Fooled by Randomness (10 page)

For an idea, age is beauty (it is premature to discuss the mathematics of the point).The applicability of Solon’s warning to a life in randomness, in contrast with the exact opposite message delivered by the prevailing media-soaked culture, reinforces my instinct to value distilled thought over newer thinking, regardless of its apparent sophistication—another reason to accumulate the hoary volumes by my bedside (I confess that the only news items I currently read are the far more interesting upscale social gossip stories found in
Tatler, Paris Match,
and
Vanity Fair—
in addition to
The Economist
). Aside from the decorum of ancient thought as opposed to the coarseness of fresh ink, I have spent some time phrasing the idea in the mathematics of evolutionary arguments and conditional probability. For an idea to have survived so long across so many cycles is indicative of its relative fitness. Noise, at least
some
noise, was filtered out. Mathematically, progress means that some new information is better than past information, not that the average of new information will supplant past information, which means that it is optimal for someone, when in doubt, to systematically reject the new idea, information, or method. Clearly and shockingly, always. Why?

The argument in favor of “new things” and even more “new new things” goes as follows: Look at the dramatic changes that have been brought about by the arrival of new technologies, such as the automobile, the airplane, the telephone, and the personal computer. Middlebrow inference (inference stripped of probabilistic thinking) would lead one to believe that all new technologies and inventions would likewise revolutionize our lives. But the answer is not so obvious: Here we only see and count the winners, to the exclusion of the losers (it is like saying that actors and writers are rich, ignoring the fact that actors are largely waiters—and lucky to be ones, for the less comely writers usually serve French fries at McDonald’s). Losers? The Saturday newspaper lists dozens of new patents of such items that can revolutionize our lives. People tend to infer that because
some
inventions have revolutionized our lives that inventions are good to endorse and we should favor the new over the old. I hold the opposite view. The opportunity cost of missing a “new new thing” like the airplane and the automobile is minuscule compared to the toxicity of all the garbage one has to go through to get to these jewels (assuming these have brought some improvement to our lives, which I frequently doubt).

Now the exact same argument applies to information. The problem with information is not that it is diverting and generally useless, but that it is toxic. We will examine the dubious value of the highly frequent news with a more technical discussion of signal filtering and observation frequency farther down. I will say here that such respect for the time-honored provides arguments to rule out any commerce with the babbling modern journalist and implies a minimal exposure to the media as a guiding principle for someone involved in decision making under uncertainty. If there is anything better than noise in the mass of “urgent” news pounding us, it would be like a needle in a haystack. People do not realize that the media is paid to get your attention. For a journalist, silence rarely surpasses any word.

On the rare occasions when I boarded the 6:42 train to New York I observed with amazement the hordes of depressed business commuters (who seemed to prefer to be elsewhere) studiously buried in
The Wall Street Journal,
apprised of the minutiae of companies that, at the time of writing now, are probably out of business. Indeed it is difficult to ascertain whether they seem depressed because they are reading the newspaper, or if depressive people tend to read the newspaper, or if people who are living outside their genetic habitat both read the newspaper and look sleepy and depressed. But while early on in my career such focus on noise would have offended me intellectually, as I would have deemed such information as too statistically insignificant for the derivation of any meaningful conclusion, I currently look at it with delight. I am happy to see such mass-scale idiotic decision making, prone to overreaction in their postperusal investment orders—in other words I currently see in the fact that people read such material an insurance for my continuing in the entertaining business of option trading against the fools of randomness. (It takes a huge investment in introspection to learn that the thirty or more hours spent “studying” the news last month neither had any predictive ability during your activities of that month nor did it impact your current knowledge of the world. This problem is similar to the weaknesses in our ability to correct for past errors: Like a health club membership taken out to satisfy a New Year’s resolution, people often think that it will surely be the next batch of news that will really make a difference to their understanding of things.)

Shiller Redux

Much of the thinking about the negative value of information on society in general was sparked by Robert Shiller. Not just in financial markets; but overall his 1981 paper may be the first mathematically formulated introspection on the manner in which society in general handles information. Shiller made his mark with his 1981 paper on the volatility of markets, where he determined that if a stock price is the estimated value of “something” (say the discounted cash flows from a corporation), then market prices are way too volatile in relation to tangible manifestations of that “something” (he used dividends as proxy). Prices swing more than the fundamentals they are supposed to reflect, they visibly overreact by being too high at times (when their price overshoots the good news or when they go up without any marked reason) or too low at others. The volatility differential between prices and information meant that something about “rational expectation” did not work. (Prices did not rationally reflect the long-term value of securities and were overshooting in either direction.) Markets had to be wrong. Shiller then pronounced markets to be not as efficient as established by financial theory (efficient markets meant, in a nutshell, that prices should adapt to all available information in such a way as to be totally unpredictable to us humans and prevent people from deriving profits). This conclusion set off calls by the religious orders of high finance for the destruction of the infidel who committed such apostasy. Interestingly, and by some strange coincidence, it is that very same Shiller who was trounced by George Will only one chapter ago.

The principal criticism against Shiller came from Robert C. Merton. The attacks were purely on methodological grounds (Shiller’s analysis was extremely rough; for instance, his using dividends in place of earnings was rather weak). Merton was also defending the official financial theory position that markets needed to be efficient and could not possibly deliver opportunities on a silver plate. Yet the same Robert C. Merton later introduced himself as the “founding partner” of a hedge fund that aimed at taking advantage of market inefficiencies. Setting aside the fact that Merton’s hedge fund blew up rather spectacularly from the
black swan problem
(with characteristic denial), his “founding” such a hedge fund requires, by implication, that he agrees with Shiller about the inefficiency of the market. The defender of the dogmas of modern finance and efficient markets started a fund that took advantage of market inefficiencies! It is as if the Pope converted to Islam.

Things are not getting any better these days. At the time of writing, news providers are offering all manner of updates, “breaking news” that can be delivered electronically in a wireless manner. The ratio of undistilled information to distilled is rising, saturating markets. The elder’s messages need not be delivered to you as imminent news.

This does not mean that all journalists are fooled by randomness noise providers: There are hordes of thoughtful journalists in the business (I would suggest London’s Anatole Kaletsky and New York’s Jim Grant and Alan Abelson as the underrated representatives of such a class among financial journalists; Gary Stix among scientific journalists); it is just that prominent media journalism is a thoughtless process of providing the noise that can capture people’s attention and there exists no mechanism for separating the two. As a matter of fact, smart journalists are often penalized. Like the lawyer in
Chapter 11
who does not care about the truth, but about arguments that can sway a jury whose intellectual defects he knows intimately, journalism goes to what can capture our attention, with adequate sound bites. Again, my scholarly friends would wonder why I am getting emotional stating the obvious things about the journalists; the problem with my profession is that we depend on them for what information we need to obtain.

Gerontocracy

A preference for distilled thinking implies favoring old investors and traders, that is, investors who have been exposed to markets the longest, a matter that is counter to the common Wall Street practice of preferring those that have been the most profitable, and preferring the youngest whenever possible. I toyed with Monte Carlo simulations of heterogeneous populations of traders under a variety of regimes (closely resembling historical ones), and found a significant advantage in selecting aged traders, using as a selection criterion their cumulative years of experience rather than their absolute success (conditional on their having survived without blowing up). “Survival of the fittest,” a term so hackneyed in the investment media, does not seem to be properly understood: Under regime switching, as we will see in
Chapter 5
, it will be unclear who is actually the fittest, and those who will survive are not necessarily those who appear to be the fittest. Curiously, it will be the oldest, simply because older people have been exposed longer to the rare event and can be, convincingly, more resistant to it. I was amused to discover a similar evolutionary argument in mate selection that considers that women prefer (on balance) to mate with healthy older men over healthy younger ones, everything else being equal, as the former provide some evidence of better genes. Gray hair signals an enhanced ability to survive—conditional on having reached the gray hair stage, a man is likely to be more resistant to the vagaries of life. Curiously, life insurers in renaissance Italy reached the same conclusion, by charging the same insurance for a man in his twenties as they did for a man in his fifties, a sign that they had the same life expectancy; once a man crossed the forty-year mark, he had shown that very few ailments could harm him. We now proceed to a mathematical rephrasing of these arguments.

PHILOSTRATUS IN MONTE CARLO:
ON THE DIFFERENCE BETWEEN NOISE
AND INFORMATION

The wise man listens to meaning; the fool only gets the noise. The modern Greek poet C. P. Cavafy wrote a piece in 1915 after Philostratus’ adage “For the gods perceive things in the future, ordinary people things in the present, but the wise perceive things about to happen.” Cavafy wrote:

I thought hard and long on how to explain with as little mathematics as possible the difference between noise and meaning, and how to show why the time scale is important in judging a historical event. The Monte Carlo simulator can provide us with such an intuition. We will start with an example borrowed from the investment world, as it can be explained rather easily, but the concept can be used in any application.

Let us manufacture a happily retired dentist, living in a pleasant, sunny town. We know
a priori
that he is an excellent investor, and that he will be expected to earn a return of 15% in excess of Treasury bills, with a 10% error rate per annum (what we call volatility). It means that out of 100 sample paths, we expect close to 68 of them to fall within a band of plus and minus 10% around the 15% excess return, i.e., between 5% and 25% (to be technical; the bell-shaped normal distribution has 68% of all observations falling between -1 and 1 standard deviations). It also means that 95 sample paths would fall between -5% and 35%.

Clearly, we are dealing with a very optimistic situation. The dentist builds for himself a nice trading desk in his attic, aiming to spend every business day there watching the market, while sipping decaffeinated cappuccino. He has an adventurous temperament, so he finds this activity more attractive than drilling the teeth of reluctant little old Park Avenue ladies.

He subscribes to a Web-based service that supplies him with continuous prices, now to be obtained for a fraction of what he pays for his coffee. He puts his inventory of securities in his spreadsheet and can thus instantaneously monitor the value of his speculative portfolio. We are living in the era of connectivity.

A 15% return with a 10% volatility (or uncertainty) per annum translates into a 93% probability of success in any given year. But seen at a narrow time scale, this translates into a mere 50.02% probability of success over any given second as shown in Table 3.1. Over the very narrow time increment, the observation will reveal close to nothing. Yet the dentist’s heart will not tell him that. Being emotional, he feels a pang with every loss, as it shows in red on his screen. He feels some pleasure when the performance is positive, but not in equivalent amount as the pain experienced when the performance is negative.