"The Fat-Tailed Straw Man
My Time article about the quant meltdown of August, 2007 started 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 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 of the "where did that come from" variety. I am firmly in the camp of those who understand there are unanticipatable risks; as far back as an article I co-authored in 1985, I have argued for the need to recognize that we face uncertainty from the unforeseeable. To get an idea of how far back the appreciation of this sort of risk goes in economic thought, consider the fact that it is sometimes referred to as Knightian uncertainty.
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. Weird stuff happens. 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 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 unexpected 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 a 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. This cycle evolves unrelated to historical relationships, out of the reach of VaR-types of models, but that does not mean it is beyond analysis.
Granted it is not easy to trace the risk of these potential liquidity crisis cycles. To do so with 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 regulator. 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."
Me:Don said...
"An exogenous shock occurs in a 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."
I look at this through a Fisher lens. It seems to me that one problem is that the leverage, while high, appears contained if it can be wound down in a contained manner, which it often is. What needs to be added is panic, which precludes an organized and efficient winding down, because its effects go outside of the immediate investment environment. So, while focusing on leverage and linkages seems like a good idea, panic, once started, is hard to predict or contain. So we need to ask if there is a way to preclude panic, in the way that FDIC insurance is used to preclude bank runs.
Truthfully speaking, following Bagehot, if there is a LOLR, it is going to be assumed to be a guarantor. Yet, ideas of insurance seem to be too expensive for banks or too little to cover losses.
The solution, to me, is to have a government guaranteed narrow/limited banking system, alongside a regulated/self-insured/non-guaranteed financial sector. Hopefully, because there is a LOLR, and a solid banking system under it, along with some insurance, perhaps bought from the government, that would be enough to stop a Calling Run breaking out system wide.
The problem with assessing risk is that it can vary. In one instance, it can be contained, in another, it can't.
As best as I can tell, VaR, CDSs, CDOs, have valid uses. In hearing calls for banning them or other investment instruments, we're involved in a kind of Debt-Deflation of human ability. We've gone from hubris to impotence and skipped the sensible middle. It doesn't seem to me to be a valid argument that, since we can't predict everything, we can't predict anything. There is also a difference between not seeing risk, and ignoring it. I think that our situation was caused by the latter.
Don the libertarian Democrat
Posts
Here's a post I came across today which says some of what I was trying to say, as a simple citizen:
"Modelling financial turmoil through endogenous risk"
http://www.voxeu.org/index.php?q=node%2F3243
It begins:
"Financial crises are often accompanied by large price changes, but large price changes by themselves do not constitute a crisis. Public announcements of important macroeconomic statistics, such as the US employment report, are sometimes marked by large, discrete price changes at the time of announcement. However, such price changes are arguably the signs of a smoothly functioning market that is able to incorporate new information quickly. The market typically finds composure quite rapidly after such discrete price changes.
A crisis feeds on itself
In contrast, the distinguishing feature of crisis episodes is that they seem to gather momentum from the endogenous responses of the market participants themselves. Rather like a tropical storm over a warm sea, they gather more energy as they develop. As financial conditions worsen, the willingness of market participants to bear risk seemingly evaporates. They curtail their exposures and generally attempt to take on a more prudent, conservative stance.
However, the shedding of exposures results in negative spillovers on other market participants from the sale of assets or withdrawal of credit. As prices fall, measured risks rise, or previous correlations break down, market participants respond by further cutting exposures. The global financial crisis of 2007-9 has served as a live laboratory for many such distress episodes."
Don the libertarian Democrat
This point of endogenous responses is what I am talking about with the liquidity crisis cycle, discussed towards the end of the post.
In that cycle, what makes for the endogenous acceleration of the initial exogenous shock, and thus precipitates the crisis, is the leverage of the participants, which forces them to liquidate. This in turn drops prices further, forcing more liquidation. And, as I point out in this post and in other places (including my book), the next step is selling in other markets, leading to contagion.