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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.

EQUALIZATION OF DOLLAR VOLATILITY
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
TEN-YEAR-NOTES Ty
˜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
TABLE II-1

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
2.38
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

102.50
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
203
100 227 147 ,a2 282 305 204

180.78
217.40 2c0.70 200.74 251.10 208.01 ,048, 210.04
140
130 137 104 113 130 172 ,20

0,022
351.12 201.05 254.05 351.75 332.50 201.30 332.05
40
81 37 11, 81 85 141 0.5

317.34 338.40 1021.57. 024.30 713.80 ooo.,o 081.03 583.44
40
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.

BASIC TEST PORTFOLIO AND PLATFORM
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.
CHAPTER S
.-.

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.

KINDS OF BREAKOUTS
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
84




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.

CHARACTERISTICS OF BREAKOUTS
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.

TESTING BREAKOUT MODELS
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).
CHANNEL BREAKOUT ENTRIES
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;
88




] ,, process next bar
I

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-

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