# Why the math blew up....

Interesting article in Alphaville (FT) today about a paper that goes into the gory details about how the mathematical assumption behind most of the pricing models that blew up last year was flawed at the most basic level.

Chart 1 is Exhibit A…

Those curves, short term v long term, could be replicated almost everywhere in the inputs that went into the pricing models.

Base your model on a data set (multi-years) that gives you a 'Golden Decade" curve (light color) and sooner or later you have a market reversion to mean that gets you back closer to the ‘Whole Sample’ curve (dark color). Those bits of the dark curve on either side of the light curve are what caused financial instruments to blow up and bankrupt the banking system.

Just read that the majority of CDO’s written on ABS’s have now defaulted. Who said those calculus classes were n’t going to be useful in real life…

There’s a real problem with including bubbles in the mean. Mean reversion theory postulates (as far as I understand it) that an excess will head towards the mean and overshoot it before coming up to it on the other side. But if you include the bubble in your calculation of the mean, then of course it will overshoot as it heads to an underlying mean (i.e. mean excluding the bubble). If we are to believe we are in a thirty year bubble (starting in 1979ish), then we should be looking at an mean based on the previous trend-line. I suspect the mean would look very different.

That is, of course, if you believe that any system reverts to mean and is not simply chaotic - regular in an irregular way.

PSst. so far from understanding any of the little maths that I learned that I am almost certainly talking bollocks…

Thats the problem with the mean, it keeps changing…

Like all complex multi-variate systems the financial system has a tendency to return to some equilibrium point but as the system is dynamically evolving and the relationships between the variables are slowly (or sometimes quickly) changing the long term equilibrium point can get stuck for long periods of time in strange places. The data set for property prices over very long periods of time show this tendency. But over very long time periods the effect of bubbles on the mean tends to be dampened out.

For the current debt bubble implosion the change in investment psychology will be long term. Just like the 1930’. So I’ll think we will have a full reversion with a noticeable overshoot and then long term semi-stability. They wont be able to blow a bubble another asset inflation bubble for a quite a while . The start of Baby Boomer pension draw down will guarantee this.

“Measures of kurtosis - the fatness of the tails "
Kurtosis, I like it and I can’t wait to use it.
" your dog is very kurtotic!”

I think we should blame Excel for the current crisis!
If we werent able to analyse a multitude of risks, measure historical distributions, apply those to the future etc…Then maybe, just maybe we would have used the Old “back of the envelope” mentality in assigning whether the black swan was around the corner…Common sense would probably have been more accurate!!

I always thought that kurtosis is what you got from eating too many gyros.

You see quite a few kurtotic older women in Greece…

Modelling did take over from good judgement but it would , would it not, when the rating agencies gave everyone an AAA score no matter what pile of poo they cooked up as an asset class .

I think the book on the blow up of LTCM first made this connection… no spreadsheets, no modern finance. Not just financial engineering but almost all M&A activity depended on serious number crunching.

So it is all Dan Bricklins fault…

The Dutch studied the population and noted they were getting a bit fat . Then a mathematics guru got his hands on it

studweb.north.londonmet.ac.uk/~s … ower23.pdf

and off they went to do their thing

Like the fuck like . And they were not finished

Right . Is there a fucking conclusion here ??

In other words they are getting fatter but we cannot agree on a model .

They are still getting fat

Reminds me of a paper I read years ago that proved, using Bayesian analysis and stochastic partial differential equations, that there is a strong correlation between the ratio of equations to body text in a paper and a) lack of anything substantive and original to say and b) desperation to get on the tenure track.

I think it took them 6 pages of equations and five pages of footnotes for the proof. Pretty terse, all things considered…

There is an interesting topic in here somewhere. Let me try to dig it out for you.

Francis Galton was the victorian genius who came up with the idea of The Widsom of Crowds. The story is that when hundreds
of people guess the weight of an ox at a fare, you get a normal distribution of results with average = the weight of the ox.

Deh market fundamentalists use this idea to argue that the market prices stuff correctly, because it distills the wisdom of thousands of
market participants. And this often works. For a lot of stuff, like the probability of a rate cut at the next ECB meeting, the market is the best guide
you will get.

For other stuff, the market provides no guide at all. Basically any events with a fat-tailed distribution. Like the growth of google, the severity of a war,
the size of an earthquake, the depth of a credit crunch. These are scalable, can get arbitrarily large, and ordinary statistics don’t work. Estimates of risk based on the variance of historical data are wrong because the variance does not exist in reality (its infinite). Nassim Taleb calls this world extremistan.

By pretending that the real world is like a casino, where risk is bounded and predictable (Taleb calls this world mediocristan), financial risk managers greatly underestimate risk.

This is Nassim Taleb’s black swan argument. It makes a nonsense of modern financial economics.

Thats why you get dopes like Goldman Sachs head of risk David Viniar talking about 25-sigma events. A 25-sigma event can never happen in mediocristan. It just proves their risk models are wrong, which the dogs on the street now know anyway.

There is no fix for this. In future large insititutions will not be allowed to concentrate financial risk.

Hey, you found the fix!

I fear the lesson may not be learned so well.

This is either the event that breaks the markets completely - or frighteningly, the one that shows them that they will always have a safety net - if so the drunk with liver disease would like one more drink please Mr. Barman!

“That is, of course, if you believe that any system reverts to mean and is not simply chaotic - regular in an irregular way”

Chaos is often used in this way, but in fact that’s not what chaos is. Chaos isregular in an iregular way; i.e. chaotic systems are predictable provided you have an accurate measurement. Personally I think the term ‘chaos theory’ is a misnomer. The system is chaotic until it starts, then it becomes predictable, but arguably, every system is chaotic until it starts!!

The other point is the models used by banks. From what I’ve read, they are really no different than the models used by LTCM (Long Term Capital Management). These guys almost brought down the system in the 90’s, after that happened, the system started using models that were scarily close to the LTCM models as their models for how much capital they need to keep in reserve. Basically NO LESSONS WERE LEARNED BY THE COLLAPSE OF LTCM.

I don’t want to get into the moral hazard brought about by saving the system back then (I only mention it now to prevent it coming up later!!).

You’re right, I should have said “dynamic in a non-linear way”…

Actually there is nothing wrong with the math that goes into pricing models and risks models. There is nothing wrong with the theory and implementation of derivatives. What just happened was mainly a failure of regulators by allowing over extended periods of time the chronic and systemic deliberate misuse of both the math and implementation of derivatives.

The instruments that blew up first were those that were not exchange traded, there were no market signals to rein in the exponential growth. CDS’s and CDO’s being a good example. Nothing inherently wrong with either and nothing inherently opaque about them either, once you understanding the nuts and bolts of how they are put together. This is not rocket science.

The main problem with risk models was the Basle II mandated use of VaR methodologies. Other methodologies predicted and weathered the storm a lot better than VaR.

As for Taleb, like all very rich and very intelligent quants he thinks that because he is very rich and very intelligent that he has some special insight into how the world works. He has some very interesting observations to make but is ultimately facile. I’ll take Frank Partnoy any day.

Oh dear, I agree with almost none of that, sorry.

I am intrigued by

VaR and its variants is the industry standard. Which other risk-management methodologies are you referring to?

From Frank Portnoy’s Infectious Greed:

I believe Mr. Portnoy and Mr. Taleb are saying the same thing, just looking at it from different ends. Mr. Portnoy is saying VaR is broken because the models used do not (cannot) adequately convey the amounts at risk. Mr. Taleb tells us why this is the case (standard deviation-based models exclude ‘weird shit’ events. ‘Weird shit’ is the most expensive type of event that can happen; why? because if it wasn’t weird, it would be within the bell curve and if it wasn’t shit, you’d make a lot of money.

My weekend reading was a huge cache of internal handbooks and research docs from Morgan Stanley, JP Morgan, Lehman Bros, et al covering most derivate instruments. Gives one a very different view from the short summaries one sees else where or the view one gets from the financial engineering books and papers.

After walking though a worked example of a particular CDO or CDS for example one has a very good idea of exactly what the mechanics is. I know that the final documentation for an issue runs to many hundreds of pages (or more) and that there can be some real nasties in the fine print, but that’s what all those very high paid analytical minds (legal and quant) are paid for.

So the math, at least the more esoteric stuff, was just pure obfuscation to make the instruments sound more whizzy and sophisticated than they actually were.

If I remember correctly I read discussions on both the Wilmott forum and The Institutional Risks Analyst site, to name but two, about the subject over the last few years. Not my area of interest but the gist was the superiority of actuarial based methodologies over financial model driven ones if I remember correctly.

I dont have my risk management text books to hand but I remember VaR as just one of at least a dozen different methodologies for assessing and quantifying risk.

Taleb approached the problem as a quant, Partnoy as a lawyer. So I think Partnoy got the bigger picture. Taleb books descend pretty quickly into a wishy washy quant world view of things, whereas Partnoy is suitably outraged and takes a lawyers world view of how to stop the more dangerous and disingenuous practices and create a more stable system before it is too late.

But it was too late. Too many people were making too much money from the Cargo Cult. And too many politicians got off from having to make difficult and unpopular decisions while the waterfall of cheap credit continued.