Casino math (PDF) may be the most important wisdom you can know to be a successful trend follower. In fact, I feature much of this thinking in my documentary film.
“Someone who has made a successful living as a poker player for a few years would more likely be a good trader than someone who hasn’t,” said Aaron Brown, a 53-year-old former poker pro who is now a risk manager at AQR Capital Management LLC in Greenwich, Connecticut, which oversees $23 billion. “They know to push when they have the edge and they know how not to bust, and that’s a tough combination to find.”
I love it when people tell me the trend following ‘winners’ are the lucky survivors. In my humble opinion people who think like that are either ignorant in the short-term willing to learn/be corrected or, and I say this bluntly, losers in life unable to accept reality. If trend following winners are the lucky monkeys hitting the keyboards, than the king of the monkeys must be Warren Buffett. Buffett himself makes the case for why this is bullshit (there is no other word) in an excerpt from Snowball:
The most recent review of my book “Trend Following” on Amazon is this:
For 200 pages you read how much trend followers made, trend followers are so great, they are always winners…. It’s almost like the book is promoting some money managers. Seriously the book is pretty bad, I almost feel embarrassed to write a review. According to the author you don’t need to know anything about what you are really buying, as long as it trends up. So I wonder if Mr. Covel would buy a bag of dirt for $10 just because it was $7 last week. I don’t want to get to the dynamics of trends and explain that after you buy a up-trending security you may lose money. But I wonder if Mr. Covel plays rulette and bets on red after red hits 3 in a row, thinking the new trend is red. I had the feeling that this book is written to increase the number of trend followers so when the time comes some people can dump the stocks easier. I wonder how Mr. Covel knows that you wont be the one standing without a chair when the music stops. Anyway, I will say one thing, buying this book may cost you a lot more than its price.
I will not bother with the vast majority of the above reviewer’s lack of understanding on my blog (others are welcome to use his comments as an entry into a teaching rebuttal), but his comment about “promoting some money managers” gives me a great opportunity to clarify with hard data. For example, most people have NEVER heard of Dunn Capital unless they have read my book, read Futures Magazine, or are involved in the money management industry. So there is a very compelling reason for me to pass along data like this (PDF of Dunn’s 2008 performance). Personally, whether you want to be the next Dunn, let Dunn trade your money, or just sit there in your mutual fund and wet your pants trying to figure out if someone can give you permission to think for yourself — Dunn’s performance data is NEWS. Not news cause I have some business dealing with Dunn (I don’t), but because most people just lost their *** in 2008 and he just made +50% on his WMA program (inception 1984). And for those who might want to whack at me and say Dunn was an anomaly, no dice on that angle. He is one of many trend traders who just whacked 2008 markets like a piñata.
Notice his really bad spell (03, 04, 05) was right when Greenspan was engineering the credit/real estate/stock bubbles? I wonder if in hindsight most people would take Dunn or buy and hold.
“Life is nothing more than a series of bets and bets are really nothing more than questions and their answers. There is no real difference between, “Should I take another hit on this Blackjack hand?” and “Should I get out of the way of that speeding and wildly careening bus?” Each shares two universal truths: a set of probabilities of potential outcomes and the singular outcome that takes place. Everyday we place hundreds if not thousands of bets – large and small, some seemingly well considered and others made without a second thought. The vast majority of the latter, life’s little gambles made without any thought, might certainly be trivial. “Should I tie my shoes?” Seems to offer no big risk, nor any big reward. While others, such as the aforementioned – speeding and wildly careening bus – would seem to have greater impact on our lives. However, if deciding not to tie your shoes that morning causes you to trip and fall down in the middle of the road when you finally decide to fold your hand and give that careening bus plenty of leeway, well then, in hindsight the trivial has suddenly become paramount.”
If you are involved in financial markets, you have gotten the memo about fat tails by now.
But awareness of extreme events is not enough. Thoughtful investors must understand two interrelated aspects of the market. The first is the statistical properties of price movements, including important deviations from the bell-shaped distribution. Academics, risk managers, and quantitative investors have explored this aspect extensively. Researchers recognized decades ago that the distribution of price changes includes fat tails.
The second aspect, and one often overlooked or misunderstood, is the mechanism that leads to the statistical imprint. Much of the work on the market’s statistical properties is divorced from the propagating mechanism, while traditional theories of market efficiency assume the mechanisms. Crucially, understanding the mechanism provides insight into how and why markets fail.
Our focus here is on nonlinearity. Many complex systems, including markets, have critical points where small incremental condition changes lead to large-scale effects. Researchers in both the physical and social sciences have known about these critical points for a long time; so much so that terms like phase transition and tipping point have slipped into our day-to-day language. Still, critical points throw a monkey wrench into our mostly linear cause-and-effect thinking.
Critical points help explain our perpetual surprise at fat-tail events: We don’t see them coming because the state change is much greater than the perturbation suggests. Water does not undergo a dramatic change as it drops from 35 to 33 degrees Fahrenheit, but two degrees of additional cooling changes its state from liquid to solid. Likewise, large changes can occur in markets without visible manifestation in asset price change, while small additional changes can flip the price switch.
A conversation about a friend’s cancer came up today. I immediately thought of a chapter in Stephen Jay Gould’s book “Full House”:
The Median Isn’t the Message by Stephen Jay Gould
Stretching the Truth: The median isn’t the message by evolutionary biologist Stephen Jay Gould. Image from Wikipedia.
My life has recently intersected, in a most personal way, two of Mark Twain’s famous quips. One I shall defer to the end of this essay. The other (sometimes attributed to Disraeli), identifies three species of mendacity, each worse than the one before – lies, lies, and statistics.
Consider the standard example of stretching the truth with numbers – a case quite relevant to my story. Statistics recognizes different measures of an “average,” or central tendency. The mean is our usual concept of an overall average – add up the items and divide them by the number of sharers (100 candy bars collected for five kids next Halloween will yield 20 for each in a just world). The median, a different measure of central tendency, is the half-way point. If I line up five kids by height, the median child is shorter than two and taller than the other two (who might have trouble getting their mean share of the candy). A politician in power might say with pride, “The mean income of our citizens is $15,000 per year.” The leader of the opposition might retort, “But half our citizens make less than $10,000 per year.” Both are right, but neither cites a statistic with impassive objectivity. The first invokes a mean, the second a median. (Means are higher than medians in such cases because one millionaire may outweigh hundreds of poor people in setting a mean; but he can balance only one mendicant in calculating a median).
The larger issue that creates a common distrust or contempt for statistics is more troubling. Many people make an unfortunate and invalid separation between heart and mind, or feeling and intellect. In some contemporary traditions, abetted by attitudes stereotypically centered on Southern California, feelings are exalted as more “real” and the only proper basis for action – if it feels good, do it – while intellect gets short shrift as a hang-up of outmoded elitism. Statistics, in this absurd dichotomy, often become the symbol of the enemy. As Hilaire Belloc wrote, “Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.”
This is a personal story of statistics, properly interpreted, as profoundly nurturant and life-giving. It declares holy war on the downgrading of intellect by telling a small story about the utility of dry, academic knowledge about science. Heart and head are focal points of one body, one personality.
In July 1982, I learned that I was suffering from abdominal mesothelioma, a rare and serious cancer usually associated with exposure to asbestos. When I revived after surgery, I asked my first question of my doctor and chemotherapist: “What is the best technical literature about mesothelioma?” She replied, with a touch of diplomacy (the only departure she has ever made from direct frankness), that the medical literature contained nothing really worth reading. Of course, trying to keep an intellectual away from literature works about as well as recommending chastity to Homo sapiens, the sexiest primate of all. As soon as I could walk, I made a beeline for Harvard’s Countway medical library and punched mesothelioma into the computer’s bibliographic search program. An hour later, surrounded by the latest literature on abdominal mesothelioma, I realized with a gulp why my doctor had offered that humane advice. The literature couldn’t have been more brutally clear: mesothelioma is incurable, with a median mortality of only eight months after discovery. I sat stunned for about fifteen minutes, then smiled and said to myself: so that’s why they didn’t give me anything to read. Then my mind started to work again, thank goodness.
If a little learning could ever be a dangerous thing, I had encountered a classic example. Attitude clearly matters in fighting cancer. We don’t know why (from my old-style materialistic perspective, I suspect that mental states feed back upon the immune system). But match people with the same cancer for age, class, health, socioeconomic status, and, in general, those with positive attitudes, with a strong will and purpose for living, with commitment to struggle, with an active response to aiding their own treatment and not just a passive acceptance of anything doctors say, tend to live longer. A few months later I asked Sir Peter Medawar, my personal scientific guru and a Nobelist in immunology, what the best prescription for success against cancer might be. “A sanguine personality,” he replied. Fortunately (since one can’t reconstruct oneself at short notice and for a definite purpose), I am, if anything, even-tempered and confident in just this manner.
Hence the dilemma for humane doctors: since attitude matters so critically, should such a sombre conclusion be advertised, especially since few people have sufficient understanding of statistics to evaluate what the statements really mean? From years of experience with the small-scale evolution of Bahamian land snails treated quantitatively, I have developed this technical knowledge – and I am convinced that it played a major role in saving my life. Knowledge is indeed power, in Bacon’s proverb.
The problem may be briefly stated: What does “median mortality of eight months” signify in our vernacular? I suspect that most people, without training in statistics, would read such a statement as “I will probably be dead in eight months” – the very conclusion that must be avoided, since it isn’t so, and since attitude matters so much. I was not, of course, overjoyed, but I didn’t read the statement in this vernacular way either. My technical training enjoined a different perspective on “eight months median mortality.” The point is a subtle one, but profound – for it embodies the distinctive way of thinking in my own field of evolutionary biology and natural history.
We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. (Thus we hope to find an unambiguous “beginning of life” or “definition of death,” although nature often comes to us as irreducible continua.) This Platonic heritage, with its emphasis in clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as the hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and variation around the median just a device for its calculation, the “I will probably be dead in eight months” may pass as a reasonable interpretation.
But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions. Therefore, I looked at the mesothelioma statistics quite differently – and not only because I am an optimist who tends to see the doughnut instead of the hole, but primarily because I know that variation itself is the reality. I had to place myself amidst the variation.
When I learned about the eight-month median, my first intellectual reaction was: fine, half the people will live longer; now what are my chances of being in that half. I read for a furious and nervous hour and concluded, with relief: ****ed good. I possessed every one of the characteristics conferring a probability of longer life: I was young; my disease had been recognized in a relatively early stage; I would receive the nation’s best medical treatment; I had the world to live for; I knew how to read the data properly and not despair.
Another technical point then added even more solace. I immediately recognized that the distribution of variation about the eight-month median would almost surely be what statisticians call “right skewed.” (In a symmetrical distribution, the profile of variation to the left of the central tendency is a mirror image of variation to the right. In skewed distributions, variation to one side of the central tendency is more stretched out – left skewed if extended to the left, right skewed if stretched out to the right.) The distribution of variation had to be right skewed, I reasoned. After all, the left of the distribution contains an irrevocable lower boundary of zero (since mesothelioma can only be identified at death or before). Thus, there isn’t much room for the distribution’s lower (or left) half – it must be scrunched up between zero and eight months. But the upper (or right) half can extend out for years and years, even if nobody ultimately survives. The distribution must be right skewed, and I needed to know how long the extended tail ran – for I had already concluded that my favorable profile made me a good candidate for that part of the curve.
The distribution was indeed, strongly right skewed, with a long tail (however small) that extended for several years above the eight month median. I saw no reason why I shouldn’t be in that small tail, and I breathed a very long sigh of relief. My technical knowledge had helped. I had read the graph correctly. I had asked the right question and found the answers. I had obtained, in all probability, the most precious of all possible gifts in the circumstances – substantial time. I didn’t have to stop and immediately follow Isaiah’s injunction to Hezekiah – set thine house in order for thou shalt die, and not live. I would have time to think, to plan, and to fight.
One final point about statistical distributions. They apply only to a prescribed set of circumstances – in this case to survival with mesothelioma under conventional modes of treatment. If circumstances change, the distribution may alter. I was placed on an experimental protocol of treatment and, if fortune holds, will be in the first cohort of a new distribution with high median and a right tail extending to death by natural causes at advanced old age.
It has become, in my view, a bit too trendy to regard the acceptance of death as something tantamount to intrinsic dignity. Of course I agree with the preacher of Ecclesiastes that there is a time to love and a time to die – and when my skein runs out I hope to face the end calmly and in my own way. For most situations, however, I prefer the more martial view that death is the ultimate enemy – and I find nothing reproachable in those who rage mightily against the dying of the light.
The swords of battle are numerous, and none more effective than humor. My death was announced at a meeting of my colleagues in Scotland, and I almost experienced the delicious pleasure of reading my obituary penned by one of my best friends (the so-and-so got suspicious and checked; he too is a statistician, and didn’t expect to find me so far out on the right tail).
Still, the incident provided my first good laugh after the diagnosis. Just think, I almost got to repeat Mark Twain’s most famous line of all: the reports of my death are greatly exaggerated.
