### Tuesday, March 3, 2009

#### The techies understand.

##### Recipe for Disaster: The Formula That Killed Wall Street

For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels. *** This was definitely a catalyst to the crisis as it allowed "simple modelling of CDOs" ***

## 28 thoughts on “The techies understand.”

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## devo says:

“The techies understand” – but not enough to prevent causing financial Armageddon it would appear.

Ha Ha! Gotta laugh 51ck!

## Potnoddle says:

The real problem was Gaussian part of this function; the spread it’s gaussian isn’t nature it has a Lévy stable distributions; please see the Misbehavior of Markets: A Fractal View of Financial Turbulence.

## refusetobuy says:

One reason for failure I heard was that most CDO’s are CDO^2’s.

All the mortgages from a certain area were all bundled together and sold as one asset that was then bundled with other assets into a CDO. The problem was that the mortgages grouped by area also had a tranch like structure. The assets that were in the CDO were CDO’s themselves.

The correlation between CDO’s is quite high because they only default in a tail event, and the tail events are mainly caused by systematic risk, so tail risks tend to happen together. Use too low a correlations in a CDO model and you get too high a value for the CDO. Fine when you are selling them, awful when you have to take them back onto your book (and you now know their proper value).

The CDO model is a nice model, it was just used to model the wrong thing.

## yorkshireman says:

The formula did not kill Wall Street, the damn fools who applied it did.

## 51ck-6-51x says:

devo – I think you have the wrong end of the stick. The techies I refer to are those who write Wired, i.e. computer techies, who would have understood the problems if they were the ones designing the products, but they were not there, so they can only write about it after the event – although this does not imply that no-one understood the issues!

refusetobuy… CDO^2 is even more dangerous that’s true, but CDO is enough. You are correct that the fact that defaults become more correlated as more defaults occur is a big problem, and the fact that as more defaults occur recovery goes south does not help those Senior tranche holders much either!

I agree the model is a nice model …on it’s own. However modelling default risk on it’s own is not easy and correlation would appear to be even more unstable that volatility, especially when the correlation one is trying to model is in something as unobservable as default.

## 51ck-6-51x says:

yorshireman – how very true!

## letthemfall says:

An interesting article. The notion that a single constant reliably sums up complex information occurs fairly often in physics, but no one bets the house on it. Here lies the ultimate failure of mathematical modelling in finance – the long-term invalidity of the assumptions on which it is based.

## 51ck-6-51x says:

yorkshireman – excuse my typo!

## 51ck-6-51x says:

letthemfall – now you see where I’m coming from and why I think it’s important that people who want to make the system better should be studying the mathematics that has been used (and abused) in the pursuit of profit – yet I still get knocked for “being a banker” or a “financial engineer who caused this mess”, I like to think that most of the financial engineering driven market failures arise from a lack of thought rather than someone thinking how this idea will screw everyone over, but I may well be wrong.

## Dbc Reed says:

The Black Scholes formula, which got Nobel prizes, and is formidable to look at could n’t cope with the unexpected and Long Term Capital Management which had two of the Nobel laureates on board had to be bailed out in 1998.

## letthemfall says:

Hi 51ck

Well, I always thought I knew where you were coming from – as well as one can on a blog. I don’t actually know what you do, although you obviously know something about maths and stats, and I certainly don’t hold that against you, nor indeed your occupation, even if you are a banker! (I’ll cross myself just in case). I’m inclined to agree that the failures are not the product of malicious individuals, but possibly down in part to those who are perhaps overconfident in their abilities (and paid too much), as well as separation of management and analysts, as the article suggests.

Anyway, keep up the good posts. Watch out for the ankle biters.

## refusetobuy says:

More comments on Slashdot

## 51ck-6-51x says:

The mezzanine tranche is the most sensitive to correlation and it looks like the UK Taxpayer has just bought the biggest one ever:

The Mother Of All CDOs – Paul Wilmott

Agggh.

## 51ck-6-51x says:

^^ actually probably worth a post of it’s own…

## flashman says:

etthemfall & 51ck

“not the product of malicious individuals, but possibly down in part to those who are perhaps overconfident in their abilities”

“most of the financial engineering driven market failures arise from a lack of thought”

Both of these statements are reasonable assumptions, but in fact, the market failure was caused by a carnage of willful, deliberate, devil may care, profiteering. Some of the greatest minds in the world work in this industry (unfashionable comment now) but their collective intellect is only targeted at making obscene profits for themselves as quickly as possible. ‘Consequences are for poor people’. This man’s eloquent formula was used to throw a cloak of respectability over this con. That this guy won acclaim for his formula was ‘manna from heaven’. What a great cover! Everyone knew it would one day end in tears but nobody cared. Most people ,if offered the chance to earn a few million would do the same. No one cares about consequences, (particularly because they will affest other people), if they can retire at 40. Mathematicians in this industry are generally thought of as gullible nerds and stooges. Their work is only accepted if it aids the cause. Their efforts to model the industry with eloquent formulas will always be overwhelmed by the barbaric profiteering of market participants. The Black Scholes options pricing formula was similarly used, abused then discredited. Black and Scholes eventually lost all their money in the markets because they didn’t realise that traders could destroy any tidy formula or strategy they devised and even more crucially that anything that appears to work will provide an opportunity for abuse. There is an old book ‘when genius failed’, that illustrates this point beautifully

Please do not think I am criticising mathematicians. I am not. I have the greatest respect for their craft, but they are no match for the greedy bullies found on the trading floor..

## devo says:

13. flashman

A fascinating insight, which confirms many of my (our?) suspicions about where it all went wrong.

Thanks

## devo says:

51ck-6-51x

A few months ago you posted a link to a paper containing mathematical formulae of mind-boggling complexity. In fact I inferred from a footnote that only the author himself had a true understanding of his hypothesis!

Can you give an estimate of how many people, mathematicians or otherwise, truly understand the workings on which the trading described by flashman were based?

## bellwether says:

The problem wasn”t so much the rationale of the CDO’s within their abstracted frame of reference but the false assumption upon which they were built namely the economy and and value of the underlying assets (mostly property) cannot shrink.

In a sufficiently severe contraction everything is correlated.

## bellwether says:

I suppose underlying assumption suggests the assumption was acutally made, within the Flashman model it was more of a fraud or a lie that everyone was aware of but no-one cared

## Tenyearstogetmymoneyback says:

An interesting article.

Perhaps they should have used this branch of mathematics (which they seem to have completely ignored

http://en.wikipedia.org/wiki/Chaos_theory

Now we just have Chaos.

:- Duncan

## flashman says:

The banking industry has had several practice runs at this economic fiasco:

The Long Term Capital Management disaster almost brought the system down in 2000. The enormous leverage used by the hedge fund industries was implicated.

The Savings and Loan crisis of the 80 and 90’s caused massive budget deficits. One of its major causes was a slowing real estate market and eventually only massive government bailouts saved the day.

These scenarios are so eerily similar and so incredibly recent. With this in mind, how can anyone possibly believe that the consequences of over leveraged debt were unknown to the industry?

The Victorians called it ‘bad paper’ in their day. Even they would have known.

## bellwether says:

with Goverment complicit throughout

## devo says:

From the comments:

‘The model was doomed to fail as soon as housing prices started to fall’

Are you avin’ that 51ck?

Doesn’t sound like the most robust formula to underpin the global economy, but hey, what do I know?

## refusetobuy says:

@ Tenyearstogetmymoneyback

“Perhaps they should have used this branch of mathematics (which they seem to have completely ignored http://en.wikipedia.org/wiki/Chaos_theory”

Not ignored. Chaos theory is the basis for most computer based random number generation, on which the banking industry relies.

see http://en.wikipedia.org/wiki/Randomness#Generating_randomness

## phdinbubbles says:

@flashman

“Some of the greatest minds in the world work in this industry”

LOL. Some of the world’s most deluded minds more like.

@refusetobuy

“Chaos theory is the basis for most computer based random number generation”

Is it? All of the random number generators I’ve ever used are pseudo-random number sequences generated using simple formulae, seeded with the CPU’s clock.

@flashman

“These scenarios are so eerily similar and so incredibly recent. With this in mind, how can anyone possibly believe that the consequences of over leveraged debt were unknown to the industry?”

Quite, but does anyone with half a brain seriously believe that nobody saw this coming? It really doesn’t take a genius to work out that the profiteering, bullying, short-termist, make a huge pile of cash before it collapses culture within the financial services industry is mostly responsible for the subsequent and inevitable collapse.

## refusetobuy says:

Yep. Chaos only needs a simple formula to create complex results.

Compare the Park Miller algorithm to

the Mandelbrot set equation.

Both have a multiply and an add. The random number generator has the modulus function to make sure the number stays within bounds.

The Horseshoe mapping is a nice way of thinking about chaos. It’s a bit like kneading doh. A set of numbers gets mapped back onto itself, so bits of flour that started together could end up in any position to each other.

## refusetobuy says:

Sorry, I meant a Linear congruential generator, of which the park miller algorithm is a special case where nothing is added.

## 51ck-6-51x says:

devo said “Can you give an estimate of how many people, mathematicians or otherwise, truly understand the workings on which the trading described by flashman were based?” –

I don’t know to what trading you are referring. But there are many people who understand the mathematics, just probably not that many trading. I also agree with much of what Flashman said. As far as I know traders, generally, do not think about the mathematics, even if they are using the models, and often times the model will say one thing but their (or a colleagues) gut will say another, and there seems little replacement for this instinct. Furthermore there seems to have evolved a culture of short term positions which suit the narcissistic individual [credit to Paul Wilmott again for this] to which Flashman seems to point.

devo said “‘The model was doomed to fail as soon as housing prices started to fall'”

– yep I agree, although I would abstract to the credit bubble bursting, rather than it all being about houses themselves.