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8 deals with seasonality, which is construed in different ways by different traders. For our purposes, seasonalify is defined as cyclic or recurrent phenomena that are consistently linked to the calendar, specifically, market behavior affected by the time of the year or tied to particular dates. Because they are predictive (providing trading signals weeks, months, or years ahead), these models are countertrend in nature. Of the many ways to time entries that use seasonal rhythms, two basic approaches will be examined: momentum and crossover. The addition of several rules for handling confirmations and inversions will also be tested to determine whether they would produce results better than the basic models.
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Lunar and Solar Phenomena
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Do lunar and solar events influence the markets Is it possible for an entry model to capitalize on the price movements induced by such influences The moon s role in the instigation of tides is undisputed. Phases of the moon correlate with rainfall and with certain biological rhythms, and they influence when farmers plant crops. Solar phenomena, such as solar flares and sunspots, are also known to impact events on earth. During periods of high solar activity, magnetic storms occur that can disrupt power distribution systems, causing serious blackouts. To assume that solar and
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lunar phenomena influence the markets is not at all unreasonable; but how might these influences be used to generate predictive, countertrend entries Consider the lunar rhythm: It is not hard to define a model that enters the mar ket a specified number of days before or after either the full or new moon. The same applies to solar activity: An entry can be signaled when the sunspot count rises above some threshold or falls below another threshold. Alternatively, moving averages of solar activity can be computed and crossovers of these moving averages used to time market entries. Lunar cycles, sunspots, and other planetary rhythms may have a real, albeit small, impact on the markets, an impact that might be profitable with a properly constructed entry model. Whether lunar and solar phenomena actually affect the markets sufficiently to be taken advantage of by an astute trader is a question for an empirical investigation, such as that reported in 9. Cycles and Rhythms 10 explores cycles and rhythms as a means of timing entries into the market. The idea behind the use of cycles to time the market is fundamentally simple: Extrapolate observed cycles into the future, and endeavor to buy the cycle lows and sell short the cycle highs. If the cycles are sufficiently persistent and accurately extrapolated, excellent countertrend entries should be the result. If not, the entries are likely to be poor. For a very long time, traders have engaged in visual cycle analysis using charts, drawing tools, and, more recently, charting programs. Although cycles can be analyzed visually, it is not very difficult to implement cycle recognition and analysis algorithms in software. Many kinds of algorithms are useful in cycle analysis-everything from counting the bars between tops or bottoms, to fast Fourier transforms (FITS) and maximum entropy spectral analyses (MESAS). Getting such algorithms to work well, however, can be quite a challenge; but having reliable software for cycle analysis makes it possible to build objective, cyclebased entry models and to test them on historical data using a trading simulator. Whether detected visually or by some mathematical algorithm, market cycles come in many forms. Some cycles are exogenous, i.e., induced by external phenomena, whether natural or cultural. Seasonal rhythms, anniversary effects, and cycles tied to periodic events (e.g., presidential elections and earnings reports) fall into the exogenous category: these cycles are best analyzed with methods that take the timing of the driving events into account. Other cycles are endogenous; i.e., their external driving forces are not apparent, and nothing other than price data is needed to analyze them. The 3-day cycle occasionally observed in the S&P 500 is sn example of an endogenous cycle, as is an S-minute cycle observed by the authors in S&P 500 tick data. Programs based on band-pass filters (Katz and McCormick, May 1997) and maximum entropy (e.g., MESA96 and TradeCycles) are good at finding endogenous cycles.
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We have already discussed the exogenous seasonal cycles, as well as lunar and solar rhythms. In 10, endogenous cycles are explored using a sophisticated wavelet-based, band-pass filter model. Neural Networks
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As discussed in 11, neural network technology is a form of artiiicial intelligence (or AI) that arose from endeavors to emulate the kind of information pmcessing and decision making that occurs in living organisms. Neural networks (or nets ) are components that learn and that are useful for pattern recognition, classification, and prediction. They can cope with probability estimates in uncertain situations and with fuzzy patterns, i.e., those recognizable by eye but difficult to dehe using pmcise rules. Nets can be used to directly detect turning points or forecast price changes, in an effort to obtain good, predictive, countertrend entry models. They can also vet entry signals generated by other models. In addition, neural network technology can help integrate information from both endogenous sources, such as past prices, and exogenous sources, such as sentiment da@ seasonal data, and intermarket variables, in a way that benefits the trader. Neural networks can even be trained to recognize visually detected patterns in charts, and then serve as pattern-recognition blocks within traditional rule-based systems (Katz and McCormick, November 1997). Genetically Evolved Entry Rules
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12 elaborates a study (Katz and McCormick, December 1996) demonstrating that genetic evolution can be used to create stable and profitable rulebased entry models. The process involves putting together a set of model fragments, or rule templates, and allowing a genetic algorithm (GA) to combine and complete these fragments to achieve profitable entries. The way the methodology can discover surprising combinations of rules that consider both endogenous and exogenous variables, traditional indicators, and even nontraditional elements (e.g., neural networks) in making high-performance entry decisions will be examined. Evolutionary model building is one of the most advanced, cuttingedge, and unusual techniques available to the trading system developer. STANDARDIZED EXITS
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To study entries on their own, and to do so in a way that permits valid comparisons of different strategies, it is essential to implement a srandardized exit that will be held constant across various tests; this is an aspect of the scientific method that was discussed earlier. The scientific method involves an effort to hold everything, except that which is under study, constant in order to obtain reliable information about the element being manipulated.
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The standardized exit, used for testing entry models in the following chapters, incorporates the three functions necessary in any exit model: getting out with a profit when the market moves sufficiently in the trade s favor, getting out with a limited loss when the market moves against the trade, and getting out from a languishing market after a limited time to conserve margin and reduce exposure. The standard exit is realized using a combination of a stop order, a limit order, and a market order. Stop and limit orders are placed when a trade is entered. If either order is filled within a specified interval, the trade is complete, the remaining order is canceled, and no additional orders are placed. If, after the allotted interval, neither the stop nor limit orders are filled, they are canceled and a market order is placed to force an immediate exit from the trade. The stop order, called a money management stop, serves to close out a losing position with a small, manageable loss. Taking a profit is accomplished with the limit order, also called a profit target. Positions that go nowhere are closed out by the market order. More elaborate exit strategies are discussed in Part III: The Study of Exits, where the entries are standardized. Money management stops and profit target limits for the standardized exits are computed using volatility units, rather than fixed dollar amounts, so that they will have reasonably consistent meaning across eras and markets. Because, e.g., a $1,000 stop would be considered tight on today s S&P 500 (yet loose on wheat), fixed-dollar-amount stops cannot be used when different eras and markets are being studied. Volatility units are like standard deviations, providing a uniform scale of measurement. A stop, placed a certain number of volatility units away from the current price, will have a consistent probability of being triggered in a given amount of time, regardless of the market. Use of standardized measures permits meaningful comparisons across markets and times. EQUALIZATION OF DOLLAR VOLATILITY Just as exits must be held constant across entry models, risk and reward potential, as determined by dollar volatility (different from raw volatility, mentioned above), must be equalized across markets and eras. This is done by adjusting the number of contracts traded. Equalization of risk and reward potential is important because it makes it easier to compare the performance of different entry methods over commodities and time periods. Equalization is essential for portfolio simulations, where each market should contribute in roughly equal measure to the performance of the whole portfolio. The issue of dollar volatility equalization arises because some markets move significantly more in dollars per unit time than others. Most traders are aware that markets vary greatly in size, as reflected in differing margin requirements, as well as in dollar volatility. The S&P 500, for example, is recognized as a big contract, wheat as a small one; many contracts of wheat would have to be traded to achieve the same bang as a single S&P 500 contract. Table II-l shows, broken down by year and market, the dollar volatility of a single contract
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Dollar Volatilities (First Line) and Number of Contracts Equivalent to 10 New S&P 500s on 12/31/l 998 (Second Line) Broken Down by Market and Year
NAME 86PJNDM NY8EJNDEx WMB SP ,881 1183.50 24 825.50 45 348.13 81 82.81 342 235.3, 12, 842.88 44 487.3, 81 8M.38 53 413.50 88 108.00 283 84.38 338 213.25 133 288.05 105 275.83 102 143.55 ,811 113.W 1882 848.37 30 MD.75 88 342.81 83 82.38 344 302.34 84 887.81 4 1 801.88 57 881.58 43 388.88 73 184.20 154 9l.W 282 181.80 175 24421 ,,8 238.17 120 123.90 228 H3.75 249 128.73 220 74.25 332 ,883 1884 ,885 18W ,887 1888
823.80 1124.37 1125.25 1888.00 4188.50 2838.50 3d 25 25 14 7 10 452.80 83 43422 85 50.25 5e4 257.80 H O 534.88 53 387.00 13 481.44 58 818.55 48 MO.80 14, 44.13 843 178.80 158 200.80 141 205.0, 138 252.10 113 324.12 88 145.40 181 128.83 220 813.75 48 510.00 58 88.25 288 352.50 80 528.50 84 998.37 84 43(I.M 85 531.W 83 138.75 204 8&00 288 2,4.65 132 238.78 118 282.10 100 141.35 20, 211.25 105 558.00 51 438.84 84 12.38 382 2,422 103 358.75 78 478.00 80 668.75 42 572.25 33 115.25 182 88.15 4007 150.10 188 180.82 ,87 214.05 133 97.45 291 288.85 08 887.87 1888.82 285~.00 28 14 11 475.83 80 84.83 518 283.88 100 288.52 108 247.88 It4 387.8, 73 408.19 88 83.05 305 48.81 588 244.85 82 374.9, 78 377.03 75 84.80 335 186.72 144 74.83 318 97.85 280 388.58 77 48.12 511 204.10 138 311.88 75 532.31 85 428.94 84 588.50 48 143.50 198 38.12 725 232.00 122 258.87 H O 2B4.51 88 178.40 158 488.84 80 15.54 318 216.41 103 338.81 84 282.08 101 418.12 88 805.W 35 IW.80 148 50.15 500 252.60 H2 237.87 118 211.18 105 158.25 111
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