That mathematics is dangerous stuff. According to the article, a single formula — the Gaussian copula — killed Wall Street. But according to this article, it’s all the fault of physicists. The only explanation I can come up with that makes sense of these two conflicting versions of events? Mathematics is dangerous only when it falls into the wrong hands.
The common thread through both articles is that the mathematics and those that could actually understand it were brought in by business droids that could not understand either. In reality the mathematics was done in a vacuum on selected historical data then applied by people who could barely pronounce it to situations that were not appropriate. If a monkey bought a gun you would expect it to be used inappropriately…
While I am of the opinion that the crash was not entirely caused by the quants (at which level I think it is meaningless to distinguish between mathematicians and physicists), it is disingenuous to claim that they were just innocent bystanders.
People aren’t just randomly pulled out of the streets and given these jobs. These quants have struggled and fought to get these jobs, often because they were disillusioned by their prior academic past and are hungry for the money. So, they are as much driven by greed and fear as the less academically gifted traders who work with them. In most cases, when the resultant analysis of a model is on a threshold of some major decision, I find it hard to believe that they didn’t subtly cooperate with the side that determined their annual bonus.
Having said that, of course, the larger course of events had little to do with the quantitative strategies. But the quants were as much part of the cultural setup that resulted in the bubble as the managers!
Ultimately the Gaussian copula was to price leverage, and as should be obvious from any leverage calculation, there is no limitation as to the direction or force of the effects of leverage.
In addition, quantitative data exists within a larger universe [remember those exogenous non-quantifiable variables], which is best sensed with intuition and qualitative reasoning. Further, any equation that does not include an error component is immediately suspect. Os, what about those goodness-of-fit tests?
And, trying to accurately predicate the future behavior of humans is, ultimately, an exercise in futility. Ask any psychologist.
If a monkey bought a gun you would expect it to be used inappropriately…
If a monkey bought a gun I’d be *extremely* impressed. Plus, I’d want to know who gave it the credit card…
I wish to clarify something here, in contrast with the two articles that seem to imply that mathematics somehow deceived some people. Mathematics are not an agent, it’s just a tool, that may be employed to various ends.
People in the financial world were not deceived by mathematics, they were deceived by their own greed (that is the ultimate cause of the present crisis), mathematics were just used to justify this greed, to rationalize it. In doing so, some mathematicians (coming from physics or mathematics) along with a part of the mathematical finance academia made themselves accomplice of the ongoing deception, which consisted in disguising good old irrational greed as mathematically sound.
However, for those who used mathematics honestly, in order to genuinely understand the markets, there was no doubt that the Gaussian model was irrelevant. Proper models of market behaviors exist, with a good data-fit, unfortunately, they don’t say things agreeable to the greed of speculators, and have therefore been carefully ignored for over 40 years, by financial academia.
JP
You’ve already shown your bias by the title of your post.
Interesting. I suppose this means that people should stay in their respective fields.
But it also has implications for the idea of what it means to be truly multidisciplinary.
Many academicians in the economic community are always looming over Wall Street, having them beware of triumphant theories. Burton Malkiel is one, just to pick an example off the top of my head.
NS
Another aspect of the stories is that many of these physicists and mathematicians gravitated to finance because of the money. Why is it that (at least in the US) research and professional work in these fields is less remunerative?
I am not familiar with the copula function, but based on the description provided in the article it sounds like it relies on circular logic. A formula for setting the price of securities is based on the price behavior of the securities. I suspect I am missing something. Could someone explain the underlying mathematical implications further?
Tim: That’s, to a surprisingly large extent, true. The copula-based models used to price CDOs and other structured financial products relied on market indices (like the Markit CDX indices http://www.markit.com/information/products/category/indices/cdx.html) to back out an implied correlation structure to price other securities. It is a bit circular, but it’s a common approach used in financial mathematics / economics: estimate some key pricing parameters from market data, then use your estimates to price something new. It works fine most of the time (emphasis on most).
When the CDO market seized up in mid-2007, the issue you mentioned was a large reason. When credit risk increased dramatically, people stopped trading CDOs and other such products. As a result, the market indices everyone had been using became unreliable. Thus, no one could accurately price these assets with internal models; to do so, they would have needed to make extremely strong assumptions about complex default correlation structures, and no one was prepared to put any money behind such assumptions. As a result, there was a vicious circle: no data meant no trading which meant no data etc. This also led to some tense situations on trading floors; I heard rumors of near fights between salespeople trying to get clients to trade and traders unwilling to quote prices without reliable correlation structures.
I hope that this illuminates things a bit.
actually, i think the crucial problem was the assumption that the correlation structure was constant through time. it is known even in quant research arms of banks that when the market tanks, correlation spikes. that is what happens when the housing market tanks - defaults spike. of course it is hard to incorporate this into the model.
What happened was not a failure of quantitative methods per se but rather a lesson in the perils of ignoring real-world complexities in favor of deceptively elegant shortcuts. What happened in essence was that the CDO market ran up against one of the most challenging of quantitative modeling problems: the dimensionality curse. This refers to what happens in complex environments where numerous variables interact with each other and all of the resulting combinatorial possibilities influence the economic value.
To continue reading this insight on this topic:
You Can’t Punt Away the Dimensionality Curse
http://blog.sentrana.com/2009/04/06/you-cant-punt-away-the-dimensionality-curse/
In Economic Modeling, Can Hindsight Lead to Foresight?
http://blog.sentrana.com/2009/04/21/in-economic-modeling-can-hindsight-lead-to-foresight/
Joe Smiley
Sentrana
http://www.sentrana.com