Thursday, April 30, 2009

But I will never understand why banks held these assets on their balance sheets

From Free Exchange:

"Further thoughts on copulas
Posted by: | NEW YORK
Financial markets

OUR RECENT post on the Gaussian copula generated many outstanding comments. Commenter chaintzean offers a defence of the proposition that quants did not appreciate the limitations of their models:

Working as a quant in credit I hear a lot of this "don't blame the formula, blame the people who trusted it wrongfully" argument. I think it's beside the point. The astonishing growth of structured credit was not a consequence of the appearance of quotes based on an oversimplifying formula; it merely facilitated the fulfillment of a growing financial need.

A better statement would go along the line that the gaussian copula was not strong enough a model to prevent a crisis that was already in the making, just like the "pre-smile" option pricing of the 80s cannot itself (or its wrongful use) be held responsible (in a causal sense) for the Black Monday.

The world today is neither much smaller nor less complex than it was before the crisis. While the pricing method will evolve in order to account for the weaknesses of the previous approach, structured credit is bound to come back, in the long run, to levels close to where it was before the crisis; the financial need is still there.

It's a sentiment I've heard from other quants. The argument faults the insatiable demand for the holy grail in investment: predictable, high returns hedged from any downside. It cites the appalling management and cultural divide that exists in many banks. The business side demanded products that could deliver. The quants were charged with creating these perfectly hedged vehicles. Management accepted the products and their stamp of approval from rating agencies. Banks and investors made lots of money and demanded more of the same. There's just one problem: The existing models (and technology) cannot, and perhaps never will, provide a high return and low risk under all circumstances.

You might argue that this only shows these models are dangerous because they promise something they cannot deliver. But that misses the point. They can deliver lower-risk investment at higher returns when used properly. Financial models provide invaluable guidance and information about market risk. But proper use involves accepting a model's limitations and tempering them with good business sense.

I've built financial models under a variety of different management styles. The better managers (who often lacked quantitative skills) asked about the assumptions I made and forced me to explain, in simple terms, what my model did. It was often a painful process, but in retrospect it improved my modeling skills. If some managers at financial firms accepted models blindly, without performing the necessary diligence, then they did not do their job. It does not reflect an innate failure of the model.

To be fair, if such managers did their jobs properly it may have meant putting the breaks on building and selling these products. Chaintzean points this out in another comment:

[F]or a number of structured products the financial need is somehow driven by considerations other than profit or value. For instance, buyers of super-senior protection are sometimes forced into buying for regulatory purpose, almost "at any cost", one might say.

If buyers demand these products at any price, banks are unlikely to eschew them. But I will never understand why banks held these assets on their balance sheets. Surely someone must have known there is no such thing as a high-return-zero-risk investment. If something seems to good to be true, it probably is.

The other comments are great too, I recommend reading the full thread. "


Don the libertarian Democrat wrote:

April 30, 2009 17:34

I think that the problem has to do with the name. Here's Gauss:

"Johann Carl Friedrich Gauss (IPA: /ˈ?aʊs/, De-carlfriedrichgauss.ogg Audio (help·info), German: Gauß, Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy and optics. Sometimes known as the Princeps mathematicorum[1] (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.[2] He referred to mathematics as "the queen of sciences."[3]

Gauss was a child prodigy. There are many anecdotes pertaining to his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day."

So, he was a great mathematician, and he's been dead for a while. I wonder how he feels having this copula named after him. I just took a look at this paper:

On Default Correlation: A Copula Function Approach
David X. Li

I can't find Gauss mentioned at all. So, what if it had been call David Li's Copula, or Mario's Copula, or, better yet, Ponzi's Copula. Let's say that it's the exact same copula. Would people have found it as trustworthy? I rather doubt it.

By the way, here are a few quotes from that paper:

"Surprising though it may seem, the default correlation has not been well
defined and understood in finance."

Count me as not surprised.

"However the choice of a specific period like one year is more or less arbitrary"

I love the precision of math.

"The probability of dying within one year for a
person aged 50 years today is about 0.6%, but the probability of dying for the same person within 50 years is
almost a sure event. Similarly default correlation is a time dependent quantity"

Put it like that, and we might want to call it the Grim Reaper's Copula. Any takers?

"Also there are strong links between the economic cycle and defaults."

Sorry chaps, no excuses after reading that.

"1A company who is observed, default free, by Moody’s for 5-years and then withdrawn from the Moody’s study must have
a survival time exceeding 5 years. Another company may enter into Moody’s study in the middle of a year, which implies that
Moody’s observes the company for only half of the one year observation period. In the survival analysis of statistics, such incomplete
observation of default time is called censoring. According to Moody’s studies, such incomplete observation does occur in Moody’s
credit default samples."

Good work Moody's.

"Let us consider an existing security A. This security’s time-until-default, TA, is a continuous random variable
which measures the length of time from today to the time when default occurs. For simplicity we just use T
which should be understood as the time-until-default for a specific securityA"

See how easy it is?

"The function S(t) is called the survival function"

I wonder if this phrase was used in the marketing?

"Rating agencies reacts much slower than the market in anticipation of future credit quality. A typical
example is the rating agencies reaction to the recent Asian crisis.
• Ratings are primarily used to calculate default frequency instead of default severity. However, much
of credit derivative value depends on both default frequency and severity."

Now you tell us.

"Frank Copula The Frank copula function is defined as"

Well, there goes my thesis. Anyway, the paper is interesting and not that hard to follow, even for the mathematically inept like me. Give it a read.

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