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optimizations, and generate output for each combination of moving average type, model, and entry order. The code below is more complex than for breakouts: Instead of a different routine for each combination of moving average, entry rule, and trading order, there is one larger routine in which parameters control the selection of system elements. This technique is required when systems are genetically evolved. Although no genetics are used here, such algorithms are employed in later chapters. This code uses parameters to control model elements, making it easier to handle all the combinations tested in a clean, systematic way.
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local // // I/ I/ I/ I/ I/ //
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variables for clearer reference period for faster moving average period for slower moving average type Of entry model type of moving average type Of entry order maximum holding period profit target in volatility units stop loss in volatility units
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// skip invalid parameter combinations if(fastmale" >= slovmlale") { set-"ector~eqcls, 1, rib, 0.01; return; ) I/ perform whole-series computations using vector routines // ATR for exit *"gTr"eRa"ses(exitatr, hi, 10, ClS, 50, "b); switchbvgtype) ( // select type of moving average case 1: // simple moving averages A"erageS~fastma, cls, fastmale", "b); AverageSislovmla, ClS, slowmale*, nbl; break; ,, exponential mo"i"g averages case 2: xA"erageS(fastma, ClS, fastmale", "b, ; xA"erageS~slowma, CL%, s1ovmden. "b) ; break; case 3: // front-weighted triangular moving averages FwTn"erages~fastma, ClS, fastmale", nb,; FwTAverageS ~slowma, ClS, slowmale", "b, ; break; case 4: // "IDYA-style adaptive moving averages "rn"erages~fastma, ClS. fastmale". 10, "b, ; "IA"erageS~slowma, ClS. *lowmale", 10. &I; break; default: "rerror~"I""alid mo"i"g average selected"); 1;
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// avoid placing orders on possibly limit-locked days if (hi L&+11 == lo L&+11 1 continue; ,, generate entry signals, stop prices and limit // using the specified moving average entry model prices
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// enter trades using specified order type ifCts.positionO c= 0 && signal == 1) ( switch(ordertype1 ( // select desired order type case 1: ts.b"yopen~ 1'. ncontracts,; break; case 2: ts.buylimitC~Z', limprice, ncontracts); break;
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The code contains three segments. The first segment calculates moving averages. A parameter (avgrype) selects the kind of average: 1 = simple; 2 = exponential: 3 = front-weighted triangular; and 4 = the modified VIDYA. Even if the model requires only one moving average, two of the same type are computed, this allows the selection of the moving average to be independent of model selection. The average true range is also computed and is required for setting stop-losses and profit targets in the standard exit strategy. Two additional parameters, fastmalen and slowmalen, specify the period of the faster and the slower moving averages, respectively. The moving averages are saved in the vectors,fismzma and slowma. The next block uses the selected model to generate entry signals, stop prices, and limit prices. First, simple relationships (CrossesAbove, CrossesBelow, TurnsUp, and TurnsDown) are defined. Depending on modeltype, one of four moving average models then generates the signals: 1 = the classic, trend-following dual moving average crossover; 2 = a slope-based trend-following model; 3 = a countertrend crossover model; and 4 = a countertrend support/resistance model. In the classic, trend-following dual moving average crossover, the trader goes long if a faster moving average of the closing price crosses above a slower moving average, and goes short if the faster moving average crosses below the slower one. As a special case, this model contains the classic crossover that compares prices to a moving average. The special case is achieved when the period of the shorter moving average is set to 1, causing that moving average to decay to the original series, i.e., the closing prices. With a slope-based trend-following model, the trader buys when the moving average was decreasing on previous bars but increases on the current bar (slope turns up), and sells when the opposite occurs. This model requires only
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the fast moving average. The countertrend model is the opposite of the classic trend-following crossover: The trader buys when the shorter moving average (or the price itself) crosses below the longer moving average, and sells when it crosses above. This model is the contnuian s delight: Doing exactly the opposite of the trend-followers. Last is a crude countertrend support/resistance model in which prices are expected to bounce off the moving average, as if off a line of support or resistance. The rules are almost identical to the countertrend crossover model, except that the slower moving average must be moving in the direction of the entry: If the slower moving average is trending upward, and prices (or the faster moving average) move from above that slower moving average into or below it, the trader buys; conversely, if prices (or the faster moving average) are currently below a downward trending slower moving average, and prices bump into or penetrate that moving average from below, then the trader sells. The additional trend rule prevents an immediate reversal of position after contact or penetration. Without the trend rule, a quick penetration followed by a reversal would trigger two entries: The fast would be the desired countertrend entry, occurring when the prices penetrate the moving average, and the second entry (in the opposite direction) would occur as the prices bounce back, again crossing the moving average. The trend check only allows entries to be taken in one direction at a time. A penetration, followed by a bounce in an up-trending market, will take the long entry; a penetration and reversal in a down-trending market will result in a short entry. In the last block of code, the entry order to be posted is determined by the ordertype parameter: 1 = market at open; 2 = limit; 3 = stop. Whether a buy or sell is posted, or no order at all, is determined by whether any signal was generated in the previous block of code; a variable called signal carries this information: 1 = buy; - 1 = sell (go short); 0 = do nothing. The limit price (limpn ce) is computed as the sum of today s high and low prices divided by two. Because many of the models have no natural price for setting a stop, a standard stop was used. The standard entry stop price (stpprice) is obtained by taking the closing price of the previous bar and adding (if a long position is signalled) or subtracting (if a short is signalled) the 50-bar average true range multiplied by 0.50; the market must move at least one-half of its typical daily range, in the direction of the desired entry, for the entry to occur. This type of stop order adds a breakout test to the moving average system: Once a signal is given, the market must move a certain amount in the direction of the trade to trigger an entry. Because of the large number of tests, statistical significances were not reported unless something notable occurred. TESTS OF TREND-FOLLOWING MODELS The group of tests presented here involve moving averages as trend-followers. The models vary in the kinds of moving average, the rules that generate signals, and the orders posted to effect entry. The moving averages tested include the simple,
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the exponential, the front-weighted triangular, and a modification of VIDYA. Both single and dual moving average crossovers, and models that use slope (rather than crossover) to determine entry, are examined. Entry orders are market-at-open, stop, and limit. Tests 1 through 12 were of the crossover models, Optimization was performed 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. Only cases in which the longer moving average was strictly longer than the shorter moving average were examined. Brute force optimization was used, controlled by the testing script. The parameters were chosen to maximize the risk-to-reward ratio or, equivalently, minimize the probability (based on a t-test of daily returns) that any profitable performance was due to chance. In Tests 13 through 24 (the slope models), brute-force optimization was performed by stepping the length of the first and, in this case, only moving average from 3 to 40, in increments of 1. As in Tests 1 through 12, the risk-to-reward ratio was maximized. Optimization was only carried out on in-sample data. Tables 6-l and 6-2 show, for each of the 24 tests, the specific commodities that the model traded profitably and those that lost, for the in-sample (Table 1) and outof-sample (Table 6-2) runs. The SYM column represents the market being studied; the first row identifies the test. The data provides relatively detailed information about which markets were and were 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 (+ +) indicates a large gain per trade, i.e., $2,000 or more; a blank cell means that the loss was between $0 and $1,999 or the profit was between $0 and $1,000 per trade. Table 6-3 shows, for the entire portfolio, the return-on-account (ROA%) and average dollar-per-trade ($TRD) broken down by the moving average, model, entry 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 have been averaged over all combinations of moving average type and model. The numbers at the right are averaged over order type. None of the trend-following moving average models was profitable on a portfolio basis. More detailed examination reveals that for the crossover models the limit order resulted in a dramatic benefit on the in-sample data. When compared with an entry at open or on a stop, the limit cut the loss of the average trade almost in half. Out-of-sample, the improvement was not as dramatic, but still significant. The return-on-account showed a similar pattern: The least loss was with the limit order. For slope models, the limit order worked best out-of-sample in terms of dollars per trade. The return-on-account was slightly better with a stop (due to distortions in the ROA% numbers when evaluating losing systems), and worse for entry at open. In-sample, the stop order performed best, but only by a trivial amount.
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