Follow that igon value!

Perhaps fittingly, the first use of "igon value" was in a profile of (then obscure) hedge fund philosopher Nassim Taleb. (See earlier post Pinker on Gladwell.)

New Yorker, April 22 & 29, 2002: [this version retrieved from gladwell.com] ... As the day came to an end, Taleb and his team turned their attention once again to the problem of the square root of n. Taleb was back at the whiteboard. Spitznagel was looking on. Pallop was idly peeling a banana. Outside, the sun was beginning to settle behind the trees. "You do a conversion to p1 and p2," Taleb said. His marker was once again squeaking across the whiteboard. "We say we have a Gaussian distribution, and you have the market switching from a low-volume regime to a high-volume. P21. P22. You have your igon value." He frowned and stared at his handiwork. The markets were now closed. Empirica had lost money, which meant that somewhere off in the woods of Connecticut Niederhoffer had no doubt made money. That hurt, but if you steeled yourself, and thought about the problem at hand, and kept in mind that someday the market would do something utterly unexpected because in the world we live in something utterly unexpected always happens, then the hurt was not so bad. Taleb eyed his equations on the whiteboard, and arched an eyebrow. It was a very difficult problem. "Where is Dr. Wu? Should we call in Dr. Wu?"

I doubt the New Yorker and its famous fact checkers caught the error. Possibly not a single New Yorker employee knows any linear algebra. Who needs all that geeky math stuff? [Update: Apparently the New Yorker did correct the electronic version now available on its site, although one can find references to the error online in 2003. See here and comments below for more.]

Leave it for the Asians like Dr. Wu... :-)

... a man whom Taleb refers to, somewhat mysteriously, as Dr. Wu wandered in. Dr. Wu works for another hedge fund, down the hall, and is said to be brilliant. He is thin and squints through black-rimmed glasses. He was asked his opinion on the square root of n but declined to answer. "Dr. Wu comes here for intellectual kicks and to borrow books and to talk music with Mark," Taleb explained after their visitor had drifted away. He added darkly, "Dr. Wu is a Mahlerian."

Taleb or not Taleb?

Nassim Taleb, love him or hate him, has appeared quite a few times on this blog. Personally I find him quite amusing. I like his irreverence for "expert" opinion (especially that of economists) and his skepticism toward finance theory (in particular, towards Black Scholes and assumptions about perfect hedging and normally distributed risks). His earlier book Fooled By Randomness is largely devoted to making the simple point (amazingly, not appreciated by many otherwise very smart people) that it is quite difficult to tell whether success is due to ability or plain luck. In Wall Street terms, when is there enough data to be confident about someone's alpha?

I recently found this interesting essay by Eric Falkenstein, which is quite critical of Taleb and his book The Black Swan. Many of Falkenstein's points are well taken, although one should evaluate his arguments carefully -- his background (worked on VAR, an economics PhD) might predispose him to dislike Taleb. He criticises Taleb's hero Mandelbrot and the use of fractal ideas in finance, but these criticisms point to the fact that the ideas do not lead to easily implementable models, not that they are wrong as a fundamental description of the underlying phenomena. See, e.g., here and here for more discussion. Eventually, he cuts to the chase and notes that Taleb's earlier hedge fund was probably a loser, and that if he had had any success as a trader he wouldn't be out there hawking books and giving lectures on the rubber chicken circuit :-)

Taleb's trading strategy, based on the idea that others in the market are insufficiently aware of fat tailed distributions, was to buy out of the money puts in hopes of a profiting from a catastrophe. Under this strategy his fund constantly lost small amounts of money in hopes of making a big killing. Sadly for Taleb, he never hit the jackpot, although (see the Fooled By Randomness comment above) that doesn't necessarily undermine the validity of the strategy. More damaging, however, is the fact that insurance companies are basically on the other side of Taleb's trade all the time, and they seem capable of generating steady profits for long periods of time. My guess is that any trader who sold a put to Taleb's fund would pad out the price so much that even if their probability distribution were off at the tails, they would still exact a premium over the real value of the option. The deeper out of the money you go, the more careful and suspicious your counterparty is likely to be.

Finally, here's a recent paper by Taleb which is harshly critical of Black-Scholes-Merton.

Falkenstein: ...Taleb argues that the unpredictability of important events implies we should basically forget about all that is predictable, because that’s not where the real money or importance is. So from a risk management perspective, we should ignore Value at Risk, which measures anticipated fluctuations. Further, we should ‘go long’ on these unanticipated events by engaging in quirky activities on the off-chance that we randomly find something, or someone, really valuable.

Success in markets, like life, is a combination of ability, effort, and chance. Much of intelligent thought is distinguishing between what is predictable v. what is unpredictable; it is to any organism's advantage to find out what we can figure out and change, and what is forever mysterious and unalterable (eg, the Serenity Prayer). The brain is constantly predicting the environment, trying to figure out cause and effect so it can better understand the world. Most of what humans process is predictable, but because we take predictable things for granted, they are uninteresting. We can't predict some things, but instead of resorting to nihilism, we merely buy insurance or manage our portfolios--in the broad sense of the term--to have an appropriate robustness. Discovering certain things are basically unpredictable does not diminish our constant focus on trying to predict more and more things. People will disagree on which risks at the margin are predictable, but that's to be expected, and we all hope to be making the right choices that optimize our serenity at the margin of our predictable prowess.

Of course, in the face of being totally wrong in his evaluation of the usefulness of VAR as a tool — it’s ubiquitous in practical management of diverse trading books — Taleb now says he merely warned against naive usage of VAR. However, it was only his absurdly strong statement that VAR was for charlatans that got him mentioned in the Derivatives Strategy article that propelled him into public discourse (conveniently removed from his website, but you can read it online here). Then, as now, he points to anecdotes of imperfection to "prove" his points.

From Taleb's Wikipedia entry circa July 2006, we see where Black Swan thinking goes when applied to an investment strategy:
When he was primarily a trader, he developed an investment method which sought to profit from unusual and unpredictable random events, which he called "black swans." His reasoning was that traders lose much more money from a market crash than they gain from even years of steady gains, and so he did not worry if his portfolio lost money steadily, as long as that portfolio positioned him to profit greatly from an extremely large deviation (either a crash or an unexpected jump upwards).

In fact, Mandelbrot also argues for this strategy. Taleb co-authored a paper arguing that most people systematically underestimate volatility. Furthermore, he argues there exists not only a lack of appreciation of fat tails, but a preference for positive skew, in that people prefer assets that jump up, not down, which would imply the superiority of buying out-of-the-money puts as opposed to calls because those negative tails that increase the price of puts are unappreciated.

These assertions present some straightforward tests, which a Popperian like Taleb should embrace. Specifically, buying out-of-the-money options, especially puts (because of negative skew), should, on average, make money. But insurance companies, which basically are selling out-of-the-money options, tend to do as well as any industry (Warren Buffet has always favored insurance companies, especially re-insurers, as equity investments). Studies by Shumway and Coval (2001) and Bondarenko (2003) have documented that selling puts is where all the extranormal profit seems to be. Of all the option strategies, selling, not buying, out-of-the-money puts has been the best performer historically.

Famed New Yorker writer Malcom Gladwell in a 2002 New Yorker article contrasts the thoughtful, pensive Taleb versus the brash cowboy Victor Neiderhoffer: Taleb buys out-of-the-money puts, Neiderhoffer sells them. Taleb is betting on the big blow up, Niederhoffer on the idea that people overpay for insurance. Who was right? Well, Neiderhoffer still ran his flagship fund until September 2007 from a chalet-style mansion in Weston Connecticut . Taleb shut down his Empirica Kurtosis fund at the end of 2004, and the only public data on it suggest a rather anemic Sharpe ratio, below that of the S&P500 (60% in 2000, about zero for the next 4 years, see here), which is consistent with shutting it down, and trying to redescribe it as a hedge or laboratory, and then move into the more profitable business of teaching how to invest. While neither strategy was great, Niederhoffer's was better, if you just look at their lifetimes (management, in this case Taleb, always likes to say that people left positions of power due to desires to be with family or other opportunities, but the bottom line is, selling puts remained immune to family considerations longer than buying puts).

Taleb's big problem is that he misinterprets the mode-mean trade. A mode-mean trade is where a trader finds a strategy with a positive mode, but zero or negative mean. He then uses someone else’s capital to make money off several years of good returns, making good money for creating or managing the strategy, then, when the strategy gives it all back, the investor bears all the loss. That’s a bad strategy for the investor, and the trader who manages it is either naïve or duplicitous. That is, selling extreme options or writing insurance on extreme events at any prices generates a good mode return, but if it underestimates the probability or severity of the bad times, it may generate a zero or negative average return. Buying High Yield debt is a good example. However, just because selling puts is a bad strategy, it doesn't mean buying puts is a good strategy. A Sharpe of 0.2 is a bad long position, but a worse short (because a - 0.2 Sharpe is worse than a 0.2).

Worth a look or listen

Some recommendations from a bunch of content I consumed during recent travel.

The Black Swan by Nassim Taleb. I finally got around to reading this and recommend it highly. Physicists and others who are already familiar with nonlinear dynamics (chaos theory), the difference between Gaussian and power-law distributions, etc. will find the presentation slow and repetitious at times, but Taleb does have a lot of interesting insights. Particularly amusing: Chapter 10, The scandal of prediction, in which he recapitulates Philip Tetlock's results, chapter 17, which rails against the "Nobel" prize in economics, especially the one awarded to Merton and Scholes. I can't say I completely agree with Taleb on the (non)utility of modern finance theory. It's true that Gaussians underestimate the likelihood of rare events, but that is well known now and there are various ways to incorporate that into models (e.g., fat tails, stochastic vol). He's dismissive of these improvements in the book; it appears to me he's attacking a caricature from 10 years ago.

I also recommend a number of podcast interviews from the site Econtalk.org. Especially useful if you're going to be stuck on a plane, train or automobile. Some that I found especially good:

Taleb on the Black Swan (strange that the interviewer, an economist, didn't explore Taleb's extremely negative view of the profession! I guess they're both Hayekians so had some common ground :-)

Paul Romer on economic growth.

Ed Leamer on outsourcing and trade.

Vernon Smith on experimental economics.

Gregg Easterbrook on happiness and the American standard of living (we're 10x richer on average than 100 years ago!).

Bob Lucas on growth, poverty, monetary policy.

Nassim Taleb on Charlie Rose

Anyone read The Black Swan yet? I liked his earlier book Fooled By Randomness. I skimmed the Black Swan at the bookstore and liked it as well but was too cheap to part with the $20 :-) Here is an earlier post, linking to a nice podcast interview in which he discusses prediction and the dismal track record of certain prognosticators.

Taleb: "There are a lot of disciplines -- economics, political science -- where the expert is no expert. ... They don't have more predictive power than cab drivers ... do not take the experts seriously in these areas..." (He says this both on the podcast and on Charlie, but I quote from the latter. He's exaggerating -- remember his market perspective -- but not entirely wrong :-)

By the way, the current seizing up of the credit markets is not a black swan event -- a lot of people predicted it a long time ago!

Gladwell and genius

Malcolm Gladwell shows exquisite taste in the subjects he writes and talks about -- he has a nose for great topics. I just wish his logical and analytical capabilities were better (see also here). This talk at the New Yorker's recent Genius 2012 conference is entertaining, but I disagree completely with his conclusion. Ribet, Wiles, Taniyama and Shimura are probably the real geniuses, not Michael Ventris, the guy who decoded Linear B. (Gladwell also can't seem to remember that it's the Taniyama-Shimura conjecture, not Tanimara. He says it incorrectly about 10 times.) My feeling is that Gladwell's work appeals most to people who can't quite understand what he is talking about.

Gladwell is confused about the exact topic discussed in James Gleick's book Genius. In a field where sampling of talents is sparse (e.g., decoding ancient codexes) you might find one giant (even an amateur like Michael Ventris) towering above the others, able to do things others cannot. In a well-developed, highly competitive field like modern mathematics, all the top players are "geniuses" in some sense (rare talents, one in a million), even though they don't stand out very much from each other. In Gleick's book, Feynman, discussing how long it might have taken to develop general relativity had Einstein not done it, says "We are not that much smarter than each other"!

To put it simply, if I sample sparsely from a Gaussian distribution, I might find a super-outlier in the resulting set. If I sample densely and have a high minimum cutoff for acceptable points, I will end up with a set entirely composed of outliers, but who do not stand out much from each other. Every guard in the NBA is an athletic freak of nature, even though they are relatively evenly matched when playing against each other.

To counteract the intelligence-damping effect of Gladwell's talk, I suggest this podcast interview with Nassim Taleb, about his new book The Black Swan. Warning: may be psychologically damaging to people who fool themselves and others about their ability to predict the behavior of nonlinear systems.

Taleb podcast: What do we know?

Here is an excellent talk by Nassim Taleb, hedge fund manager and author of the book Fooled by Randomness, which I highly recommend. Taleb addresses the prediction problem: how do you evaluate your knowledge of the world, other than by testing your ability to make predictions about what will happen next? (Post-diction is too easy - one can always construct post-hoc stories which are consistent with the data. Sorry, historians :-) He then notes that in certain fields like finance, economics and social science, the accuracy of predictions, when carefully studied, is dismal. (See my earlier discussion of Tetlock's research, which confirms this in a quantitative way. Tetlock had to work hard at this, since he looked at softer non-quantitative predictions as in foreign affairs. If you stick to quantitative predictions, like of equity or commodity prices, it is much easier to see that prognosticators are terrible.)

Feynman once said, holding up his fist and rotating it as if it were a charged sphere or something, "Physics is about answering the question: if I do this, what happens next?" I think this is very much in the spirit of Taleb's viewpoint.

One nice experiment Taleb describes shows how overconfident we are in our ability to predict the future.

Ask a group of people to make a prediction -- for example, how many Corollas will Toyota sell next (or last) year? We're not interested in the central values of their predictions. We're more interested in their understanding of its accuracy. So we say, give me a range that covers the 98 percent confidence interval. That is, give me a range of how many Corollas were sold last year, with the real value somewhere in that range at 98 percent confidence. Even if you know nothing about the auto industry, you could incorporate this into your guess by choosing a large range (e.g., between 10,000 and 10 million).

However, people are systematically overconfident in the quality of their predictions - by at least an order of magnitude, says Taleb. Typically, their 98 percent confidence level prediction is more like a 60 percent confidence level prediction. In other words, if you try this experiment with 100 students who correctly understand their own state of knowledge, you would expect only about 2 students to choose ranges which don't include the actual value. Instead, what you find is that 40 or so of the ranges will not contain the correct number! (Their error estimate of 2% is a gross underestimate.)

Taleb claims that the worst performing groups on this kind of exercise (regardless of the prediction requested) are stock analysts and economists, probably because the two groups are selected for a systematic bias toward overconfidence in dealing with noisy data. I wonder how physicists would do? I often stress that in communicating some information to a colleague (e.g., "A neutrino with those properties is ruled out by LEP data"), it is useful to also include a confidence level ("I have thought carefully about the loopholes and have looked at the LEP analysis and am 99% confident what I just said to you is true"). Thus, rather than transmitting a single statement, it is better to transmit the statement plus a confidence estimate. The utility of the pair is dramatically greater than just the statement itself.

My feeling is that when it comes to discussing the implications of a particular experiment, physicists are trained to accurately understand the confidence intervals. However, when it comes to a question like "How likely is it that supersymmetry solves the hierarchy problem?" I suspect we are as overconfident as any other group in the accuracy of our predictions.