Encyclopedia Of Trading Strategies
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THE ENCYCLOPEDIA OF
TRADING STRATEGIES
JEFFREY OWEN KATZ, Ph.D.
DONNA 1. M C CORMICK
T R A D E M A R K S A N D S E R V I C E M A R K S
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sidered as trademarks or service marks of the company indicated. The use of a reg-
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C ONTENTS
. ~.
PREFACE xiii
INTRODUCTION xv
What Is a Complete Mechanical Trading System? - What Are Good Entries and Exits?
* The Scientific Approach to System Development * Tools and Materials Needed for
the Scientific Approach
PART I
Tools of the Trade
Introduction 1
Chapter 1
Data 3
Types of Data * Data Time Frames * Data Quality l Data Sources and Vendors
Chapter 2
Simulators 13
Types of Simulators * Programming the Simulator * Simulator Output @erformance
summnry reports; trade-by-trade reports) * Simulator Perfomxmce (speed: capacity:
power) l Reliability of Simulators - Choosing the Right Simulator * Simulators Used
in This Book
Chaoter 3
Optimizers and Optimization 29
What Optimizers Do * How Optimizers Are Used * ?Lpes of Optimization (implicit
optimizers; brute force optimizers; user-guided optimization; genetic optimizers; optimization
by simulated annealing; analytic optimizers; linearpmgrwnming) l How to Fail with
Optimization (small samples: large fxmztneter sets; no veri~cation) . How to Succeed
with O&mization (h-ge, representative samples; few rules andparameters; veriicatim
@results) * Alternatives to Traditional Optimization * Optimizer Tools and Information *
Which Optimizer Is forYou?
Chapter 4
Statistics 51
Why Use Statistics to Evaluate Trading Systems? l Sampling * Optimization and
Curve-Fitting l Sample Size and Representativeness . Evaluating a System Statistically
* Example 1: Evaluating the Out-of-Sample Test (what ifthe distribution is not normal?
what if there is serial dependence? what if the markets change?) l Example 2:
Evaluating the In-Sample Tests * Interpreting the Example Statistics (optimization
i-esults; verification results) l Other Statistical Techniques and Their Use (genetically
evoJved systems; multiple regression; monte car10 simulations; out-of-sample testing;
walk-forward testing) * Conclusion
PART II
The Study of Entries
Introduction 71
What Constitutes a Good Entry? * Orders Used in Entries (stop orders; limit orders;
market orders; selecting appropriate orders) * Entry Techniques Covered in This Book
(breakouts and moving averages; oscillators; seasonality: lunar and solar phenomena:
cycles and rhythms; neural networks; geneticaNy evolved entry rules) * Standardized
Exits * Equalization of Dollar Volatility * Basic Test Portfolio and Platfcnm
Chapter 5
Breakout Models 83
Kinds of Breakouts l Characteristics of Breakouts . Testing Breakout Models l
Channel Breakout Entries (close only channel breakouts; highest higMowest low
bnxzkouts) l Volatility Breakout Entries l Volatility Breakout Variations (long positions
only; currencies only; adx tremififilter) . Summary Analyses (breakout types: entry
orders; interactions; restrictions andjilters; analysis by market) * Conclusion l
What Have We Lamed?
Chapter 6
Moving Average Models 109
What is a Moving Average? - Purpose of a Moving Average * The Issue of Lag l
Types of Moving Averages l Types of Moving Average Entry Models l Characteristics
of Moving Average Entries l Orders Used to Effect Entries * Test Methodology ’
Tests of Trend-Following Models * Tests of Counter-Trend Models * Conclusion l
What Have We Learned?
ix
Chapter 7
Oscillator-Based Entries 133
What Is an Oscillator? l Kinds of Oscillators * Generating Entries with Oscillators *
Characteristics of Oscillator Entries . Test Methodology l Test Results (teas of
overbought/oversold models; tests of signal line models; tests of divergence models;
summary analyses) - Conclusion * What Have We Learned?
Chapter S
Seasonality 153
What Is Seasonality? l Generating Seasonal Entries l Characteristics of Seasonal
Entries . Orders Used to Effect Seasonal Entries . Test Methodology . Test Results
(test of the basic crossover model; tests of the basic momentum model: tests of the
crossover model with con$mtion; tests of the C~SSOV~~ model with confirmation and
inversions: summary analyses) * Conclusion * What Have We Learned?
Chmter 9
Lunar and Solar Rhythms 179
Legitimacy or Lunacy? l Lunar Cycles and Trading (generating lunar entries: lunar test
methodology; lunar test results; tests of the basic cmmo~er model; tests of the basic
momentum model: tests of the cnx~mer model with confirmation; test.s of the crmmver
model with confirmation and inversions; summary analyses; conclusion) * Solar
Activity and Trading (generazing solar entries: solar test results: conclusion) *
What Have We Learned?
Chapter 10
Cycle-Based Entries 2Q3
Cycle Detection Using MESA l Detecting Cycles Using Filter Banks (butterworth
jilters; wavelet-basedjilters) * Generating Cycle Entries Using Filter Banks *
Characteristics of Cycle-Based Entries . Test Methodology . Test Results .
Conclusion l What Have We Learned?
Chapter 11
Neural Networks 227
What Are Neural Networks? (feed-forward neural networks) . Neural Networks
in Trading l Forecasting with Neural Networks l Generating Entries with Neural
Predictions . Reverse Slow %K Model (code for the reverse slow % k model: test
methodology for the reverse slow % k model; training results for the reverse slow %k
model) l Turning Point Models (code for the turning point models; test methodology
for the turning point models; training resulrs for the turning point models) * Trading
Results for All Models (@ading results for the reverse slow %k model: frading results
for the bottom ruming point model; trading results for the top turning poinf model) *
Summary Analyses l Conclusion * What Have We Learned?
Chapter 12
Genetic Algorithms 257
What Are Genetic Algorithms? * Evolving Rule-Based Entry Models * Evolving an
Entry Model @he rule remplares) * Test Methodology (code for evolving an entry
model) l Test Results (solutions evolved for long entries; solutions evolved for short
enrries; fesf results for the standard portfolio; market-by-market tesf resulrs: equify
curves; the rules for rhe solurions tesred) * Conclusion * What Have We Learned?
PART III
The Study of Exits
Introduction 281
The Importance of the Exit l Goals of a Good Exit Strategy * Kinds of Exits
Employed in an Exit Strategy (money management exits; trailing exits; projir tnrgef
exiW rime-based exits; volarilify airs: barrier exits; signal exits) * Considerations
When Exiting the Market (gunning; trade-offs with prorecrive stops: slippage;
conC?nian rrading: conclusion) * Testing Exit Strategies * Standard Entries for Testing
Exits (the random entry model)
Chaoter 13
The Standard Exit Strategy 293
What is the Standard Exit Strategy? * Characteristics of the Standard Exit * Purpose of
Testing the SES l Tests of the Original SES (test results) * Tests of the Modified SES
(test resulrs) * Conclusion - What Have We Learned?
Chapter 14
Improvements on the Standard Exit 309
Purpose of the Tests l Tests of the Fixed Stop and Profit Target * Tests of Dynamic
Stops (rest of the highest higWlowest low stop; fesf of the dynamic arr-based stop: fat
of the modified exponential moving average dynamic stop) * Tests of the Profit Taget *
Test of the Extended Time Limit - Market-By-Market Results for the Best Exit *
Conclusion l What Have We Learned?
xi
Chapter 15
Adding Artificial Intelligence to Exits 335
Test Methodology for the Neural Exit Component . Results of the Neural Exit Test
(baseline results; neural exit portjolio results: neural exit market-by-market results) .
Test Methodology for the Genetic Exit Component (top 10 solutions with baseline exit:
results of rule-based exits for longs and shorts; market-by-market resu1t.s (If rule-based
exits for longs: market-by-market results
P R E F A C E
I n this book is the knowledge needed to become a mc~re successful trader of com-
modities. As a comprehensive reference and system developer’s guide, the book
explains many popular techniques and puts them to the test, and explores innova-
tive ways to take profits out of the market and to gain an extra edge. As well, the
book provides better methods for controlling risk, and gives insight into which
methods perform poorly and could devastate capital. Even the basics are covered:
information on how to acquire and screen data, how to properly back-test systems
using trading simulators, how to safely perform optimization, how to estimate and
compensate for curve-fitting, and even how to assess the results using inferential
statistics. This book demonstrates why the surest way to success in trading is
through use of a good, mechanized trading system.
For all but a few traders, system trading yields mm-e profitable results than
discretionary trading. Discretionary trading involves subjective decisions that fre-
quently become emotional and lead to losses. Affect, uncertainty, greed, and fear
easily displace reason and knowledge as the driving forces behind the trades.
Moreover, it is hard to test and verify a discretionary trading model. System-
based trading, in contrast, is objective. Emotions are out of the picture. Through
programmed logic and assumptions, mechanized systems express the trader’s
reason and knowledge. Best of all, such systems are easily tested: Bad systems
can be rejected or modified, and good cntes can be improved. This book contains
solid information that can be of great help when designing, building, and testing
a profitable mechanical trading system. While the emphasis is on an in-depth,
critical analysis of the various factors purported to contribute to winning systems,
the essential elements of a complete, mechanical trading system are also dissected
and explained.
To be complete, all mechanical trading systems must have an entry method
and an exit method. The entry method must detect opportunities to enter the mar-
ket at points that are likely to yield trades with a good risk-to-reward ratio. The
exit method must protect against excessive loss of capital when a trade goes wrong
or when the market turns, as well as effectively capture profits when the market
moves favorably. A considerable amount of space is devoted to the systematic
back-testing and evaluation of exit systems, methods, and strategies. Even the
trader who already has a trading strategy or system that provides acceptable exits
is likely to discover something that can be used to improve the system, increase
profits, and reduce risk exposure.
Also included in these pages are trading simulations on entire pqrtfolios of
tradables. As is demonstrated, running analyses on portfolios is straightforward, if
not easy to accomplish. The ease of computing equity growth curves, maximum
drawdowns, risk-to-reward ratios, returns on accounts, numbers of trades, and all
xiv PREFACE
the other related kinds of information useful in assessing a trading system on a
whole portfolio of commodities or stocks at once is made evident. The process of
conducting portfolio-wide walk-forward and other forms of testing and optimiza-
tion is also described. For example, instruction is provided on how to search for a
set of parameters that, when plugged into a system used to trade each of a set of
commodities, yields the best total net profit with the lowest drawdown (or perhaps
the best Sharpe Ratio, or any other measure of portfolio performance desired) for
that entire set of commodities. Small institutional traders (CTAs) wishing to run a
system on multiple tradables, as a means of diversification, risk reduction, and liq-
uidity enhancement, should find this discussion especially useful.
Finally, to keep all aspects of the systems and components being tested
objective and completely mechanical, we have drawn upon our academic and sci-
entific research backgrounds to apply the scientific method to the study of entry
and exit techniques. In addition, when appropriate, statistics are used to assess
the significance of the results of the investigations. This approach should provide the
most rigorous information possible about what constitutes a valid and useful com-
ponent in a successful trading strategy.
So that everyone will benefit from the investigations, the exact logic behind
every entry or exit strategy is discussed in detail. For those wishing to replicate
and expand the studies contained herein, extensive source code is also provided in
the text, as well as on a CD-ROM (see offer at back of book).
Since a basic trading system is always composed of two components, this
book naturally includes the following two parts: “The Study of Entries” and “The
Study of Exits.” Discussions of particular technologies that may be used in gener-
ating entries or exits, e.g., neural networks, are handled within the context of devel-
oping particular entry or exit strategies. The “Introduction” contains lessons on the
fundamental issues surrounding the implementation of the scientific approach to
trading system development. The first part of this book, “Tools of the Trade,” con-
tains basic information, necessary for all system traders. The “Conclusion” pro-
vides a summary of the research findings, with suggestions on how to best apply
the knowledge and for future research. The ‘Appendix” contains references and
suggested reading.
Finally, we would like to point out that this book is a continuation and elab-
oration of a series of articles we published as Contributing Writers to Technical
Analysis of Stocks and Commodities from 1996, onward.
Jeffrey Owen Katz, Ph.D., and Donna L. McCormick
I N T R O D U C T I O N
There is one thing that most traders have in common: They have taken on the
challenge of forecasting and trading the financial markets, of searching for those
small islands of lucrative inefficiency in a vast sea of efficient market behavior.
For one of the authors, Jeffrey Katz, this challenge was initially a means to indulge
an obsession with mathematics. Over a decade ago, he developed a model that pro-
vided entry signals for the Standard & Poor’s 500 (S&P 500) and OEX. While
these signals were, at that time, about 80% accurate, Katz found himself second-
guessing them. Moreover, he had to rely on his own subjective determinations of
such critical factors as what kind of order to use for entry, when to exit, and where
to place stops. These determinations, the essence of discretionary trading, were
often driven more by the emotions of fear and avarice than by reason and knowl-
edge. As a result, he churned and vacillated, made bad decisions, and lost more
often than won. For Katz, like for most traders, discretionary trading did not work.
If discretionary trading did not work, then what did? Perhaps system trading
was the answer. Katz decided to develop a completely automated trading system
in the form of a computer program that could generate buy, sell, stop, and other
necessary orders without human judgment or intervention. A good mechanical
system, logic suggested, would avoid the problems associated with discretionary
trading, if the discipline to follow it could be mustered. Such a system would pro-
vide explicit and well-defined entries, “normal” or profitable exits, and “abnor-
mal” or money management exits designed to control losses on bad trades,
A fully automated system would also make it possible to conduct historical
tests, unbiased by hindsight, and to do such tests on large quantities of data.
Thorough testing was the only way to determine whether a system really worked
and would be profitable to trade, Katz reasoned. Due to familiarity with the data
series, valid tests could not be performed by eye. If Katz looked at a chart and
“believed” a given formation signaled a good place to enter the market, he could
not trust that belief because he had already seen what happened after the forma-
tion occurred. Moreover, if charts of previous years were examined to find other
examples of the formation, attempts to identify the pattern by “eyeballing” would
be biased. On the other hand, if the pattern to be tested could be formally defined
and explicitly coded, the computer could then objectively do all the work: It
would run the code on many years of historical data, look for the specified for-
mation, and evaluate (without hindsight) the behavior of the market after each
instance. In this way, the computer could indicate whether he was indeed correct in
his hypothesis that a given formation was a profitable one. Exit rules could also
be evaluated objectively.
Finally, a well-defined mechanical trading system would allow such things
as commissions, slippage, impossible tills, and markets that moved before he
xvi
could to be factored in. This would help avoid unpleasant shocks when moving
from computer simulations to real-world trading. One of the problems Katz had in
his earlier trading attempt was failing to consider the high transaction costs
involved in trading OEX options. Through complete mechanization, he could
ensure that the system tests would include all such factors. In this way, potential
surprises could be eliminated, and a very realistic assessment could be obtained of
how any system or system element would perform. System trading might, he
thought, be the key to greater success in the markets.
WHAT IS A COMPLETE, MECHANICAL TRADING SYSTEM?
One of the problems witb Katz’s early trading was that his “system” only provided
entry signals, leaving the determination of exits to subjective judgment; it was not,
therefore, a complete, mechanical trading system. A complete, mechanical trading
system, one that can be tested and deployed in a totally objective fashion, without
requiring human judgment, must provide both entries and exits. To be truly com-
plete, a mechanical system must explicitly provide the following information:
1. When and how, and possibly at what price, to enter the market
2. When and how, and possibly at what price, to exit the market with a loss
3. When and how, and possibly at what price, to exit the market with
a profit
The entry signals of a mechanical trading system can be as simple as explic-
it orders to buy or sell at the next day’s open. The orders might be slightly more
elaborate, e.g., to enter tomorrow (or on the next bar) using either a limit or stop.
Then again, very complex contingent orders, which are executed during certain
periods only if specified conditions are met, may be required-for example, orders
to buy or sell the market on a stop if the market gaps up or down more than so
many points at the open.
A trading system’s exits may also be implemented using any of a range of
orders, from the simple to the complex. Exiting a bad trade at a loss is frequently
achieved using a money management stop, which tertninates the trade that has
gone wrong before the loss becomes seriously damaging. A money management
stop, which is simply a stop order employed to prevent runaway losses, performs
one of the functions that must be achieved in some manner by a system’s exit strat-
egy; the function is that of risk control. Exiting on a profit may be accomplished
in any of several different ways, including by the use of pm@ targets, which are
simply limit orders placed in such a way that they end the trade once the market
moves a certain amount in the trader’s favor; trailing stops, which are stop orders
used to exit with a profit when the market begins to reverse direction; and a wide
variety of other orders or combinations of orders.
In Katz’s early trading attempts, the only signals available were of probable
direction or turning points. These signals were responded to by placing buy-at-
market or sell-at-market orders, orders that are often associated with poor fills and
lots of slippage. Although the signals were often accurate, not every turning point
was caught. Therefore, Katz could not simply reverse his position at each signal.
Separate exits were necessary. The software Katz was using only served as a par-
tially mechanical entry model; i.e., it did not provide exit signals. As such, it was
not a complete mechanical trading system that provided both entries and exits.
Since there were no mechanically generated exit signals, all exits had to be deter-
mined subjectively, which was one of the factors responsible for his trading prob-
lems at that time. Another factor that contributed to his lack of success was the
inability to properly assess, in a rigorous and objective manner, the behavior of the
trading regime over a sufficiently long period of historical data. He had been fly-
ing blind! Without having a complete system, that is, exits as well as entries, not
to mention good system-testing software, how could such things as net profitabil-
ity, maximum drawdown, or the Sharpe Ratio be estimated, the historical equity
curve be studied, and other important characteristics of the system (such as the
likelihood of its being profitable in the future) be investigated? To do these things,
it became clear-a system was needed that completed the full circle, providing
complete “round-turns,” each consisting of an entry followed by an exit.
WHAT ARE GOOD ENTRIES AND EXITS?
Given a mechanical trading system that contains an entry model to generate entry
orders and an exit model to generate exit orders (including those required for
money management), how are the entries and exits evaluated to determine whether
they are good? In other words, what constitutes a good entry or exit?
Notice we used the terms entry orders and exit orders, not entry or exit sig-
nals. Why? Because “signals” are too ambiguous. Does a buy “signal” mean that
one should buy at the open of the next bar, or buy using a stop or limit order? And
if so, at what price? In response to a “signal” to exit a long position, does the exit
occur at the close, on a profit target, or perhaps on a money management stop?
Each of these orders will have different consequences in terms of the results
achieved. To determine whether an entry or exit method works, it must produce
more than mere signals; it must, at smne point, issue highly specific entry and exit
orders. A fully specified entry or exit order may easily be tested to determine its
quality or effectiveness.
In a broad sense, a good entry order is one that causes the trader to enter the
market at a point where there is relatively low risk and a fairly high degree of
potential reward. A trader’s Nirvana would be a system that generated entry orders
to buy or sell on a limit at the most extreme price of every turning point. Even if
xviii lNTR”D”Cn”N
the exits were only merely acceptable, none of the trades would have more than
one or two ticks of adverse excursion (the largest unrealized loss to occur within
a trade), and in every case, the market would be entered at the best obtainable
price. In an imperfect world, however, entries will never be that good, but they can
be such that, when accompanied by reasonable effective exits, adverse excursion
is kept to acceptable levels and satisfying risk-reward ratios are obtained.
What constitutes an elective exit? An effective exit must quickly extricate the
trader from the market when a trade has gone wrong. It is essential to preserve cap-
ital from excessive erosion by losing trades; an exit must achieve this, however,
without cutting too many potentially profitable trades short by converting them into
small losses. A superior exit should be able to hold a trade for as long as it takes to
capture a significant chunk of any large move; i.e., it should be capable of riding a
sizable move to its conclusion. However, riding a sizable move to conclusion is not
a critical issue if the exit strategy is combined with an entry formula that allows for
reentry into sustained trends and other substantial market movements.
In reality, it is almost impossible, and certainly unwise, to discuss entries
and exits independently. To back-test a trading system, both entries and exits
must be present so that complete round-turns will occur. If the market is entered,
but never exited, how can any completed trades to evaluate be obtained? An entry
method and an exit method are required before a testable system can exist.
However, it would be very useful to study a variety of entry strategies and make
some assessment regarding how each performs independent of the exits.
Likewise, it would be advantageous to examine exits, testing different tech-
niques, without having to deal with entries as well. In general, it is best to manip-
ulate a minimum number of entities at a time, and measure the effects of those
manipulations, while either ignoring or holding everything else constant. Is this
not the very essence of the scientific, experimental method that has achieved so
much in other fields? But how can such isolation and control be achieved, allow-
ing entries and exits to be separately, and scientifically, studied?
THE SCIENTIFIC APPROACH TO SYSTEM DEVELOPMENT
This book is intended to accomplish a systematic and detailed analysis of the
individual components that make up a complete trading system. We are propos-
ing nothing less than a scientific study of entries, exits, and other trading system
elements. The basic substance of the scientific approach as applied herein is
as f0110ws:
1. The object of study, in this case a trading system (or one or more of its
elements), must be either directly or indirectly observable, preferably
without dependence on subjective judgment, something easily achieved
with proper testing and simulation software when working with com-
plete mechanical trading systems.
2. An orderly means for assessing the behavior of the object of study must
be available, which, in the case of trading systems, is back-testing over
long periods of historical data, together with, if appropriate, the applica-
tion of various models of statistical inference, the aim of the latter being
to provide a fix or reckoning of how likely a system is to hold up in the
future and on different samples of data.
3. A method for making the investigative task tractable by holding most
parameters and system components fixed while focusing upon the effects
of manipulating only one or two critical elements at a time.
The structure of this book reflects the scientific approach in many ways.
Trading systems are dissected into entry and exit models. Standardized methods for
exploring these components independently are discussed and implemented, leading
to separate sections on entries and exits. Objective tests and simulations are run,
and statistical analyses are performed. Results are presented in a consistent manner
that permits direct comparison. This is “old hat” to any practicing scientist.
Many traders might be surprised to discover that they, like practicing scien-
tists, have a working knowledge of the scientific method, albeit in different guise!
Books for traders often discuss “paper trading” or historical back-testing, or pre-
sent results based on these techniques. However, this book is going to be more
consistent and rigorous in its application of the scientific approach to the prob-
lem of how to successfully trade the markets. For instance, few books in which
historical tests of trading systems appear offer statistical analyses to assess valid-
ity and to estimate the likelihood of future profits. In contrast, this book includes
a detailed tutorial on the application of inferential statistics to the evaluation
of trading system performance.
Similarly, few pundits test their entries and exits independently of one
another. There are some neat tricks that allow specific system components to be
tested in isolation. One such trick is to have a set of standard entry and exit strate-
gies that remain fixed as the particular entry, exit, or other element under study is
varied. For example, when studying entry models, a standardized exit strategy will
be repeatedly employed, without change, as a variety of entry models are tested
and tweaked. Likewise, for the study of exits, a standardized entry technique will
be employed. The rather shocking entry technique involves the use of a random
number generator to generate random long and short entries into various markets!
Most traders would panic at the idea of trading a system with entries based on the
fall of the die; nevertheless, such entries are excellent in making a harsh test for
an exit strategy. An exit strategy that can pull profits out of randomly entered
trades is worth knowing about and can, amazingly, be readily achieved, at least for
the S&P 500 (Katz and McCormick, March 1998, April 1998). The tests will be
done in a way that allows meaningful comparisons to be made between different
entry and exit methods.
To summarize, the core elements of the scientific approach are:
1. The isolation of system elements
2. The use of standardized tests that allow valid comparisons
3. The statistical assessment of results
TOOLS AND MATERIALS NEEDED FOR THE SCIENTIFIC
APPROACH
Before applying the scientific approach to the study of the markets, a number of
things must be considered. First, a universe of reliable market data on which to
perform back-testing and statistical analyses must be available. Since this book is
focused on commodities trading, the market data used as the basis for our universe
on an end-of-day time frame will be a subset of the diverse set of markets supplied
by Pinnacle Data Corporation: these include the agriculturals, metals, energy
resources, bonds, currencies, and market indices. Intraday time-frame trading is
not addressed in this book, although it is one of our primary areas of interest that
may be pursued in a subsequent volume. In addition to standard pricing data,
explorations into the effects of various exogenous factors on the markets some-
times require unusual data. For example, data on sunspot activity (solar radiation
may influence a number of markets, especially agricultural ones) was obtained
from the Royal Observatory of Belgium.
Not only is a universe of data needed, but it is necessary to simulate one or
more trading accounts to perform back-testing. Such a task requires the use of a
trading simulator, a software package that allows simulated trading accounts to be
created and manipulated on a computer. The C+ + Trading Simulator from
Scientific Consultant Services is the one used most extensively in this book
because it was designed to handle portfolio simulations and is familiar to the
authors. Other programs, like Omega Research’s TradeStation or SystemWriter
Plus, also offer basic trading simulation and system testing, as well as assorted
charting capabilities. To satisfy the broadest range of readership, we occasionally
employ these products, and even Microsoft’s Excel spreadsheet, in our analyses.
Another important consideration is the optimization of model parameters.
When running tests, it is often necessary to adjust the parameters of some compo-
nent (e.g., an entry model, an exit model, or some piece thereof) to discover the
best set of parameters and/or to see how the behavior of the model changes as its
parameters change. Several kinds of model parameter optimizations may be con-
livmOD”CTlON xxi
ducted. In manual optimization, the user of the simulator specifies a parameter that
is to be manipulated and the range through which that parameter is to be stepped;
the user may wish to simultaneously manipulate two or more parameters in this
manner, generating output in the form of a table that shows how the parameters
interact to affect the outcome. Another method is brute force optimization, which
comes in several varieties: The most common form is stepping every parameter
through every possible value. If there are many parameters, each having many pos-
sible values, running this kind of optimization may take years. Brute force opti-
mization can, however, be a workable approach if the number of parameters, and
values through which they must be stepped, is small. Other forms of brute force
optimization are not as complete, or as likely to find the global optimum, but can
be run much more quickly. Finally, for heavy-duty optimization (and, if naively
applied, truly impressive curve-fitting) there are genetic algorithms. An appropri-
ate genetic algorithm (GA) can quickly tind a good solution, if not a global opti-
mum, even when large numbers of parameters are involved, each having large
numbers of values through which it must be stepped. A genetic optimizer is an
important tool in the arsenal of any trading system developer, but it must be used
cautiously, with an ever-present eye to the danger of curve-fitting. In the inves-
tigations presented in this book, the statistical assessment techniques, out-of-
sample tests, and such other aspects of the analyses as the focus on entire portfolios
provide protection against the curve-fitting demon, regardless of the optimization
method employed.
Jeffrey Owen Katz, Ph.D., and Donna E McCormick
P A R T I
Tools of the Trade
Introduction
T o obJectlve1y study the behavior of mechanical trading systems, various exper-
‘.
imental materials and certain tools are needed.
To study the behavior of a given entry or exit method, a simulation should be
done using that method on a portion of a given market’s past performance; that
requires data. Clean, historical data for the market on which a method is being
tested is the starting point.
Once the data is available, software is needed to simulate a trading account.
Such software should allow various kinds of trading orders to be posted and
should emulate the behavior of trading a real account over the historical period of
interest. Software of this kind is called a trading simulator.
The model (whether an entry model, an exit model, or a complete system)
may have a number of parameters that have to be adjusted to obtain the best results
from the system and its elements, or a number of features to be tamed on or off.
Here is where an optimizer plays its part, and a choice must be made among the
several types of optimizers available.
The simulations and optimizations will produce a plethora of results. The sys-
tem may have taken hundreds or thousands of trades, each with its own profiVloss,
maximum adverse excursion, and maximum favorable excursion. Also generated
will be simulated equity curves, risk-to-reward ratios, profit factors, and other infor-
mation provided by the trading simulator about the simulated trading account(s). A
way to assess the significance of these results is needed. Is the apparent profitabili-
ty of the trades a result of excessive optimization? Could the system have been prof-
itable due to chance alone, or might it really be a valid trading strategy? If the system
is valid, is it likely to hold up as well in the future, when actually being traded, as in
2
the past? Questions such as these require the basic machinery provided by inferen-
tial statistics.
In the next several chapters, we will cover data, simulators, optimizers, and
statistics. These items will be used throughout this book when examining entry
and exit methods and when attempting to integrate entries and exits into complete
trading systems.
C H A P T E R 1
Data
A determination of what works, and what does not, cannot be made in the realm
of commodities trading without quality data for use in tests and simulations.
Several types of data may be needed by the trader interested in developing a prof-
itable commodities trading system. At the very least, the trader will require his-
torical pricing data for the commodities of interest.
TYPES OF DATA
Commodities pricing data is available for individual or continuous contracts.
Individual contract data consists of quotations for individual commodities con-
tracts. At any given time, there may be several contracts actively trading. Most
speculators trade thefront-month contracts, those that are most liquid and closest
to expiration, but are not yet past first notice date. As each contract nears expira-
tion, or passes first notice date, the trader “rolls over” any open position into the
next contract. Working with individual contracts, therefore, can add a great deal of
complexity to simulations and tests. Not only must trades directly generated by the
trading system be dealt with, but the system developer must also correctly handle
rollovers and the selection of appropriate contracts.
To make system testing easier and more practical, the continuous contract was
invented. A continuous contract consists of appropriate individual contracts strung
together, end to end, to form a single, continuous data series. Some data massaging
usually takes place when putting together a continuous contract; the purpose is to
close the gaps that occur at rollover, when one contract ends and another begins,
Simple back-aajustment appears to be the most reasonable and popular gap-closing
3
method (Schwager, 1992). Back-adjustment involves nothing more than the sub-
traction of constants, chosen to close the gaps, from all contracts in a series other
than the most recent. Since the only operation performed on a contract’s prices is the
subtraction of a constant, all linear price relationships (e.g., price changes over time,
volatility levels, and ranges) are preserved. Account simulations performed using
back-adjusted continuous contracts yield results that need correction only for
rollover costs. Once corrected for rollover, simulated trades will produce profits and
losses identical to those derived from simulations performed using individual con-
tracts. However, if trading decisions depend upon information involving absolute
levels, percentages, or ratios of prices, then additional data series (beyond back-
adjusted continuous contracts) will be required before tests can be conducted.
End-of-day pricing data, whether in the form of individual or continuous
contracts, consists of a series of daily quotations. Each quotation, “bar,” or data
point typically contains seven fields of information: date, open, high, low,
close, volume, and open interest. Volume and open interest are normally
unavailable until after the close of the following day; when testing trading
methods, use only past values of these two variables or the outcome may be a
fabulous, but essentially untradable, system! The open, high, low, and close
(sometimes referred to as the settlement price) are available each day shortly
after the market closes.
Intraday pricing data consists either of a series of fixed-interval bars or of
individual ticks. The data fields for fixed-interval bars are date, time, open, high,
low, close, and tick volume. Tick volume differs from the volume reported for end-
of-day data series: For intraday data, it is the number of ticks that occur in the peri-
od making up the bar, regardless of the number of contracts involved in the
transactions reflected in those ticks. Only date, time, and price information are
reported for individual ticks: volume is not. Intraday tick data is easily converted
into data with fixed-interval bars using readily available software. Conversion soft-
ware is frequently provided by the data vendor at no extra cost to the consumer.
In addition to commodities pricing data, other kinds of data may be of value.
For instance, long-term historical data on sunspot activity, obtained from the
Royal Observatory of Belgium, is used in the chapter on lunar and solar influ-
ences. Temperature and rainfall data have a bearing on agricultural markets.
Various economic time series that cover every aspect of the economy, from infla-
tion to housing starts, may improve the odds of trading commodities successfully.
Do not forget to examine reports and measures that reflect sentiment, such as the
Commitment of Traders (COT) releases, bullish and bearish consensus surveys,
and put-call ratios. Nonquantitative forms of sentiment data, such as news head-
lines, may also be acquired and quantified for use in systematic tests. Nothing
should be ignored. Mining unusual data often uncovers interesting and profitable
discoveries. It is often the case that the more esoteric or arcane the data, and the
more difficult it is to obtain, the greater its value!
