not follow a Normal distribution. Really, we all get it. We should be constructive in trying to move risk management beyond the point of simply noting that there are fat tails, beyond admonitions like “hey, you know, shit happens, so be careful.” And that means understanding the dynamics that create the fat tails, in particular, that lead to market crisis and sudden linkages between markets.

What are these dynamics?

One of them, which I have written about repeatedly, is the liquidity crisis cycle. An exogenous shock occurs in highly leveraged market, and the resulting forced selling leads to a cascading cycle downward in prices. This then propagates to other markets as those who need to liquidate find the market that is under pressure no longer can support their liquidity needs. Thus there is contagion based not on economic linkages, but based on who is under pressure and what else they are holding.

It is not easy to trace the risk of these potential liquidity crisis cycles. To do so with high accuracy, we need to know the leverage and positions of the market participants. In my previous post, “Mapping the Market Genome“, I argued that this should be the role of a market regulatory. But even absent that level of detail, perhaps we can get some information indirectly from looking at market flows.

No doubt there are other dynamics that lead to the fat tailed events currently frustrating our efforts to manage risk in the face of market crises. We need to move beyond the fat-tail critiques and the ‘be careful’ mantra to discover and analyze them.

Originally published at the Rick Bookstaber weblog and reproduced here with the author’s permisssion.

6 Responses to "The Fat-Tailed Straw Man"

  1. Anonymous   March 10, 2009 at 1:17 pm

    The question is not whether people believe in the normal distribution but whether they actually use the normal distribution.Additionally the advice be careful is actually useful. If you are careful you don’t take as much leverage.

  2. Anonymous   March 10, 2009 at 2:21 pm

    >> It is because quant methods sometimes fail.Shouldn’t this be “quant methods will eventually fail”. Its like playing Russian roulette but with an unknowable number of chambers instead of six. If you bet with enough leverage eventually you’ll blow up the firm. If you are lucky you’ll blow up the entire financial universe and get a bailout.

  3. Anonymous   March 11, 2009 at 3:26 am

    You are right that certain methodologies have practical utility in routine trading. You are wrong that the primary criticism is that fat tails should have been incorporated. The primary criticism is that these methodologies created a false sense of security for the dimwits in management. Moreover, the eggheads were simply to weak to make a strong case that dangers lurked in the shadows, even though symptoms like LTCM have popped up on numerous occasions in the past. The false sense of security spread all the way up the chain to the FED. It lead the financial services industrial establishment to build giant towers of leverage in a known earth quake zone. What would we say if Tokyo changed its building codes to ignore seismic risk?The quants do not have the muscle to steer the ship, therefore they should stay off the bridge.WilliamBanzai7MOVIN TO BERMUDA SOON GONNA BE A SUBPRIME LOSS TYCOON(Movin to Montana Soon, Frank Zappa)WilliamBanzai7Sing along link: might be movin’ to Bermuda soonJust to write me up a crop of structured subprime dross, Writin it upMarkin it downIn a little black boxThat I can sell downtownBy myself I wouldn’tHave no coins to toss,But I’d be writin my lowly Subprime drossWritin’ my lowly Subprime drossWell I just might hire me some quantitative geeksAnd I’d sell that geek stuffTo somebody else…but then, on the other handI’d Keep take some toxic subprime snacks N’ melt it downTake some geek greek sauce N’ swish it aroun’I’d have me a crop of crapAn’ it’d be AAA on top(that’s why I’M movin’ to Bermuda)Movin’ to Bermuda soonGonna be a Subprime loss tycoon(yes I am)Movin’ to Bermuda soonGonna be a structured loss flykune[Solo]I’m securitizing’ the ol’ Subprime drossThat’s growin’ in Greenspan’s scary bubblePluckin’ the dross!I plucked all day an’ all nite an’ all Afternoon…I’m ridin’ a small tiny hoss(His name is GAUSS)He’s a good hossEven though He’s a bit dim witted to strap a hedge straddle orsecurity blanket on anywayAny way I’m writin’ the ol’ Subprime drossEven if you think it is a little silly, folksI don’t care if you think it’s silly, folksI don’t care if you think it’s silly, folksI’m gonna find me a derivative counterparty horseWith a brain just about this bigAn’ ride him all along the inefficient frontierWith a Pair of heavy-dutyMagic alpha-encrusted tweezers in my handEvery other structured finance geek would sayI was mighty grandBy myself I wouldn’tHave no coin to tossBut I’d be writin’ my lowly Subprime drossWell I might Ride along the Level 3 borderWith my tweezers gleamin’In the moon-lighty nightAnd then I’d Get a cuppa cawfeeN’ give my CRO a kick in the tush…Just me ‘n the pymgy ponyOver the Subprime dross BushN’ then I might just Jumb back onAn’ ride Like a Wall Street cowboyInto the dawn to BermudaMovin’ to Bermuda soon(Yippy-Ty-O-Ty-Ay)Movin’ to Bermuda soon”Without deviation from the norm, progress is not possible.”Frank Zappa

  4. V. Ray   March 14, 2009 at 5:56 pm

    So, which is the American Airlines flight with a “fat tail” that I should not book for my upcoming trip from New York to Los Angeles?