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Source link: http://archive.mises.org/9494/the-math-function-that-cratered-wall-street/

The Math Function That Cratered Wall Street

February 23, 2009 by

Can you imagine any reader of Human Action being fooled by this?

Teaser quote:

It was a brilliant simplification of an intractable problem. And Li didn’t just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number — one clean, simple, all-sufficient figure that sums up everything …

Read the whole thing. This has got to be the most powerful illustration yet of the fallacy of mistaking a math function for real phenomena in the market.

{ 10 comments }

geoih February 24, 2009 at 6:38 am

It’s amazing to me that otherwise intelligent people insist on treating human beings as if they are inanimate gas molecules that will act in a completely random, but collectively logical fashion.

I Hate Space Aliens February 24, 2009 at 7:15 am

Worse,

They treat human beings as if they are the property of the government, have no feelings or needs.

Cattle and wildlife is treated with more respect than humans.

ProudCapitalist February 24, 2009 at 7:51 am

To sum up the essence of the article, the error was to rely on the short history of CDS (credit default swap) prices as a model for future risks in house prices. CDS price history isn’t older that the 1990s and their volume 62-folded between 2001 and 2007.

So all data about house price risks was based on a period of exceptionally great credit expansion. Conclusions drawn from such were is of course not applicable during other circumstances. The model as it was applied, was basically based on only one single empirical observation…

The reason to use data from the CDS market with its short history, instead of the long series of housing prices directly, was lazyness. It would be quite complicated to derive the risk of a certain collateral debt obligation from the many kinds of properties from which its cashflow comes from.

But also, most people in this business DID make a lot of money. They took advantage of the situation. They’d been worse off if they had priced those obligations lower by factoring in real risk estimates. Credits isn’t a market anyway, interest rate isn’t a market price. So why should financial managers have pretended that they were market players? It’s gov planned a grab and run exercise.

Billy Beck February 24, 2009 at 9:58 am

“It’s amazing to me that otherwise intelligent people insist on treating human beings as if they are inanimate gas molecules that will act in a completely random, but collectively logical fashion.”

A reading:

“Political economists — including the advocates of capitalism — defined their science as the study of the management or direction or organization or manipulation of a ‘community’s’ or a nation’s ‘resources’. The nature of these ‘resources’ was not defined; their communal ownership was taken for granted — and the goal of political economy was assumed to be the study of how to utilize these ‘resources’ for ‘the common good’.

The fact that the principal ‘resource’ involved was man himself, that he was an entity of a specific nature with specific capacities and requirements, was given the most superficial attention, if any. Man was regarded simply as one of the factors of production, along with land, forests, or mines — as one of the less significant factors, since more study was devoted to the influence and quality of these others than his role or quality.

Political economy was, in effect, a science starting in midstream: it observed that men were producing and trading, it took for granted that they had always done so and always would — it accepted this fact as the given, requiring no further consideration — and it addressed itself to the problem of how to devise the best way for the ‘community’ to dispose of human effort.”

(Ayn Rand,“Capitalism: The Unknown Ideal”, 1966, New American Library, Part I, “Theory And History”, ch. 1, “What Is Capitalism?”, p. 4)

Pat February 24, 2009 at 10:13 am

This article is interesting in the sense that it tells only one part of the story. After all, it was the scope of the article. It is nothing new for those with some knowledge in quantitative finance (Of course, such knowledge is not necessary to realize mathematical functions cannot explain the market process. My exhibit A is the company present on this website).

One question I come out and I have been asking lately is the reason behind the push for mathematics in finance, especially when playing such a huge game. For example, it is a fact that a large number of investment banks had a leverage of 33-to-1 (http://mercatus.org/PublicationDetails.aspx?id=26042). The logic was that the bigger the leverage ratio was, the bigger the gains would be. Knowing that the financial sector is more regulated than any other private sectors (It is arguable, I recognize, to call the financial sector as unambiguously private), isn’t it surprising that banks would work on developing financial instruments in order to increase their profits? After all, their clients and themselves have needs to and monetary gains help fund those needs. Why, with all those cars, jets, and huge mansions. But my point is that those math equations were only the accomplices (Not even a good one). But the story is interesting from a quant perspective. So, kudos on the story.

Raja February 24, 2009 at 11:28 am

I remember taking a computational finance class during my masters (financial engineering) and thinking how absolutely simplified and divorced from reality the computational models used on wall street are, Gaussian copula included. Unfortunately, there is no alternative. They are simplified not because these quants really believe that a single correlation number can capture human behavior, but rather because anything more complicated will be either highly intractable or lack historical data, or both.

As Austrians, we should recognize the problems with this approach. However, that does not mean to imply that financial engineering or mathematical models are completely irrelevant in the markets. Although they rest on a false epistemology, that is mainly a problem in economics, not in finance. If one understands both the economics (Austrian, of course) and the math (it actually is quite novel and interesting how these models are designed) there are certainly many profitable applications.

I find that a lot people are over reacting to this crisis. The problem is not the mathematical models, tranching, risk shifting, or financial engineering in general. All of these serve a very important market function. The problem was the skewed incentives created by the Fed and the fiat fractional reserve system as well the government regulated environment. Although, I do agree that the financial engineering exacerbated the problem.

diego joachin February 24, 2009 at 12:36 pm

Fellows: misunderstanding models based on Gaussian principles by bankers is also part of human action.

Incentives are just not efficient across the financial industry, so let’s take some losses and rebuild a new business cycle.

As Mises noted, scarcity is the natural situation of human being.

Ken February 24, 2009 at 2:29 pm

What amazes me is that a correlation coefficient was treated as if it were anything other than orthogonal to causation (the parable of the sneaker companies in the Wired article illustrates why correlation and causation are orthogonal).

Criminy, I practically had to sign a paper saying, “Yes, I the undersigned do in fact recognize that correlation is not causation” before they let me fire up SAS for the first time. :-)

Vincent Cook February 24, 2009 at 3:42 pm

Bloomberg News ran an interesting series of articles offering the accounts of former insiders of the ratings agencies. It seems that people in positions of responsibility within these agencies did object to the use of the new quant models, but were overruled by higher-ups who were more interested in harvesting large fees for helping set up CDOs (the ratings agencies were actively involved in fixing tranche levels, etc.) than in preserving their reputation for the integrity of their ratings. SEC regulations make S&P, Moodys, and Fitch the gatekeepers to massive quantities of capital, so security issuers must still pay for their ratings services–integrity is expendable.

Another critical factor, which you can find buried in a paper on the Federal Reserve website, is that the new regulations for bank capitalization (known as Basel II) helped set the stage for the disaster. Prior to Basel II, banks would hold riskier non-conforming mortgages (i.e. the subprime, alt-A, jumbos, etc. that Fannie and Freddie wouldn’t buy) in their own portfolios, and maintain a hefty capital reserve as a hedge against correlated defaults.

Under the Basel II regime, banks could exchange these mortgages for the more highly rated CDO paper and get a substantial reduction in their capital requirements. In theory, they were merely selling the correlated default risk to other investors–that is, Basel II itself is based on the model, so the new international bank regulations were written accordingly.

In reality banks weren’t just selling the correlated default risk; they were also multiplying the correlated default risk, since the banks (and other mortgage lenders who got into the CDO game) no longer had the incentive to maintain the appropriate underwriting standards as they did when they held the mortgages themselves.

In addition to the CDO-squared phenomena mentioned in the article, there was also the problem that the originators of the CDO paper (the Wall Street investment banks) were also issuing massive quantities of related CDS paper to give the riskier CDO tranches the illusion of being less risky. The net effect of leveraged purchases of the riskier tranches and of issuance of unbacked CDS guarantees was to effectively eliminate any capital cushion. Once correlated defaults began to occur (as they always do in any bust phase of the business cycle), there was nothing to prevent the entire house of cards from collapsing.

ehmoran February 24, 2009 at 3:44 pm

I’ve built ground-water models, surface-water models, water-quality models, climate models, ecological models, etc., and even Stock Market models. All using higher math and sophisticated stats. The problem is you begin to believe the models too much and forget that predictions are based on past data. That’s your first mistake.

The second mistake, however, is often you don’t believe the models and the models were right because the model parameters themselves vary over time and you end up having to model the model or parameters.

The Black-Scholes derivative model is an example of a failed not-fully developed model that helped cause the DOT.com crisis. The Nobel model didn’t use enough historic data. The constants were wrong. And we can refer to many other Financial models.

Financial, Market, and Economic models need to account for human action. Mathematics can be used to do this, but when building these models, one must be able to explain the model in praxiological terms. I believe that’s the biggest mistake on understanding and developing these kinds of models.

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