Uncertainty

-- By PeterPark - 17 Apr 2010

According to one Felix Salmon, bad math destroyed our economy. That math looks something like this:

This is called a Gaussian-Copula formula. Simply put, it posits that the probability of two events occurring simultaneously can be determined by probabilities of each event occurring independently and a correlation factor which expresses how closely the two events are related. Easy.

Modeling Uncertainty on Wall Street.

If a Caucasian male in his twenties earning $300,000/yr defaults on his mortgage on a million dollar condo in NYC, how does that affect the chance of an Asian female in her fifties who makes $50,000/yr defaulting on her modest house in Chicago? If someone who earns six times as much defaults on his mortgage, then surely, probability of the woman’s default be up. But wait – maybe white guys making six figures in their twenties tend to be inexperienced and irresponsible whereas middle-aged Asian women are wise and conservative with their money, so perhaps there is no correlation. But then again, maybe the first default occurred because of an emerging trend where Americans are sick of condos - maybe condo prices plummeted while house prices soared, in which case the probability of the woman’s defaulting actually went down.

These lines of reasoning and empirical conjectures - sufficient perhaps for judicial decisions - will not comfort an investor who just bought a bond backed by thousands of mortgage obligations. His bet is that even as some of these mortgages inevitably go into default, the remaining “good” mortgages will be enough to pay him off when he cashes out. If default on one house is strongly correlated to default on the next house, which is strongly correlated to default on the next house, and so on, then there is a chance that the investor will be wiped out as a consequence of the first default. So he needs to know just how interrelated these events are. Less is better, of course.

Psychology of Uncertainty.

Uncertainty is all around us. Although we count on a lot of things in our lives, in reality, we don’t even know for sure that the sun will rise tomorrow morning. We don’t even know if the world outside our minds truly exists. And yet, ours is a history of tackling uncertainties. Lightening was first caused because one god or another was angry. Now it’s because negatively charged particles dissipate by connecting to the positively charged particles on the ground. The world was once flat, with hell below and heaven on top. Now the world is large beyond our comprehension, but at least we can explain its birth, life, and death. We don’t know what a big chunk of it looks like, but at least we know the collective effect that chunk has on us.

Psychologists consistently connect uncertainty to such negative feelings as dread and anxiety. Dread and anxiety elicit fear, which sets off a variety of pathological behaviors. On the one end of the spectrum are people who wear an armor of dogma. They insist on permanence where there is none. To them, the world operates under absolute and unyielding rules. We may not know all the rules, but they are there, maintained by a supernatural being or the nature itself. This is a classic defense mechanism, whereby irrationality trumps having to confront uncertainty and the resulting unpleasantries. By stifling uncertainties, they also stifle open-mindedness and the potential for creativity. On the other end of the spectrum are people who succumb to a solipsistic stupor. Somewhere in between, there are people who dismiss uncertainty for practical purposes while acknowledging it at a fundamental level. Scientific instrumentalists are a good example. So what if one cannot explain how penicillin works? The point is that it works. Also in the murky middle are the statisticians, economists, every manner of gamblers, and of course, psychologists, all of whom seek to tame uncertainty with operating rules derived from empirical data.

Back to Wall Street

Modernity gave birth to a new and dangerous kind of instrumentalists. Having gained an unconscionable degree of asymmetrical advantage, these people formed organizations whose sole purpose was to exploit the anxiety of everyone else. Under a countenance of professionalism and expertise, they sold compelling but not legally binding promises to everyone else (See for example, Stocks for the Long Run by Jeremy Siegel). And yet, as individuals, these Harvard-trained math Ph.D.’s were just as vulnerable to the anxiety of uncertainty as the rest of us. It is not surprising, then, that bad math destroyed our economy.

Enter David Li, a math genius turned Wall Street “quant.” Li came up with an elegant solution to the correlation problem above. Instead of thoroughly investigating the qualities of each event and drawing meaningful connections - a prohibitively expensive task - he figured out a shortcut. He tracked credit default swaps (CDS) associated with each event and compared them. If they moved in the same direction, there was positive correlation. CDS is an insurance policy which one investor buys from another, just in case the investment goes bust – it would be a good proxy for the risk of investment, if the primary investors could correctly price the risk. Thus, Li’s model was a fatally circular one – e.g. this derivative investment is not risky because higher order investors said it wasn’t. How did those guys know? They used Li’s model, of course. The model suggested, among other things, that one default was not correlated to another. Therefore, mortgage-backed securities were bullet-proof. As it turned out, the only available CDS data was from the boom years and was not at all applicable during a downturn. In a bad economy, as one might suspect, one default could easily signal an onslaught of others - and triple-A, first tranche, risk-free bonds could become worthless. And they did. Thus began the apocalypse.

The primary lesson here is to be wary of anyone who claims to have tamed uncertainty. Chances are, it's a con and you are the mark.