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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

11 4 cups rolled oats 11 4 cups whole-wheat flour 1 teaspoon baking powder 2 cups fresh or frozen (thawed) blueberries 1 4 cup canola oil 1 3 cup honey 3 tablespoons water 1 large egg or 1 4 cup egg substitute 1 teaspoon fresh lemon or lime rind (optional)* 2 tablespoons lemon or lime juice

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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

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to 45, with a grid of 01; 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, 26; moving average length, 15; and average true range period, 18 The best parameters produced an annualized return of 530%, and a risk-to-reward ratio of 117 (p < 00002; p < 002, 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, eg, 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 -146% 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.

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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.

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