### A conversation with Fat Tony and Dr. John

In his popular book *The Black Swan,* Nassim Nicholas Taleb provides an interesting alternative to modern statistical theory. He theorizes that the world is driven by singular events that are highly improbable and bear an extreme impact. Along the way, Taleb heavily bashes statistics, essentially calling it an irrelevant, concocted pseudoscience (he especially enjoys haranguing about the fallacies of the bell curve).

In one fictional example, Taleb tries to show why statistics is so irrelevant to the real world by facilitating a conversation between a street-wise Brooklyner, Fat Tony, and the prototypical nerd/stats star, Dr. John. Let’s have a look (Ch. 4 The Ludic Fallacy, or the Uncertainty of the Nerd):

NNT (that is, me): Assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it nineny-nine times and get heads each time. What are the odds of my getting tails on my next throw?

Dr. John: Trivial question. One half, of course, since you are assuming 50 percent odds for each and independence between draws.

NNT: What do you say, Tony?

Fat Tony: I’d say no more than 1 percent, of course.

NNT: Why so? I gave you the initial assumption of a fair coin, meaning that it was 50 percent either way.

Fat Tony: You are either full of crap or a pure sucker to buy into that “50 pehcent” business. The coin gotta be loaded. It can’t be a fair game. (Translation : It is far more likely that your assumptions about the fairness are wrong than the coin delivering the ninety-nine heads in ninety-nine throws.)

And then Taleb proceeds to bash statisticians and their “inside the box” thinking. Now I hate to do this, but let’s apply some simple stats to this problem. Anyone who has take any kind of stats class should be able to follow along (although most won’t remember anything from stats beyond feeling their eyes becoming heavier and drifting off slowly into sweet…).

Let’s test the hypothesis that the coin is fair (p=0.5) given that the last 99 flips produced heads every time.

We have:

H_{0}: P = 0.5 n = 99 pˆ = 1 (99 heads for the last 99 flips)

Let’s decide to reject H_{0 }if the difference between our sample p (pˆ) and the p according to our hypothesis is “significant” with a 1% significance level. In other words, if we are less than 99% sure that the difference between what we sampled and what the hypothesis we are testing holds is *not *due to random sampling error, then we cannot say that our hypothesis that the coin is fair is wrong.

Using the test statistic (a test we can use since what we’re looking at looks like a bell curve) we can determine the distance from what we sampled to what we think is the right number in a general unit, the standard error.

Basically, what we want to know is whether the number we got, 1, is far enough from 0.5, the original condition, for us to question if the original condition is true. Since we are trying to prove with 99% accuracy that the original condition *isn’t *true, we are looking for a value of z that is greater than 2.575. **In other words, if the sample we got (1) is 2.575 standard errors (an arbitrary generalized unit) away from .5 then we can say with 99% accuracy that the coin is not fair. **

**Pluggin’ in some values, we get a z value equal to around 9.95. Way, way, way over 2.575**. We can most definitely say with at least 99% accuracy that the coin is not fair.

So let’s go back to Dr. John. If Dr. John was an actual statistician, instead of some dude with a medical degree (or a PhD in psychology, I don’t know), he would have *clearly *rejected the initial condition of the test, based on the fact that if it were true, he would be getting results much closer to the initial condition (around 50/50 heads and tails). So statistics isn’t as useless as you thought. And Taleb isn’t as right as he thought. Taleb certainly makes very interesting points about Black Swans (it’s true, stats has a hard time accounting for them) and the normal distribution, but we mustn’t forget to be as skeptical of Taleb as he is of statistics. One of Taleb’s main arguments throughout the book is to be skeptical and keep your mind open to unforeseen possibilities.

If you haven’t read *The Black Swan*, I would highly recommend it. Of course, as Taleb might say, don’t believe everything you see on paper.

I think Dr Taleb just tries to show the problems is larger than the box. In my opinion, he is not sceptical of stats per se, but of the use of stats. Even statisticians can forget stats principles in their daily lives.

Warm regards,

Y

Taleb is aiming at people like the ones described in this inteview, who allow themselves to become mesmerized by their algorithms, when their fitting experience is manifestly too thin to justify their confidence in the results:

http://www.ritholtz.com/blog/2010/12/part-ii-scott-patterson-quants/

A: He would discover inefficiencies between the price of the stock and the bond and became really good at putting these trades on, so he ended up running Deutsche Bank’s global bond desk at the age of 33, and he was in charge of this other prop trading arm at Deutsche Bank that he called ‘saba,’ which is a Hebrew word for ‘grandfather,’ and he was this incredibly powerful guy making huge bets…

Q: And a kid, essentially.

A: Yeah, but in a way, he was representing the evolution of Wall Street, the older guys who were used to playing vanilla bonds, they had no idea how to use these new derivatives, and to him, it was natural, that’s just how he grew up trading, so it was an evolution of the market, he road that wave, he was very good at it, and when Lehman went down, the CDS market just froze, and it screwed up his trades, because he’d hedged these positions with CDS, and the CDS market just froze, it wasn’t moving, so he ended up having these losses on his books that if the CDS market was working as it should have, he probably would have been OK, but it didn’t, and he was using quantitative formulas to put all these trades together, and it’s just another example of how when things don’t work out in panics, which seems to happen a lot on Wall Street, these very careful, calibrated trades, if you’re using a lot of leverage, which he was, can blow up in your face, and they ended up losing about two billion dollars in the course of about a month or two.

Q: Which, in the scheme of things, is not a huge amount of money relative to what it threw off in profits. Some shops seem to have wiped out previous decades worth of profits.

A: When you add up how much he’d made over the past few years to how much he lost, he ended up kind of flat.

Q: So he gave back all the profits he made?

A: Yeah, it looks like Boaz did not make money for Deutsche Bank over the three or four years leading up to, at least on that prop desk. Now he was also running the flow desk, which can raise questions itself, Chinese walls…he was in charge of that flow desk, which had billions of dollars flowing through it, and I’m sure they were profitable.

Q: I was going to ask about the Gaussian Copula, but I don’t know if you really want to get that far into the weeds.

A: It’s difficult to talk about, it’s the formula that most of Wall Street was using, and the rating agencies, to price these CDOs or synthetic CDOs, more than anything, the bundles of credit default swaps that were designed to mimic cash CDOs, and they were basically, in a nutshell, trying to calculate the correlations between the various tranches of the synthetic CDOs, and it was a very complicated formula. It was also based on correlation, so if one tranche of triple As is trading at 99 cents on the dollar based on historical performance, the triple B tranche is going to be at 92, so you ended up having, based on this formula, a new breed of trader that rose up in Wall Street in the 2000s called correlation traders, and they were making bets on the various tranches of synthetic CDOs, shorting some tranches, going long other tranches, using the model, and that is basically what blew up Morgan Stanley. Morgan Stanley was doing correlation bets on synthetic CDOs.

Q: And heavily leaned into it.

A: Yeah.

More good discussion on this here:

http://www.scribd.com/doc/6765643/Why-We-Have-Never-Used-the-BlackScholesMerton-Option-Pricing-Formula