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Portfolio Performance with Best In-Sample Parameters on Both InSample and Out-of-Sample Data
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trade. The long side was slightly profitable with entry at open, was somewhat more profitable with entry on limit, and lost with entry on stop. The behavior out-of-sam ple, with entry at open and on limit, was a lot worse than the behavior of the model in-sample. The loss per trade grew to $3,741 for entry at open and to $3,551 for entry on limit. The percentage of winning trades also declined, to 34%. The performance of the cycle model on the verification sample was among the worst observed of the various models tested. The deterioration cannot be attributed to optimization: Several other parameter sets were examined, and regardless of which was chosen, the cycle model still performed much worse out-of-sample. With entry on stop, the out-of-sample performance did not deteriorate. In this case, the loss ($944) was not too different from the in-sample loss. Although the stop order appears to have prevented the deterioration of the model that was seen with the other orders, in more recent times the system is a loser. The decline of system performance in recent years was unusually severe, as observed from the results of the other models tested. One possible reason may be the recent proliferation of sophisticated cycle trading tools. Another explanation might be that major trading firms are conducting research using sophisticated techniques, including wavelets of the kind studied here. These factors may have contributed to making the markets relatively efficient to basic cycle trading. Table 10-2 shows the in-sample and out-of-sample behavior of the cycle model broken down by market and entry order (test). The SYM column represents the market being studied. The center and rightmost columns (COUhrr, contain the number of profitable tests for a given market. The numbers in the first row represent test identifiers: 01, 02, and 03 represent entry at open, on limit, and on stop, respectively. The last row (COUNT) contains the number of markets on which a given model was profitable. The data in this table provides relatively detailed information about which markets are and are not profitable when traded by each of the models: One dash (-) indicates a moderate loss per trade, i.e., $2,000 to $4,000; two dashes (--) represent a large loss per trade, i.e., $4,000 or more; one plus sign (+) means a moderate profit per trade, i.e., $1,000 to $2,000; two pluses (++) indicate a large gain per trade, i.e., $2,000 or more; and a blank cell means that the loss was between $0 and $1,999 or the profit was between $0 and $1,000 per trade. (For information about the various markets and their symbols, see Table 11-l in the Introduction to Part II.) Only the IO-Year Notes and Cotton showed strong profits across all three entry orders in-sample. Out-of-sample, performance on these markets was miserable. The S&P 500, a market that, in our experience, has many clear and tradable cycles, demonstrated strong profitability on the in-sample data when entry was at open or on limit. This market was strongly profitable out-of-sample with entry on limit and on stop, but somewhat less profitable with entry at open. Interestingly, the NYFE, although evidencing strong in-sample profits with entry at open and on limit, had losses out-of-sample across all three orders. There are a few other prof-
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Performance Data Broken Down by Market and Test
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itable in-sample market-order combinations, as well as out-of-sample marketorder combinations, However, very little correspondence between the two was observed. Perhaps markets that have not had cycles in the past (in-sample) have cycles in the present (out-of-sample), and vice versa. At least the S&P 500 behaved as expected on the basis of prior research and may be one of the few markets consistently amenable to cycle trading in this crude form. Figure 10-4 depicts the equity for the portfolio with entry at open. Equity declined slowly and then became rather flat until about August 1992, at which time it began a steady and rapid decline.
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