It would be nice to think that this crisis was a huge math error. Some geek in a cubicle hit the wrong button on his HP12-C. Doh! Alas, it is not the case. Any error this pervasive is not from some obscure assumption, but an assumption that everyone was comfortable with. If an obscure technical assumption drove investors into various bonds, there should be a large group of investors who would have quants who disagreed, and they would have not been exposed. That is, quants may have no common sense, but on obscure technical results, they are smart and often disagree. Yet not one of the major investment banks worldwide escaped this craze. It's as if all the geeks thought the 5th digit of Pi was 6.
The only reason everyone made the mistake was that it was from an assumption that everyone seemed to think was reasonable, something quants did not have the authority to affect: that housing prices would not fall significantly. Look at Shiller's updated Irrational Exuberance from 2005, and there's a chapter on the Housing Bubble, where he notes that recent housing price increases 'probably won't continue', hardly a clarion call to avoid housing.
When everyone is doing something, and think it's right, the quants will perforce generate supporting documentation. Scientists in that way are like lawyers, advocates not for a paid client, but rather, the ephemeral verities of the current zeitgeist. With $4B for global warming research, and much less for anti-global warming research, it is no surprise many scientists are documenting various evidence of global warming: people like the results, they aren't as skeptical, more likely to get published, get a grant, get on a government project, etc.
UBS used a 10-day Value-at-Risk on its residential mortgage backed portfolio to assess its risk, using data from the benign 2000-2005 period. This was an error. But UBS was going to invest in mortgages anyway, because presumably this collateral does not decline much if ever, so this was all standard rationalization of preconceived objectives.
Felix Salmon wrote a piece in Wired, where he fingers the copula function as the primary culprit.
And (David) Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.
He then quotes some quants, like Darrell Duffie, who states that "corporate CDO world relied almost exclusively on this copula-based correlation model". Well, derivatives textbook authors might like to believe that their formulas underlie most financial activity, but I suspect the number of people using copulas in their sales pitch was low, no more than 5%, because most investors, big shots who actually make portfolio decisions, do not like pretentious mathematics. Perfunctory metrics may be ubiquitous, but they are still perfunctory. The decision makers are rich, powerful, kind of smart, do not feel embarrassed by their lack of knowledge in obscure technical trivia, and surely are not intimidated by it. Of that limited set, the copula itself, irrespective of the broader knowledge about mortgages and housing price trends, was probably the driver of 10% of those purchases, because even for investors who like formulas, most require a bigger picture. Thus, I generously estimate about 0.5% of all mortgages were bought because of David Li's Frankenstein formula.
Copulas, value at risk, correlations, credit scores, one might add standard deviations, means, and Microsoft Excel's 'solver'. These concepts can get tricky, but the basic assumption, that housing prices would not fall significantly, was not tricky, and people with the authority to make decisions were not swayed by these technical issues, rather, they used them to validate their earlier beliefs. Further, you can't avoid them. My favorite flâneur, Nassim Taleb, notes in the article that
"Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."
Well, I would agree that anything that 'relies' on a specifically precise correlation is a bad idea, but that is merely about accurately assessing the correlation's standard error, an eminently feasible objective. To say something is not measurable, or can not be relied on at all, even after making accommodations for the standard errors of correlations, is simply untrue. You make an assumption about correlations whether you want to or not. For example, if you assume 'nothing', that could be that the correlation is 0. But then you get too much expected diversification. You could assume the correlation is 1.0, but then you would never own a portfolio of risky assets, which is generally suboptimal. You could assume correlations are -1.0, but then the hedges would appear to work too well. You could assume correlations move randomly between -1.0 and 1.0 (correlations being bounded at -1 and +1), but this would imply various dispersion trades based on mean reversion in correlation. Thus, saying one should avoid estimating worst-case scenarios (eg, Value at Risk), or expected returns (averages), standard deviations, etc., do not realize that you can't avoid them. Even if you say you are not 'using' them, you are making an assumption about them implicitly.
Now, one could try to make one's portfolio robust to various assumptions in correlations and Value at Risk, etc., and this would then necessitate various discussion of particularities with the strategy in question, the data, comparable data from similar asset classes or other countries, etc. This all gets very detailed rather quickly, and is considered a special case not relevant to the generalization that correlations, Value at Risk, or copulas are useless.
But every case is detailed like that. It's like people who say, 'my company has a lot of petty politics', as if most, or even some companies work on an Olympian plain where ideas are discussed honestly, without pretext, and projects are always chosen for their stated reason. The statement 'my strategy makes no assumptions', is both pretentious and illogical.
So leave the geeks alone. They merely prove what the suits want them to prove.
