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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.
TABLE 5-l

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
92




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.

HIGHEST HIGH / LOWEST LOW BREAKOUTS
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




S-2
TABLE

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;
I
else if(cls[cblcLoweat(lo,n.cbl) && ts.positionO˜-0) {
94




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
improvement.
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



FIGURE S-1

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.

VOLATILITY BREAKOUT ENTRIES
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.

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