Fooled by Randomness (15 page)

Visibly, the statistic that 90% of all option positions lost money is meaningless, (i.e., the
frequency
) if we do not take into account
how much
money is made on average during the remaining 10%. If we make 50 times our bet on average when the option is in the money, then I can safely make the statement that buying options is another way to go to the palazzo rather than the poorhouse. Mr. Jim Rogers seems to have gone very far in life for someone who does not distinguish between probability and expectation (strangely, he was the partner of George Soros, a complex man who thrived on rare events—more on him later).

One such rare event is the stock market crash of 1987, which made me as a trader and allowed me the luxury of becoming involved in all manner of scholarship. Nero of the smaller house in
Chapter 1
aims to get out of harm’s way by avoiding exposure to rare events—a mostly defensive approach. I am far more aggressive than Nero and go one step further; I have organized my career and business in such a way as to be able to benefit from them. In other words, I aim at profiting from the rare event, with my asymmetric bets.

Symmetry and Science

In most disciplines, such asymmetry does not matter. In an academic pass/fail environment, where the cumulative grade does not matter, only frequency matters. Outside of that it is the magnitude that counts. Unfortunately, the techniques used in economics are often imported from other areas—financial economics is still a young discipline (it is certainly not yet a “science”). People in most fields outside of it do not have problems eliminating extreme values from their sample, when the difference in payoff between different outcomes is not significant, which is generally the case in education and medicine. A professor who computes the average of his students’ grades removes the highest and lowest observations, which he would call
outliers,
and takes the average of the remaining ones, without this being an unsound practice. A casual weather forecaster does the same with extreme temperatures—an unusual occurrence might be deemed to skew the overall result (though we will see that this may turn out to be a mistake when it comes to forecasting future properties of the ice cap). So people in finance borrow the technique and ignore infrequent events, not noticing that the effect of a rare event can bankrupt a company.

Many scientists in the physical world are also subject to such foolishness, misreading statistics. One flagrant example is in the global-warming debate. Many scientists failed to notice it in its early stages as they removed from their sample the spikes in temperature, under the belief that these were not likely to recur. It may be a good idea to take out the extremes when computing the average temperatures for vacation scheduling. But it does not work when we study the physical properties of the weather—particularly when one cares about a cumulative effect. These scientists initially ignored the fact that these spikes, although rare, had the effect of adding disproportionately to the cumulative melting of the ice cap. Just as in finance, an event, although rare, that brings large consequences cannot just be ignored.

ALMOST EVERYBODY IS ABOVE AVERAGE

Jim Rogers is not the only person committing such traditional fallacy of mistaking mean and median. In all fairness to him, some people who think for a living, such as the star philosopher Robert Nozik, have committed versions of the same mistake (Nozik, besides, was an admirable and incisive thinker; before his premature death he was perhaps the most respected American philosopher of his generation). In his book
The Nature of Rationality
he gets, as is typical with philosophers, into amateur evolutionary arguments and writes the following: “Since not more than 50 percent of the individuals can be wealthier than average.” Of course, more than 50% of individuals can be wealthier than average. Consider that you have a very small number of very poor people and the rest clustering around the middle class. The mean will be lower than the median. Take a population of 10 people, 9 having a net worth of $30,000 and 1 having a net worth of $1,000. The average net worth is $27,100 and 9 out of 10 people will have above average wealth.

Figure 6.1 shows a series of points starting with an initial level W
₀
and ending at the period concerned Wt. It can also be seen as the performance, hypothetical or realized, of your favorite trading strategy, the track record of an investment manager, the price of a foot of average Palazzo real estate in Renaissance Florence, the price series of the Mongolian stock market, or the difference between the U.S. and Mongolian stock markets. It is composed of a given number of sequential observations W
₁
, W
₂
, etc., ordered in such a way that the one to the right comes
after
the one to the left.

Figure 6.1 A Primer on Time Series

If we were dealing with a deterministic world—that is, a world stripped of randomness (the right-column world in
Table P.1
), and we knew with certainty that it was the case, things would be rather easy. The pattern of the series would reveal considerable and predictive information. You could tell with precision what would happen one day ahead, one year ahead, and perhaps even a decade ahead. We would not even need a statistician; a second-rate engineer would do. He does not even need to be armed with a modern degree; someone with nineteenth-century training under Laplace would be able to solve the equations, called
differential equations,
or, equivalently,
equations of motion—
since we are studying the dynamics of an entity whose position depends on time.

If we were dealing with a world where randomness is charted, things would be easy as well, given that there is an entire field created for that called
Econometrics
or
Time Series Analysis.
You would call a friendly econometrician (my experience of econometricians is that they are usually polite and friendly to practitioners). He would run the data in his software, and provide you with diagnostics that would tell you if it is worth investing in the trader generating such a track record, or if it is worth pursuing the given trading strategy. You can even buy the student version of his software for under $999 and run it yourself during the next rainy weekend.

But we are not sure that the world we live in is well charted. We will see that the judgment derived from the analysis of these past attributes may on occasion be relevant. But it may be meaningless; it could on occasion mislead you and take you in the opposite direction. Sometimes market data becomes a simple trap; it shows you the opposite of its nature, simply to get you to invest in the security or mismanage your risks. Currencies that exhibit the largest historical stability, for example, are the most prone to crashes. This was bitterly discovered in the summer of 1997 by investors who chose the safety of the pegged currencies of Malaysia, Indonesia, and Thailand (they were pegged to the U.S. dollar in a manner to exhibit no volatility, until their sharp, sudden, and brutal devaluations).

We could be either too lax or too stringent in accepting past information as a prediction of the future. As a skeptic, I reject a sole time series of the past as an indication of future performance; I need a lot more than data. My major reason is the
rare event,
but I have plenty of others.

On the surface, my statement here may seem to contradict earlier discussions, where I blame people for not learning enough from history. The problem is that we read too much into shallow recent history, with statements like “this has never happened before,” but not from history in general (things that never happened before in one area tend eventually to happen). In other words, history teaches us that things that never happened before do happen. It can teach us a lot outside of the narrowly defined time series; the broader the look, the better the lesson. In other words, history teaches us to avoid the brand of naive empiricism that consists of learning from casual historical facts.

THE RARE-EVENT FALLACY

The Mother of All Deceptions

The rare event, owing to its dissimulative nature, can take a variety of shapes. It is in Mexico that it was spotted first, where it was called by academics the
peso problem.
Econometricians were puzzled by the behavior of the Mexican economic variables during the 1980s. The money supply, interest rates, or some similar measure of small relevance to the story exhibited some moody behavior, thwarting many of their efforts at modeling them. These indicators erratically switched between periods of stability and brief bursts of turbulence without warning.

By generalization, I started to label a rare event as any behavior where the adage “beware of calm waters” can hold. Popular wisdom often warns of the old neighbor who appears to remain courtly and reserved, the model of an excellent citizen, until you see his picture in the national paper as a deranged killer who went on a rampage. Until then, he was not known to have committed any transgression. There was no way to predict that such pathological behavior could emanate from such a nice person. I associate rare events with any misunderstanding of the risks derived from a narrow interpretation of past time series.

Rare events are always unexpected, otherwise they would not occur. The typical case is as follows. You invest in a hedge fund that enjoys stable returns and no volatility, until one day, you receive a letter starting with “An unforeseen and
unexpected
event, deemed a rare occurrence . . .” (emphasis mine). But rare events exist precisely because they are unexpected. They are generally caused by panics, themselves the results of liquidations (investors rushing to the door simultaneously by dumping anything they can put their hands on as fast as possible). If the fund manager or trader expected it, he and his like-minded peers would not have invested in it, and the rare event would not have taken place.

The rare event is not limited to one security. It can readily affect the performance of a portfolio. For example, many traders engage in the purchase of mortgage securities and hedge them in some manner to offset the risks and eliminate the volatility, hoping to derive some profits in excess of the Treasury bond returns (which is used as the benchmark of the minimum expected returns on an investment). They use computer programs and draw meaningful assistance from Ph.D.s in applied mathematics, astrophysics, particle physics, electrical engineering, fluid dynamics, or sometimes (though rarely) plain Ph.D.s in finance. Such a portfolio shows stable returns for long periods. Then, suddenly, as if by accident (I consider that
no
accident), the portfolio drops by 40% of its value when you expect, at the worst, a 4% drop. You call the manager to express your anger and he tells you that it was not his fault, but somehow the relationship dramatically changed (literally). He will also point out to you that similar funds also experienced the same problems.

Recall that some economists call the rare event a “peso problem.” The designation peso problem does not appear to be undeservedly stereotypical. Things have not gotten better since the early 1980s with the currency of the United States’ southern neighbor. Long periods of stability draw hordes of bank currency traders and hedge fund operators to the calm waters of the Mexican peso; they enjoy owning the currency because of the high interest rate it commands. Then they “unexpectedly” blow up, lose money for investors, lose their jobs, and switch careers. Then a new period of stability sets in. New currency traders come in with no memory of the bad event. They are drawn to the Mexican peso, and the story repeats itself.

It is an oddity that most fixed-income financial instruments present rare events. In the spring of 1998, I spent two hours explaining to a then-important hedge fund operator the notion of the peso problem. I went to great lengths to explain to him that the concept was generalized to every form of investment that was based on a naive interpretation of the volatility of past time series. The reply was:“ You are perfectly right. We do not touch the Mexican peso. We only invest in the Russian ruble.” He blew up a few months later. Until then, the Russian ruble carried attractive interest rates, which invited yield hogs of all types to get involved. He and other holders of investments denominated in rubles lost close to 97% of their investment during the summer of 1998.

We saw in
Chapter 3
that the dentist does not like volatility as it causes a high incidence of negative pangs. The closer he observes his performance, the more pain he will experience owing to the greater variability at a higher resolution. Accordingly investors, merely for emotional reasons, will be drawn into strategies that experience
rare but large
variations. It is called pushing randomness under the rug. Psychologists recently found out that people tend to be sensitive to the presence or absence of a given stimulus rather than its magnitude. This implies that a loss is first perceived as just a loss, with further implications later. The same with profits. The agent would prefer the number of losses to be low and the number of gains to be high, rather than optimizing the total performance.