. 3
( 9)


the market. Trades that languish before finally taking off tie up money that might
be better used elsewhere; not only do such trades increase market exposure, but
they waste margin and lead to “margin-ineffCent” trading or portfolios. Perfect
entries would involve buying the exact lows of bottoming points and selling the
exact highs of topping points. Such entries hardly ever occur in the real world and
are not necessary for successful trading. For trading success it is merely necessary
that entries, when coupled with reasonable exits, produce trading systems that
have good overall performance characteristics.
Entries may be executed using any of several kinds of orders, including stop
orders, limit orders, and market orders.

Stop Orders
A stop order enters a market that is already moving in the direction of the trade.
A buy or sell is triggered when the market rises above a buy stop or falls below a
sell stop; this characteristic often results in stop orders being used with trend-fol-
lowing entry models. A nice feature of a stop order is that the market must be mov-
ing in a favorable direction at the time of entry. Because of this, the order itself can
act as a contlrming “filter” of the signals generated by the entry model. If a par-
ticular entry happens to be a good one, momenhnn will cause the trade to quickly
turn profitable with hardly any adverse excursion,
On the negative side, an entry executed on a stop order may experience con-
siderable slippage, especially in fast moves, and the market will be bought high or
sold low. Consider the case in which prices begin to move rapidly in favor of a
trade: Buying or selling into such movement is like jumping onto an accelerating
train and is likely to result in large amounts of slippage; the faster the move, the
greater the slippage. Sli˜ppage is the difference between the price at which the stop
is set and the price at which it is actually tilled. Because slippage eats into the
profit generated by the trade, it is undesirable. The most unpleasant situation is
when the entry order gets tilled far past the stop, just as the market begins to
reverse! Because buying or selling takes place on a stop, the market entry occurs
significantly into any move and at a relatively poor price.

Limit Orders
In contrast to a stop order, a limit order results in entry when the market moves
against the direction of the trade. A limit order is an order to buy or to sell at a
specified price or better. For a buy limit to be filled, the market must move below
the limit price; for a sell order, the market must move above the limit price. At least
in the short term, buying or selling takes place against the trend. The count&rend
nature of a limit order and the fact that the market may never move to where the
order can be tilled are the primary disadvantages. However, when working with
predictive, countertrend entry models, the countertrend nature of the limit order
may not be a disadvantage at all. The advantage of a limit order is that there is no
slippage and that entry takes place at a good, known price.

Market Orders
A market order is a simple order to buy or sell at the prevailing market price. One
positive feature of a market order is that it will be executed quickly after being
PART II The Study Of Entries 73

placed; indeed, many exchanges require market orders to be tilled within a few
minutes at most. Stop or limit orders, on the other hand, may sit for some time
before market activity triggers a till. Another benefit is guaranteed execution:
After placing a market order, entry into the trade will definitely take place. The
drawback to the market order is that slippage may occur. However, in contrast to
the stop order, the slippage can go either way-sometimes in the trade™s favor,
sometimes against it--depending on market movement and execution delay.

Selecting Appropriate Orders
Determining which kind of order to use for an entry must include not only con-
sideration of the advantages and disadvantages of the various kinds of orders, but
also the nature of the model that generates the entry signals and its theory regard-
ing market behavior.
If the entry model predicts turning points slightly into the future, a limit
order may be the most appropriate, especially if the entry model provides some
indication of the price at which the turning point will occur. If the entry model
contains specification of price, as do systems based on critical retracement levels,
entry on a limit (with a tight money management exit stop) is definitely the way
to go: A bounce from the retracement level can be expected, and the limit order
will enter at or near the retracement level, resulting in a trade that either quickly
turns profitable (if the market has responded to the critical level as expected) or is
stopped out with a very small loss.
If the entry model requires some kind of confirmation before entry that the
market is moving in the appropriate direction, a stop order might be the best
choice. For example, a breakout system can be naturally married to a stop-based
entry. If the market moves in a favorable direction and passes the breakout thresh-
old price (the same price at which the entry stop is set), entry will occur automat-
ically, and it will be possible to capture any ensuing move. If the breakout price is
not penetrated, the stop will not be triggered and no entry will take place. In this
example, the entry order actually becomes part of the entry model or system.
Market orders are most useful when the entry model only provides timing
information and when the cost (in terms of slippage and delay) of confirming the
entry with a stop order is too great relative to the expected per-trade profit. A mar-
ket order is also appropriate when the timing provided by the system is critical.
For some models, it would make sense to place a stop or a limit order and then, if
the order is not filled within a specified period of time, to cancel the order and
replace it with a market order.
When developing an entry model, it is often worthwhile to examine various
entry orders to determine which are most manageable and which perform best.
The original entry model will probably need modification to make such tests pos-
sible, but the outcome may prove worth the trouble. Examples of various entry
systems tested using these three types of orders (entry at open, on limit, and on
stop) appear throughout the study of entries.

This part of the book explores entry techniques that range from trend-following to
countertrend, from endogenous to exogenous, from traditional to exotic, and from
simple to complex. Since there are an infinite number of entry models, spatial lim-
itations forced us to narrow our focus and discuss only a subset of the possibili-
ties. We attempted to cover popular methods that are frequently discussed, some
of which have been around for decades, but for which there is little objective, sup-
portive evidence. We will systematically put these models to the test to see how
well they work. We have also tried to expand upon some of our earlier, published
studies of entry models in which readers (primarily of ZMtnicul Analysis of Stocks
and Commodities) have expressed great interest.

Breakouts and Moving Averages
Traditional trend-following entry models that employ breakouts and moving aver-
ages are examined in Chapters 5 and 6, respectively. Breakout entn™es are simple and
intuitively appealing: The market is bought when prices break above an upper band
or threshold. It is sold short when prices break below a lower band or threshold.
Operating this way, breakout entries are certain to get the trader on-board any large
market movement or trend. The trend-following entries that underlie many popular
trading systems are breakout entries. Breakout models differ from one another main-
ly in how the threshold bands are computed and the actual entry is achieved.
Like breakouts, moving averages are alluring in their simplicity and are
extremely popular among technical traders. Entries may be generated using mov-
ing averages in any of several ways: The market may be entered when prices cross
over a moving average, when a faster moving average crosses a slower one, when
the slope of a moving average changes direction, or when prices pull back to a mov-
ing-average line as they might to lines of support or resistance. Additional variety
is introduced by the fact that there are simple moving averages, exponential mov-
ing averages, and triangular moving averages, to mention only a few. Since the
entry models of many trading systems employ some variation of breakouts or mov-
ing averages, it seems important to explore these techniques in great detail.

Oscillators are indicators that tend to fluctuate quasi-cyclically within a limited
range. They are very popular among technical traders and appear in most charting
packages. Entry models based on oscillators are “endogenous” in nature (they do
not require anything but market data) and are fairly simple to implement, charac-
teristics they share with breakout and moving-average models. However, breakout
and moving-average models tend to enter the market late, often too late, because
they are designed to respond to, rather than anticipate, market behavior. In con-
trast, oscillators anticipate prices by identifying turning points so that entry can
occur before, rather than after, the market moves. Since they attempt to anticipate
prices, oscillators characteristically generate countertrend entries.
Entries are commonly signaled by divergence between an oscillator and
price. Divergence is seen when prices form a lower low but the oscillator forms a
higher low, signaling a buy; or when prices form a higher high but the oscillator
forms a lower high, signaling the time to sell short.
A signal line is another way to generate entries. It is calculated by taking a
moving average of the oscillator, The trader buys when the oscillator crosses above
the signal line and sells short when it crosses below. Although typically used in
“trading range” markets for countertrend entries, an oscillator is sometimes
employed in a trend-following manner: Long or short positions might be entered
when the Stochastic oscillator climbs above 80 or drops below 20, respectively.
Entry models that employ such classic oscillators as Lane™s Stochastic, Williams™s
RSI, and Appel™s MACD are studied in Chapter 7.

Chapter 8 deals with seasonality, which is construed in different ways by dif-
ferent traders. For our purposes, seasonalify is defined as cyclic or recurrent
phenomena that are consistently linked to the calendar, specifically, market
behavior affected by the time of the year or tied to particular dates. Because
they are predictive (providing trading signals weeks, months, or years ahead),
these models are countertrend in nature. Of the many ways to time entries that
use seasonal rhythms, two basic approaches will be examined: momentum and
crossover. The addition of several rules for handling confirmations and inver-
sions will also be tested to determine whether they would produce results bet-
ter than the basic models.

Lunar and Solar Phenomena
Do lunar and solar events influence the markets? Is it possible for an entry model to
capitalize on the price movements induced by such influences? The moon™s role in
the instigation of tides is undisputed. Phases of the moon correlate with rainfall and
with certain biological rhythms, and they influence when farmers plant crops. Solar
phenomena, such as solar flares and sunspots, are also known to impact events on
earth. During periods of high solar activity, magnetic storms occur that can disrupt
power distribution systems, causing serious blackouts. To assume that solar and
lunar phenomena influence the markets is not at all unreasonable; but how might
these influences be used to generate predictive, countertrend entries?
Consider the lunar rhythm: It is not hard to define a model that enters the mar
ket a specified number of days before or after either the full or new moon. The same
applies to solar activity: An entry can be signaled when the sunspot count rises above
some threshold or falls below another threshold. Alternatively, moving averages of
solar activity can be computed and crossovers of these moving averages used to time
market entries. Lunar cycles, sunspots, and other planetary rhythms may have a real,
albeit small, impact on the markets, an impact that might be profitable with a prop-
erly constructed entry model. Whether lunar and solar phenomena actually affect the
markets sufficiently to be taken advantage of by an astute trader is a question for an
empirical investigation, such as that reported in Chapter 9.

Cycles and Rhythms
Chapter 10 explores cycles and rhythms as a means of timing entries into the mar-
ket. The idea behind the use of cycles to time the market is fundamentally simple:
Extrapolate observed cycles into the future, and endeavor to buy the cycle lows
and sell short the cycle highs. If the cycles are sufficiently persistent and accu-
rately extrapolated, excellent countertrend entries should be the result. If not, the
entries are likely to be poor.
For a very long time, traders have engaged in visual cycle analysis using
charts, drawing tools, and, more recently, charting programs. Although cycles can
be analyzed visually, it is not very difficult to implement cycle recognition and
analysis algorithms in software. Many kinds of algorithms are useful in cycle
analysis-everything from counting the bars between tops or bottoms, to fast
Fourier transforms (FITS) and maximum entropy spectral analyses (MESAS).
Getting such algorithms to work well, however, can be quite a challenge; but hav-
ing reliable software for cycle analysis makes it possible to build objective, cycle-
based entry models and to test them on historical data using a trading simulator.
Whether detected visually or by some mathematical algorithm, market
cycles come in many forms. Some cycles are exogenous, i.e., induced by external
phenomena, whether natural or cultural. Seasonal rhythms, anniversary effects,
and cycles tied to periodic events (e.g., presidential elections and earnings reports)
fall into the exogenous category: these cycles are best analyzed with methods that
take the timing of the driving events into account. Other cycles are endogenous;
i.e., their external driving forces are not apparent, and nothing other than price data
is needed to analyze them. The 3-day cycle occasionally observed in the S&P 500
is sn example of an endogenous cycle, as is an S-minute cycle observed by the
authors in S&P 500 tick data. Programs based on band-pass filters (Katz and
McCormick, May 1997) and maximum entropy (e.g., MESA96 and TradeCycles)
are good at finding endogenous cycles.
We have already discussed the exogenous seasonal cycles, as well as lunar
and solar rhythms. In Chapter 10, endogenous cycles are explored using a sophis-
ticated wavelet-based, band-pass filter model.

Neural Networks
As discussed in Chapter 11, neural network technology is a form of artiiicial intelli-
gence (or AI) that arose from endeavors to emulate the kind of information pmcess-
ing and decision making that occurs in living organisms. Neural networks (or “nets”)
are components that learn and that are useful for pattern recognition, classification,
and prediction. They can cope with probability estimates in uncertain situations and
with “fuzzy” patterns, i.e., those recognizable by eye but difficult to dehe using pm-
cise rules. Nets can be used to directly detect turning points or forecast price changes,
in an effort to obtain good, predictive, countertrend entry models. They can also vet
entry signals generated by other models. In addition, neural network technology can
help integrate information from both endogenous sources, such as past prices, and
exogenous sources, such as sentiment da@ seasonal data, and intermarket variables,
in a way that benefits the trader. Neural networks can even be trained to recognize
visually detected patterns in charts, and then serve as pattern-recognition blocks with-
in traditional rule-based systems (Katz and McCormick, November 1997).

Genetically Evolved Entry Rules
Chapter 12 elaborates a study (Katz and McCormick, December 1996) demon-
strating that genetic evolution can be used to create stable and profitable rule-
based entry models. The process involves putting together a set of model
fragments, or “rule templates,” and allowing a genetic algorithm (GA) to combine
and complete these fragments to achieve profitable entries. The way the method-
ology can discover surprising combinations of rules that consider both endoge-
nous and exogenous variables, traditional indicators, and even nontraditional
elements (e.g., neural networks) in making high-performance entry decisions will
be examined. Evolutionary model building is one of the most advanced, cutting-
edge, and unusual techniques available to the trading system developer.

To study entries on their own, and to do so in a way that permits valid comparisons
of different strategies, it is essential to implement a srandardized exit that will be
held constant across various tests; this is an aspect of the scientific method that
was discussed earlier. The scientific method involves an effort to hold everything,
except that which is under study, constant in order to obtain reliable information
about the element being manipulated.
The standardized exit, used for testing entry models in the following chapters,
incorporates the three functions necessary in any exit model: getting out with a prof-
it when the market moves sufficiently in the trade™s favor, getting out with a limited
loss when the market moves against the trade, and getting out from a languishing
market after a limited time to conserve margin and reduce exposure. The standard
exit is realized using a combination of a stop order, a limit order, and a market order.
Stop and limit orders are placed when a trade is entered. If either order is
filled within a specified interval, the trade is complete, the remaining order is can-
celed, and no additional orders are placed. If, after the allotted interval, neither the
stop nor limit orders are filled, they are canceled and a market order is placed to
force an immediate exit from the trade. The stop order, called a money management
stop, serves to close out a losing position with a small, manageable loss. Taking a
profit is accomplished with the limit order, also called a profit target. Positions that
go nowhere are closed out by the market order. More elaborate exit strategies are
discussed in “Part III: The Study of Exits,” where the entries are standardized.
Money management stops and profit target limits for the standardized exits
are computed using volatility units, rather than fixed dollar amounts, so that they
will have reasonably consistent meaning across eras and markets. Because, e.g., a
$1,000 stop would be considered tight on today™s S&P 500 (yet loose on wheat),
fixed-dollar-amount stops cannot be used when different eras and markets are
being studied. Volatility units are like standard deviations, providing a uniform
scale of measurement. A stop, placed a certain number of volatility units away
from the current price, will have a consistent probability of being triggered in a
given amount of time, regardless of the market. Use of standardized measures per-
mits meaningful comparisons across markets and times.

Just as exits must be held constant across entry models, risk and reward potential,
as determined by dollar volatility (different from raw volatility, mentioned above),
must be equalized across markets and eras. This is done by adjusting the number
of contracts traded. Equalization of risk and reward potential is important because
it makes it easier to compare the performance of different entry methods over
commodities and time periods. Equalization is essential for portfolio simulations,
where each market should contribute in roughly equal measure to the performance
of the whole portfolio. The issue of dollar volatility equalization arises because
some markets move significantly more in dollars per unit time than others. Most
traders are aware that markets vary greatly in size, as reflected in differing margin
requirements, as well as in dollar volatility. The S&P 500, for example, is recog-
nized as a “˜big” contract, wheat as a “small” one; many contracts of wheat would
have to be traded to achieve the same bang as a single S&P 500 contract. Table II-l
shows, broken down by year and market, the dollar volatility of a single contract
Dollar Volatilities (First Line) and Number of Contracts Equivalent to
10 New S&P 500s on 12/31/l 998 (Second Line) Broken Down by
Market and Year

NAME WMB ,881 1882 ,883 1884 ,885 18W ,887 1888

86PJNDM SP 1183.50 848.37 823.80 1124.37 1125.25 1888.00 4188.50 2838.50
24 30 3d 25 25 14 7 10

NY8EJNDEx Yx 825.50 MD.75 452.80 813.75 558.00 887.87 1888.82 285˜.00
45 88 83 48 51 28 14 11

T-BONDS US 348.13 438.84
342.81 43422 510.00 475.83 388.58 488.84
81 83 85 58 84 80 77 80

T˜BIU8˜8OJ4YS TB 82.81 82.38 50.25 88.25 12.38 84.83 48.12 15.54
342 344 5e4 288 382 518 511 318

235.3, 2,422
302.34 257.80 352.50 283.88 204.10 216.41
˜12, 84 HO 80 103 100 138 103

BRITISH-POUND BP 842.88 358.75
887.81 534.88 528.50 288.52 311.88 338.81
44 4™1 53 84 78 108 75 84

DEUTSCHEMARK DM 487.3, 801.88 387.00 998.37 478.00 247.88 532.31 282.08
81 57 13 84 80 It4 85 101

SWISS-FRANC SF 8M.38 881.58 481.44 43(I.M 668.75 387.8, 428.94 418.12
53 43 58 85 42 73 84 88

JAPANESE-YEN Jy 413.50 572.25
388.88 818.55 531.W 408.19 588.50 805.W
88 73 48 83 33 88 48 35

CANADIANJXLAR CD 108.00 184.20 MO.80 138.75 115.25 83.05 143.50 IW.80
283 154 14, 204 182 305 198 148

E”RODcnLAR8˜3M ED 84.38 9l.W 44.13 8&00 88.15 48.81 38.12 50.15
338 282 843 288 4007 588 725 500

CRUDE˜LIGnT CL 213.25 181.80 178.80 2,4.65 150.10 244.85 232.00 252.60
133 175 158 132 188 82 122 H2

HEATING_OIL_X2 HO 288.05 180.82
24421 200.80 238.78 374.9, 258.87 237.87
105 ,,8 141 118 ,87 78 HO 118

UNLEADED˜GA8Ol. H” 275.83 238.17 205.0, 282.10 214.05 377.03 2B4.51 211.18
102 120 138 100 133 75 88 105

GOLD oc 143.55 123.90 252.10 141.35 97.45 84.80 178.40 ˜158.25
,811 228 113 20, 291 335 158 111

SI 269.15 310.52
SILVER 113.W 288.85
H3.75 324.12 211.25 186.72
183 249 88 105 08 144 105 81

PLATINUM PI. 131.53 135.45
131.00 128.73 145.40 74.83 212.12 185.52
207 220 181 218 208 318 134 152

PAUWJM PA 86.30 74.25 128.83 ,02.,8 121.14 97.85 301.82 887.2l
328 332 220 278 234 280 82 80

Dollar Volatilities (First Line) and Number of Contracts Equivalent to
10 New S&P 500s on 12/31/1998 (Second Line) Broken Down by
Market and Year (Continued)

125.04 12657
10602 1Y.40
132.09 80.81 130.08 123.78
225 224
170 2˜8
213 284 218 21,

03.50 150.08 115.58
103.10 01.04 94.31 1oo.so 234.02
232 300 301 286 121 180 24s

70.00 100.50 130.50 ea.38 72.01
78.00 80.50 30.50
370 152 328 380
350 317 352 232

157.31 15™1.04 137.00 223.00 330.13 207.84 150.50
175 04 130 188
180 187 207 124

221.81 338.87 227.3, 142.00
128 3.4 125 200

130.01 ,08.08 02.88 130.33
145.38 124.80 183.42 151.03
100 227 147 ,a2 282 305 204

217.40 2c0.70 200.74 251.10 208.01 ,048, 210.04
130 137 104 113 130 172 ,20

351.12 201.05 254.05 351.75 332.50 201.30 332.05
81 37 11, 81 85 141 0.5

317.34 338.40 1021.57. 024.30 713.80 ooo.,o 081.03 583.44
88 84 28 3, 32 42 43
and the number of contracts that would have to be traded to equal the dollar
volatility of 10 new S&P 500 contracts at the end of 1998.
For the current studies, the average daily volatility is computed by taking a
200-day moving average of the absolute value of the difference between the current
close and the previous one. The average daily volatility is then multiplied by the dol-
lar value of a point, yielding the desired average daily dollar volatility. The dollar
value of a point can be obtained by dividing the dollar value of a tick (a market™s
minimum move) by the size of a tick (as a decimal number). For the new S&P 500
contract, this works out to a value of $250 per point (tick value/tick size = $25/0.10).
To obtain the number of contracts of a target market that would have to be traded to
equal the dollar volatility of IO new S&P 500 contracts on 12/31/1998, the dollar
volatility of the new S&P 500 is divided by the dollar volatility of the target market;
the result is multiplied by 10 and rounded to the nearest positive integer.
All the simulations reported in this book assume that trading always involves
the same amount of dollar volatility. There is no compounding; trade size is not
increased with growth in account equity. Equity curves, therefore, reflect returns
from an almost constant investment in terms of risk exposure. A constant-investment
model avoids the serious problems that arise when a compounded-investment
approach is used in simulations with such margin-based instruments as futures. With
margin-based securities, it is difficult to define return except in absolute dollar
amounts or in relationship to margin requirements or risk, simple ratios cannot be
used. In addition, system equity may occasionally dip below zero, creating problems
with the computation of logarithms and further obscuring the meaning of ratios.
However, given a constant investment (in terms of volatility exposure), monthly
returns measured in dollars will have consistent significance over time, t-tests on
average dollar return values will be valid (the annualized risk-to-reward ratio used to
assess performance in the tests that follow is actually a resealed t-statistic), and it
will be easy to see if a system is getting better or worse over time, even if there are
periods of negative equity. The use of a fixed-investment model, although carried out
more rigorously here by maintaining constant risk, rather than a constant number of
contracts, is in accord with what has appeared in other books concerned with futures
trading. This does not mean that a constant dollar volatility portfolio must always be
traded. Optimal f and other reinvestment strategies can greatly improve overall
returns; they just make simulations much more difficult to interpret. In any case,
such strategies can readily and most appropriately be tested after the fact using
equity and trade-by-trade data generated by a fixed-investment simulation.

A standardportfolio of futures markets is employed for all tests of entry methods
reported in this section. The reason for a standard portfolio is the same as that for
a fixed-exit strategy or dollar volatility equalization: to ensure that test results will
be valid, comparable, and consistent in meaning. All price series were obtained
from Pinnacle Data in the form of continuous contracts, linked and back-adjusted
as suggested by Schwager (1992). The standard portfolio is composed of the fol-
lowing markets (also see Table II-l): the stock indices (S&P 500, NYFE), interest
rate markets (T-Bonds, 90-day T-Bills, lo-Year Notes), currencies (British Pound,
Deutschemark, Swiss Franc, Japanese Yen, Canadian Dollar, Eurodollars), energy
or oil markets (Light Crude, #2 Heating Oil, Unleaded Gasoline), metals (Gold,
Silver, Platinum, Palladium), livestock (Feeder Cattle, Live Cattle, Live Hogs,
Pork Bellies), traditional agriculturals (Soybeans, Soybean Meal Soybean Oil,
Corn, Oats, Wheat), and other miscellaneous commodities (Coffee, Cocoa, Sugar,
Orange Juice, #2 Cotton, Random Lumber). Selection of markets was aimed at
creating a high level of diversity and a good balance of market types. While the
stock index bond, currency, metal, energy, livestock, and grain markets all have
representation, several markets (e.g., the Nikkei Index and Natural Gas) would
have improved the balance of the portfolio, but were not included due to the lack
of a sufficient history. In the chapters that follow, entry models am tested both on
the complete standard portfolio and on the individual markets that compose it.
Since a good system should be able to trade a variety of markets with the same
parameters, the systems were not optimized for individual markets, only for the
entire portfolio. Given the number of data points available, optimizing on specific
markets could lead to undesirable curve-fitting.
Unless otherwise noted, quotes from August 1, 1985, through December 31,
1994, are treated as in-sample or optimization data, while those from January 1,
1995, through February 1,1999, are used for out-of-sample verification. The num-
ber of contracts traded is adjusted to achieve a constant effective dollar volatility
across all markets and time periods; in this way, each market and time period is
more comparable with other markets and periods, and contributes about equally to
the complete portfolio in terms of potential risk and reward. All tests use the same
standardized exit technique to allow meaningful performance comparisons
between entry methods.

Breakout Models

A breakout model enters the market long when prices break above an upper band
or threshold, and enters short when they drop below a lower band or threshold.
Entry models based on breakouts range from the simple to the complex, differing
primarily in how the placement of the bands or thresholds is determined, and in
how entry is achieved.

Breakout models are very popular and come in many forms. One of the oldest is the
simple trendline breakour used by chartists. The chartist draws a descending trend-
line that serves as the upper threshold: When prices break above the trendline, a long
position is established; if the market has been rising, and prices break below an
ascending trendline, a short entry is taken. Support and resistance lines, drawn using
Gann angles or Fibonacci retracements, can also serve as breakout thresholds.
Historically, channd breakout modds, employing support and resistance lev-
els determined by previous highs and lows, followed chart-based methods. The
trader buys when prices rise above the highest of the last n bars (the upper chan-
nel), and sells when prices fall below the lowest of the last n bars (the lower chan-
nel). Channel breakouts are easily mechanized and appeal to traders wishing to
avoid the subjectivity of drawing trendlines or Gann angles on charts.
More contemporary and sophisticated than channel breakouts are volatility
breakout models where the points through which the market must move to trigger
long or short positions are based on volatility bands. Volatility bands are placed a
certain distance above and below some measure of current value (e.g., the most
recent closing price), the distance determined by recent market volatility: As

volatility increases, the bands expand and move farther away from the current
price; as it declines, the bands contract, coming closer to the market. The central
idea is statistical: If the market moves in a given direction more than expected
from normal jitter (as reflected in the volatility measurement), then some force
may have impinged, instigating a real trend worth trading. Many $3,000 systems
sold since the late 1980s employed some variation on volatility breakouts,
Breakout models also differ in how and when they enter the market. Entry
can occur at the open or the close, requiring only a simple market order. Entry
inside the bar is accomplished with stops placed at the breakout thresholds. A
more sophisticated way to implement a breakout entry is to buy or sell on a limit,
attempting to enter the market on a small pull-back, after the initial breakout, to
control slinpage and achieve entry at a better price.

Breakouts are intuitively appealing. To get from one place to another, the market
must cross all intervening points. Large moves always begin with small moves.
Breakout systems enter the market on small moves, when the market crosses one of
the intermediate points on the way to its destination: they buy into movement.
Breakout models arc, consequently, trend-following. Another positive characteristic
of breakout models is that, because they buy or sell into momentum, trades quickly
become profitable. Sometimes a very tight stop-loss can be set, an approach that can
only be properly tested with intraday, tick-level data. The intention would be to enter
on a breakout and to then set a very tight stop loss, assuming momentum at the
breakout will carry the market sufficiently beyond the stop-loss to prevent it from
being triggered by normal market fluctuations; the next step would be to exit with a
quick profit, or ratchet the protective stop to break-even or better. Whether a profit
can be taken before prices reverse depends on the nature of the market and whether
momentum is strong enough to carry prices into the profit zone.
On the downside, like many trend-following models, breakouts enter the
market late-sometimes too late, after a move is mostly over. In addition, small
moves can trigger market entries, but never become the large moves necessary for
profitable trading. Since breakout systems buy or sell into trends, they are prone
to sizeable slippage; however, if well-designed and working according to theory,
occasional strong trends should yield highly profitable trades that make up for the
more frequent (but smaller) losers. However, the consensus is that, although their
performance might have been excellent before massive computational power
became inexpensive and widespread, simple breakout methods no longer work
well. As breakout systems were developed, back-tested, and put on-line, the mar-
kets may have become increasingly efficient with respect to them. The result is
that the markets™ current noise level around the prices where breakout thresholds
are often set may be causing many breakout systems to generate an excessive num-
ber of bad entries; this is especially likely in active, volatile markets, e.g., the S&P
500 and T-Bonds. Finally, it is easy to encounter severe slippage (relative to the
size of a typical trade) when trying to implement trading strategies using breakout
entries on an intraday time frame; for longer term trading, however, breakout entry
strategies may perform acceptably.
A well-designed breakout model attempts to circumvent the problem of mar-
ket noise to the maximum extent possible. This may be accomplished by placing
the thresholds at points unlikely to be reached by movements that merely represent
random or nontrending market activity, but that are likely to be reached if the mar-
ket has developed a significant and potentially profitable trend. If the bands are
placed too close to the current price level, a large number of false breakouts (lead-
ing to whipsaw trades) will occur: Market noise will keep triggering entries, first in
one direction, then in the other. Because such movements do not constitute real
trends with ample follow-through, little profit will be made; instead, much heat (in
the form of commissions and slippage) will be generated and dissipate the trader™s
capital. If the bands are set too wide, too far away from the prevailing price, the sys-
tem will take few trades and entry into the market will be late in the course of any
move; the occasional large profit from a powerful trend will be wiped out by the
losses that occur on market reversals. When the thresholds are set appropriately
(whether on the basis of trendlines, volatility bands, or support and resistance),
breakout entry models can, theoretically, be quite effective: Frequent, small losses,
occurring because of an absence of follow-through on noise-triggered entries,
should be compensated for by the substantial profits that accrue on major thrusts.
To reduce false breakouts and whipsaws, breakout systems are sometimes
married to indicators, like Welles Wilder™s “directional movement index” (1978),
that supposedly ascertain whether the market is in a trending or nontrending mode.
If the market is not trending, entries generated by the breakouts are ignored; if it
is, they are taken. If popular trend indicators really work, marrying one to a break-
out system (or any other trend-following model) should make the trader rich:
Whipsaw trades should be eliminated, while trades that enter into strong trends
should yield ample profits. The problem is that trend indicators do not function
well, or tend to lag the market enough to make them less than ideal.

Tests are carried out on several different breakout models, trading a diversified
portfolio of commodities, to determine how well breakout entries perform. Do
they still work? Did they ever? Breakout models supposedly work best on com-
modities with persistent trends, traditionally, the currencies. With appropriate fil-
tering, perhaps these models can handle a wider range of markets. The
investigations below should provide some of the answers. The standard portfolio
and exit strategy were used in all tests (see “Introduction” to Part II for details).
The initial tests address several variations of the channel breakout entry. First
examined are close-only channel breakout models, in which the price channels or
bands are determined using only closing prices. A model involving breakouts that
occur beyond the highest high or lowest low will also be studied. In these mod-
els, the price channels approach the traditional notion of support and resistance.

Close-Only Channel Breakouts
Test I: Close-Only Channel Breakout with Entry on Market Order at Next
Open, No Z™ransaction Costs. The rules are: “If the current position is either
short or flat and the market closes above the highest close of the last n days, then
buy tomorrow™s open.” Likewise, “If the current position is either long or flat
and the market closes below the lowest close of the preceding n days, then sell
(go short at) tomorrow™s open.” The channel breakout entry model has only one
parameter, the look-back (a). The number of contracts to buy or sell (nconrracfs)
was chosen to produce, for the market being traded, an effective dollar volatili-
ty approximately equal to that of two new S&P 500 contracts at the end of 1998.
Exits occur either when a breakout entry reverses an existing position or
when the standard exit closes out the trade, i.e., when a money management stop
is triggered, a profit target is hit, or the position has been open more than a speci-
fied number of days (bars), whichever comes first. The money management stop
is computed as the entry price plus (for short positions) or minus (for long posi-
tions) some multiple (a parameter, mmsrp) of the 50-bar average true range. Profit
target limits are at the entry price plus (long) or minus (short) another multiple
(ptlim) of the same average true range. Finally, an “exit at close” order (a form of
market order) is posted when a position has been held for more than a specified
number of days (manhold). All exit orders are “close-only,” i.e., executed only at
the close: this restriction avoids ambiguous simulations when testing entries with
intrabar limits or stops. Were exits not restricted to the close, such cases would
involve the posting of multiple intrabar orders. Simulations become indeterminate
and results untrustworthy when multiple intrabar orders are issued: The course of
prices throughout the period represented by the bar, and hence the sequence of
order executions, is unknown.
The average true range (a measure of volatility) is calculated as the mean of
the true range of each of a specified number of previous bars (in this case, 50). The
true range is the highest of the day™s high minus the day™s low, the day™s high
minus the previous day™s close, or the previous day™s close minus the day™s low.
Below is a C+ + implementation of the close-only channel breakout entry
model mated with the standard exit strategy. When calculating the number of con-
tracts, no correction is explicitly made for the S&P 500 split. The new contract is
CHAFTER 5 Breakout Models 8,

treated as identical to the old one, both by the simulator and by the code. All sim-
ulations are, nevertheless, correct under the assumption that the trader (not the
simulator) trades two new contracts for every old contract: The simulator is
instructed to sell half as many new contracts as it should, but treats these contracts
as twice their current size. Limit-locked days are detected by range checking: A
zero range (high equal to the low) suggests poor liquidity, and a possibly limit-
locked market. Although this detection scheme is not ideal, simulations using it
resemble results obtained in actual trading. Compiling the information from the
exchanges needed to identify limit-locked days would have been almost impossi-
ble; therefore, the zero-range method is used. The code allows re-entry into per-
sistent trends as long as new highs or lows are made.

// declare local scratch variables
static int cb, n, ncontracts, maxhold;
static float mlnstp, ptlim, atr;

] ,, process next bar

The code was compiled and linked with the development shell and associat-
ed libraries; in TradeStationTM, this is called “verifying” a system. Using develop-
ment shell commands, the look-back parameter was brute-force optimized. The
best solution (in terms of the risk-to-reward ratio) was then verified on out-of-sam-
ple data. Optimization involved stepping the entry model look-back (n) from 5 to
100, in increments of 5. The stop-loss parameter (mmsrp) was fixed at 1 (repre-
senting 1 volatility, or average true range, unit), the profit target doflim) at 4 (4
units), and the maximum holding period (mardays) at 10 days. These values are
used for the standard exit parameters in all tests of entry methods, unless other-
wise specified. To provide a sense of scale when considering the stop-loss and
profit target used in the standard exit, the S&P 500 at the end of 1998 had an aver-
age true range of 17.83 points, or about $4,457 for one new contract. For the fist
test, slippage and commissions were set to zero.
For such a simple system, the results are surprisingly good: an annual return
of 76% against maximum drawdown. All look-back parameter values were prof-
itable; the best in terms of risk-to-reward ratio was 80 days. A t-test for daily
returns (calculated using the risk-to-reward ratio) reveals the probability is far less
than one in one-thousand that chance explains the performance; when corrected
for the number of tests in the optimization, this probability is still under one in
one-hundred. As expected given these statistics, profits continued out-of-sample.
Greater net profits were observed from long trades (buys), relative to short ones
(sells), perhaps due to false breakouts on the short side occasioned by the constant
decay in futures prices as contracts neared expiration. Another explanation is that
commodity prices are usually more driven by crises and shortages than by excess
supply. As with many breakout systems, the percentage of winners was small
(43%) with large profits from the occasional trend compensating for frequent
small losses. Some may find it hard to accept a system that takes many losing
trades while waiting for the big winners that make it all worthwhile.
Portfolio equity for the best in-sample look-back rose steadily both in- and
out-of-sample; overoptimization was not au issue. The equity curve suggests a
gradual increase in market efficiency over time, i.e., these systems worked better
in the past. However, the simple channel breakout can still extract good money
from the markets. Or can it? Remember Test 1 was executed without transaction
costs. The next simulation includes slippage and commissions.

Test 2: Close-Only Channel Breakout with Entry at Next Open, Transaction
Costs Assumed. This test is the same as the previous one except that slippage
(three ticks) and commissions ($15 per round turn) are now considered. While
this breakout model was profitable without transaction costs, it traded miserably
when realistic costs were assumed. Even the best in-sample solution had nega-
tive returns (losses); as might be expected, losses continued in the out-of-sam-
ple period. Why should relatively small commission and slippage costs so
devastate profits when, without such costs, the average trade makes thousands of
dollars? Because, for many markets, trades involve multiple contracts, and slip-
page and commissions occur on a per-contract basis. Again, long trades and
longer look-backs were associated with higher profits. The model was mildly
profitable in the 1980s but lost money thereafter. Considering the profitable
results of the previous test, it seems the model became progressively more
unable to overcome the costs of trading. When simple computerized breakout
systems became the rage in the late 198Os, they possibly caused the markets to
become more efficient.
Table 5-l shows the portfolio performance of the close-only channel break-
out system broken down by sample and market (SYM). (For information about the
various markets and their symbols, see Table II-1 in the “Introduction” to Part II.)
NETL = the total net profit on long trades, in thousands of dollars; NETS = the
total net profit on short trades, in thousands of dollars; ROA% = annualized
return-on-account; PROP = associated probability or statistical significance;
AVTR = average protlt/loss per trade.
Trend-following methods, such as breakouts, supposedly work well on the
currencies. This test confirms that supposition: Positive returns were observed
both in-sample and out-of-sample for several currencies. Many positive returns
were also evidenced in both samples for members of the Oil complex, Coffee,
and Lumber. The profitable performance of the stock indices (S&P 500 and
NYFE) is probably due to the raging bull of the 1990s. About 10 trades were
taken in each market every year, The percentage of wins was similar to that seen
in Test I (about 40%).

Test 3: Close-Only Channel Breakout with Entry on Limit on Next Bar,
Transaction Costs Assumed. To improve model performance by controlling
slippage and obtaining entries at more favorable prices, a limit order was used to
enter the market the next day at a specified price or better. Believing that the mar-
ket would retrace at least 50% of the breakout bar (cb) before moving on, the limit
price (limprice) was set to the midpoint of that bar. Since most of the code remains
unchanged, only significantly altered blocks are presented:

Trade entry took place inside the bar on a limit. If inside-the-bar profit target
and stop-loss orders were used, problems would have arisen. Posting multiple intra-
bar orders can lead to invalid simulations: The sequence in which such orders are
tilled cannot be specified with end-of-day data, but they can still strongly affect the
outcome. This is why the standard exit employs orders restricted to the close.

Performance Statistics for Close-Only Channel Breakout with Entry
at Open for All Markets in the Standard Portfolio

As before, the look-back parameter was stepped from 5 to 100, in increments
of 5, and the solution with the best risk-to-reward ratio (and t-test probability) was
selected. Commissions, slippage, exit parameters, and the ability to reenter a con-
tinuing trend (albeit on a pullback), remain unchanged.
With a best look-back of 80 (same as in Test l), this model returned about
33% annually during the in-sample period. The probability that these returns
were. due to chance is less than 5% when not corrected, or 61% when corrected
for 20 optimization runs. Although profitable in-sample, the statistics suggest the

model may fail in the future: indeed, out-of-sample returns were negative. As in
Tests 1 and 2, trades lasted about seven bars and long trades were more profitable
than short ones. The percentage of winners was 42%. Although the limit entry did
not eliminate the damaging impact of transaction costs, performance improved.
The limit order did not seriously reduce the˜number of trades or cause many prof-
itable trends to be missed, the market pulled back after most breakouts, allowing
entry at more favorable prices. That a somewhat arbitrary, almost certainly sub-
optimal, limit entry strategy could so improve performance is highly encourag-
ing. The equity curve again shows that this kind of system once worked but no
longer does.
Table 5-2 shows that, with few exceptions, there were positive returns for the
currencies and oils, both in-sample and out-of-sample, consistent with findings in
earlier tests. Coffee continued to trade well on both samples, and the S&P 500
remained profitable in the verification sample.

Conclusion A limit-based entry can significantly improve the overall perfor-
mance of a breakout model. Substantial benefit is obtained even with a fairly crude
choice for the limit price. It is interesting that the markets to benefit most from the
use of a limit order for entry were not necessarily those with the lowest dollar
volatilities and implied transaction costs, as had been expected. Certain markets,
like the S&P 500 and Eurodollars, just seem to respond well to limit entries, while
others, such as Cocoa and Live Cattle, do not.

Would placing the thresholds further from current prices reduce whipsaws,
increase winning trades, and improve breakout performance? More stringent
breakout levels are readily obtained by replacing the highest and lowest close from
the previous model with the highest high and lowest low (HHLL) in the current
model. Defined this way, breakout thresholds now represent traditional levels of
support and resistance: Breakouts occur when previous highs or lows are “taken
out” by the market. One possible way to further reduce spurious breakouts is by
requiring the market to close beyond the bands, not merely to penetrate them at
some point inside the bar. Speeding up system response by using a stop order for
entry, or reducing transaction costs by entering on a pullback with a limit order,
might also improve performance.

Test 4: Close-Only HHLL Breakout with Entry at Open of Next Bar. This
breakout buys at tomorrow™s open when today™s close breaks above the highest
high of the last n days, and sells at tomorrow™s open when today™s close drops
below the lowest low. The look-back (n) is the only model parameter. The beau-
CHArnR 5 Breakout MD&IS Y3


Performance Statistics for Close-Only Channel Breakout with Entry
at Limit for All Markets in the Standard Portfolio

ty of this model, besides its simplicity, is that no important trend will be
missed, and tomorrow™s trades are fully known after today™s close.

,, file = x09mod04.c
,, HHLL channel breakout system with entry next bar on open
i f lcls[cbl zHighest(hi,n,cb-1) && t˜.positionOc=Oi {
tS.buyOpenc™l™, ncontractsl;
else if(cls[cblcLoweat(lo,n.cbl) && ts.positionO˜-0) {

Look-backs from 5 to 100 were tested in steps of 5. On the in-sample data,
the model was profitable for only four of the look-backs. The best results were
obtained with a look-back of 85, where in-sample returns were a mere 1.2% annu-
ally. Given these returns and the associated statistics, it is no surprise that this
model lost 15.9% annually out-of-sample. Winners occurred about 39% of the
time, and long trades were more profitable than short ones in-sample. As in all pre-
vious breakout simulations, the HHLL breakout performed best on the currencies,
the oils, and Coffee; it performed worst on metals, livestock, and grains. Equity
shows a model that never performed well, but that now performs disastrously.
The results were slightly better than those for the close-only breakout with
a similar entry at the open; they were not better enough to overcome transaction
costs. In the close-only model, a limit order reduced the cost of failed breakouts
and, thereby, improved performance. Because costs are higher with the HHLL
breakout, due to the more stringent breakout thresholds, a limit entry may pro-
vide a greater boost to performance. A limit entry for a breakout model also side-
steps the flurry of orders that often hit the market when entry stops, placed at
breakout thresholds, are triggered. Entries at such times are likely to occur at
unfavorable prices. However, more sophisticated traders will undoubtedly “fade”
the movements induced by the entry stops placed by more ndive traders, driving
prices back. An appropriate limit order may be able to enter on the resultant pull-
back at a good price. If the breakout represents the start of a trend, the market is
likely to resume its movement, yielding a profitable trade; if not, the market will
have less distance to retrace from the price at entry, meaning a smaller loss. Even
though the HHLL breakout appears only marginally better than the close-only
breakout thus far, the verdict is not yet in; a limit entry may produce great
The annualized return-on-account is used as an index of performance in
these discussions and the risk-to-reward ratio is rarely mentioned, even though the
probability statistic (a t-statistic) is computed using that measure. The risk-to-
reward ratio and return-on-account are very highly correlated with one another:
They are almost interchangeable as indicators of model efficacy. Since it is easier
to understand. the annualized return-on-account is referred to more often.

For the
Test 5: Close-Only HHLL Breakout with Enhy on Limit on Next Bar.
close-only channel breakout, use of a limit order for entry greatly improved per-
formance. Perhaps a limit entry could similarly benefit the HHLL breakout model.
For the sake of consistency with the model examined in Test 3, the limit price is
set to the mid-point of the breakout bar.

The look-back parameter was stepped through the same range as in previous
tests. All look-backs produced positive returns. The best in-sample results were
with a look-back of 85, which yielded a return of 36.2% annually; the probability
is less than 2% (33% when corrected for multiple tests) that this was due to
chance. In-sample, long positions again yielded greater profits than short posi-
tions. Surprisingly, out-of-sample, the short side produced a small profit, while the
long side resulted in a loss! With a return of -2.3%, out-of-sample performance
was poor, but not as bad as for many other systems tested. In-sample, there were
43% wins and the average trade produced an $1,558 profit; out-of-sample, 41%
were winners and the average trade lost $912.
The equity curve in Figure 5-l may seem to contradict the negative out-of-
sample returns, but the trend in the out-of-sample data was up and on par with the
trend in the latter half of the in-sample period. The apparent contradiction results
from a bump in the equity curve at the start of the out-of-sample period.
Nevertheless, the HHLL breakout with entry on a limit (together with the standard
exit) is not a system that one would want to trade after June 1988: The return was
too low relative to the risk represented by the fluctuation of equity above and
below the least-squares polynomial trendline (also shown in Figure 5-l).
All currencies and oils had positive in-sample results. Strong out-of-sample
returns were seen for the Swiss Franc, Canadian Dollar, and Deutschemark, as
well as for Heating Oil and Light Crude; small losses were observed for the British
Pound, Eurodollar, and Unleaded Gasoline. Coffee was profitable in both samples.

Test 6: Close-Only HHLL Breakout with Entry on Stop on Next Bar. This
model buys on a stop at a level of resistance defined by recent highs, and sells on
a stop at support as defined by recent lows. Because the occurrence of a breakout
PART II The Study of Entries


Equity Curve for HHLL Breakout, Entry at Limit

is decided on the entry bar by the stop itself, the highest high and lowest low are
calculated for bars up to and including the current bar. The relative position of the
close, with respect to the breakout thresholds, is used to avoid posting multiple
intrabar orders. If the close is nearer to the upper threshold, then the buy stop is
posted; if the close is closer to the lower threshold, the sell stop is posted. Both
orders are never posted together. By implementing the HHLL breakout with stop
orders, a faster response to breakout conditions is achieved; there is no need to
wait for the next bar after a signal is given to enter the market. Entry, therefore,
occurs earlier in the course of any market movement and no move will ever be
missed, as might happen with a limit while waiting for a pull-back that never takes
place. However, the reduced lag or response time may come at a cost: entry at a
less favorable price. There is greater potential for slippage, when buying into
momentum on a stop, and entry takes place at the breakout price, rather than at a
better price on a retracement.
The look-back parameter was optimized as usual. The best in-sample look-
back was 95, with look-backs of 65 through 100 being profitable. Annual returns
were 8.7%. Although the results were better than those for Test 4, they were not
as good as for Test 5. Faster response bought some advantage, but not as much as
waiting for a retracement where entry can occur at a more favorable price. The
percentage of winning trades was 41% and the average trade yielded a $430 prof-
it. Out-of-sample, the picture was much worse, as might be expected given the low
returns and poor statistics on the in-sample data. This model lost an average of
$798 per trade. About 37% of the trades were winners. The model made most of
its profits before June 1988, and lost money after January 1992.
All currencies, except Eurodollars, had positive returns in the optimization peri-
od. In the verification period, the Japanese Yen, Canadian Dollar, and Deutschemark,
had solid returns in the 30% to 50% range. The model also generated moderate
retmns on the oils. Coffee traded well, with a 21.2% return in-sample and a 61.8%
return out-of-sample. Random Lumber also had positive returns in both samples.

The next three tests evaluate volatility breakout entry models, in which the trader
buys when prices rise above an upper volatility band, and sells short when they fall
below a lower volatility band. Volatility bands are bands placed above and below
current prices. When volatility increases, the bands expand; when it decreases, they
contract. The balance point around which the bands are drawn may be the most
recent closing price, a moving average, or some other measure of current value.

Test 7: Volatdity Breakout wdth Entry at Next Open. This model buys at tomor-
row™s open when today™s close pushes above the upper volatility band, and sells
short at the next open when the close drops below the lower volatility band. The
volatility bands are determined by adding to (for the upper band) and subtracting
from (for the lower band) the estimate of current value a multiple (bw) of the
at&n-bar average true range (a measure of volatility). The estimate of value is a
m&n-bar exponential moving average of the closing price. If the moving average
length (m&n) is one, this estimate degrades to the closing price on the breakout
or “signal” bar.
Because the volatility breakout model has three parameters, genetic optimiza-
tion was chosen for the current test. Using genetic optimization, the bandwidth para-
meter (bw) was evaluated over a range of 1.5 to 4.5, with a grid size (increment) of
0.1; the period of the average true range (&&VI) was studied over a range of 5 to SO,
with a grid size of 1; and the moving average length (m&n) was examined over a
range of 1 to 25, also with a unit grid size. The genetic optimization was allowed to
run for 100 generations. As in all previous tests, the highest attainable risk-to-reward
ratio (or, equivalently, the lowest attainable probability that any profits were due to
chance) on the in-sample or optimization data was sought.
The best in-sample performance was obtained with a bandwidth of 3.8, a
moving average length of 5, and an average true range of 20 bars. With these para-
meters, the annualized return was 27.4%. There was a probability of 5.6% (99.7%
when corrected for 100 tests or generations) that chance produced the observed
return. Almost every combination of parameters examined generated profits on the
long side and losses on the short side. The average trade for the best parameter set
was held for 6 bars and yielded a profit of $4,675. Only 240 trades were present in
the optimization period, about 45% of which were winners. Compared to previous
tests, the smaller number of trades, and the higher percentage of winners, are
explained by breakout thresholds placed further from current price levels. The aver-
age trade lost $7,371 in the verification sample and only 25% of the 112 trades were
profitable. Both long positions and short positions lost about the same amount.
Almost all gain in equity occurred from August 1987 to December 1988, and
then from December 1992 to August 1993. Equity declined from October 1985
through July 1986, from August 1989 through May 1992, and from May 1995 to
December 1998.
Excessive optimization may have contributed to deteriorated performance in
the verification sample. Nevertheless, given the number of parameters and para-
meter combinations tested, a good entry model should have generated a greater in-
sample return than was seen and better statistics, capable of withstanding
correction for multiple tests without total loss of significance. In other words,
excessive optimization may not be the central issue: Despite optimization, this
model generated poor in-sample returns and undesirably few trades. Like the oth-
ers, this model may simply have worked better in the past.
As before, currencies were generally profitable. Oddly, the oil complex, which
traded profitably in most earlier tests, became a serious loser in this one. Coffee and
Lumber traded well in-sample, but poorly out-of-sample, the reverse of previous
findings. Some of these results might be due to the model™s limited number of trades.

Test 8: Vokztility Breakout with Entry on Limit. This model attempts to estab-
lish a long position on the next bar using a limit order when the close of the cur-
rent bar is greater than the current price level plus a multiple of the average true
range. It attempts to establish a short position on the next bar using a limit order
when the close of the current bar is less than the current price level minus the same
multiple of the average true range. The current price level is determined by an
exponential moving average of length malen calculated for the close. The multi-
plier for the average true range is referred to as bw, and the period of the average
true range as atrlen. Price for the limit order to be posted on the next bar is set to
the midpoint price of the current or breakout bar. Optimization was carried out
exactly as in Test 7.
For all parameter combinations, long positions were more profitable (or lost
less) than short positions. The best in-sample results were achieved with a band-
width of 3.7, a moving average length of 22, and a period of 41 for the average
true range measure of volatility; these parameter values produced a 48.3% annu-
alized return. Results this good should occur less than twice in one-thousand
experiments; corrected for multiple tests (100 generations), the probability is less
than 13% that the observed profitability was due to chance. On the in-sample data,
1,244 trades were taken, the average trade lasted 7 days, yielded $3,6 16, and was
a winner 45% of the time. Both long and short trades were profitable.
Given the statistics, there was a fair probability that the model would con-
tinue to be profitable out-of-sample; however, this was not the case. The model
lost heavily in the out-of-sample period. Equity rose rather steadily from the
beginning of the sample until August 1990, drifted slowly lower until May 1992,
rose at a good pace until June 1995, then declined. These results primarily
reflect the decreasing ability of simple breakout models to capture profits from
the markets.
All currencies had positive in-sample returns and all, except the British
Pound and Canadian Dollar, were profitable out-of-sample-confirmation that
breakout systems perform best on these markets, perhaps because of their trendi-
ness. Curiously, the currency markets with the greatest returns in-sample are not
necessarily those with the largest returns out-of-sample. This implies that it is
desirable to trade a complete basket of currencies, without selection based on his-
torical performance, when using a breakout system. Although this model per-
formed poorly on oils, it produced stunning returns on Coffee (both samples
yielded greater than 65% annually) and Lumber (greater than 29%).

Tesf 9: Volatility Breakout with Entry on Stop. This model enters immediately
at the point of breakout, on a stop which forms part of the entry model. The advan-
tage is that entry takes place without delay: the disadvantage is that it may occur
at a less favorable price than might have been possible later, on a limit, after the
clusters of stops that are often found around popular breakout thresholds have
been taken out. To avoid multiple intmbar orders, only the stop for the band near-
est the most recent closing price is posted; this rule was used in Test 6. The volatil-
ity breakout model buys on a stop when prices move above the upper volatility
band, and sells short when they move below the lower volatility band.
The optimum values for the three model parameters were found with the aid
of the genetic optimizer built into the C-Trader toolkit from Scientific Consultant
Services, Inc. The smallest risk-to-reward ratio occurred with a bandwidth of X.3, a
moving average length of 11, and an average true range of 21 bars. Despite opti-
mization, this solution returned only 11.6% annually. There were 1,465 trades
taken; 40% were winners. The average trade lasted 6 days and took $931 out of the
market. Only long positions were profitable across parameter combinations.
Both long and short trades lost heavily in the verification sample. There were
610 trades, of which only 29% were winners. The equity curve and other simula-
tion data suggested that deterioration in the out-of-sample period was much
greater for the volatility breakout model with a stop entry than with entry on a
limit, or even at the open using a market order.
Can excessive optimization explain the rapid decay in the out-of-sample
period? No. Optimization may have merely boosted overall in-sample perfor-
mance from terrible to poor, without providing improved out-of-sample perfor-
mance. Optimization does this with models that lack real validity, capitalizing on
chance more than usual. The greater a model™s real power, the more helpful and
less destructive the process of optimization. As previously, the detrimental effects
of curve-fitting are not the entire story: Performance declined well before the out-
of-sample period was reached. The worsened out-of-sample performance can as
easily be attributed to a continued gain in market efficiency relative to this model
as it can to excessive optimization.
The model generated in-sample profits for the British Pound, Deutschemark,
Swiss Franc, and Japanese Yen; out-of-sample, profits were. generated for all of
these markets except the British Pound. If all currencies (except the Canadian
Dollar and Eurodollar) were traded, good profits would have been obtained in both
samples. The Eurodollar lost heavily due to the greater slippage and less favorable
prices obtained when using a stop for entry; the Eurodollar has low dollar volatil-
ity and, consequently, a large number of contracts must be traded, which magni-
ties transaction costs. In both samples, Heating Oil was profitable, but other
members of the oil group lost money. The out-of-sample deterioration in certain
markets, when comparison is to entry on a limit, suggests that it is now more dif-
ficult to enter on a stop at an acceptable price.

Would restricting breakout models to long positions improve their performance?
How about trading only the traditionally trendy currencies? Would benefit be
derived from a trend indicator to filter out whipsaws? What would happen without
m-entries into existing, possibly stale, trends? The last question was answered by
an unreported test in which entries took place only on breakout reversals. The
results were so bad that no additional tests were completed, analyzed, or reported.
The first three questions, however, are addressed below.

Long Positions Only
In the preceding tests, the long side almost always performed better than the short
side, at least on in-sample data. What if one of the previously tested models was
modified to trade only long positions? Test 10 answers that question.

Test IO: Vohdity Breakout with Limit Entry Zkading Only Long Posilims. T h e
best in-sample model (Test 8) was modified to trade only long positions. A genetic
algorithm optimized the model parameters. Band-width (bw) was optimized from 1.5
to 4.5, with a grid of 0.1; the period of the average true range (arrlen) from 5 to 50,
with a grid of 1; and the length of the moving average (malen) from 1 to 25, with a
grid of 1. Optimization was halted after 100 generations.
In-sample, the model performed well. The best parameter values were: band-
width, 2.6; moving average length, 15; and average true range period, 18. The best
parameters produced an annualized return of 53.0%, and a risk-to-reward ratio of
1.17 (p < 0.0002; p < 0.02, corrected). There were 1,263 trades, 48% profitable
(a higher percentage than in any earlier test). The average trade lasted 7 days, with
a $4,100 profit after slippage and commissions. Even suboptimal parameter val-
ues were profitable, e.g., the worst parameters produced a 15.5% return!
Out-of-sample, despite the high levels of statistical significance and the
robustness of the model (under variations in parameter values when tested on in-
sample data), the model performed very poorly: There were only 35% wins and a
loss of -14.6% annually. This cannot be attributed to in-sample curve-fitting as all
in-sample parameter combinations were profitable. Suboptimal parameters should
have meant diminished, but still profitable, out-of-sample performance. Additional
tests revealed that no parameter set could make this model profitable in the out-of-
sample period! This finding rules out excessive optimization as the cause for out-
of-sample deterioration. Seemingly, in recent years, there has been a change in the
markets that affects the ability of volatility breakout models to produce profits,
even when restricted to long positions. The equity curve demonstrated that the
model had most of its gains prior to June 1988. The remainder of the optimization
and all of the verification periods evidenced the deterioration.
As before, most currencies traded fairly well in both samples. The average
currency trade yielded $5,591 in-sample and $1,723 out-of-sample. If a basket of
oils were traded, profits would be seen in both samples. Coffee was also profitable
in both samples.
Overall, this system is not one to trade today, although it might have made a
fortune in the past; however, there may still be some life in the currency, oil, and
Coffee markets.

Currencies Only
The currency markets are believed to have good trends, making them ideal for
such trend-following systems as breakouts. This belief seems confirmed by the
tests above, including Test 10. Test I1 restricts the model to the currencies.

Test 11: Vokztility Breakout with Limit Entry Trading Only Currencies. This
model is identical to the previous one, except that the restriction to long trades
was removed and a new restriction to trading only currencies was established.
No optimization was conducted because of the small number of markets and,
consequently, data points and trades; instead, the best parameters from Test 8
were used here.
This is the first test where a breakout produced clearly profitable results in
both samples with realistic transaction costs included in the simulation! In-sam-
ple, the model returned 36.2% annually. Out-of-sample, the return was lower
(17.7%), but still good. There were 268 trades, 48% wins, with an average profit
per trade (in-sample) of 53,977. Out-of-sample, the model took 102 trades, won
43%, and averaged 52,106 per trade.
The equity curve in Figure 5-2 contimts the encouraging results. Almost all equi-
ty was gained in five thrusts, each lasting up to a few months. This model is potential-
ly tradeable, especially if the standard exit was replaced with a more effective one.

ADX Trend Filter
One problem with breakouts is the tendency to generate numerous whipsaw trades
in which the breakout threshold is crossed, but a real trend never develops. One
possible solution is to use a trend indicator to filter signals generated by raw break-
outs; many traders do this with the ADX, a popular trend indicator. Test 12 exam-
ines whether Wilder™s ADX is beneficial.


Equity Curve for HHLL Breakout, Entry on Limit, Currencies Only
Test 12: Volatility Breakout with Limit Entry and Trend Filter. The same
model from Tests 10 and 11 is used; instead of restriction to long positions or
currencies, the signals are “filtered” for trending conditions using the Average
Directional Movement index (or ADX; Wilder, 1978). By not entering trend-
less markets, whipsaws and languishing trades, and the resultant erosion of
capital, can hopefully be reduced. The ADX was implemented to filter break-
outs as suggested by White (1993). Trending conditions exist as long as the
18-bar ADX makes a new 6-bar high, and entries are taken only when trends

As in previous tests, a genetic algorithm optimized the parameters. All 100
parameter combinations except one produced positive returns in-sample; 88
returned greater than 20%, demonstrating the model™s tolerance of parameter vari-
ation. The best parameters were: bandwidth, 2.6; moving average length, 8; and
average true range period, 34. With these parameters the in-sample return was
68.3%; the probability that such a high return would result from chance was less
than one in two-thousand, or about one in twenty-nine instances when corrected
for optimization. There were 872 trades and 47% wins. The average trade gener-
ated about $4,500 in profit. Out-of-sample the average trade lost $2,415 and only
36% of all trades taken (373) were winners. The return was -20.9%, one of the
worst out-of-sample performances. The ADX appears to have helped more in the
past than in current times.
Most currencies, Heating Oil, Coffee, Lumber, and lo-Year Notes were prof-
itable out-of-sample. The S&PSOO, Kansas Wheat, and Comex Gold were profitable
out-of-sample, but lost money it-sample. The pattern is typical of what has been
observed with breakout systems, i.e., the currencies, oils, and Coffee tend to be con-
sistently profitable.

Table 5-3 summarizes breakout results broken down by model, sample, and order
type. ARRR = the annualized risk-to-reward ratio, ROA = the annualized return
on account, and AVTR = the average trade™s profit or loss.

Breakout Types
In the optimization sample (1985 to 1995). volatility breakouts worked best, the
highest-high/lowest-low breakout fell in-between, and the close-only breakout did
worst: this pattern was consistent across all three order types. In the verification
period (1995 through 1998), the highest-higMowest-low continued to do slightly
better than the close-only, but the volatility model performed much worse. For rea-
sons discussed earlier, optimization cannot account for the relatively dramatic
deterioration of the volatility breakout in recent years. Perhaps the volatility break
out deteriorated more because of its early popularity. Even the best breakout mod-
els, however, do poorly in recent years.
When broken down by model, three distinct periods were observed in the aver-
aged equity curves. From August 1985 through June 1988, all models were about
equally profitable. From June 1988 to July 1994, the HHLL and close-only models
were flat and choppy. The volatility model showed a substantial gain from August
1992 through July 1994. From July 1994 until December 1998, the HHLL and
close-only breakouts were choppy and slightly down, with the HHLL model some-
what less down than the close-only model; equity for the volatility model declined

Entry Orders
Both in- and out-of-sample, and across all models, the limit order provided the
greatest edge; the stop and market-at-open orders did poorly. The benefit of the
limit order for entering the market undoubtedly stemmed from its ability to
obtain entries at more favorable prices, The dramatic impact of transaction costs
and unfavorable entry prices is evident in Tests 1 and 2. Surprisingly, the limit
order even worked with a trend-following methodology like breakouts. It might
be expected that too many good trends would be missed while waiting to enter
on a limit; however, the market pulls back (even after valid breakouts) with
Summary of Breakout Entry Results Arranged for Easy

enough frequency to enter on a limit at a better price without missing too many
good trends.
The same three periods, evident when average equity was broken down by
breakout type, appeared when entry orders were analyzed. For the limit and stop
entries, equity surged strongly from August 1985 to June 1988. Equity increased,
but to a lesser extent, with a stop order. For entry at the open and on a stop, equity
was choppy and down-trending from June 1988 to July 1994, when the limit
order modestly gained. From July 1994 to December 1998, equity for entry at the
open mildly declined, the stop evidenced a serious decline, and the limit had no
consistent movement. The stop did better than average during the first period and
much worse than average during the third, more decay in performance over time
occurred with a stop order than with the other orders. In all periods, the limit
order performed best.
When equity was analyzed for all models and order types combined, most of
its gains were in the first period, which covered less than the first third of the in-
sample period. By the end of this period, more than 70% of the peak equity had
already accumulated. In the second period, equity drifted up a little. In the third
period, equity declined, at first gradually and then, after July 1997, at a faster pace.

Interactions seemed strongest between breakout types and time. The most
notable was between volatility breakouts (versus the others) and time (in-san-
ple versus out-of-sample). Volatility breakouts performed best early on, but
later became the worst. The volatility breakout with stop entry deteriorated
more in recent years than it did with entry on a limit, perhaps due to the com-
mon use of stops for entry in trend-following models. Finally, the highest-
higMowest-low breakout sometimes favored a stop, while the volatility model
never did.

Restrictions and Filters
Restricting trades to long positions greatly improved the performance of the
volatility breakout in-sample, and improved it to some extent out-of-sample.
Breakout models do better on the long side than on the short one. The ADX
trend filter had a smaller benefit in-sample and provided no benefit out-of-
Restricting trading to currencies produced lessened in-sample perfor-
mance, but dramatic improvements out-of-sample. The gain was so great that
the model actually profited out-of-sample, which cannot be said for any of the
other combinations tested! The currencies were not affected by the rising effi-
ciency other markets had to simple breakout systems, perhaps because the cur-
rency markets are huge and driven by powerful fundamental forces. The poorer
in-sample performance can be explained by the reduced number of markets

Analysis by Market
Net profit and annual return were averaged for each market over all tests. The cal-
culated numbers contained no surprises. Positive returns were seen in both samples
for the Deutschemark, Swiss Franc, Japanese Yen, and Canadian Dollar, and for
Light Crude and Heating Oil. Trading a basket of all six currencies, all three oils, or
both, would have been profitable in both samples. Although no other market group
demonstrated consistent profitability, some individual markets did. In order of min-
imum net profit, Coffee, Live Hogs, and Random Lumber had positive retarns.
The S&P 500, NYFE, Comex Gold, Corn, and the wheats had positive out-
of-sample returns with in-sample losses. The index markets™ profitability may
have resulted from the strong trends that developed out-of-sample. Positive in-
sample returns, associated with out-of-sample losses, were somewhat more
common; T-Bonds, IO-Year Notes, Palladium, Feeder Cattle, Pork Bellies,
Soybeans, Soybean Meal, Bean Oil, Oats, Orange Juice, and Cotton had this pat-
tern. T-Bills, Silver, Platinum, Live Cattle, Cocoa, and Sugar lost in both sam-
ples. A correlation of 0.15 between net in-sample and net out-of-sample profits
implies markets that traded well in the optimization period tended to trade well
in the verification period.

No technique, except restricting the model to the currencies, improved results
enough to overcome transaction costs in the out-of-sample period. Of course,
many techniques and combinations were not tested (e.g., the long-only restriction
was tested only with the volatility breakout and not with the HHLL breakout, a
better out-of-sample performer), although they might have been effective. In both
samples, all models evidenced deterioration over time that cannot be attributed to
overoptimization. Breakout models of the kind studied here no longer work, even
though they once may have. This accords with the belief that there are fewer and
fewer good trends to ride. Traders complain the markets are getting noisier and
more countertrending, making it harder to succeed with trend-following methods.
No wonder the countertrend limit entry works best!
Overall, simple breakout models follow the aforementioned pattern and do
not work very well in today™s efficient markets. However, with the right combina-
tion of model, entry order, and markets, breakouts can yield at least moderate prof-
its. There are many variations on breakout models, many trend filters beyond the
ADX, and many additional ways to improve trend-following systems that have not
been examined. Hopefully, however, we have provided you with a good overview
of popular breakout techniques and a solid foundation on which to begin your own

If possible, use a limit order to enter the market. The markets are noisy and

usually give the patient trader an opportunity to enter at a better price; this
is the single most important thing one can do to improve a system™s prof-
itability. Controlling transaction costs with limit orders can make a huge
difference in the performance of a breakout model. Even an unsophisticated
limit entry, such as the one used in the tests, can greatly improve trading
results. A more sophisticated limit entry strategy could undoubtedly pro-
vide some very substantial benefits to this kind of trading system.
. Focus on support and resistance, fundamental verities of technical
analysis that are unlikely to be “traded away.” The highest-high/lowest-
low breakout held up better in the tests than other models, even though

it did not always produce the greatest returns. Stay away from popular
volatility breakouts unless they implement some special twist that
enables them to hold up, despite wide use.
. Choose “trendy” markets to trade when using such trend-following mod-
els as breakouts. In the world of commodities, the currencies traditionally
are good for trend-following systems. The tests suggest that the oils and
Coffee are also amenable to breakout trading. Do not rely on indicators
like the ADX for trendiness determination.
. Use something better than the standard exit to close open positions.
Better exit strategies are available, as will be demonstrated in Part III. A
good exit can go a long way toward making a trading system profitable.

Moving Average Models

Moving averages are included in many technical analysis software packages and
written about in many publications. So popular arc moving averages that in 1998,
5 of the 12 issues of Technical Analysis of Stocks and Commodities contained art-
cles about them. Newspapers often show a 50-day moving average on stock charts,
and a 20.day moving average on commodities charts.

To help understand moving averages, it is first necessary to discuss time series,
i.e., series of data points that are chronologically ordered. The daily closing prices
for a commodity are one example: They form a string of “data points” or “bars”
that follow one another in time. In a given series, a sample of consecutive data
points may be referred to as a “time window.” If the data points (e.g., closing
prices) in a given time window were added together, and the sum divided by the
number of data points in the sample, an “average” would result. A moving aver-
age is when this averaging process is repeated over and over as the sampling peri-
od is advanced, one data point at a time, through the series. The averages
themselves form a new time series, a set of values ordered by time. The new series
is referred to as “the moving average of the original or underlying time series” (in
this case, the moving average of the close). The type of moving average just
described is known as a simple moving average, since the average was computed
by simply summing the data points in the time window, giving each point equal
weight, and then dividing by the number of data points summed.
A moving average is used to reduce unwanted noise in a time series so that the
underlying behavior, unmasked by interference, can be more clearly perceived; it
serves as a data smoother. As a smoothing agent, a moving average is a rudimen-
tary low-passJ%er, i.e., a filter that permits low frequency activity to pass through
unimpeded while blocking higher frequency activity. In the time domain, high fre-
quency activity appears as rapid up-and-down jiggles, i.e., noise, and low fre-
quency activity appears as more gradual trends or undulations. Ehlers (1989)
discusses the relationship between moving averages and low-pass filters. He pro-
vides equations and compares several formal low-pass filters with various moving
averages for their usefulness. Moving averages may be used to smooth any time
series, not just prices.

Besides their ability to decrease the amount of noise in a time series, moving aver-
ages are versatile, easy to understand, and readily calculated. However, as with
any well-damped low-pass filter or real-time data smoothing procedure, reduced
noise comes at a cost: lag. Although smoothed data may contain less noise and,
therefore, be easier to analyze, there will be a delay, or “lag,” before events in the
original time series appear in the smoothed series. Such delay can be a problem
when a speedy response to events is essential, as is the case for traders.
Sometimes lag is not an issue, e.g., when a moving average of one time series
is predictive of another series. This occurs when the predictor series leads the series
to be predicted enough to compensate for the lag engendered by the moving aver-
age. It is then possible to benefit from noise reduction without the cost of delay.
Such a scenario occurs when analyzing solar phenomena and seasonal tendencies.
Also, lag may not be a serious problem in models that enter when prices cross a
moving average line: In fact, the price must lead the moving average for such mod-
els to work. Lag is more problematic with models that use the slope or turning
points in the average to make trading decisions. In such cases, lag means a delayed
response, which, in turn, will probably lead to unprofitable trades.
A variety of adaptive moving averages and other sophisticated smoothing
techniques have been developed in an effort to minimize lag without giving up
much noise reduction. One such technique is based on standard time series fore-
casting methods to improve moving averages. To eliminate lag, Mulloy (1994)
implements a linear, recursive scheme involving multiple moving averages. When
the rate of movement in the market is appropriate to the filter, lag is eliminated;
however, the filters tend to “overshoot” (an example of insufficient damping) and
deteriorate when market behavior deviates from filter design specifications.
Chande ( 1992) took a nonlinear approach, and developed a moving average that
adapts to the market on the basis of volatility. Sometimes lag can be controlled or
eliminated by combining several moving averages to create a band-pass filter.
Band-pass filters can have effectively zero lag for signals with periodicities near
the center of the pass-band; the smoothed signal can be coincident with the origi-
nal, noisy signal when there is cyclic activity and when the frequency (or period-
icity) of the cyclic activity is close to the frequency maximally passed by the filter.

All moving averages, from the simple to the complex, smooth time series data by
some kind of averaging process. They differ in how they weigh the sample points
that are averaged and in how well they adapt to changing conditions. The differ-
ences between moving averages arose from efforts to reduce lag and increase
responsiveness. The most popular moving averages (equations below) are the sim-
ple moving average, the exponential moving average, and the front-weighted tri-
angular moving average. Less popular is Chande™s adaptive moving average

ai = (2m + 1 - k) si-k] / ( J?u (2m + 1 - k) ] Front-weighted triangular

In the equations, aj represents the moving average at the i-th bar, si the i-th
bar or data point of the original time series, m the period of the moving average,
and c (normally set to 2 / (m + I)) is a coefficient that determines the effective
period for the exponential moving average. The equations show that the moving
averages differ in how the data points are weighted. In a simple moving average,
all data points receive equal weight or emphasis. Exponential moving averages
give more weight to recent points, with the weights decreasing “exponentially”
with distance into the past. The front-weighted triangular moving average
weighs the more recent points more heavily, but the weights decline in a linear
fashion with time; TradeStation calls this a “weighted moving average,” a pop-
ular misnomer.
Adaptive moving averages were developed to obtain a speedier response. The
goal was to have the moving average adapt to current market behavior, much as
Dolby noise reduction adapts to the level of sound in an audio signal: Smoothing
increases when the market exhibits mostly noise and little movement (more noise
attenuation during quiet periods), and smoothing declines (response quickens) dur-
ing periods of more significant market activity (less noise suppression during loud
passages). There are several adaptive moving averages. One that seems to work
well was developed by Mark Jurik (www.jurikres.com). Another was “VIDYA”
(Variable Index Dynamic Moving Average) developed by Chande.
A recursive algorithm for the exponential moving average is as follows: For
each bar, a coefficient (c) that determines the effective length (m) of the moving
average is multiplied by the bar now being brought into the average and, to the
result, is added 1.0 - c multiplied by the existing value of the moving average,
yielding an updated value. The coefficient c is set to 2.0/(1.0 + m) where m is the
desired length or period. Chande (1992) modified this algorithm by changing the
coefficient (c) from a fixed number to a number determined by current market
volatility, the market™s “loudness,” as measured by the standard deviation of the
prices over some number of past bars. Because the standard deviation can vary
greatly between markets, and the measure of volatility needs to be relative,
Chande divided the observed standard deviation on any bar by the average of the
standard deviations over all bars on the S&P 500. For each bar, he recomputed the
coefficient c in the recursive algorithm as 2.0 / (1.0 + m) multiplied by the rela-
tive volatility, thus creating a moving average with a length that dynamically
responds to changes in market activity.
We implemented an adaptive moving average based on VIDYA that does not
require a fixed adjustment (in the form of an average of the standard deviations over
all bars) to the standard deviation. Because markets can change dramatically in their
average volatility over time, and do so in a way that is irrelevant to the adaptation of


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