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In-Sample Performance Broken Down by Test and Market
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In-sample, the simple moving average provided the best results in average dollars-per-trade. The worst results were for the adaptive moving average. The other two moving averages fell in-between, with the exponential better in the crossover models, and the front-weighted triangular in the slope models. Of the crossover models, the ROA% was also the best for the simple moving average. Overall, the crossover models did as well or better than the slope models, possibly because of a faster response to market action in the former. Out-of-sample, the simple moving average was the clear winner for the crossover models, while the front-weighted triangular was the best for the slope models. In terms of the
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Out-of-Sample Performance Broken Down by Test and Market
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ROA%, the exponential moving average appeared the best for the crossover
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models, with the front-weighted triangular still the best for the slope models. When looking at individual tests, the particular combination of a frontweighted triangular moving average, the slope model, and entry on stop (Test 21) produced the best out-of-sample performance of all the systems tested. The out-ofsample results for the front-weighted triangular slope models seemed to be better across all order types. There apparently were some strong interactions between the various factors across all tests, e.g., for the crossover model on the in-sample data, entry at the open was consistently close to the worst, entry on stop was somewhere in between, and entry on limit was always best, regardless of the moving average
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Performance of Trend-Following Moving Average Entry Models Broken Down by Order, Moving Average Type, Model, and Sample
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used. Out-of-sample, the findings were much more mixed: With the simple moving average, the pattern was similar to that for the in-sample period; however, with the exponential moving average, the limit performed worst, the stop best, and the open not far behind. Out-of-sample, with the front-weighted triangular average, the stop performed by far the worst, with the limit back to the best performer. These results indicate interaction between the moving average, entry order, and time. The slope model, in-sample, had the entry at open always performing worst; however, although the results were often quite close, the limit and stop orders were hvice seen with the limit being favored (simple moving average and adjusted moving
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average), and twice with the stop being favored (exponential moving average and
front-weighted triangular moving average). As before, great variation was seen outof-sample. For the simple moving average, the limit order performed best and the stop worst. The more typical pattern was seen for the exponential moving average: The entry at open performed worst, the limit best, and the stop was on the heels of the limit. As already stated, the front-weighted triangular moving average performed very unusually when combined with the stop order. The limit was best for the adaptive moving average, the stop was worst, and the open was slightly better albeit very close to the stop. As a whole, these models lost on most markets. Only the JapaneseYen and Pork Bellies were profitable both in- and out-of-sample; no other markets were profitable in-sample. Out-of-sample, some profits were observed for Heating Oil, Unleaded Gasoline, Palladium, Live Hogs, Soybean Meal, Wheat, and Coffee. The strong outof-sample profit for Coffee can probably be explained by the major run-up during the drought around that time. On an individual model-order basis, many highly profitable combinations could be found for Live Hogs, JapaneseYen, Pork Bellies, Coffee, and Lumber. No combinations were profitable in either sample for Oats. In terms of equity averaged over all averages and models, entry at the open performed, by far, the worst. Entry on limit or stop produced results that were close, with the limit doing somewhat better, especially early in the test period. It should be noted that, with the equity curves of losing systems, a distortion takes place in their reflection of how well a system trades. (In our analyses of these losing systems, we focused, therefore, on the average return-per-trade, rather than on risk-reward ratios, return-on-account, or overall net profits.) The distortion involves the number of trades taken: A losing system that takes fewer trades will appear to be better than a losing system that takes more trades, even if the better appearing system takes trades that lose more on a per-trade basis. The very heavy losses with entry at open may not be a reflection of the bad quality of this order; it may simply be reflecting that more trades were taken with an entry at the open than when a stop or limit order was used. Figure 6-l presents the equity curves for all eight model and moving average combinations. The equity curves were averaged across order type. Figure 6-l provides a useful understanding of how the systems interact with time. Most of the systems had their heaviest losses between late 1988 and early 1995. The best performance occurred before 1988, with the performance in the most recent period being intermediate. In Curve 3, the simple moving average crossover model was the most outstanding: This pattern was greatly exaggerated, making the equity curve appear very distinct; it actually showed a profit in the early period, a heavier relative loss in the middle period, and levelled off (with a potential return to flat or profitable behavior) toward the end of the third period. Finally, it is dramatically evident that the crossover systems (Curves 1 through 4) lost much less heavily than the
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