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Test 6: Close-Only HHLL Breakout with Entry on Stop on Next Bar.
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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
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Equity Curve for HHLL Breakout, Entry at Limit
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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 lookback 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
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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 profit. 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 period. 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 tomorrow 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 optimization was chosen for the current test. Using genetic optimization, the bandwidth parameter (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 parameters, the annualized return was 27.4%. There was a probability of 5.6% (99.7%
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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 average 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 parameter combinations tested, a good entry model should have generated a greater insample 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 others, 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 establish a long position on the next bar using a limit order when the close of the current 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 multiplier 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 bandwidth 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% annualized return. Results this good should occur less than twice in one-thousand
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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 continue 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 trendiness. 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 historical performance, when using a breakout system. Although this model performed 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 advantage 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 nearest the most recent closing price is posted; this rule was used in Test 6. The volatility 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 optimization, 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 simulation 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.
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Can excessive optimization explain the rapid decay in the out-of-sample period No. Optimization may have merely boosted overall in-sample performance from terrible to poor, without providing improved out-of-sample performance. 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 outof-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 volatility and, consequently, a large number of contracts must be traded, which magnities 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 difficult to enter on a stop at an acceptable price. VOLATILITY BREAKOUT VARIATIONS
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: bandwidth, 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 values 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 insample 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-ofsample period! This finding rules out excessive optimization as the cause for outof-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.
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,
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