Trend Following Strategy for Big Winnings is the subtitle of Michael Covel’s latest book (link on Amazon), an addition to the “Little Book of…” series (“Trading” in this instance).

I find it quite surprising for an author to come out with two books roughly at the same time but this book is fairly different from the recent Trend Commandments.

Similarly, this is an easy, short read – good for one sitting on the beach or by the pool, as the cliche has it.
And once again, one should not expect an actual specific strategy per se, in the form of a ready-to-be-traded system, delivered in the book – for this, a better place would probably be the Trading Blox forums or even this humble blog (start with the State of Trend Following report, which uses and points to several basic Trend Following systems provided by Trading Blox). Unless you prefer to purchase the author’s course…

No, this book is mostly about inspiration from successful (Trend Following) stories. Whereas Trend Commandments is all about “principles over personalities”, this latest Covel instalment revolves around some famous Trend Following personalities. And successful stories are one of the best ways to get inspiration and motivation, in my opinion. I actually felt this was one aspect missing from Trend Commandments, especially compared with the original Trend Following book (which contains a variety of philosophy, trading aspects, successful stories, performance charts, trader insights, etc.).

It seems that Covel decided to split out several concepts in two different books). In this Little Book, each of the twelve chapters cover Trend Following personalities, with their story and insights on trend trading.

Below are the personalities/firms covered (a large share of them being part of the Trend Following Wizards report) with chosen quote(s) from each chapter.

Sunrise Capital (Gary Davis, Jack Forrest, Rick Slaughter)

Trend Following can be simple, but sticking with it is the hard part.

Make sure you never miss a potential big trend. You always want to put some kind of trade when your system says enter as your price trigger hits. If you are wrong, you have stops to protect your capital, to protect your downside. After all, you never know which move is going to be the mother of all moves.

David Druz

Trend traders are trying to capture risk premium from the hedgers. […]
Hedgers hope to minimize their exposure to unwanted risk. Speculators (i.e. trend followers assume risk for hedgers. […]
Hedgers are net losers in futures markets over the long run, and Druz’s trend trading approach is based on capturing this risk premium.

The more robust a system, the more volatile it tends to be!
There are whole families of trend trading ideas that seem to work forever on any market. The down side is they are very volatile because they are not curve-fit

Paul Mulvaney

How you compute the amount you are willing to risk for every trade, and how you exit your big winners, that’s what counts.

Mulvaney’s trend trading is profitable on 54 to 55 percent of days, but only on 25 percent of trades. Obviously those 25 percent of trades are more profitable than the 75 percent of trades that are losers.

Kevin Bruce

There is great truth in the idea that if you take care of the downside, the upside will take care of itself.

Larry Hite

Hite has two basic rules about trading and life:
1) If you don’t bet, you can’t win.
2) If you lose all your chips, you can’t bet

David Harding

Don’t get caught up constantly trying to lower your risks. Think of yourself as running a risk targeting business where you go find risk. No risk, no reward!

I think the efficient market hypothesis is quite useful too. One prediction it makes is that it is difficult to beat the markets. It’s just saying that the markets know better than you do. So the assumption that the markets know better than you do is quite a sensible and useful assumption. It certainly would lead you to approach [beating the markets] with humility and modesty.

Determination is the same as having wings. If at first you don’t succeed, try, try, and try again. Madonna always says, ‘I’m like a cockroach.’

Bernard Drury

I made the decision that I would give up the use of my experience as a sector specialist in favour of adopting a systematic approach in which the most important benefits are the application of very extensive research, consistency of method, and diversification. For example, if we are curious about a trading rule, we run a simulation across a portfolio of about 70 instruments and 15 years of data. If we run a simulation on three or four systems together, then we get an even more robust result. This type of research provides some benefits that are difficult for a discretionary or fundamental trader to have.

Justin Vandergrift

While entry and exit is an overwhelming focus for new traders, it is only a small part of the recipe for winning in the trend follower’s cookbook. Money management is far more imperative to your success than worrying about a perfect entry.

Vandergrift, like many of the trend following traders, found through intense research that the only systems that really worked over time were long term trend following in nature. However, his real Aha! moment came when he put money management into his trading system equation. […] If you have a portfolio of markets, […] you want t risk an equal amount on every trade.

Eric Crittenden and Cole Wilcox

Wilcox, for example, has a constant process of asking, “Am I wrong?” while he sees everyone else asking, “Am I right?” If you don’t ask the correct probing question with genuine curiosity, like a scientist, you cannot arrive at the correct answer.
The scientific method doesn’t allow you to prove anything. All you can do is disprove theories, and then, with a preponderance of evidence still left, you can accept and keep the remainder as long as you can’t disprove it.

A few key lessons from Basso helped Crittendedn and Wilcox from the beginning. Basso was blunt, “It really is simple. You hold your winners, have discipline and cut your losers. You take what the market gives and you’ll be successful in this business”. Crittenden added: “One. Don’t over-bet. Two. Diversify across markets.”

Michael Clarke

You want to look for trend following models that remain robust over long time periods and you want to include models that have flat to negative performance for periods of up to two years. The principles that allow a good model to work successfully may fall out of favour and stop working for a period of time, but if the model has validity, the long-term principles will reassert themselves over time. Don’t jump the gun in throwing away your models.

In order for a model to be accepted, you want it to trade all markets using the same rules and parameters. Your results should yield good performance across 90-plus percent of all markets tested. Also, no model should be accepted unless it shows stability of performance during tests involved with shifting parameters and altering rules. This is the definition of robust.

Charles Faulkner

Stay in the moment of right Now.

The idea of cutting your losses quickly and letting your gains run is in fact going against human biology.

Successful trend following trading is about developing a belief deep in your belly that you are part of a larger system.

Ed Seykota

The Whipsaw song:

• Ride your Winners
• Cut your Losses
• Manage your Risk
• Use Stops
• Stick to the System
• File the News

 
Interesting and an easy read, a good book to round off the Summer…

You want confidence and inspiration? It’s here.

Michael Covel’s Trend Commandments is a new book on Trend Following, which focuses mostly on the psychological and philosophical aspects of this trading strategy.

You want a “how-to” book, including a “turn-key” Trend Following system? It is not there (The Complete Turtle Trader did this with the original Turtle system rules though).

It is a fact that you need to have faith in a system or idea before you can start trading it. This is a central premise of this book, which seems aimed at “would-be” trend followers, to give them the conviction required to start and keep trading this strategy – “a real, proven way to make money in the markets”.

The contents and format of the book make for an easy read, good to pick up for the beach (or the metro if you are not blessed with a Summer holiday). It is divided in many short chapters (50+) each dealing with a specific topic in a few pages.

In some way, there is some overlap with Covel’s first book, Trend Following (after all, the main principles have not changed since), but this book does it in its own ways:

I thought a different approach to get that story out was required.

About 25% of the book is composed of footnotes for the numerous quotes or references that illustrate or complement the author’s points, and provide the reader ways to explore some concepts further. As part of these references, Covel makes an analogy with the movie The Matrix, which could apply to the overall message in the book.

Pushing the analogy further, one could say that Covel plays Morpheus, and you get to play Neo[-phyte] (the book is mostly aimed at beginner trend followers, in my view).

The tone is quite different from the first books, more direct; almost that of a missionary on a crusade against the Matrix robots and their agents, and to evangelise the crowds on Trend Following.

Reading Covel’s words is similar to taking the red pill, going down the rabbit hole… You get access to an “alternative truth”, which can be divided into a dual view:

1. The principles of a winning philosophy and strategy (Trend Following that is – just in case you’re not… following)
2. “Removing junk from people’s heads” (the crusade against the Matrix robots and their agents)

Covering the principles of Trend Following, each chapter provides a nugget of insight with topics such as:

• Irrationality of the markets
• Buy High
• “Price is the only true reality in trading”
• No prediction
• Calculated Risks
• Discipline in following a system
• Diversification: “trade everything”
• Drawdowns are inevitable
• Let your profits run
• Handling losers
• Statistical reasons why Trend Following works
• Low winning percentages: no need to be right

But in the words of Covel:

Getting rich is a fight

It’s you [...] against the world

The well-constructed fortress of government, media and Wall Street, all designed to bleed you dry [...]

great trend trading knowledge and wisdom are found by removing junk from people’s heads.

And as a complement to presenting Trend Following principles, the second main aspect of the book fights the “junk” that is part of the “establishment”.

Wall Street, financial academics, Buy-and-Hold, use of fundamentals in trading, gold bugs, politicians and government, media, CNBC, Jim Cramer and other “market gurus”, even Warren Buffet all get the “irreverent Covel treatment”, exposing the myths, misconceptions or biases surrounding them. This aims to act as “reality check” against what most people are led to believe all their (trading) life.

Throw in a bit of “self-help” advice (lessons in happiness, finding truth, living big) and you have a book which is indeed quite accessible and distils the insights and over-arching principles of Trend Following, which Covel has amassed in his 15 years of tracking down and studying the most successful trend traders.

Do not expect a full combat training though. The chapters are short and subjects covered are not explored in-depth; but this is not what the book pretends to:

This book is the primer that unlocks the path of trend trading.

You will not be ready to jump from building to building after reading this book, rather it aims to “free your mind” and give you that “push” to take a leap of faith into Trend Following.

As a non-novice in the principles of Trend Following, and having previously read Mike Covel’s first book, I personally prefer the format of Trend Following, which I feel will still retain its role as a reference in my library. I find it more thorough (filled with facts and figures, philosophical principles, trading concepts, quotes and stories of successful trend following traders) but I can understand the need for simplifying its message for newcomers.

To a friend (or reader) still “plugged into” the system and wanting to get started in trading, I would definitely recommend reading Trend Commandments as an introductory volume. If you are well-versed and/or a believer in Trend Following and have read the previous books, do not expect any “ground-breaking” discoveries in these pages, rather similar concepts and principles presented in a different angle and tone, with added rhetoric against the establishment.

The book on Amazon:

Previous Covel books:

	Trend Following – Michael Covel See Why and How Trend Following works. Over a dozen of top CTAs covered. – Link to review Look up on Amazon US | CA | UK
	The Complete Turtle Trader – Michael Covel The Turtle story and their complete rules –No review/summary yet– Look up on Amazon US | CA | UK

The book is really divided into two main parts: first the classical modern finance theory, later opposed to Mandelbrot’s fractal view of the Markets, risk, ruin and reward – where he introduces his two main model components: H: the exponent of price dependence and α: the parameter characterizing volatility.

A History of Modern Finance Theory

Mandelbrot traces the origins of Modern Finance Theory back to little-known French mathematician: Louis Bachelier, who, in 1900, published his Théorie de la Spéculation thesis, mostly ignored at the time. The theory introduced its key model: the random walk or brownian motion, which forms a large part of Modern Finance Theory’s foundations. It is not until the 1960′s that Bachelier’s ideas would catch up, when translated to English and republished. Fama’s Efficient Market Hypothesis simply represents a broader version of Bachelier’s work, which “would be developed into a great edifice of modern economics and finance (and five Nobel Memorial Medals in economic science)”.

Mandelbrot first presents the stepping stones of Modern Finance before arguing that there are basic flaws in the theory:

The principal building blocks with which the modern house of finance is constructed all sit on the theoretical foundations laid by Bachelier a century ago.
This book argues that the foundation needs re-pouring, before any more repairs are done to the building. To understand why this matters, let us first look more closely at the structure as it exists today

The presentation of Modern Finance is an interesting chronological re-telling of how the theory shaped itself throughout its various developments.

It starts with Harry Markowitz, who applied Bachelier’s theory to develop his Modern Portfolio Theory using the Mean Variance model. This is often considered as the start of financial engineering. William Sharpe then simplified some of Markowitz’s work with the Capital Asset Pricing Model. Black and Scholes followed suit by contributing their famous eponymous option pricing model.
The book describes the discoveries and explains the main concepts more in detail, which makes for an interesting recap.

But then, Mandelbrot starts to deconstruct these theories:

The whole edifice hung together – provided you assume Bachelier and his latter-day disciples are correct. Variance and standard deviation are good proxies for risk, as Markowitz posited – provided the bell curve correctly describes how prices move. Sharpe’s beta and cost-of-capital estimates make sense – provided Markowitz is right and, in turn, Bachelier is right. And Black-Scholes is right – again, provided you assume the bell curve is relevant and that prices move continuously. Taken together, this intellectual edifice is an extraordinary testament to human ingenuity. But the whole is no stronger than its weakest member

The rest of the first part of the book forms Mandelbrot’s case against the Modern Theory of Finance. In it, he explains that some of the assumptions in the models are wrong, borrowing from behavioural finance principles, to mention that investors are not rational for example. The easier assumption to refute using simple facts, is that of price changes following a brownian motion. The presence of fat-tails in market returns distribution or the P/E effect are such evidence contradicting the theory. In here, Mandelbrot even takes the example of a simple moving average strategy being profitable:

A by-now substantial body of economics research suggests that there is, indeed, money to be made in such a “trend following” strategy.

Fractals Applied to the Markets

Mandelbrot is the inventor of fractals. He actually coined the term and founded a new branch of mathematics based on fractal geometry.

My life’s work has been to develop a new mathematical tool to add to man’s survival kit. I call it fractal and multifractal geometry. It is the study of roughness, of the irregular and jagged. I coined its name in 1975. Fractal is from fractious, past participle of frangere, to break, as I was reminded by one of my son’s Latin dictionaries. The same root survives in many common words, including fraction and fragment. I developed these ideas over many decades of intellectual wanderings – pulling together many stray, forgotten, under-explored, and seemingly unrelated artifacts and issues of the mathematical past, extending them in every direction, and creating a new, coherent body of mathematics. Fractal geometry has come to be viewed as “natural”. It is used today for an improbably diverse set of tasks: compressing digital images over the internet, measuring meta-structures, analysing brain waves in an EEG machine, designing ultra-small radio antennae, making better optical cables, and studying the anatomy of lung bronchia.

After an introduction to fractals in general, the second part dives into the two main tenets of Mandelbrot’s theory.

The first one is fractal scaling, basically based on the fact that market price changes do not follow a gaussian distribution but instead a power-law distribution, in which the tails drop off much slower than in the usually assumed bell curve (ie. fat tails), giving infinite variance and explaining why extreme price movements are much more frequent than anticipated by the “classic” models – something which is arguably a good reason for trend following to work.
Mandelbrot describes how he came to that conclusion starting with his study of cotton prices in 1961 while working as an IBM researcher, and coming across similar concepts by George Zipf, Vilfred Pareto or Paul Levy.

The power law distributions are characterised by their parameter α describing how fast the tails drop off (ie linking intensity to frequency).

The second main concept is that of long memory or long range dependence, characterized by the Hurst exponent H. Presenting some studies in the Nile river hydrology, Mandelbrot establishes the concept of trend persistence in natural phenomenon: periods of floods or droughts tend to come in streaks: they exhibit more serial correlation and for longer than one would expect. Applying similar calculations to market prices shows that financial instruments display more (trend persistence) or less (anti-persistence) long-term memory than the normal case (when H = 0.5).

To measure these two effects, I developed new statistical tools. Some focus on α, the index mentioned earlier. A low-α market would be risky, prone to wild price swings. A market with a higher α differs less from the classic coin-tossing market. Other of my statistical test focus on H, the Hurst coefficient for long-range dependence described earlier. An H of one half implies each price change is independent of the last. A larger H suggests the data are “persistent”, trending in the same direction. A smaller H implies “anti-persistence”, a tendency to double back on themselves.

To separate the two effects, measured by H and α, I developed a statistical test called rescaled range analysis or R/S. It is of a type known by statisticians as “non-parametric”, tests that make no simplifying assumptions about how the data are organised.

Now, as fate would have it, under some circumstances these two effects are so closely interrelated that H is simply equal to 1/α. Take the coin-tossing case: its H is one half and its α is two. Mathematically the relation between the two effects is quite profound; it presents what mathematicians call a dual relationship.

Mandelbrot then quickly presents his “current best model” of how a market works, the fractional Brownian motion of multifractal time, and how to use it to generate graphically synthetic market data exhibiting desired H and α.

Disappointment in the Conclusion?

The book ends without a direct practical application of the fractal concepts to trading or managing money, which can be disappointing for some readers. Mandelbrot is not shy of admitting that his work is still in-progress and to be developed by further generations. Indeed, his models could be compared to those of Bachelier, which took decades to begin having a practical application in finance. Nevertheless, the new concepts are interesting and might give some food for thought for further research. I did try a while ago to implement and use the rescaled range analysis test for trading without much success. I’d be interested to hear other readers’ experience using fractal concepts in trading…
 
 
UPDATE: A reader kindly pointed me to another review/summary pdf of the book which can be found there

With the AMH, Lo attempts to reconcile the Efficient Markets Hypothesis with behavioral models, which often seem to contradict each other. The AMH is based on “Darwinian” evolutionary principles:

Based on evolutionary principles, the Adaptive Markets Hypothesis implies that the degree of market efficiency is related to environmental factors characterizing market ecology such as the number of competitors in the market, the magnitude of profit opportunities available, and the adaptability of the market participants.

Behavioral biases are, in fact, consistent with an evolutionary model of individuals adapting to a changing environment via simple heuristics.

The EMH model can be seen as the equilibrium state in a perfect/ideal world where market efficiency runs at 100%. However, reality is often more complex than a simple theoretical model. Because of ever-changing factors, real market efficiency oscillates towards and away from the “perfect” EMH model, without necessarily converging towards it.

The framework that Lo describes is mostly qualitative and as such its applications might not be immediate.

The Behavioral Side

Lo covers some well-known behavioral biases to illustrate how “investor idiosyncrasies” contradict the EMH assumption: investors are not always rational.

Examples of behavioral biases used for illustration are:

• Over-confidence
• Probability assessment
• Risk aversion

These behavioral biases are presented as being investor heuristics:

Within this paradigm, behavioral biases are simply heuristics that have been taken out of context.

Given enough time and enough competitive forces, any counterproductive heuristic will be reshaped to better fit the current environment. The dynamics of natural selection and evolution yield a unifying set of principles from which all behavioral biases may be derived.

The EMH Response

The way EMH proponents address these questions raised by behavioralists is by affirming that markets as a whole gravitate towards efficiency. All “small” inefficiencies are arbitraged away and their effect counteract each other. The argument is that behavioral biases are negligible and irrelevant.

But this last conclusion relies on the assumption that market forces are sufficiently powerful to overcome any type of behavioral bias, or equivalently, that irrational beliefs are not so pervasive as to overwhelm the capacity of arbitrage capital dedicated to taking advantage of such irrationalities.

Lo then uses anecdotal evidence in the form of various classic financial manias and panics (tulip mania, South Sea Bubble, Dot-Com Crash, etc.) as examples that sometimes, forces of irrationality can dominate the forces of rationality.

A Look from the Neuroscience Angle

Behavioral finance falls into the field of psychology rather than economy and Lo takes a look at neuroscience to get a better understanding of behavioral biases.

EMH proponents sometimes criticize the behavioral literature as primarily observational, an intriguing collection of counterexamples without any unifying principles to explain their origins. To a large extent, this criticism is a reflection of the differences between economics and psychology.

The field of psychology has its roots in empirical observation, controlled experimentation, and clinical applications. From the psychological perspective, behavior is often the main object of study, and only after carefully controlled experimental measurements do psychologists attempt to make inferences about the origins of such behavior.

In contrast, economists typically derive behavior axiomatically from simple principles such as expected utility maximization, resulting in sharp predictions of economic behavior that are routinely refuted empirically.

In this section, Lo gives us (succinct) explanation of how the brain works and how it can be split in three parts: reptilian, mammalian and hominid brains, all traces of our evolutionary past. These “three” brains react to and manage situations differently. The way they interact when presented with “emotional distress” (fear and greed for example) is likely the root of behavioral biases: Emotion is at the heart of irrational decision.

The Hypothesis and its Implications

Lo’s theory falls in the “Darwinian alternatives to the EMH”, arguing that individual investors develop heuristics to solve various economic challenges, based on their experience. They learn by receiving positive or negative reinforcement from the outcomes. If the environment remains stable, heuristics will tend towards optimal solutions. However, with changing market environments, heuristics become unsuited and need to adapt: this is when behaviors can appear irrational.

This means:

1. Individuals act in their own self-interest.
2. Individuals make mistakes.
3. Individuals learn and adapt.
4. Competition drives adaptation and innovation.
5. Natural selection shapes market ecology.
6. Evolution determines market dynamics.

Any market will be more or less efficient depending on its ecology (ie number and variety of market participants, availability of profit opportunities). However, convergence to equilibrium is neither guaranteed nor likely to occur at any point in time (as per concepts of evolutionary biology).

Lo concludes with applications of the AMH, to try and render his model more practical.

• Investor’s preferences matter and need to be managed to meet their objectives.
• Risk/Reward relations are likely to evolve over time.
• Arbitrage opportunities do exist from time to time. The market does not necessarily tend to higher efficiency but is subject to more complex market dynamics with cycles and market trends.
• Specific investment strategies’ profitability evolves over time
• A better way to achieve a consistent level of expected returns is to adapt to changing market conditions

As Lo warned us in the introduction, this work is still at a level of qualitative framework of thoughts, and as such still needs to be developed if it wants to compete with the EMH theory – which, despite being flawed, provides more practical applications for an investor.

The main practical application from the above points hints at the idea of using regime switching to adapt a trading strategy to the changing market environment.

As mentioned in the Evidence-based Technical Analysis review post, the main value of the book lies in the presentation of the two methods allowing for computing the statistical significance of trading strategy results, despite having a single sample of data:

Both methods solve the problem of estimating the degree of random variation in a test statistic when there is only a single sample of data and, therefore, only a single value of the test statistic.

Today, let’s look at the bootstrap test, with a practical application of it.

In very brief terms, the concept uses hypothesis testing to verify whether the test statistic (such as mean return of the back-testing sample) is statistically significant. This is done by establishing the p-value of the test statistic based on the sampling distribution. (Aronson covers the basics of statistical analysis earlier in the book. I have also mentioned previously The Cartoon Guide to Statistics, which covers these concepts too)

The problem with back-testing is that the results generated represent a single sample, which does not provide any information on the sample statistic’s variability and its sampling distribution. This is where bootstrapping comes in: by systematically and randomly resampling the single available sample many times, it is possible to approximate the shape of the sampling distribution (and therefore calculate the p-value of the test statistic).

Bootstrap on Single Rule Back-Test

In the context of hypothesis testing, the bootstrap tests for the null hypothesis that the rule does not have any predictive power. In practical terms, this is translated to the population distribution of rule returns having an expected value of zero or less.

The bootstrap uses the daily returns of a back-test (run on detrended data) and performs a resampling with replacement.

In practice:

1. A back-test is run on detrended data and the mean daily return, based on n observations, is calculated.
2. The mean daily return is substracted from each day’s return (zero-centering), This gives a set of adjusted returns.
3. For each resample, select n instances of adjusted returns, at random (with replacement), and calculate their mean daily return (bootstrapped mean).
4. Perform a large number of resamples to generate a large number of bootstrapped means.
5. Form the sampling distribution of the means generated in the step above.
6. Derive the p-value of the initial back-test mean return (non zero-centered) based on the sampling distribution

A Practical Application

To illustrate the concept, we can look at a back-test and apply the bootstrap method to its daily return series. I decided to look at a back-test I presented in Better Trend Following via improved Roll Yield. Remember: a standard 50/20 Moving Average cross-over system applied to Crude Oil was improved by adding a roll yield optimisation process.

In that instance, the benchmark is the standard strategy and we want to check that the strategy improvement was not the result of random chance. In Aronson’s book, benchmarking is achieved by detrending the data. However, this case is different as the benchmark is the standard strategy. The improved strategy results can be thought of 2 distinct parts:

• Results from standard Trend Following strategy
• Results from Roll Yield Optimisation

I therefore generated a composite, “Roll Yield-only” equity curve (by removing from the improved strategy equity curve the returns that could be attributed to the Trend Following component). I then computed the daily returns based on that equity curve.

1. This set of daily returns is the original sample of 5120 observations, with an arithmetic mean of 0.216%.
2. Substracting 0.216% to all 5120 returns adjusts those returns (zero-centering), ready to be picked for resampling.
3. The 10,000 resamples all pick at random, with replacement, 5120 observations from the zero-centered, adjusted returns. A mean is computed for each resample.
4. Each of the resample means are used to form the sampling distribution of the mean return:
    
   

5. The last step is the comparison of the non-adjusted original sample mean (0.216%) to the sampling distribution to establish the p-value, which is 0.006 in this example.

Once the p-value is obtained, it is simply a matter of deciding which threshold qualifies for statistical significance. Scientists usually determine the statistical significance threshold at 0.05 (ie. the null hypothesis would be rejected for any p-value less or equal to 0.05).

Note on Arithmetic Mean vs. Geometric Mean

As discussed above, the assumption that the rule does not have predictive power is translated to the arithmetic mean of its returns being equal to zero. In the bootstrap method, rejecting the null hypothesis occurs when the mean arithmetic return is statistically significantly positive.

I am usually no big fan of arithmetic mean of returns as it is a flawed indicator of profitability. In effect, a system can have a positive mean arithmetic return and still be unprofitable – think about a return of 50% followed by a return of -40%: arithmetic mean return is +5%, yet the overall return is minus 5.1%

Proving that the mean arithmetic return is significantly positive, and deducing that the trading system is therefore profitable is flawed. It is ironically amusing that Aronson spends quite a lot of time talking about logic reasoning and usual traps people fall into, to actually present a flawed deduction logic. To use an example from the book:

A dog having four legs (a profitable rule having a positive mean arithmetic return) does not imply that any four-legged animal is a dog (ie. any rule with a positive mean arithmetic return is not necessarily profitable).

On the other hand, any profitable rule has a positive mean geometric return, and any rule with positive mean geometric return is profitable. On that basis, using the mean geometric return as the test-statistic in the bootstrap must be more appropriate.

I’ll be running this post in 2 parts, and this concludes part 1…
In part 2, we’ll look at how the bootstrap method can be modified to handle the data mining process and its associated bias. I’ll also make the code used for the practical application above available for download (this will be a simple bootstrap resample tool developed on the .net platform for Windows). Finally we’ll explore the idea of using the geometric mean return as the test-statistic instead of its arithmetic cousin.

 
Today I’ll be talking about an excellent book, which was recommended on several “quant” blogs I read: Evidence-Based Technical Analysis by David Aronson. One of the main reasons I picked this book is because it teaches you to fish (instead of giving you a fish). So, if you’re after a book with great trading strategies or indicators, this might not be the ideal one, however if you want to learn about strategy testing and methodology, it’s probably a great addition to your trading library. It had been on my list for a while and I wish I’d read it earlier as it has the potential to add cornerstone methods to trading research and testing procedures. Read on for a summary with a review right at the end…

Intro

One of the early quotes from the book defines the concept it covers:

The scientific method is the only rational way to extract useful knowledge from market data and the only rational approach for determining which TA methods have predictive power. I call this evidence-based technical analysis (EBTA).

Aronson introduces early on the concept of objective (TA) vs. subjective (TA). An objective claim is a meaningful proposition, which can be unambiguously verified. For us mechanical system trading developers: a set of rules that can be back-tested. On the other hand, subjective technical analysis would consist of approaches such as Elliot Wave Analysis.

However, objective technical analysis is not sufficient on its own: you still need rigourous statistical inference to draw conclusions on its predictive power.

Part One: the Foundations

Part one of the book establishes the methodological, philosophical, psychological and statistical foundations of EBTA.

The first topic covered is the need for benchmarking to evaluate objective rules and introduces the concept of detrending, which I have previously discussed.

The second topic deals with cognitive psychology and gives examples of different types of behavioral biases that can fool us and make us believe in subjective technical analysis:

• Pattern recognition
• Confirmation bias
• Hindsight bias
• Over-confidence
• Illusory correlations
• Mis-perception of randomness

The antidote for these “mind traps” is the scientific method. The generic scientific method is covered in the third chapter with some history and philosophy of science and logic reasoning. The scientific method – which can and should be applied to Technical Analysis – contains 5 stages:

1. Observation
2. Hypothesis
3. Prediction
4. Verification
5. Conclusion

Subjective TA does not conform to the scientific method and the author presents an interesting study of objectification of a subjective TA pattern (Head and Shoulders) to make it testable (it shows that Head and Shoulders is worthless on stocks and has doubtful value on currencies).

Statistical Analysis of Back-Test Results

The next three chapters introduce and cover statistical analysis. The beginning of this part gives a good refresher on statistical inference, starting with concepts such as frequency distribution, standard deviation, probabilities and p-values. The example of sampling and statistical inference using beads in a box makes for a good illustration and a fairly clear parallel with the world of trading rules back-testing.

The book moves on to concepts such as hypothesis testing, statistical significance and confidence interval, etc. and how they relate to rule testing.

One of the main issue of back-testing results is that they only represent one sample of how the systems/rule(s) perform. Aronson presents the classical statistical approach to derive the sampling distribution (required to perform the statistical inference) based on a single observation/sample. However this assumes normality of the distribution, which is unlikely to be correct when dealing with financial data.

New Scientific Methods for Back-Testing

This last concept leads to the introduction of the two alternative methods to derive the sampling distribution and perform statistical inference on the back-tested results. These are two computer-based methods:

• The Bootstrap
• The Monte Carlo permutation

Both methods estimate the sampling distribution by randomly resampling (reusing) the original sample of observation. A test statistic is then computed for each resample.

In practice, the bootstrap method uses resampling with replacement of the daily strategy returns to generate numerous random test statistics used to approximate a sampling distribution.
The Monte Carlo permutation method achieves the same result by decoupling and permuting the position direction (ie. long or short) with the daily instrument returns.

Using the statistical inference covered in earlier chapters, one can decide whether results found in the back-test are statistically significant or the product of random chance.

These two methods are the main take-away from the book, as they are valuable to identify the degree of randomness in a back-tested rule. This should probably be part of a standard trading system research methodology and I will cover these two methods in more detail in later posts.

On Data Mining

The methods above only deal with one rule/back-test. However, we rarely test the one rule in isolation: most back-testing would test multiple parameter values, rules and combinations to try and identify the best performing ones: this is data mining.

It is however wrong to expect future performance of the best performing systems to keep in line with past, back-tested results. The best performing systems might have intrinsic value, but some of their over-performance is due to random variations. If you run 1,000 different rules with no predictive power, all of them will contain some random chance producing a variable departure from the zero-mean. The “most lucky” rule will be furthest away on the right-hand side of the zero-mean (and therefore picked up by the data miner), despite having no intrinsic value.

Data mining introduces a bias, which overstates the value of the “best” rule compared to expected random variations. The data mining bias is linked to several factors:

• Increases with the number of rules back-tested
• Decreases with sample size used in back-testing.
• Decreases with the correlation of back-tested rules results.
• Increases with the frequency of outliers in the back-test sample.
• Decreases with the variation in back-tested returns among rules considered.

This is illustrated with examples and charts. The rest of the chapter concentrate on methods to reduce/correct for the data mining bias and adapts the bootstrap method (using White’s reality check) and Monte Carlo permutation to be used in “data mining” mode (instead of single rule testing).

In conclusion, data mining is a valid method to discover the best rule(s) but the researcher should ensure that the results are statistically significant to avoid the risk of discovering “most lucky” rules.

A Tour of the EMH and Application of Methods

The following chapter deals with the Efficient Market Hypothesis, which takes a bit of a beating by the author. The main point is that both from an empirical and theoretical point of view, the EMH contains flaws, which supports the idea of succesful TA.

The last part of the book presents a diverse set of rules and parameters (6,402 combinations) and attempts to test for their statistical significance. The rules are fairly simple and the results do not highlight significant predictive power in any rule.

Review Conclusion

This book is a very interesting read, on the long side, with 450+ pages. Even though I enjoyed it throughout, I was sometimes finding myself hoping for the author not to expand so much on some introductory topics (the history and philosophy of science is quite interesting but could well be skim-read to get to the “juicier” parts quicker). If you’re in a rush I’d advise to concentrate on chapters 4, 5 and 6 where the actual bootstrap and Monte Carlo methods get presented and discussed, and the discussion on data mining bias is interesting and very relevant. For a reader new to these concepts, the initial chapters would provide a comprehensive introduction of the foundational concepts of scientific reasoning and statistical analysis before putting them all together in application.

For more info, some of the reviews on amazon are quite insightful (mostly positive – although the book’s got its share of 1-star reviews). There is also a companion website to the book with more info and detailed results of the tests performed in the last part of the book.

The book for today’s review is A Practical Guide to ETF Trading Systems by Anthony Garner, who is a Trend Follower and fund manager (and user of Trading Blox). The book is aimed at investors wanting to investigate rule-based trading and explains, with numerous examples, the path to designing, building and testing mechanical trading systems, with an emphasis on how this can be applied to the ETF instruments.

The book is a quick read (170 pages) with lots of charts to illustrate the testing.

Introductory information

The author starts by presenting systematic/mechanical trading by the way of a very simple system example and the track records of systematic funds such as Renaissance and many of the Trend Following Wizards.

The next chapter deals with Data. Stressing the importance of good quality data, the author lists a few sources to get historical data to be used as a proxy for the (fairly recent) ETFs. An example of investing with/without dividends makes a compelling case for trying to source that data as well (over slightly more than one century, including and reinvesting dividends nearly double the annual return – and with compounding, that means multiplying your end balance by a factor of over 150!). Finally, Garner touches on commodities and the need to construct indices including less obvious factors such as roll return.

A quick chapter on Backtesting software follows on (Garner uses Trading Blox throughout the book) leads to the final chapter of Part 1 on Strategy and System design.

Aspects such as optimisation and curve-fitting are discussed as well as the need for realistic testing assumptions, in simulating slippage and transaction costs – which can also have a dramatic impact on the simulation results.

Part 2: The meat of the book

The second and final part introduces several investing strategies including systematic (or rule-based) trading. As highlighted by the author, asset allocations is a one of the most important source of return. The good news is that most major asset classes (and more) are available in the form of an ETF. Various asset allocations are tested using the different systems throughout this part.

Benchmarks

As a base for comparison, various statistics (CAGR, drawdown, etc.) are calculated for different Buy and Hold portfolios (Equities-only, Equities with Bonds and Commodities, Commodities-only, etc.). One conclusion is that a diversified portfolio helps generate smoother and higher returns. Another point is how regular rebalancing is important to keep an appropriate level of diversification in the portfolio.

Garner uses the ill-named risk-adjusted return metric to compare strategies. Let’s just call this a semantic error (it is widly used throughout the industry), the astute reader should be able to mentally translate this to volatility-adjusted return. (sorry… a bug bear of mine: Variance != Risk)

Finally, an interesting side note specific to commodities and their equivalent ETCs for long-term holdings. The author demonstrates that because of negative roll yields (for markets in contango) and additional ETC sponsor fees eroding much of the returns, these instruments are not an ideal option for long-term holding.

BBBO system

The first rule-based system that Garner introduces is a Bollinger Band BreakOut. He describes the full system using rules, not only for entry and exit, but also for risk and position sizing, rebalancing, money management, etc. (as any good system should). The nice extra for Trading Blox users is that the system is made available on the forums over there.

The author runs comparisons with the various asset allocation benchmarks discussed in the prior chapter, which fairly conclusively demonstrate the superiority of this Trend Following system over any Buy and Hope Buy and Hold strategies. Playing with the system parameters also shows some form of robustness, with the performance staying fairly constant.

One point is made about trading short. It is recommended not to.
This is mainly in the light of bad performance of short-only strategies tested in the book. But the problem with this reasoning is that most backtests go back only to 1982! I believe the author might have fallen prey to a biased view of the markets, making macro predictions on the continuity of market conditions (suggesting that despite very good performance in 2007-2008 short-positioned systems will “go back to negative performance when stock markets recover”).

I have several problems with this:

• Who knows if markets will recover any time soon? Without getting into macro-economics discussions in much detail here: since the 80′s, the world markets have been subjected to the greatest inflationary expansion in the last 100 years (ever?), helping support (create?) the major macro bull run (bubble?) in most asset classes, globally. I do not want to be making any prediction about where we are heading next, but who knows if the next 25 years will not rhyme with 1931-1955 (ie and/or give us a long “Japan-style” deflationary decline spiral).
• The assumption has not been tested on earlier markets (mostly because of lack of data prior to 1982).

As a side note to the above: it would be interesting to measure and test the impact of a macro filter on a Trend Following system (ie something in the vein of: “favour long trades in the system when the macro indicators indicate a period of expansion and short trades during declines”). Maybe exploring a mechanized version of Schumpeter Business Cycles or Kondratiev Waves as a very long-term filter would be a worthy approach.

Increasing Returns

This is an interesting chapter addressing one of the shortfalls of ETFs versus futures as systematic trading instruments: leverage (or rather lack of). The new altered Money Management algorithm dictates to the system to concentrate the equity on the available signals, rather than separating the equity equally by instrument (and sitting in Cash where there are no signals). This is an interesting concept that deserves further investigation.

The performance improvement that this Money Management rule change generates is quite interesting. The conclusion is that it is possible to increase returns without increasing leverage.

Momentum System

The last chapter gives the same comparison treatment to a momentum system (buy strongest performing markets), which seems to over-perform the BBBO system (and obviously Buy and Hold as well).

Again, this system code is available on the Trading Blox forums.

After Word

A fairly short and pleasant read from a seasoned and real-life Trend Follower and Trading System Developer. There are a few ideas to take away, which is always appreciable. A bit on the expensive side (but I somehow managed to get it at nearly -50% on amazon…).

Another area of statistics which very often comes up in the context of serious trading system development is Robust Statistics. I have not found a good book to leave unread on my bookshelf on Robust Statistics yet so I’ll have to make do with with an unused bookmark on the wikipedia article ;-)

William Eckhardt

Anyway, Bill Eckhardt is a succesful automated trend follower with a strong background in Mathematics (although he apparently never finished his PhD – abandonning his studies for the trading pits). He was also Richard Dennis partner in the Turtle Trading experiment. I re-read his interview in New Market Wizards where he emphasises on a few concepts such as understanding statistics, bet size, and even psychology.

Here are some interesting inssights from the book interview (starting pg 107):

- Statistics are an important element of mathematics for trading:

- “The analysis of commodity markets is prone to pitfalls in statistical inference, and if one uses these tools without having a good foundational understanding, it’s easy to get in trouble.”

- “Classic Statistics work well if you are correct about data distribution assumptions. Because distributions are pathological, we need robust techniques”

- “define what you mean by robust?
A robust statistical estimator is one that is not perturbed much by mistaken assumptions about the nature of the distribution.”

- He mentions the concept of infinite variance in market prices distribution and particularly Mandelbrot and his precursor work on this topic.

- Traders should be more conservative in risk control than might be implied from statistical interpretations using normal distribution

- Less degrees of freedom is better – a degree of freedom is a parameter that produces a different system for every value (e.g. length of Moving Average in crossover systems).

- Chart patterns do not work

- Wished he’d focus more on money management at the start of his trading career (and mentions that in trading, Money Management is the most tractable problem, mathematically speaking)

- Mentions Utility functions and states that all the utility functions used in his risk management model are bounded. He takes the example that if utility functions were unbounded, there would be an amount for which a billionaire would be willing to bet his whole net worth at the flip of a coin.

- Interesting remark about bet size: if you plot system performance against bet size, you obtain a curve in the shape of a rightward-facing cartoon whale, going up in a straight line before dropping dramatically.

Eckhardt's righward-facing whale

- “Trading size is one aspect you dont want to optimize: the optimum comes just before the precipice. You want to be at the left of the optimal point, in the high zone of the straight curve”

- Gives his point of view on psychology and trading.

Will Christmas bring the Bear back? We shall not care - we are systems traders... image credits: alicepopkorn@flickr

I certainly seem to have hit a (small) motivation “roadblock” and slowed down in my research/development of a trading system in the last few weeks. So these few days break are most welcome to “recharge the batteries”.

Looking back at the last 3-4 months the blog has been live, I feel pretty happy of the experience and the path it has taken. Traffic has been decent for this kick-start period so it seems that you are happy too – which is encouraging. It takes time to keep a blog, up but it helps keep me on track! I have also “met” (by email, blog comments, forums, etc.) some great people that pushed me to further some of my reflexions and learn new things. You are part of this, so thank you!

If you have any further suggestions about the blog, please let me know by email or by commenting below – I always appreciate every single comment.

Selection of posts

If you have joined recently you might want to catch up on these selected posts:

• Series of posts on the e-ratio: use it to measure your edge, code it up in TradersStudio and AmiBroker.
• A bit more personal: why I write the blog and what’s in the pipeline.
• Michael Covel dropped by to comment (and argue a bit) on the review post of his book Trend Following.
• Continuous Futures contracts and their different options, with some C# code to generate the data using the CSI API.

Xmas Reading Linkfest

Also, I did not want to let you with nothing “to chew on” while I’m away, so I am sharing a list of reading material that I will probably go through in the Christmas break:

• I have come across Futures and Options Trader magazine, an interesting quarterly publication with free PDF download (requires email registration). Some good articles for automated trading systems, with a finger on the “market pulse” (Futures calendars, etc.).
• On the nature and origins of trend following by Stig Ostgaard.
• For those that have not come across it before: Mebane Faber’s updated tactical asset allocation paper, also a paper discussing its conclusions.
• A couple of articles from Taleb: the Fourth Quadrant – a map of the limits of statistics, Bleed or Blowup? Why Do We Prefer Asymmetric Payoffs?
• To balance with the above – a critic of Taleb’s views.
• Stats book:
  A stats book is always a good idea as this is an often “skill for life” – as illustrated in the excellent – and definitely required understanding for the data analysis that comes with trading systems development. My short-list, in no particular order: this one, that one and 2 other ones.
  But as it is Christmas, I will probably make it easy on myself, and start with this illustrated cartoon Stats guide, which seems to have great reviews and will surely be more fun to read (and learn – it is still a serious book).
• Mandelbrot: (Mis)behavior of the Markets
  I found this a very enjoyable read and I am planning on re-reading it during the break. Despite the subject matter (fractal analysis of financial time-series and “review” of the Efficient Market Hypothesis/CAPM, etc.) this is an easy read, which expands on some of the concepts popularised by Taleb. Hopefully a more detailed review will be coming in the new year.
• Vince’s Portfolio Mathematics
  This one has been sitting on my desk for a while. It is a reference in the Risk/Money Management/Position Exposure and introduces the Optimal f and Leveraged Space Model – I think every trader should read this, if only to understand some of the concepts. I will aim to finish it and post a review of it in January.
• And finally some non-trading related books that might provide philosophy insights on how to approach life, recommended by Tim Ferris (from The 4-Hour Workweek):
  Zorba the Greek: Epicurean and Stoic philosophies wrapped into a laugh-out-loud story you will never forget.
  Letters from a Stoic (Seneca): Common Sense, Roman Decadence, and the Meaning of Life – A timeless masterpiece!

Note about the FTC

Note that the FTC (Federal Trade Commission) has changed some rules regarding blogging endorsements. As I get paid (a little – literally pennies) off the links to Amazon – including purchases you make while on Amazon that I did not link directly to – I added a disclosure page highlighting just that and other things about the blog. I am not sure I have to (as I am based in London) but a little transparency does not hurt – and it’s also a friendly reminder that you can support the Au.Tra.Sy blog by starting all your Amazon shopping here ;-)
Rest assured that when I review or recommend books, I only do so if I liked them/found them useful (or not in case of negative reviews…) and all my library books actually sit on my bookshelf (+ some that I have not deemed relevant, or read yet!…).

2009 Closing

These are most likely my last online words for 2009… Have fun and see you on the other side for a great new decade!

What this book is not

If you are looking for the Holy Grail of trading systems and/or a complete “turn-key” trading system: look elsewhere as this is not what this book is set to achieve. It will not reveal any trading secrets; however reading this book will make you realise that this is not what is important…

Trend Following: essentials of a trading philosophy

It looks like Michael Covel appreciated the concept of Market Wizards from Jack Schwager and drew inspiration from it. In a clever mix, Covel managed to overlay and enrich all the foundations of trend following with great trend follower insights.

The book covers the principles of the trend following trading philosophy and its multiple aspects: discipline, drawdowns, risk and money management, behavioral biases, prediction vs. reaction, etc. It makes for a very interesting read – both instructive and interactive.

Even with an automated trading system, you have to be in agreement with the strategy philosophy. This book helps you understand the philosophy of trend following in greater detail – you can then decide whether it suits you. Additionally it can help you strengthen your belief during the inevitable low points such as drawdowns while trading a trend following system.

Inside Trend Wizard minds: 10 years of research

The world of trend followers is relatively discreet: barely anybody has heard of Ed Seykota or Bill Dunn – but John Meriwether opening up his third hedge fund (after blowing up his previous 2 – including LTCM!) makes it to the first page of Bloomberg and the FT.

Michael Covel has spent 10 years researching and interviewing for this book. This allowed him to get in the head of the greatest trend following traders. This results in extensive quotes/pearls of wisdon from Ed Seykota, Dave Harding, Bill Dunn, John W Henry, all the greatest Trend Following Wizards. It really gives you great insights on the way they think and how they apply their market philosophy to trend following. And this is information that is not readily available anywhere else.

New Edition addition

I have read both earlier and newest (post-2008) editions and I think the later version is worth it. Many references to the major events of 2008 help to put the text in the present context and add some relevancy (especially with trend followers outstanding performance during these times).

Additonally there is a new appendix covering in detail Trend Following for Stocks, which is of interest.

Controversies

One of the main message of Trend Following (the trading philosophy and the book) is that we cannot predict. It forces society to admit that we are no as sophisticated as we think. It also points to the fact that chance might have much more to do with success of so-called “experts” rather than their “expert prediction abilities”.
One such “expert trader” Victor Niederhoffer slams the book:

I get the same sort of value from these books [Trend Following] as I do from studying the Keech cult, supernatural operators such as Uri Geller and horosope readers

You can tell that Covel takes some pleasure describing the latest blow-up from Niederhoffer’s fund in 2007 in his “Big Events” chapter.
Some people have also raised the question as to why Michael Covel primarily seems to be marketing his books and courses rather than trading for himself. Whether this is a valid point or not, this does not remove any quality from the book.

You can check and follow Michael Covel on his trend following blog to make your opinion.

In closing

I find this book very inspiring and motivating.
If you are new to trend following, this is a must-read: it will introduce you to all the basic concepts.
If you already believe in trend following, this is a must-read: it will reinforce your beliefs and motivation.
If you do not believe in trend following: this is a must-read: it is not too late to change your mind and this is the best book for it!

I have read Trend Following about 3 times now; this is a book that lives on my trading bookshelf – I know that every time I need a boost for motivation, a re-read will provide me just that.

As Larry Hite says:

The way I see it, you have two choices – you can do what I did and work for 30-plus years, cobbling together scraps of information, seeking to create a money-making strategy, or you can spend a few days reading Covel’s book and skip that three-decade learning curve.