Isegoria

Felix Salmon calls David Li‘s Gaussian copula function the formula that killed Wall Street:

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.) 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.

D’oh!

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.

All the ratings agencies needed was one variable, correlation, to rate a tranche:

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.

The CDS and CDO markets grew together, feeding on each other. 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. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.

We know it all doesn’t end well:

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 percent of the time. The other 1 percent of the time they blew up. Those explosions may have been rare, but they could destroy all previous gains, and then some.

Li’s copula function was used to price hundreds of billions of dollars’ worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.

Managers didn’t understand how the black box worked:

Bankers should have noted that very small changes in their underlying assumptions could result in very large changes in the correlation number. They also should have noticed that the results they were seeing were much less volatile than they should have been — which implied that the risk was being moved elsewhere. Where had the risk gone?

They didn’t know, or didn’t ask. One reason was that the outputs came from “black box” computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula’s weaknesses, weren’t the ones making the big asset-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked. They could, however, understand something as simple as a single correlation number. That was the problem.

Taleb of course proclaims, “Anything that relies on correlation is charlatanism.”

Nassim Nicholas Taleb (The Black Swan, Fooled by Randomness) maps decisions onto four quadrants — much like any MBA, really. In his case, the two criteria are whether the decision itself is simple (binary) or complex, and whether the probability distribution is known and thin-tailed (Mediocristan) or unknown and/or fat-tailed (Extremistan).

The Fourth Quadrant, naturally, is where all hell breaks loose:

In response, Taleb has developed a list of Phronetic Rules — What Is Wise To Do (Or Not Do) In The Fourth Quadrant:

1) Avoid Optimization, Learn to Love Redundancy. Psychologists tell us that getting rich does not bring happiness — if you spend it. But if you hide it under the mattress, you are less vulnerable to a black swan. Only fools (such as Banks) optimize, not realizing that a simple model error can blow through their capital (as it just did). In one day in August 2007, Goldman Sachs experienced 24 x the average daily transaction volume — would 29 times have blown up the system? The only weak point I know of financial markets is their ability to drive people & companies to “efficiency” (to please a stock analyst’s earnings target) against risks of extreme events.

Indeed some systems tend to optimize — therefore become more fragile. Electricity grids for example optimize to the point of not coping with unexpected surges — Albert-Lazlo Barabasi warned us of the possibility of a NYC blackout like the one we had in August 2003. Quite prophetic, the fellow. Yet energy supply kept getting more and more efficient since. Commodity prices can double on a short burst in demand (oil, copper, wheat) — we no longer have any slack. Almost everyone who talks about “flat earth” does not realize that it is overoptimized to the point of maximal vulnerability.

Biological systems — those that survived millions of years — include huge redundancies. Just consider why we like sexual encounters (so redundant to do it so often!). Historically populations tended to produced around 4-12 children to get to the historical average of ~2 survivors to adulthood.

Option-theoretic analysis: redundancy is like long an option. You certainly pay for it, but it may be necessary for survival.

2) Avoid prediction of remote payoffs — though not necessarily ordinary ones. Payoffs from remote parts of the distribution are more difficult to predict than closer parts.

A general principle is that, while in the first three quadrants you can use the best model you can find, this is dangerous in the fourth quadrant: no model should be better than just any model.

3) Beware the “atypicality” of remote events. There is a sucker’s method called “scenario analysis” and “stress testing” — usually based on the past (or some “make sense” theory). Yet I show in the appendix how past shortfalls that do not predict subsequent shortfalls. Likewise, “prediction markets” are for fools. They might work for a binary election, but not in the Fourth Quadrant. Recall the very definition of events is complicated: success might mean one million in the bank …or five billions!

4) Time. It takes much, much longer for a times series in the Fourth Quadrant to reveal its property. At the worst, we don’t know how long. Yet compensation for bank executives is done on a short term window, causing a mismatch between observation window and necessary window. They get rich in spite of negative returns. But we can have a pretty clear idea if the “Black Swan” can hit on the left (losses) or on the right (profits).

The point can be used in climatic analysis. Things that have worked for a long time are preferable — they are more likely to have reached their ergodic states.

5) Beware Moral Hazard. Is optimal to make series of bonuses betting on hidden risks in the Fourth Quadrant, then blow up and write a thank you letter. Fannie Mae and Freddie Mac’s Chairmen will in all likelihood keep their previous bonuses (as in all previous cases) and even get close to 15 million of severance pay each.

6) Metrics. Conventional metrics based on type 1 randomness don’t work. Words like “standard deviation” are not stable and does not measure anything in the Fourth Quadrant. So does “linear regression” (the errors are in the fourth quadrant), “Sharpe ratio”, Markowitz optimal portfolio, ANOVA shmnamova, Least square, etc. Literally anything mechanistically pulled out of a statistical textbook.

My problem is that people can both accept the role of rare events, agree with me, and still use these metrics, which is leading me to test if this is a psychological disorder.

The technical appendix shows why these metrics fail: they are based on “variance”/”standard deviation” and terms invented years ago when we had no computers. One way I can prove that anything linked to standard deviation is a facade of knowledge: There is a measure called Kurtosis that indicates departure from “Normality”. It is very, very unstable and marred with huge sampling error: 70-90% of the Kurtosis in Oil, SP500, Silver, UK interest rates, Nikkei, US deposit rates, sugar, and the dollar/yet currency rate come from 1 day in the past 40 years, reminiscent of figure 3. This means that no sample will ever deliver the true variance. It also tells us anyone using “variance” or “standard deviation” (or worse making models that make us take decisions based on it) in the fourth quadrant is incompetent.

7) Where is the skewness? Clearly the Fourth Quadrant can present left or right skewness. If we suspect right-skewness, the true mean is more likely to be underestimated by measurement of past realizations, and the total potential is likewise poorly gauged. A biotech company (usually) faces positive uncertainty, a bank faces almost exclusively negative shocks. I call that in my new project “concave” or “convex” to model error.

8) Do not confuse absence of volatility with absence of risks. Recall how conventional metrics of using volatility as an indicator of stability has fooled Bernanke — as well as the banking system.

9) Beware presentations of risk numbers. Not only we have mathematical problems, but risk perception is subjected to framing issues that are acute in the Fourth Quadrant. Dan Goldstein and I are running a program of experiments in the psychology of uncertainty and finding that the perception of rare events is subjected to severe framing distortions: people are aggressive with risks that hit them “once every thirty years” but not if they are told that the risk happens with a “3% a year” occurrence. Furthermore it appears that risk representations are not neutral: they cause risk taking even when they are known to be unreliable.

I didn’t realize he also has a seminar DVD out, Nassim Nicholas Taleb: The Future Has Always Been Crazier Than We Thought.

Michael Lewis (Liar’s Poker, The Real Price of Everything) looks Inside Wall Street’s Black Hole:

One of the revolt’s leaders is Nassim Nicholas Taleb, the bestselling author of The Black Swan and Fooled by Randomness and a former trader of currency options for a big French bank. Taleb can precisely date the origin of his own personal gripe with Black-Scholes: September 22, 1985. On that day, central bankers from Japan, France, Germany, Britain, and the United States announced their intention to torpedo the U.S. dollar — to reduce its value in relation to the other countries’ currencies. Every day, Taleb received a list of his trading positions from his firm and a matrix describing his risks. The matrix told him how much money he stood to make or lose, given various currency fluctuations. That September 22, when the central bankers announced their plan to lower the dollar’s value, he made money but didn’t know it. “I didn’t know what my position was,” he says, “because the movement was outside the matrix they’d given me.” The French bank’s risk-analysis program assumed that a currency crash of this magnitude would occur once in several million years and therefore wasn’t worth considering.

Taleb made a killing that day, but it wasn’t thanks to a grand plan and it wasn’t happy money. “People in dark suits started coming from Paris,” he says. “They said that the only way I could have made that much was to have taken far too much risk.” But he hadn’t. They had simply failed to account for the true nature of risk in financial markets. “Then I started looking at the history of markets,” he says. “And I saw that these sorts of things happened all the time.” Taleb became obsessed with the way prices in the options market, based on the famous Black-Scholes model, underestimated the risk of extreme and rare events. He set up his trading to profit from such events by buying up disaster insurance that would, according to Black-Scholes, be considered overpriced. When October 19, 1987, arrived, he was prepared. “Ninety-seven percent of all the returns I ever made as a trader, I made on that day,” he says.