Saturday, October 18, 2008

Greed, Not Bad Models, Doomed Wall Street

http://upload.wikimedia.org/wikipedia/commons/thumb/9/96/Pearson_type_VII_distribution_PDF.png/800px-Pearson_type_VII_distribution_PDF.png
Megan McArdle, The Atlantic's libertarian economics blogger, had a post in which she wrote the following:
The people who, it seems to me, have been truly vindicated by this are Nassim Taleb and Benoit Mandelbrot. They nailed what to me is the core issue: bankers pricing security risk as if it were distributed along a normal curve with thin tails.
This assertion was made at the end of a long blog post decrying the precognitive failings of Paul Krugman. The thing is that Krugman correctly identified housing as a bubble that would burst, even if he didn't know precisely when. McArdle seems really reluctant to give him credit for it, and indeed writes off all prognosticators by saying only Taleb and Mandelbrot deserve praise, and that if anyone got anyone else got any prediction right, it was just chance. Only hindsight bias makes them seem wise now. Now aside from the ungenerousness of this (after all, quite a few people warned that housing was overpriced and could suffer a correction, and I doubt they were right purely by accident), the praise for Taleb is fantastically undeserved! (Mandelbrot I can see maybe, since he appears to be one of the earliest to see that financial returns were not normally distributed.)

The thing that McArdle doesn't seem to realize is that everyone on Wall Street worth his or her salt knows that returns are not normally distributed and therefore, models that are based on such a distribution of returns must be adjusted. She seems to think that Taleb was some kind of Cassandra, when the notion of fat tails is widely known, a major aspect of financial academic research, and something that traders and financial engineers constantly deal with.

A normal distribution can be described with two numbers, a mean and a standard deviation. If you are looking at a time series of returns, you can easily find a mean and standard deviation. The standard deviation here is what we call volatility--how much can a security go up or down? Risky assets have high volatility, safe assets low volatility. The problem is that if you make a histogram of those returns, the result rarely looks quite like a normal curve. You see fat tails. The reason for this is that volatility isn't really a constant. Just because you get a single unique number when you used the STDEV function in Excel doesn't mean it really exists.

This is a bit scary. You can look at a data series and feel like the volatility is about X, but what you can't see is that there could be some event you haven't seen yet and can't predict that would push that volatility way above X. This kind of event is what Taleb calls a "black swan"--something you don't think exists until you actually encounter it. But the thing is, if the volatility isn't constant but is ever-changing (as is actually the case in most financial returns), you can never be sure whether a "black swan" is lurking out in the future. You get a distribution of returns with leptokurtosis (aka, fat tails, which indicates that extreme outcomes are more likely to happen than in a normal distribution).

Like I said, none of this is secret. It's why the VIX exists. It shows the implied volatility of S&P 500 options. If Wall Street was full of people who didn't know about fat tails, they would not bother creating a VIX--because this volatility would just be assumed to be a flat line.

What is "implied volatility" and why do traders care? Back in the early 70s (or late 60s?), an options pricing tool called the Black-Scholes model was created. B-S assumed that the underlying asset had normally distributed returns. But since every options trader knows this not to be true, they often take the actual current option price and treat the volatility as the unknown. That's the implied volatility--implied by the current option price. (Figuring out current volatility turns out to be pretty hard.) Why do they do this? It turns out that having a better idea of the real volatility is useful for many financial activities. For example, they can use it to better delta hedge and gamma hedge their positions.

They could also try to get volatility using GARCH. This is a model for volatility that uses previous data to find volatility (as you normally would in getting a standard deviation), but weighs the data heavily to the most recent data-points, so that you can see volatility changing over time. It won't help you see the future, but it will help you see the present, which is hard enough. Well, this all sounds pretty obscure, huh? Except that its discoverers won the Noble prize in economics for it in 2003. So maybe it is obscure to Megan McArdle and other readers of pop-finance books, but not to actual practitioners.

The reason I'm going on and on about this is to demonstrate that despite what McArdle claims, people who built pricing models on Wall Street were well aware of fat tails on the probability curves of returns. And knowing these things did nothing to prevent this financial meltdown.

Why? Reading The Plight of the Fortune Tellers (excellent book on financial risk, far better than Taleb) suggests an answer. It wasn't stupidity but greed overcoming prudence.

Imagine a bank as having two groups--the risk-management group and the traders. They both use complex models to help them make their decisions. The risk group are always saying, "No." Don't leverage so high, don't have inadequate cash on hand to handle possible forecasted losses, don't engage in that risky strategy, etc. They are naysayers and scolds, and are pretty much unloved but necessary. The traders, on the other hand, are always saying yes. Yes, let's take this huge risk because the returns will be freaking orgasmic. Let's leverage to the hilt to multiply our returns. Let's not have a bunch of cash sitting around because that ain't making me a fat bonus, baby!

Now the top management is supposed to weigh these two necessarily competing urges. But because all the big banks are public and in competition with one another, they lean to what their traders are telling them. Hell, they got to be CEOs by being risk-taking traders themselves--no pussy risk-manager ever gets to be CEO. So they lean towards the risky trades and (as Michael Lewis observed) don't really understand these complex financial products and strategies that their big swinging dick rocket scientist traders have invented. (Do you think the top brass of AIG knew how to value a credit default swap? No, but they knew the CDS desk was making them a shitload of money.) They are just dazzled by the complexity and promise of returns. And if any of the risk-managers understand the shit themselves, they just come across as party pooper Deputy Dawgs. So blow them off! Go with the traders and make the big bucks!

This will always happen. That's why you need regulation. You need a brake from outside the company to prevent it from commiting suicide in its quest for ever higher returns. That regulatory brake gives the CEO cover if shareholders ask him why their stock is not higher. He can say that regulations prevent him from taking the kinds of risks necessary to produce higher returns. Without regulation, the trader mentality of high return/high risk will always prevail. That's fine if the industry we're talking about is not intimately tied to the functioning of the entire economy, but when you talk about big banks, it's unacceptable. Their greed must be tempered with sensible risk-avoidance regulation from the government.

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