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slope-based models (Curves 5 through S), although this reflects a larger number of trades, not greater losses on a per trade basis. TESTS OF COUNTER-TREND MODELS As with trend-following models, countertrend models vary in the moving averages used, the rules that generate signals, and the orders posted to effect entry. The same moving averages used in the trend-following models are studied here. Both single and dual moving average models are examined. Entry orders studied are the market-at-open, stop, and limit. Tests 25 through 36 evaluate the standard moving average crossover model turned upside-down. As before, entry signals occur when prices cross the average, or when a shorter average crosses a longer one. In traditional trend-following crossover models, the trader buys when the price (or a shorter moving average) crosses above a longer moving average, and sells when it crosses below. In the contrarian crossover model, the trader sells when prices cross above, and buys when prices cross below. In these tests, brute force optimization was performed on the in-sample data by stepping the length of the shorter moving average from 1 to 7, in increments of 1; the longer moving average was stepped from 5 to 50, in
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increments of 5. Only cases where the longer moving average was longer than the shorter moving average were considered. The parameters minimized the probability that any observed profitable performance was due to chance. The model was run on the out-of-sample data using the best parameter set found in-sample. In tests of the support/resistance model (37 through 48), the trader buys when prices bounce off a moving average from above, and sells when they hit a moving average from below. In this way, the moving average serves as a line of support or resistance where prices tend to reverse. The rules are almost the same as for Tests 25 through 36, except that not every penetration of a moving average results in an entry. If prices are above the moving average and penetrate it, a buy is generated; however, when prices bounce back up through the moving average, the second crossover is not allowed to trigger a sell. If prices arc below the moving average and rise into it, a sell is triggered, no buy is triggered when the prices bounce back down. This behavior is achieved by adding one element to the contrarian crossover model: A signal is generated only if it is in the direction of the slope of the slower moving average. Performance was brute force optimized on the in-sample data by stepping the length of the shorter moving average from 1 to 5, in increments of 1, and the longer moving average from 5 to 50, in increments of 5. A moving average length of 1 caused the shorter moving average to become equivalent to the prices; therefore, in the optimization, the model in which prices were compared to the moving average was tested, as was the model in which one moving average was compared to anotb er. Only cases where the longer moving average was strictly longer than the shorter moving average were examined. The parameters were chosen to minimize the probability that any profitable performance was due to chance. The model was then run on the out-of-sample data using the best parameter set found in-sample. Tables 6-4 and 6-5 show, for Tests 25 through 48, the commodities that the model traded profitably and those that lost, in-sample (Table 6-4) and out-of-sample (Table 6-S). The plus and dash symbols may be interpreted in the same manner as for Tables 6-1 and 6-2. Table 6-6 provides the results broken down by the moving average, model, order, and sample. The last two columns on the right, and the last four rows of numbers on the bottom, are averages. The numbers at the bottom were averaged over all combinations of moving average type and model. The numbers at the right were averaged over order type. Overall, the best models in-sample were the simple moving average support/resistance and the front-weighted triangular average support/resistance. The simple average support/resistance with a stop order was unique in that it showed small profits in both samples: an average trade of $227 and a 4.2% retum-onaccount in-sample, $482 per trade and a 14.8% return-on-account out-of-sample. The front-weighted triangular average with the stop was profitable in-sample, but lost heavily out-of-sample. Both models, especially when combined with a stop, had relatively few trades: consequently, the results are less statistically stable.
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