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Solutions Evolved for Long Entries
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Table 12-I furnishes some of the performance data for the top 20 solutions for long entries at the open (GFile 1). Each line represents a different trading model. The parameters are not shown, but the line or generation number (LINE), the probability or statistical significance (PROB, the decimal point is omitted but implied in the formatting of these numbers), the average dollars-per-trade ($TRD), the total number of trades taken (TRDS), the profit factor (PFAC ), the annualized return-on-account (%ROA), and the net profit or loss (NET) in raw numbers are provided.
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The Top 20 Solutions Evolved for Long Entries at the Open
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The performance of most of these models is nothing short of impressive. The better models are statistically significant beyond the 0.00007 level, which means these solutions have a very high probability of being real and holding up in the future. Many of the returns were greater than 50% annualized. In some cases, they reached much higher levels. While the limit order had many of the best solutions, all orders had many good, if not great, solutions. As in OUT earlier study, the GA succeeded admirably in finding many tradable models.
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Solutions Evolved for Short Entries
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Table 12-2 provides a small proportion of GFtile 4, the file for evolved models generated for short entries at the open. As in Test 1, the top 20 solutions, in terms of statistical significance or risk-to-reward ratio, are presented. Again, it can be seen that there were many good solutions. However, they were not as good as those for the longs. The solutions were not as statistically significant as for the longs, and the return-on-account numbers were somewhat smaller. A somewhat more distressing difference is that, in most cases, the number of trades was very small; the models appear to have been picking rare events. All else aside, the evolutionary process was able to find numerous, profitable rule sets for the short entries.
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The Top 20 Solutions Generated for Short Entries at the Open
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Test Results for the Standard Portfolio The best solution shown in Table 12-1 (long trades) and the best solution from Table 12-2 (short trades) were run with all three entry orders. Tests 1 through 3 represent the best evolved model for long entry at the open tested with entry at open, on limit, and on stop (respectively). Tests 4 through 6 represent the best evolved model for short entry over all three orders. Table 12-3 contains the performance data for the best evolved entry-at-open models, both long and short, on the optimization and verification samples using each of the three entry orders. In the table, SAMP = whether the test was on the optimization sample (IN or OUT); ROA% = the annualized return-on-account; ARRR = the annualized risk-toreward ratio: PROB = the associated probability or statistical significance; TRDS = the number of trades taken across all commodities in the portfolio; WZN% = the percentage of winning trades; $TRD = average profit/loss per trade; BARS = the
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T A B L E
12-S
Performance of the Best Evolved Entry-at-Open Model on the $Jeyzation and Verification Samples with Each of the Three Entry
I I I I Test 03 Short entry-at-open model, entry on stop IN / 23.11 0.6oI 0.0311 OUT 1 -13.01 -0.251 0.W 131
average number of days a trade was held, NETL = the total net profit on long trades, in thousands of dollars; and NETS = the total net profit on short trades, in thousands of dollars.
Tests 1 through 3: Long-Entry-At-Open Model Tested with Entry at Open, on
Limit, and on Stop. As can be seen in Table 12-3, the entry model produced by the evolutionary process was profitable across all three order types, both in-sample (as would be expected given the optimization power of GAS) and out-of-sample. In-sample, no return was less than 42% (annualized) for any order. The dollars-per-trade figures were all greater than $14,000, and not one system had less than 60% wins! Out-of-sample, there was more variation. With entry at open and on limit, performance continued to be stellar, with the average trade above $10,000 and the return on account above 60%. With a stop order, performance was not quite as good: The return on account was only 11%, and the average trade yielded $4,246. The only distressing aspect of the results is the small number of trades taken. For example, in-sample, with entry at open, there were only 43 trades taken over a lo-year span on a portfolio of 36 commodities. Out-of-sample, there were only 17 trades over a 5-year period; the trading frequency was roughly constant at approximately 4 trades per year. The rules were apparently detecting unusual (but tradable) market events; the model engaged in what might be termed rare event trading, which is not necessarily a bad thing. An assortment of systems, each trading different rare events, could yield excellent profits. When working with a system such as this, trading a portfolio of systems, as well as a portfolio of commodities, would be suggested. In the current situation, however, few trades would place the statistical reliability of the findings in question. The entire problem can be dealt with by using a somewhat more complex way of handling larger combinations of rules.
Tests 4 through 6: Short-Entry-at-Open Model Tested on Entry at Open, on Limit, and on Stop. In all cases, the performance of the best evolved short entry
at open model, when tested over the three order types, was poorer on the in-sample data than the long model. Out-of-sample, the results deteriorated significantly and losses occurred. Unlike the long model, this one did not hold up. It should be noted, however, that if both the long and short models had been traded together on out-ofsample data, the profits from the long side would have vastly outweighed the losses from the short side; i.e., the complete system would have been profitable. The pattern of longs trading better than shorts is a theme that has been recurrent throughout the tests in this book. Perhaps the pattern is caused by the presence of a few markets in the standard portfolio that have been in extreme bullish mode for a long time. The way commodities markets respond to excess supply, as contrasted to the way they respond to shortages, may also help explain the tendency.
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