# V.12:5 (218-221): The c-Test by William Eckhardt

By transaction costs I mean not only commissions but also the skid in placing an order. The desire to maximize the number of winning trades or minimize the number of losing trades works against the trader. Here are some interesting inssights from the book interview starting pg The firm's international clientele includes " fund of funds ", corporate, private, and institutional investors. Typically we would have 15, trades of a certain kind before we would make an inference as to whether we want to do it. Jun 12, , 2:

Feb 28, · William Eckhardt: The man who launched 1, systems Q&A. In addition to building trading systems, Eckhardt has developed a science of trading and written academic papers on the philosophy of.

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Incredibly, this difference is detectable using trading systems. Trading systems can be highly sensitive to non-linear relations in price series. Statistical estimators probe particular features of the price series; they are equipped with confidence levels, give information about possible models, and are useful for prediction. From the point of view of the modeler, trading systems do not locate specific features of the price series; they have no confidence levels and are useless for prediction.

Worst of all, they say little about any possible model. In the same way models, although valuable in other respects, do not help in designing trading systems. You have spent a lifetime in trading and in research. Name a couple of simple truths that you have discovered. Finally, use only robust estimators and very large samples, not dozens, but thousands. Eckhardt and Dennis honored at Pinnacle Awards. New era, new leaders. The man who launched 1, systems. Is it time to add managed futures to your holiday shopping list?

Price is definitely the variable traders live and die by, so it is the obvious candidate for investigation. Pure price systems are close enough to the North Pole that any departure tends to bring you farther south. A price chart is an attempt to model relevant aspects of price change.

Price change is not linear displacement, whether vertical, horizontal or oblique. Nonetheless, price change can be represented as vertical displacement and time elapsed as horizontal displacement. Such a model, however, invariably supports relationships that does not correspond to anything in the original process. The angular inclination of a trend on a price chart is a visually striking feature of this representation.

Such angles have no intrinsic meaning for the price series, but this is one of the many factors along with our facility for pattern recognition and wishful thinking that contributes to our interpreting more from price charts than rigorous testing reveals is there. Look at the Detailed Structural Information in Price Data and Not Just Summary Results Our aversion to summary statistics that obliterate structure extends to the trading systems themselves. For instance, we avoid moving averages of price in making trades.

Another popular tool, the price breakout, may be far better than the moving average, but it still eliminates most of the relevant structure.

A breakout trader keeps two pieces of structural information, the high and the low for a given time period, but ignores all the price structure in between.

For this and for other reasons we judiciously avoid breakout trading in all parts of all our systems. Have an Erraticness Filter In our case specifically, we have an erraticness filter which is influenced by volatility.

Erraticness incorporates different measures of market spread. If market erraticness rises above a certain threshold, new trades in that market are blocked. We introduced the erraticness filter near the end of March , and it turned out to be very beneficial. For the first few years after we implemented the erraticness filter, in examining our Sharpe ratio the numerator got bigger and the denominator got smaller simultaneously. A few months before things really began to fall apart [in ], our systems essentially shut down.

They judged the market to be too erratic. When the crisis hit, we had small positions. Holding Periods We have three packages which consist of 19 systems in all. The short-term package has an average trading length of about 6 days; the medium term package has an average of about 12 days.

The long-term package is over 60 days. All of the systems trade independently and are designed to be profitable on their own. Win Rate Looking back, about one third of the trades have been winners, and two thirds losers. The idea is you win in only a modest percentage of trades but you make these wins count. Why Trend Following Works I would offer a few reasons, all based on human nature. We are good at other things, such as estimating speed and distance. Take the ability to catch a baseball, for example; physicists tell us this requires integrating differential equations, which is of course quite complex.

By comparison, we make mistakes in easy probability problems. One consequence is that we tend to have only two responses to extremely small probabilities, neither of which is helpful: I would give the Anthrax scare some years back as an example of the latter. The probability that any single person would be infected with Anthrax was incredibly small, yet a lot of people were in hysterics.

That should make beans go up a penny. Then they tend to respond discontinuously to this continuous development. Another example of how people behave unreasonably when faced with probabilities is the way they respond to lotteries. Traders tend to follow the same—they take profits and they play with losses.

This bias generates trends. The trendiness of prices seems to be grounded in human nature. Looking back, about one third of the trades have been winners, and two thirds losers. This does not mean that we avoid market risk, for market risk is the raw material from which profit is fashioned, but we are conservative about what we know and about what can be done. My experience with Decision Theory indicates that knowing what it is you are ignorant of is in fact a powerful position to be in. The task of the trader is to locate those few areas where ignorance is not complete and to convert this information into profitability in an efficient way.

False knowledge can be very detrimental to this process, but acknowledged ignorance can be quite beneficial. What these patterns make during market consolidations, they lose during trends. Formally, the mistake is the confusion between prior and posterior probabilities.

That is a very different probability. If 85 percent of all tops and bottoms have property X, but property X also occurs often enough in other places, using that indicator as a signal will rip you to shreds.

All this scientific research has failed to uncover any systematic cyclic components in price data. This failure argues strongly against the validity of various trading systems based on cycles. And, I want to stress that the techniques for finding cycles are much stronger than the techniques for finding trends. Finding cycles is a classic scientific problem.

If you allow cycle periods to shrink and expand, skip beats, and even invert-as many of these cycle theorists or, perhaps more accurately, cycle cranks do-then you can fit cycles onto any data series that fluctuates.

The bottom line is that rigorous statistical techniques, such as Fourier analysis, demonstrate that these alleged cycles are practically random.

The first part is to develop a coherent portfolio theory: The second part is brainstorming for new trading ideas. It usually takes 70 to false starts before we get something that we can use.

We pay a lot of attention to the foundations of the subject, to the soundness of our methodology, and to the correctness of our statistics. In terms of the foundations of the subject, we rely heavily on Decision Theory and Utility Theory. Prediction Models Do Not Help in Trading Systems Statistical estimators probe particular features of the price series; they are equipped with confidence levels, give information about possible models, and are useful for prediction.

From the point of view of the modeler, trading systems do not locate specific features of the price series; they have no confidence levels and are useless for prediction. Worst of all, they say little about any possible model. In the same way models, although valuable in other respects, do not help in designing trading systems. You have to concentrate on projecting losses, risk management and finding something that works, but if you are directly looking for prediction that tends to be self-stultifying.

Those are different skills. When I first began trading solely on the basis of price and was much more concerned than I should have been about the academic orthodoxy that futures market price change was pure white noise—a random walk—I made the following notebook entry: Twenty-five years later, I am less confident about the continuing correctness of this answer.

What I failed to take into consideration was the staggering explosion in information processing. This will only continue. Eventually artificial intelligence devices, superior to any human researcher, will effectively uncover all exploitable nonlinear relationships of price to price. Such relationships will be mined until technical analysis is no longer profitable. The process has already begun.

I feel these developments are nearly assured assuming no disruption of civilization. What is less clear is whether this will happen as rapidly as I predict—in 10 to 20 years. In the meantime, profitable trading will only get harder as increasingly more astute traders pursue progressively weaker statistical regularities.

This is why it is necessary for a CTA continually to improve just to hold his or her own. The only consolation I can offer is that there are profits to be made participating in this process of randomization. That is an industry standard. Now the two numbers that most determine if you are over-fitting are the number of degrees of freedom in the system. Every time you need a number to define the system, like a certain number of days back, a certain distance in price, a certain threshold, anything like that is a degree of freedom.

The more degrees of freedom that you have the more likely that you are to over-fit. Now the other side of it is the number of trades you have. The more trades you have, the less you tend to over-fit, so you can afford slightly more degrees of freedom. If you put more bells and whistles on your system it is easy to get 40 degrees of freedom but we hold it to Seven or eight [degrees of freedom] is probably too many.

Three or four is fine. That is our absolute minimum. Typically we would have 15, trades of a certain kind before we would make an inference as to whether we want to do it.

The reason you need so many is the heavy tail phenomena. It is not only that heavy tails cause extreme events, which can mess up your life, the real problem with the heavy tails is that they can weaken your ability to make proper inferences. Normal distribution people say that large samples kick in around In contrast, with the kind of distributions we have with futures trading you can have hundreds of samples and they could still be inadequate; that is why we go for 1, as a minimum.

That is strictly a function of the fatness of tails of the distribution. You have to use robust statistical techniques and these robust statistical techniques are blunt instruments. They are data hogs, so both seem to be disadvantages but they have the advantages of tending to be correct.

One can have structures within the system that can take on various alternative forms. If various alternatives are tested, it gives the system another chance to conform to past idiosyncrasies in the data. Suppose a certain degree of freedom in your system impinges only on a very few oversized trends in me data and otherwise does not affect how the system trades. By affixing to accidental features of the small sample of large trends, such a degree of freedom can substantially contribute to overfitting, even though the overall number of degrees of freedom is manageable.

Take Care of the Tail Risk The large-tail phenomenon means that most statistical tests overestimate reliability and underestimate risk. Tail risk is hard to estimate but we spent over 25 years on this project. We have worked on it really hard and we do have various techniques to deal with the fact that the tails are so heavy. It is absolutely crucial because the tail risk changes everything that we do.

Every single part of designing and implementing the system is affected by the fact that you have more extreme values than you expect under any kind of normal model. I have a little bit of trouble with the idea that the tail risk in futures trading is what is helping because I see it strictly as a hindrance, strictly as a problem to be overcome.

I guess it helps to have these really big outsized moves. It is only going to help you if you treat it like a wild tiger. In other words, once you have a system, what is the right size to trade, period. After years of working on this I convinced myself that it did not have a unique answer. Now that is subjective. There is no rule that says how averse you should be to risk, that is an integral element of your personality.

Volatility Estimating volatility determines to a large extent what your position sizes should be. A slight improvement in our volatility estimators can potentially produce a significant long-term benefit. The optimum comes just before the precipice. Instead, your trading size should lie at the high end of the range in which the graph is still nearly straight. Small improvements in risk or volatility assessment may not be exciting, but they are among the most lasting and beneficial changes.

One approach to avoid is to design the system first, then to tack on risk management. They take into account the fact that each dollar you make is a little smaller than the last one, and each dollar you lose is a little bigger than the last one. They allow you to quantify your own aversion to risk, and then to maximize expectations based on your risk aversion.

The objective of any investment is to achieve the highest returns based on your own risk tolerance, or in the case of a professional manager, the risk tolerance of your clients. Note that there are two respects in which profits and losses are not equivalent.

One is objective and has to do with nonlinearity. Through Utility Theory, such imbalances can be treated in a rigorous, quantitative manner and in this way uniform and unified procedures can be developed. We use only bounded utility functions in our work on risk management. The particular utility functions we use also have the desirable technical characteristic of optimal investment fractions being independent of absolute wealth level.

Any trader who survives any length of time knows something about his subject, but in my experience, traders simply graft risk control on top of whatever else they are doing, often in an arbitrary way.

I can look up these statistics, but this is not something I would ordinarily pay any attention to. The important thing is to limit portfolio risk, the trades will take care of themselves. System Should Maximize Expected Utility We have devised a portfolio theory quite different from the classical theory that permits factors such as risk aversion, the nonlinear imbalances between profits and drawdowns, and long-term utility growth to be built in at the ground floor. They are all part of the formulas that define what it means for a system to be good.

In this way, on even the most preliminary test run of a new idea we are forced to take into consideration the subtle and complex relations between drawdowns and long-term growth. At ETC we are dedicated utility maximizers and pay particular attention to the rate of expected utility growth.

You can express a particular form of this system as a sequence of numbers, and treat that sequence exactly like a genome a string of genes. In order to test the system, you can run it with a given set of numbers.

Then, just as in natural selection, you can cause genes to mutate or you can genetically recombine two genomes, always favoring those with higher fitness.

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Jun 29, · Quotable Quotes from William Eckhardt (Mechanical Trend-Following Systems Trading) Posted by whatheheckaboom ⋅ June 29, ⋅ 1 Comment I was reading more about William Eckhardt (or the Turtles trading experiment fame with Richard Dennis). William Eckhardt: The Man who Launched 1, Systems by Daniel P. Collins: When Bill Eckhardt left the University of Chicago and foresook his nearly completed PhD in mathematical logic in , he did not abandon his educational pursuits; rather, he focused them on a myriad of disciplines that supported his research in creating trading systems. William Eckhardt is a commodities and futures trader and fund manager. He began trading in after four years of doctoral research at the University of Chicago in mathematical logic.