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Portfolio Performance with Best In-Sample Parameters in the Optimization and Verification Samples
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Portfolio Performance with Best In-Sample Parameters for in the Optimization and Verification Samples (Continued)
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ues: PI = the threshold, P2 = the number of the neural network within the group of networks trained for the model (these numbers correspond to the numbers used in the file names for the networks shown in Tables 1 l-l through 1 l-3), P3 = not used. In all cases, the threshold parameters (column Pl) shown are those that resulted in the best in-sample performance. Identical parameters are used for verification on the out-of-sample data. The threshold for the time-reversed Slow %K model was optimized for each order type by stepping it from 50 to 90 in increments of 1. For the top and bottom predictor models, the thresholds were stepped from 20 to 80 in increments of 2. In each case, optimization was carried out only using the in-sample data. The best parameters were then used to test the model on both the in-sample and out-of-sample data sets. This follows the usual practice established in this book. Trading Results for the Reverse Slow %K Model The two networks that were selected as most likely to hold up out-of-sample, based on their shrinkage-adjusted multiple correlations with the target, were analyzed for
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trading performance, The first network was the smaller of the two, having 3 layers (18-6-l network). The second network had 4 layers (18-14-4-l network).
Results Using the 18-6-I Network. In-sample, as expected, the trading results
were superb. The average trade yielded a profit of greater than $6,000 across all order types, and the system provided an exceptional annual return, ranging from 192.9% (entry at open, Test 1) to 134.6% (entry on stop, Test 3). Results this good were obtained because a complex model containing 114 free parameters was fitted to the data. Is there anything here beyond curve-fitting Indeed there is. With the stop order, out-of-sample performance was actually slightly profitable-nothing very tradable, but at least not in negative territory: The average trade pulled $362 from the market. Even though losses resulted out-of-sample for the other two order types, the losses were rather small when compared with those obtained from many of the tests in other chapters: With entry at open, the system lost only $233 per trade. With entry on limit (Test 2), it lost $331. Again, as has sometimes happened in other tests of countertrend models, a stop order, rather than a limit order, performed best. The system was profitable out-of-sample across all orders when only the long trades were considered. It lost across all orders on the short side. In-sample performance was fabulous in almost every market in the portfolio, with few exceptions, This was true across all order types. The weakest performance was observed for Eurodollars, probably a result of the large number of contracts (hence high transaction costs) that must be traded in this market. Weak performance was also noted for Silver, Soybean Oil, T-Bonds, T-Bills, Canadian Dollar, British Pound, Gold, and Cocoa. There must be something about these markets that makes them difficult to trade, because, in-sample, most markets perform well. Many of these markets also performed poorly with other models. Out-of-sample, good trading was obtained across all three orders for the TBonds (which did not trade well in-sample), the Deutschemark, the Swiss Franc, the Japanese Yen, Unleaded Gasoline, Gold (another market that did not trade well insample), Palladium, and Coffee. Many other markets were profitable for two of the three order types. The number of markets that could be traded profitably out-of-sample using neural networks is a bit surprising. When the stop order (overall, the bestperforming order) was considered, even the S&P 500 and NYFE yielded substantial profits, as did Feeder Cattle, Live Cattle, Soybeans, Soybean Meal, and Oats. Figure 1 l-l illustrates the equity growth for the time-reversed Slow %K predictor model with entry on a stop. The equity curve was steadily up in-sample, and continued its upward movement throughout about half of the out-of-sample period, after which there was a mild decline.
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