Risk management’s perpetual-motion machine: Part 2, the magic elixir
Yesterday’s post on the quest for a magic machine to quantify correlation among disparate individual risks took us, via a terrific Wired Magazine article [Hat tip: Matthew Healy], to the point of understanding that different risks correlate differently, and if we knew their correlation rates, we could design appropriate financial instruments and appropriately price the risks.
We needed a wizard, and one soon had wizardry thrust upon him:
David X. Li
Enter Li, a star mathematician who grew up in rural
Li’s trajectory is typical of the quant era, which began in the mid-1980s.
Up, and then down …
Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics PhDs were required to create, price, and arbitrage Wall Street’s ever more complex investment structures.
In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled “On Default Correlation: A Copula Function Approach.” (In statistics, a copula is used to couple the behavior of two or more variables.)
You try finding a Google image for copula!
Using some relatively simple math—by Wall Street standards, anyway—Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.
I’ve posted at length about credit default swaps as unlicensed insurance:
What is a credit default swap? From nowandfutures.com.
Thus, if Phyllis Dietrichson thinks her husband might die, she can buy a CDS from Walter Neff, and if Dietrichson dies, she wins big.
“I have a terrible premonition my husband may die.”
CDS’s are derivatives, in that instead of being secured by an object or item itself (a mortgage representing a piece of property), CDS’s are secured by other securities – indeed, by a slice of another security.
If you’re an investor, you have a choice these days: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income stream—interest payments or insurance payments—and either way, if the borrower defaults, you lose a lot of money. The returns on both strategies are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn’t constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly.
Once you get the bugs out, the thing runs forever
Also, because a CDS is a side bet, it can motivate the holder to root for the insured’s demise:
“I bet he croaks soon.”
“We bet he won’t.”
– The essential bargain in Credit Default Swaps
I think he’s very ill – lead poisoning?
As we saw yesterday, even as a Credit Default Swap has something in common with a life-insurance policy on a third party, it’s also a risk concentrate and risk shifter. [Snip] I’ve previously described them as risk moonshine or balance sheet turbochargers.
Financial eggheads used them as building blocks in “synthetic” CDO-type structures, which are based on CDSs rather than actual bonds. The market value of some tranches has slumped to less than ten cents on the dollar. And CDSs share some problems with securitisation. A paper last year by economists at the Federal Reserve Bank of
There’s the rub: opacity. For opacity implies unstated mendacity, and mendacity has an obnoxious odor.
“I smell the obnoxious odor of opacity!“
With the benefit of hindsight – I never knew anything about CDS’s until the recent unpleasantness – I think they were way, way too dangerous an instrument for investors and I’m astonished that anybody bought them. (I’m not astonished they were packaged and sold, since if it will be bought, it will be manufactured and sold.) Nevertheless, I’m an old fogy, and when first created, CDS’s were nifty, since being unconstrained by connection to physical assets, they could be printed up at warp speed.
Even ludicrous speed!
When the price of a credit default swap goes up, that indicates that default risk has risen. Li’s breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market.
Except – except that everybody knows markets move for all kinds of reasons, many of them irrational. As reader Matthew Healy – who sent me the link to this article, thanks! – put it in his email to me:
I’m hardly an expert in high finance, but it seems to me the fundamental mistake was that Wall Street got seduced by an elegant formula into thinking the map was the territory.
“The map is not the territory” – Alfred Korzybski
Because they wanted to be seduced.
But I’m a nice derivative …
It’s hard to build a historical model to predict Alice’s or Britney’s behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice.
Don’t try to predict Britney’s behavior
If it did, then there was a strong correlation between Alice’s and Britney’s default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).
Dr. Li may be a brilliant mathematician, but he’s obviously never traded stocks, or worked with financial instruments.. People are periodically crazy – frequently crazy – and the idea that markets re perfectly rational is right up there with the perpetual-motion machine as a grand folly.
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.
Too good to be true.
No really, it’ll give you muscles, too
In a five-part post (Part 1, Part 2, Part 3, Part 4, and Part 5), I’ve already excoriated the ratings agencies as willing enablers of this absurd risk-taking:
You know the old saw about the freshman in their first law school lecture? “Look to your right, gentlemen; look to your left. One of you will be gone in three years.” If S&P, Moody’s and Fitch were sitting on a bench together, I’d advise them:
Prediction: within five years, one of the three agencies will be out of business.
Possibly bankrupt, possibly taken over by a consortium of irate investors who’ve lost sums and need to re-establish credibility of the ratings function.
It’s a given they’re going to get sued. (This is
It doesn’t matter if they’re culpable. What matters is if the markets lose confidence in them. For the agencies, their reputation is critical. What is a rating agency if no one trusts it?
Worse than a crooked referee
Regarding Dr. Li’s formula, the ratings agencies should have known better, and you will have to go some distance to convince may they didn’t know better.
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.
In Parts is Parts, I lambasted the implausibility of blending discarded mortgage parts into prime cuts.
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.
At about this point, I start feeling sympathy for Dr. Li. He would have disavowed any such castles-upon-castles.
As always, should any of these instruments default, the secretary will disavow any knowledge of your actions
The CDS and CDO markets grew together, feeding on each other. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.
It grew 20x in six years.
At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion.
In six years, the CDS market grew to 70x its original size. Those are staggering, unbelievable numbers, both for the growth and for the notional value – roughly ten times the size of the
At the heart of it all was Li’s formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable.
Beautiful, simple, and tractable?
“The corporate CDO world relied almost exclusively on this copula-based correlation model,” says Darrell Duffie, a
As always, there are skeptics, and as in all bull markets, they went unheeded:
The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that “the correlations between financial quantities are notoriously unstable.” Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. Investment banks would regularly phone Stanford’s Duffie and ask him to come in and talk to them about exactly what Li’s copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.
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.
You might as well face it you’re addicted to risk
In finance, you can never reduce risk outright; you can only try to set up a market in which people who don’t want risk sell it to those who do. But in the CDO market, people used the Gaussian copula model to convince themselves they didn’t have any risk at all, when in fact they just didn’t have any risk 99% of the time. The other 1% of the time they blew up.
Look, it was statistically unlikely
Those explosions may have been rare, but they could destroy all previous gains, and then some.
[Continued next week in Part 3.]
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