Luck be a Trader...
In life, people generally don’t want to think that their success has anything to do with luck…but they are more than willing to blame their failures to a random act of misfortunes.
I have often been faced with questions of the sort: "Who do you think you are to tell me that I might have been plain lucky in my life?" Well, nobody really believes that he or she was lucky. My approach is that, with our Monte Carlo engine, we can manufacture purely random situations. We can do the exact opposite of conventional methods; in place of analyzing real people hunting for attributes, we can create artificial ones with precisely known attributes. Thus, we can manufacture situations that depend on pure, unadulterated luck, without the shadow of skills or whatever we have called non-luck. In other words, we can man-make pure nobodies to laugh at; they will be by design stripped of any shadow of ability.
Let us use the Monte Carlo generator and construct a population of 10,000 fictional investment managers. Assume that they each have a perfectly fair game; each one has a 50% probability of making $10,000 at the end of the year, and a 50% probability of losing $10,000. Let us introduce an additional restriction; once a manager has a single bad year, he is thrown out of the sample. Thus, we will operate like the legendary speculator George Soros, who was said to tell his managers gathered in a room: "Half of you guys will be out by next year." Like Soros, we have extremely high standards; we are looking only for managers with an unblemished record. We have no patience for low performers.
The Monte Carlo generator will toss a coin; heads and the manager will make $10,000 over the year, tails and he will lose $10,000. We run it for the first year. At the end of the year, we expect 5,000 managers to be up $10,000 each, and 5,000 to be down $10,000. Now we run the game a second year. Again, we can expect 2,500 managers to be up two years in a row; another year, 1,250; a fourth one, 625; a fifth, 313. We have now, simply in a fair game, 313 managers who made money for five years in a row. Out of pure luck.
Survivor Bias: Running out of Luck
Meanwhile, if we throw one of these successful traders into the real world we would get very interesting and helpful comments on his remarkable style, his incisive mind, and the influences that helped him achieve such success. Some analysts may attribute his achievement to precise elements among his childhood experiences. And the following year, should he stop outperforming would start laying blame, finding fault with the relaxation in his work ethics, or his dissipated lifestyle. The truth will be, however, that he simply ran out of luck.
Let’s push the argument further to make it more interesting. We create a cohort that is composed exclusively of incompetent managers. We will define an incompetent manager as someone who has a negative expected return, the equivalent of the odds being stacked against him. We instruct the Monte Carlo generator now to draw from an urn. The urn has 100 balls, 45 black and 55 red. By drawing with replacement, the ratio of red to black balls will remain the same. If we draw a black ball, the manager will earn $10,000. If we draw a red ball, he will lose $10,000. The manager is thus expected to earn $10,000 with 45% probability, and lose $10,000 with 55%. On average, the manager will lose $1,000 each round – but only on average.
At the end of the first year, we still expect to have 4,500 managers turning a profit (45% of them), the second, 45% of that number, 2,025. The third, 911; the fourth, 410; the fifth, 184. Let us give the surviving managers names and dress them in business suits. True, they represent less than 2% of the original cohort. But they will get attention. Nobody will mention the other 98%. What can we conclude?
The first counterintuitive point is that a population entirely composed of bad managers will produce a small amount of great track records. As a matter of fact, assuming the manager shows up unsolicited at your door, it will be practically impossible to figure out whether he is good or bad. The results would not markedly change even if the population were composed entirely of managers who are expected in the long run to lose money. Why? Because owing to volatility, some of them will make money. We can see here that volatility actually helps bad investment decisions.
Survivor Bias: Sample Size
The second counterintuitive point is that the expectation of the maximum of track records, with which we are concerned, depends more on the size of the initial sample, than on the individual odds per manager. In other words, the number of managers with great track records in a given market depends far more on the number of people who started in the investment business (in place of going to dental school), rather than on their ability to produce profits. It also depends on the volatility. Why do I use the notion of expectation of the maximum? Because I am not concerned at all with the average track record. I will get to see only the best of the managers, not all of the managers. This means that we would see more "excellent managers" in 2006 than in 1998, provided the cohort of beginners was greater in 2001 than it was in 1993 – I can safely say that it was.
The "hot hand in basketball" is another example of misperception of random sequences: It is very likely in a large sample of players for one of them to have an inordinately lengthy lucky streak. As a matter of fact it is very unlikely that an unspecified player somewhere does not have an inordinately lengthy lucky streak. This is a manifestation of the mechanism called regression to the mean. I can explain it as follows:
Generate a long series of coin flips producing heads and tails with 50% odds each and fill up sheets of paper. If the series is long enough you may get eight heads or eight tails in a row, perhaps even ten of each. Yet you know that in spite of these wins the conditional odds of getting a head or a tail is still 50%. Imagine these heads and trails as monetary bets filling up the coffers of an individual. The deviation from the norm as seen in excess heads or excess tails is here entirely attributable to luck, in other words, to variance, not to the skills of the hypothetical player (since there is an even probability of getting either).
A result is that in real life, the larger the deviation from the norm, the larger the probability of it coming from luck rather than skills: Consider that even if one has 55% probability of head, the odds of ten wins is still very small. This can be easily verified in stories of very prominent people in trading rapidly reverting to obscurity, like the heroes I used to watch in trading rooms. This applies to height of individuals or the size of dogs. In the latter case, consider that two average-size parents produce a large litter. The largest dogs, if they diverge too much from the average, will tend to produce offspring of smaller size than themselves, and vice versa. This "reversion" for the large outliers is what has been observed in history and explained as regression to the mean. Note that the larger the deviation, the more important its effect.
Again one word of warning: All deviations do not come from this effect, but a disproportionately large proportion of them do.
Survivor Bias: The Annoying Effects of Randomness
To get more technical, I have to say that people believe that they can figure out the properties of the distribution from the sample they are witnessing. When it comes to matters that depend on the maximum, it is altogether another distribution that is being inferred, that of the best performers. We call the difference between the average of such distribution and the unconditional distribution of winners and losers the survivorship bias – here the fact that about 3% of the initial cohort discussed earlier will make money five years in a row. In addition, this example illustrates the properties of ergodicity, namely, that time will eliminate the annoying effects of randomness. Looking forward, in spite of the fact that these managers were profitable in the past five years, we expect them to break even in any future time period. They will fare no better than those of the initial cohort who failed earlier in the exercise. Ah, the long term.
A few years ago, when I told a then Master-of-the-Universe type, that track records were less relevant than he thought, he found the remark so offensive that he violently flung his cigarette lighter in my direction. The episode taught me a lot. Remember that nobody accepts randomness in his own success, only his failure. His ego was pumped up as he was heading up a department of "great traders" who were then temporarily making a fortune in the markets and attributing the idea to the soundness of their business, their insights, or their intelligence. They subsequently blew up during the harsh New York winter of 1994. The interesting part is that several years later I can hardly find any of them still trading (ergodicity).
Recall that the survivorship bias depends on the size of the initial population. The information that a person derived some profits in the past, just by itself, is neither meaningful nor relevant. We need to know the size of the population from which he came. In other words, without knowing how many managers out there have tried and failed, we will not be able to assess the validity of the track record. If the initial population includes ten managers, then I would give the performer half my savings without a blink. If the initial population is composed of 10,000 managers, I would ignore the results. The latter situation is generally the case; these days so many people have been drawn to the financial markets. Many college graduates are trading as a first career, failing, and then going to dental school.
If, as in a fairy tale, these fictional managers materialized into real human beings, one of these could be the person I am meeting tomorrow at 11:45 a.m. Why did I select 11:45 a.m.? Because I will question him about his trading style. I need to know how he trades. I will then be able to claim that I have to rush to a lunch appointment if the manager puts too much emphasis on his track record.
Nassim Nicholas Taleb
for The Daily Reckoning
December 8, 2004
America’s stock was sold again yesterday; the dollar fell.
But the dollar’s nemesis, the anti-dollar – gold – fell too. Gold is probably consolidating recent gains. It would not be surprising to see it fall further, at least in the near-term. The dollar, on the other hand, is probably ready for a breather. At least, that is what the technical analysts believe.
We remind readers, too, that we have still not abandoned our view that the U.S. economy is headed towards a long, soft, slow slump – a la Japan. If we’re right, do not expect gold to zoom up, as it did in the late ’70s, at least not yet. Nor is it sure that the dollar will continue to collapse – at least not right away. Last month’s employment figures, recent sales figures, and the bond market, all whisper: "slump ahead." If we are right, this latest rally in the Dow must peak out soon…bonds could hold up for a while longer…and the dollar could surprise us.
Mr. Greenspan, meanwhile, continued his Oscar-winning performance to rave reviews from all over the planet. The celebrated economist is starring in the international blockbuster: How I Saved the World, a fantasy production brought to you by the Federal Reserve System, the U.S. Treasury Department, and the White House.
In Tokyo, poor Mr. Asakawa has another role to play; how he must sputter and choke when he sees the U.S. Fed chief on television! Or perhaps he saw the photo of Mr. Greenspan in The New York Times; there he was smiling as he strode off stage after a speech to community bankers. The Japanese central banker must gag at the sight of his American counterpart…for there is the man who put him in his misery…the man who enjoys the world’s applause while he, Mr. Asakawa, tosses and turns in anonymity.
We don’t know if his little seismic money machine went off after midnight last night…but surely he must have slept badly as the dollar fell again. You recall, dear reader, the Japanese central banker sleeps with a currency market monitor by his beside. If the dollar falls outside of an anticipated range, the infernal machine begins to beep as if the house were on fire. Yesterday, the dollar fell, but not much. We don’t know where Mr. Asakawa set his alarm. And we don’t know why he bothered.
The question came to us just this morning. Why would he bother to put a currency alarm by his bed if there was nothing he could do about it anyway? Was he merely troubling himself for no reason? Or had he planned some intervention? If the dollar fell below a certain level, would he move to boost it up? Or sell some of Japan’s $720 billion in dollar-denominated treasury bonds? Selling the bonds would have a catastrophic effect – not only on the U.S., but also on the rest of his pile. In days, the greenback might lose another 20% of its value – which would mean more than a hundred of billion in losses to Japan. But supporting the dollar at this stage would cost money – increasing Japan’s exposure to the dollar…and even greater losses in the future.
The Japanese are trapped. It is our currency, as John Connelly once put it, but it’s their problem. At least, so it appears.
Isn’t it interesting, dear reader, the way things work? At any given moment, people can make the smart decision. But smart decisions often accumulate into a very dumb position. Pursuing short-term goals in a smart way, they often end up with the exact opposite of what they had hoped to get in the long run. Surely, the Japanese were right to work and save. And surely they were right to buy U.S. Treasury bonds. What could be safer? And buying U.S. Treasuries had the added bonus of stimulating Japan’s major customer to buy more.
But now they are trapped – victims of their own smart success. It is as if a bartender had extended too much credit to a local drunk. He now has to lend him more – or recognize that his whole pile of I.O.Us is worthless. So he sets up another drink – on credit, of course – and hopes the bum will somehow pull himself together.
And who can blame Mr. Greenspan? Did not he do the smart thing too? He got a chance to play a role that the world wanted him to play – a central banker so shrewd he could make sure everyone got something for nothing…an economist so savvy he could come up with a short term lending rate better than the one that buyers and sellers of credit would choose on their own. The world wanted to be deceived; Mr. Greenspan gave it a great performance. Hocus-pocus, mumbo-jumbo, folderol and voodoo – the Fed chief used every technique known to modern economics and ancient legerdemain. And the audience loves it still!
But what will we really get from Mr. Greenspan’s sparkling performance. Something for nothing? Or nothing for something? We are on the edge of our chairs.
More news, from our team at The Rude Awakening:
Addison Wiggin, reporting from unseasonably warm Baltimore…
"We dredge up this lesson in financial history, dear reader, if only because today the pound crossed the $1.95 mark for the first time since that fateful autumn day 12 years ago. It’s a fascinating story and another glaring example of a government being humiliated by the foreign exchange market…"
Bill Bonner, back in London:
*** The average worker in America earns $21 per hour. In China, the average man gets 61 cents for his hour’s work. A great leveling has begun. We wait to see how far it will go and how long it will go on.
*** Some people will do anything to get into public office. Eliot Spritzer has been putting people in jail. At least now he’s admitted why he was doing it; yesterday he announced his bid for governor of New York. We hope the rascal gets what he deserves.
*** And here’s our favorite columnist, writing in the International Herald Tribune. "A new mission for America," proposes Thomas L. Friedman.
Friedman seems to have given up on his last great mission – invading Iraq. The troops, he told us, were doing a marvelous job of "nurturing" democracy. But the "non-healing" Bush administration bungled the job, he believes. Now, the world improver offers us a new purpose…a Great Cause as grandiose as it is imbecilic: Energy independence!
"Imagine if every American kid, in every school, were galvanized around such a vision [making America energy independent in 10 years]…" he writes.
We shudder. Surely one or two kids could galvanize themselves around some other vision – say, winning the state spelling bee…or building a fort in the backyard…or even some other world improving vision, such as teaching everyone to speak Esperanto…or making the U.S. independent in avocados.
World improvers are always looking for an excuse to boss and bully. Mr. Friedman’s particular contribution to the genre is a certain comic absurdity that leaves the reader gasping for air.
"He must be an embarrassment to the newspaper," said an acquaintance this morning. "But he writes for The New York Times and represents the middle-brow Jewish market, which must be a big part of the paper’s readership. That must be why they keep him on…either that, or he’s got photos of the publisher in a compromising position."
Mr. Friedman’s latest column tells us that oil revenues are practically the root of all evil. Take away the oil revenue, says he, and "I will give you political reform from Moscow to Riyadh to Tehran." We do not doubt that lower oil prices would shake things up in oil producing countries; but we have no reason to think that anyone would be better off as a result. For there is no reason to think that oil revenues lead to badness, nor that the lack of oil revenue leads to goodness. Texas was an oil exporter for most of the 20th century; we do not recall that the state was any worse or better than New Jersey, which imported oil. Nor can we recall any great reforms in Texas after the oil revenues dried up. Britain gained billions in oil revenue after the North Sea fields were exploited; we don’t recall any horrible consequences. Now, Britain’s income from selling oil is coming to an end. What great reforms can we expect?
Nor did North Korea become North Korea because of $45 oil. Or Iraq…or Afghanistan or Venezuela…or Zimbabwe. Nor did oil revenues finance the Hitler youth…Yes, the oil industry did wonders for Saudi Arabia and the Bush family…but what conclusion can we draw from that?
We don’t know, but to hear Friedman tell it, energy independence is the ticket to Eden:
"If Bush made energy independence his moon shot, he would dry up revenue for terrorism; force Iran, Russia, Venezuela and Saudi Arabia to take the path of reform – which they will never do with $45-a-barrel oil – strengthen the dollar; and improve his own standing in Europe, by doing something huge to reduce global warming. He would also create a magnet to inspire young people to contribute to the war on terrorism and America’s future by becoming scientists, engineers and mathematicians."
How marvelous! Let us all tie our shoelaces together and hop to work! Think of the energy we will save…and what a great world we will have.