Plight of the Fortune Tellers: two views of probability

It might seem that I’m going off the deep end. First a foray into admittedly phony astrology, and now a book entitled Plight of the Fortune Tellers. But this book is serious stuff. It’s written by Riccardo Rebonato, I assume still global head of market risk and global head of the quantitative research team at RBS, a visiting lecturer at Oxford, and adjunct professor at Imperial College; it’s subtitled Why We Need to Manage Financial Risk Differently; and it was published by Princeton University Press (2007). The fact that the Royal Bank of Scotland subsequently had to be bailed out to the tune of some $74 billion might make you snicker (yes, I guess RBS should have managed its financial risk differently). But I’m not reading this book as a call for reform, despite its subtitle. Rather I’m interested in Rebonato’s analysis of concepts we can all use in managing our trades and our portfolios. I’ll share insights from this book in dribs and drabs over time. Fortune tellers might seem like a sexy subject; risk management, I know, is not.

Today’s topic is probability. Tomes have been written about probability, but here I’m getting down to basics. There are two general ways to look at probability. The first is the frequentist view, best illustrated by coin tosses. The second is the Bayesian (or subjective) view, “often seen as a measure of belief, susceptible of being changed by new evidence.” (p. 19) The frequentist view underlies most current risk management: “We estimate the probabilities, and from these we determine the actions.” Rebonato suggests that the opposite should apply: “We observe the actions, and from these we impute the probabilities.” (p. 18)

The frequentist view requires an event such as the tossing of a coin that can, in principle, be repeated many times under virtually identical conditions. The findings can be precise, down to many decimal points. We can say, for instance, that the chance of a coin coming up heads is 0.5000001, that the probability of a newborn baby being female is 0.52345, or that the probability of a randomly chosen individual in a well-specified population having red hair is 0.1221.

But not all probabilistic statements have these characteristics. If, for instance, you are speculating about the probability of a Democrat being elected president (and are just as willing to wager on the outcome of the election as you would be on the outcome of a coin toss or the sex of the next newborn), you’ve moved outside the world of the repeatable. You have to rely on beliefs about the likelihood of a president being elected if the economy is soft, if we’re involved in war, and so on. You can look back on previous presidential elections for guidance, but they did not take place under identical conditions. Moreover, you would never make such a bizarre statement as that the probability of a Democrat being elected president is 0.520032.

A fairly strong case can be made that the frequentist view is a subset or a special case of Bayesian statistics. Rebonato illustrates this with a story about a Martian and a coin toss. You meet the Martian and, “not knowing how to strike up polite conversation, you take a coin out of your pocket.” (p. 50) The Martian has never seen a coin, so he obviously has never taken part in a coin flipping experiment. Your coin is run of the mill, nothing special about it. You toss it four times and each time it comes up heads. Rebonato then asks what you would conclude about the fairness of the coin and what the Martian is likely to conclude. You would probably just soldier on, assuming it was fair, and require odds of 50-50. The rational Martian, however, should not accept these odds; for him heads is much more likely than tails.

Rebonato continues: “You and your Martian friend have observed the same experiment, yet you reach very different conclusions. How can that be? Because, Bayesian statisticians say, we almost never approach an experiment with random outcomes without some prior ideas about the setting and the likelihood of the possible outcomes. New evidence modifies (should modify) our prior beliefs and transforms them into our posterior beliefs. The stronger the prior belief, the more difficult it will be to change it. If we really and truly have no prior beliefs about the situation at hand, as was the case with the Martian when he observed the coin flips, then and only then will we be totally guided by the evidence. This is the situation that is dealt with with infinite care and precision in ‘traditional’ statistics books. Yet it remains a rather special situation.” (p. 52)

Horoscopes for traders and investors

I’m trying something new. The seemingly mandatory disclaimer: I am not an astrologist, I don’t believe in astrology, and I’m not making any actionable predictions. If you act on any information in your horoscope and things go badly, you can’t hold me responsible. On the other hand, if things go well, feel free to think kindly of me. In these posts (weekly if I can come up with enough material, monthly otherwise) I will offer a few insights in horoscope format. I have no idea how many of these posts I’ll do; if the concept is stillborn, I will quietly bury it.

Aries March 20-April 20—Think twice before making that fearless trek into the unknown. Do you have the proper training, gear, and escape plan? If not, consider the safety of the paper world. You will not meet a real piranha in a simulated Amazon.

Taurus April 20-May 21—Get your feet out of the mud or you’re liable to get seriously stuck. Have someone throw a couple of planks across the mud. It doesn’t matter what kind of planks you use; the cheapest fir will work just as well as curly maple. By analogy, you don’t have to spring for the most expensive data provider, trading platform, or educational program to get yourself going. Free is sometimes surprisingly good.

Gemini May 21-June 21—Take advantage of your astral ability to go with the flow. You have no idea how great a gift this is. Most people end up in a dance studio for traders following footprints on the floor; you have the potential to be a Fred Astaire. Be cautious, though. Fred Astaire became more famous than his more talented sister because he had “durability.”

Cancer June 21-July 22—You can’t retract that losing trade, but stop brooding over it. If you made a mistake, learn from it; if the market simply didn’t accommodate you, suck it up. That’s part of the trading business. Some inventory you have to move at a loss—that battery-powered hula hoop for couch potato exercisers, for instance, that you thought was such a good deal at $10. Consider yourself lucky to have found a sucker to take it off your hands at $8.

Leo July 22—August 23—If you truly love being center stage, think about becoming a TV commentator or a trading guru. Both fields are crowded, but trading skills are not required. An oversized ego helps.

Virgo August 23-September 23—Continue to pursue your penchant for detail. Trading success comes in large part from perfecting the many details of trade execution, position sizing, risk management, and post-trade analytic metrics. With so much in trading beyond your control, you’ll have a genuine edge over other traders if you perfect what most ignore.

Libra September 23-October 23—Trading is a lonely business; seek companionship elsewhere. Once you opted to be an online trader you exchanged conversations around the water cooler for independence. Cultivate your social ties outside of trading hours and make these relationships count.

Scorpio October 23-November 22—If you are a discretionary trader, your keen sense of intuition should serve you well as long as you’ve done your analytic homework and have honed your intuition through many, many hours of screen time. Discretionary trading is in large measure an art where an ounce of intuition can often trump a pound of pondering.

Sagittarius November 22-December 22—So you’re feeling both lucky and smart? Dirty Harry doesn’t scare you? Well, maybe he should. Overconfidence leads to a sense of invulnerability, to overtrading, to trading in disproportionately large size. Start each trade by asking what could go wrong if it turns out you were both unlucky and made a stupid mistake. Perhaps then you really will be lucky and smart.

Capricorn December 22-January 20—Your disciplined, methodical work will pay off if only your perfectionism doesn’t get in the way. No trader has a perfect track record, not even those who advertise “no losing trades in three months.” Trading is about probabilities, so lighten up. After all, dear Capricorn, we’ve all heard that goats eat tin cans, certainly not the perfect cuisine. Oops, that report falls under the category of farmyard legend.

Aquarius January 20-February 18—Your quirkiness may be endearing, but make sure it isn’t hurting your trading. Don’t confuse Joe’s trading business with the quirky Trader Joe’s.

Pisces February 18-March 20—Take those rose-colored glasses back to the optician but keep your sense of optimism. When you’re in a positive mood your visual cortex takes in more information; negative moods result in tunnel vision. And there’s lots of actionable information that can be gleaned from the periphery.

Note: The image that accompanies this post is the horoscope of Prince Iskandar, grandson of Tamerlane, the Turkman Mongol conqueror. It shows the positions of the heavens at the moment of Iskandar’s birth on April 25, 1384. Credit: Wellcome Library, London.

Sklarew, Techniques of a Professional Commodity Chart Analyst

I enjoy reading books that others might consider outdated. Arthur Sklarew’s Techniques of a Professional Commodity Chart Analyst (Commodity Research Bureau, 1980) is a transitional book, written when “the click-buzz of computers almost drown[ed] out the shouting in the pits in Chicago and New York.” (p. xi) It covers some familiar ground—chart patterns, Elliott wave theory, trend lines, oscillators, and moving averages—all in support of trend trading. But there are twists even here; moreover, Sklarew offers some tools that are not commonplace.

Sklarew suggests that the commodity trader follow both the rule of multiple techniques (that is, the more technical indicators confirm each other the better the chance of an accurate forecast) and the principle of selective techniques. The former applies to chart analysis in general; the latter to automatic trading methods. “In very general terms, the Principle of Selective Techniques states simply that the automatic trading method that appears to work better than other methods in a particular market at a particular time is the one that should be used in that market at that time.” (p. 5)

Although Sklarew writes that “a chartist’s asset lies not so much in his being able to forecast how high or how low a market will go, or when it will get there, as in being able to identify the direction of a trend and to call the turn of a trend when it comes,” (p. 1) he offers a dozen methods for predicting how far a move will go. Here let me summarize one novel measurement technique. I haven’t tested it out, in part because I personally am not comfortable with measured targets. But a lot of people swear by them, so here is one of Sklarew’s contributions.

The rule of seven enables a trader to project one or more objectives in the direction of the new trend based on the initial leg of the trend. The formulas for uptrend and downtrend projections vary slightly. First, the uptrend formula: “Measure the size of the initial up-leg by subtracting the low price from the high; multiply that figure by seven; then divide that product by four to get the distance from the low to the first objective, divide the product by three for the second objective, and by two for the third objective.” In every case add the distance to the low. Or, in its simplified form: “Upside objective #1: High minus low, multiply by 1.75, add to low price. Upside objective #2: High minus low, multiply by 2.33, add to low price. Upside objective #3: High minus low, multiply by 3.50, add to low price.” In a downtrend, Sklarew writes, “the formula is moved back one notch. The three downside objectives are obtained by multiplying the size of the initial down-leg by 7/5, 7/4, and 7/3, or 1.40, 1.75, and 2.33 respectively, and subtracting the result from the high.” (p. 83)

Sklarew fleshes out the rule of seven, applying it to both minor and major trends, to trends of both large and small magnitude. Moreover, he suggests that in dynamic markets a fourth objective must be considered. In an uptrend, it is seven times the initial leg measured from the low of that leg; in a downtrend, it is 3.50 times the first leg projected downward from the high.

Sklarew also sets forth a 17-35 measurement. He admits that it is “difficult to find a logical reason why many sustained commodity futures price moves congest or reverse after covering a distance equal to 17% or 35% of the recent high or low price,” but he says that “this happens so frequently that it must be more than just a coincidence.” (p. 87)

This book offers tips from the former coffee and cocoa trader, mathematical formulas for many indicators, and backtested results from a study designed to find the best moving average for each of 13 commodity futures contracts. It may be thirty years old, but it offers fodder for today’s system testers.

Noise

More than once on this blog I’ve written about things I know nothing about. At least I know that I don’t know, I vet my sources to be reasonably certain that they do know, though if they don’t I’m in trouble. And, of course, if you rely on my second-hand knowledge you’re also in trouble. Well, here I go again. This time I’m trying to glean some insights from the world of sound synthesis.

Many traders try to devise ways to filter out market noise to produce tradable signals, so I thought that the world of electronic music might offer some clues. When I found a paper that talked about Brownian motion, the random walk, and algorithms, I figured that it was worth summarizing ever so briefly on the off chance that one or more of my readers might have a eureka moment.

Market noise is, of course, not same as noise in a musical setting. Let’s start with a definition of the latter. In its broadest form, “noise is an audio signal that consists of an accumulation of sinewaves of all the possible frequencies in the hearing range and with all possible amplitudes and phase relations.” Noise stands in contrast to sound, which is a sinewave signal with a single frequency. Is it possible to filter noise to produce sounds that should be hidden somewhere in the noise? The answer is no, and not just for technical reasons. “When the frequencies are filtered out correctly the amplitudes still vary wildly, making it virtually impossible to create steady tones.”

But noise signals can be differentiated according to their statistical distribution profile. Although noise has no apparent pitch, “when each possible frequency has an equal chance of occurrence . . . it sounds like a very bright hissing sound” and is what we know as white noise. We can filter white noise to produce a dull red noise, a pleasant pink noise akin to the sound of a distant ocean surf, or a very dark brown noise that is actually derived from Brownian motion. But we can’t get sound.

We know that high frequency traders function in the world of noise and presumably act on algorithms that filter cacophonous market noise into actionable “colored” noise. Noise is not, however, the exclusive property of high frequency traders. There is market noise on all time frames. Normally traders are told to stay clear of noise, but perhaps it’s time to embrace noise and simply try to filter it. One standard piece of advice is to drop down to a smaller time frame. What is noise on a 60-minute chart might appear to be a clear trend on a 5-minute chart. But are we deluding ourselves? Can we really filter 60-minute noise in such a way as to produce 5-minute “sound”? If the analogy to electronic sound holds, what we see on the 5-minute chart is still noise. The lengths of 5-minute price bars “vary wildly”; there are no steady tones here. Perhaps what we describe as a trend is really colored noise.

The gain-loss spread as an intuitive measure of risk

Today’s post relies on a paper written by Javier Estrada for the Fall 2009 issue of the Journal of Applied Corporate Finance, a Morgan Stanley publication. It is entitled “The Gain-Loss Spread: A New and Intuitive Measure of Risk.”

Estrada seeks to replace standard deviation as the benchmark way to quantify risk with a metric that is intuitive and that is based on numbers that investors consider relevant when assessing risk. “This measure is the gain-loss spread (GLS), which takes into account the probability of a loss, the average loss, and the average gain.” Estrada shows that the GLS provides basically the same kind of information as the standard deviation of returns but in a much clearer way. “Furthermore, the evidence shows that: (1) the GLS is more correlated with mean returns than both the standard deviation and beta, thus providing a tighter link between risk and return; and (2) it is better able to discriminate between high-return and low-return portfolios than beta and equal to or better than the standard deviation, and therefore is a useful tool for portfolio selection.”

The GLS is very easy to calculate. You start with annual percentage returns for an index over a specified period of time. Estrada uses the MSCI World Index for the 20-year period 1988 to 2007. During five of those years the index delivered negative returns, so the probability of a loss is 25%. Next calculate the average annual loss, in this case -13.9%. The expected annual loss is the product of these two numbers: 25% * -13.9% = -3.5%. Similar calculations will yield the expected annual gain of the asset, in this case 75% * 18.9% = 14.2%. The gain-loss spread is the difference between the expected gain and the expected loss: 14.2% - (-3.5%) = 17.6%. As risk measurements go, that’s as easy as it gets.

Can such a simple risk measurement be useful? Estrada here relies on statistical tests that are too technical for this post; the interested reader can go to the original paper. The answer (refer back to the second paragraph of this post) is clearly yes. GLS may not satisfy investors who have learned to worry about fat tails, but I consider it wonderful, even close to miraculous, that a model that requires such rudimentary arithmetical skills can compete with those that have been the provenance of statisticians.

Caplan, Profiting with Futures Options

For those who are impatient with long-winded explanations David L. Caplan provides welcome relief. Profiting with Futures Options (Center for Futures Education/Traders Press, 1994) is a pamphlet under 50 pages long that nonetheless provides a wealth of information.

Caplan is writing for futures traders, or at least those familiar with futures, who could profit from either supplementing or replacing their futures trading with trading options on futures. He outlines cases in which options should be used in place of futures contracts. For example, when a commodity is overvalued and overbought, the trader can sell an out-of-the-money, overvalued call. The options trader is also the only one who can profit in a flat commodity market. Limited-risk options strategies insulate the trader against “limit” days and can be used to prevent being stopped out on a trade that turns around and becomes profitable.

Caplan outlines a series of strategies, all spreads, that provide the trader with a significant advantage. Most of the strategies are familiar, but Caplan sometimes develops these strategies in novel ways. All in all, for anyone who trades futures this pamphlet will open the door to new opportunities for both profit and risk management.

Why winning streaks end

The Super Bowl provided the perfect opportunity for media musings on performance. Here’s a good piece from Bloomberg written by Rosabeth Moss Kanter, a professor at the Harvard Business School and author of Confidence: How Winning Streaks & Losing Streaks Begin & End.