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I magmc that tomorrow is June 7, 1997. You need to decide whether or not to
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trade. If you do trade, you will enter at the open and exit at the close. You also need to decide how to enter the market: Should you go long or short As part of the decision process, you examine the behavior of the market on all June 7s that occurred within a look-back window of some number of years (e.g., 10). You tabulate the number of June 7s on which trading occurred, the average open-to-close change in price, and the percentage of time the market rallied or collapsed. Perhaps, in the past 10 years, there were eight instances when the market was open and June 7 was a trading day: of those instances. perhaps the market closed higher than it opened six times (75%) and the average change in price was 2.50 (a reasonable figure for the S&P 500). On the basis of this information, you place a trading order to enter long tomorrow at the open and to exit at the close. Tomorrow evening you repeat the procedure for June 8, the evening after that for June 9, and so on. This is one form of seasonal trading. Will you make a profit trading this way Will your trading at least be better than chance These are the questions that arise when discussing seasonal trading and that this chapter attempts to answer. WHAT IS SEASONALITY
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The term seasondity is used in many different ways by traders. Some construe seasonality as events that are strictly related the four seasons, e.g., the increased demand for heating oil in the winter or gasoline in the summer. Others have a more liberal interpretation that includes weather patterns and election cycles. Over the years, a number of articles in academic journals have demonstrated that stocks show larger returns around the first of each month. There has been some
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discussion of the so-called January Effect, in which stocks tend to rise in January. Hannula (1991) used seasonal cycles in his own trading, providing as an example a chart for EXABYTE stock with strong seasonal patterns marked. He also discussed another phenomenon, sometimes observed with seasonal patterns, in which the highs and lows occasionally invert, a pattern that we also have witnessed and that may be worth exploring. Other factors that influence various markets have definite dates of occurrence and so should induce seasonal effects; e.g., the dates for filing taxes occur at the same time every year. The legendary trader, Gann, apparently made heavy use of recurrent yearly behavior in his trading. Bernstein s (1995) home-study course on seasonality suggests trading off significant tops and bottoms, and when there has been consistent movement in a tradable over a number of years; this approach, as well as Hannula s, may tend to involve trades lasting several weeks to several months. In 1990, we first published the Calendar Effects Chart, a set of tables and a chart that show date-specific behavior in the S&P 500 cash index. The chart illustrates a general up-trend from January through September, and then an up and down decline until October 24. The market then, on average, bottoms, after which time it steeply rises until the end of the year. On a more detailed level, rapid gains seem to occur throughout most of January, the first half of April, and the first half of June. A peak can be seen on October 8, and a very steep decline that leads to a bottom on October 24. When the tables and chart for this publication were generated, extreme movements were clipped at +2 percent to prevent them from having undue influence on the results. Consequently, the steep decline in October, and the other patterns mentioned, cannot be attributed to events in specific years, for instance, the crash in 1987. For some dates, there were incredibly consistent patterns; e.g., if an entry occurred on the close of April 14 and the trade was exited one day later, over 90% of the time a small profit would have been made. Entry on May 6, with exit one day later, resulted in a profit 100% of the time, as did entry on July 13. The market declined 90% of the time from October 18 to 19, and 89% of the time from October 16 to 17. Although the crash may have involved a much greater than normal amount of movement, the presence of a decline at the time when the crash occurred was not at all unexpected. In an attempt to capture highprobability, short-term movements, the Calendar Effects Chart could have been used to enter trades that last one or two days. For example, such a methodology would have caused a trader to go short at the close on October 16 and exit on October 19, thus capturing the crash. The data contained in this publication could also have been used to help maintain positions during periods of steep ascent or decline. There have been other studies indicating the presence of strong seasonal effects in the market that can be exploited for profitable trading. An investigation we conducted (Katz and McCormick, April 1997) found that short-term seasonal behavior could be used to trade the S&P 500: The system used fairly fast moving average
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crossovers that were computed on seasonally anticipated prices. Because the anticipated prices could be computed at least one year ahead, lag in the moving average crossover was easily compensated for with a displacement that enabled the system to take trades at crossovers occurring several days after the fact. The trades taken by the system typically lasted between 7 and 8 days, a fairly short-term seasonal trading model. The system was profitable: It pulled an astonishing $329,900 from the S&P 500 between January 3.1986, and November 8, 1996. The test did not include transaction costs, but even with $15 round-turn commissions and $75 per trade slippage, a profit of $298,310 (about a 10% reduction) resulted. The return on account was 732%, not annualized; assuming fixed contract trading, this amounted to over 70% per year, annualized, on a constant one-contract, no-reinvestment basis. There were 351 trades taken, of which 60% were winners. Both the longs and shorts were profitable. The average trade pulled $939 from the market-not bad for a simple, seasonality-based trading model, Findings like these suggest there are strong seasonal patterns in the markets producing inefficiencies that can be exploited by traders, and that are worthy of investigation. For our current purposes, seasonaliry is defined as cyclic or recurrent phenomena that are consistently linked to the calendar. The term is being used in a broad sense to mean market behavior related to the time of the year or to particular dates, including anniversaries of critical events (e.g., the October 16, 1987, crash). In short, seasonality is being construed as calendar-related cyclic phenomena. It should be made clear, however, that while all seasonality is cyclic, not all cycles are seasonal. GENERATING SEASONAL ENTRIES There are many ways to time entries using seasonal rhythms. Two basic approaches will be examined: momentum and crossover. To calculate momentum, a series of price changes is computed and centered smoothing (a smoothing that induces no delays or phase shifts, in this case, a centered triangular moving average) is applied. Each price change (or difference) in the series of price changes is then normalized: It is divided by the 50.day average true range. For every bar, the date is determined. Instances of the same date are then found in the past (or perhaps future). For each such instance, the momentum is examined. The average of the momentums becomes the value placed in the seasonal momentum series for the current bar. The seasonal momentum series measures the expected rate of change (or momentum) in prices at a given time. It is based on the historical movement of prices on the specified date in different years. The number in the seasonal momentum series for the current bar is determined only by events about 1 year or more ago. This is why it is possible to use the centered moving average and other techniques that look ahead in time, relative to the bar bei~ng considered. Entries are taken as follows: When the seasonal momentum crosses above some positive threshold, a buy is posted. When the
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momentum crosses below some negative threshold, a sell is posted. Buying or selling can happen on any of the standard three orders: at open, on limit, or on stop. Entries may also be generated by computing the price differences, normalizing them, applying an integration or summing procedure to the series (to obtain a kind of pseudo-price series, based on previous instances of each date), and then applying a moving average crossover model to the series. Because the value at any bar in the series is determined only by bars that are about 1 year old or older, the delay in the crossovers can be compensated for by simply looking ahead a small number of bars. Both of the methods described above arc somewhat adaprive in nature; i.e., they do not require specific information about which dates a buy or sell order should be placed. The adaptive quality of the aforementioned methods is important since different markets respond to seasonal influences in different ways, a fact that logic, as well as our earlier research, supports. In the current study, several rules for handling confirmations and inversions are also tested to determine whether better results can be obtained over the basic models. Confirmarion means additional data is available that supports the signals produced by the model. For example, suppose a model generated a buy signal for a given bar. If everything is behaving as it should, the market should be forming a bottom around the time of the buy. If, however, the market is forming a top, the buy signal might be suspect, in that the market may not be adhering to its typical seasonal timing. When such apparently contradictory circumstances exist, it would be helpful to have additional criteria to use in deciding whether to act upon the signal, in determining if it is correct. The crossover-with-con~rmation model implements the crossover model with an additional rule that must be satisfied before the signal to buy or sell can be acted upon: If a buy signal is issued, the Slow %K on the signal bar must be less than 25%, meaning the market is at or near the bottom of its recent range. If a sell signal is issued, Slow %K must be greater than 75%, indicating that the market is at or near the top of its range, as would be expected if following its characteristic seasonal behavior. The conjinnation-undinversion model adds yet another element: If a buy signal is issued by the basic model, and the market is near the top of its range (Slow %K greater than 75%), then it is assumed that an inversion has occurred and, instead of issuing a buy signal, a sell signal is posted. If a sell signal is generated, but the market is near the bottom of its range (Slow %K less than 25%), a buy signal is issued. CHARACTERISTICS OF SEASONAL ENTRIES Consider trading a simple moving average crossover system. Such a system is usually good at capturing trends, but it lags the market and experiences frequent whipsaws. If slower moving averages are used, the whipsaws can be avoided, but the lag is made worse. Now add seasonality to the equation, The trend-following moving average system is applied, not to a series of prices, but to a
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series that captures the seasonal ebb and flow of the market. Then compute the seasonal series so it represents that ebb and flow, as it will be several days from now-just far enough ahead to cancel out the annoying lag! The result: A system without lag (despite the use of slow, smooth, moving averages) that follows seasonal trends. The ability to remove lag in this way stems from one of the characteristics of seasonality: Seasonal patterns can be estimated far in advance. In other words, seasonality-based models are predictive, as opposed to merely responsive. Since seasonality-based models are predictive, and allow turning points to be identified before their occurrence, seasonal-based trading lends itself to countertrend trading styles. Moreover, because predictions can be made far in advance, very high quality smoothing can be applied. Therefore, the kind of whipsaw trading encountered in responsive models is reduced or eliminated. Another nice characteristic of seasonality is the ability to know days, weeks, months, or even years in advance when trades will occur--certainly a convenience. Seasonality also has a downside. The degree to which any given market may be predicted using a seasonal model may be poor. Although there may be few whipsaws, the typical trade may not be very profitable or likely to win. If inversions do occur, but the trading model being used was not designed to take them into account, sharp losses could be experienced because the trader could end up going short at an exact bottom, or long at an exact top. The extent to which seasonal models are predictive and useful and the possibility that inversion phenomena do exist and need to be considered are questions for empirical study.
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