Article here.
You will notice many similarities to the gambling universe. Including correlation, data mining, and bet sizing.
You will notice many similarities to the gambling universe. Including correlation, data mining, and bet sizing.
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What do you think Ganch?
Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk.
Probability
Specifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.
Survival times
The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.
Equality
A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.
Copula
This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.
Distribution functions
The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.
Gamma
The all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.Comment -
another excerpt...
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.
The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's—or anybody wanting to model the risk of a tranche—no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.
As a result, just about anything could be bundled and turned into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them—an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function.Comment -
Do these math equations take into account incompetence, greed etc etc..Comment -
Good read Dark Horse, thanks.
I see similiarities to Ponzi's too, primarily in this excerpt.
In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.Comment -
It's a clear article that even with a few minor mathematical inaccuracies does a good job of simplifying a complex problem.
The tale told is a familiar one on Wall Street. Fat tails and variable correlations are ignored or brushed aside and with a wave of the hands and an implicit appeal to the Central Limit Theorem every distribution is assumed to be firmly and eternally Gaussian.
Nicholas Nassim Taleb (quoted at the end of the article) discusses these issues in his classic Fooled By Randomness.Comment -
And when at last the Devil came, it was not as a cruel tyrant, nor as a beautiful woman, or a monstrous beast, or anything else one might associate with ultimate destruction. No. It slipped in under the radar in the form of perfection, with just one slight error. The Mother of all temptation, that brought a nation and world to their knees, and to tears, and to sheer panic, came in the most innocent garb of ..... a mathematical formula.
MWUAHAHAHAHAHAAAAAA
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