greater likelihood that a fester trading model will be selected. As the data shifts and that fester model is no longer good, the parameters may jump to a very slow model. This erratic pattem of shifting from fast to slow is indicative of too little test data.

Optimizing after a Major Move

When your sjstem fails to produce the right amount of profit from a major move, or when the stock markel takes an uncomfortably large plunge, it is natural to question whether the sjstem has the right parameters. Is the ttend fest enough? Is the stop-loss too close? This is the same process as retesting. if you have used enough data for your original tests, then it is very likely that the new tests wont change anything. If you make up new rules to fix this one problem, you are overfitting and accomplish nothing. If you have doubts about the test period, use more data rather than less. The new pattems will only give you a more realistic idea of the market risk than you had before. A major move that contains a price shock is a special situation discussed later in this chapter, as wen as Chapters 22 and 23.

COMPREHENSnT STUDIES6

A comprehensive shidy points out the robustness of a trading strategj. When a sjstem performs well in many markets using similar calculation intervals, it is fair to assume that the method is sound. If a technique works in the Swiss franc but not the Deutschemark, or in Euroyen but not Eurodollars, you must be able to understand the significant differences

6Iea.ler.-witLar

iicL as these .-li"Uldread tile basic matenalin . + 4 and the additional s;

before acc ting the method. Markets have individual characteristics that might justifj differences in performance; however, a strategj that can generate profits in a broad range of markets is robust. In addition to the shidies that follow. Chapter 5 ("Trend Systems") includes a section "Comparison of Major Trend Sjstems," which will be helpfiil to anyone interested in viewing the results of different sjstems side by side.

Colby and Meyers, in The Encyclopedia of TecAmical Market Indicators (Dow Jones Irwin, 1988), have given a very usefiil comparison of major market indicators simply by presenting all of their test results in a common form. Any one of the methods may have proved good or bad during the past 10 or 20 years, but taken as a whole, the consistency of various techniques adds to the robustness of that approach. For example, if one volumebased indicator was profitable, while four others generated consistent losses, you would need to understand why that one method worked before it could be used; the evidence of the four poor indicators aigues that the use of volume in this way is nol robust.

There are three previous, well-known comprehensive studies of moving average sjstems by Maxwell, Davis and Thiel, and Hochheimer. In addition, optimizations of Wilders Directional Movement and RSI will be found in the

sections that discuss those techniques. Although dated, these studies are very similar in structure to the way anyone would begin to test a trading idea, they emphasize different features of trading that were important to the authors and give us useful insight. By virtue of hindsight, we can see that along with completeness in one area often comes a deficiency in another. Davis and Thiel analyze the greatest variety of maikets, covering virtually all of the U.S. crops as well as cattle, eggs, and the soybean complex. They include about 5 years of data and use relatively fast moving averages (up to 10 dajs); they introduce variations in leadoriented plotting and in testing nonconsecutive dajs; the data used are only the closing prices. The results are clearly presented in both detail and summary, and yield generally good retums.

The authors R.E. Davis and CC. Thiel, Jr., present excellent credentials and experience in sjstems testing Their shidy of moving averages uses combinations of simple buy and sell signals, leading plots, and skips in the selection of sequential prices used (e.g., a skip of two uses every ottier price). They test a total of lOO combinations of the three factors:

A skip from 1 day (none) to 5 dajs (1 week)

An average of 5, 6, 7, 8, or lO dajs

A leap of 0 or 2 dajs

Markets tested were soybeans, bellies, catUe, cocoa, copper, com, eggs, soybean meal, oats, soybean oil, potatoes, rye, sugar, and wheat.

Ma-xwells shidy is extremely comprehensive but limited by its application to only pork bellies. His idea was to apply combinations of features and test the results. The first feature was the choice of ttend and included the possibilities of a simple mean, or a moving average of 3, 5, or 10 dajs, of either a conventional, averagemodified, or weighted tjpe. The second feature was the delay factor, used to improve timing of both entry or exit. Some of the possibilities were: (l) act without delay; (2) act if the signal condition persists for one additional day, (3) enter if the signal condition persists for 2 additional dajs, but liquidate without delay; and others. Combinations of two tjpes of moving averages and a delay factor were tested, with and without fixed or moving stops. With 10 tjpes of averages. 6 delay factors, and different stops, Ma.xwell has a lot of combinations to examine.

The study is then expanded to 3-factor sjstems with a list of 18 combinations of rules to generate 324 sjstems, of which the results of 285 are recorded, with 49°o profitable and 5 1 losers. The largest loss was generated by a sjstem with the rules:

1. Enter a new position when both the weighted 3-day and weighted lO-day moving averages cross the price-mean, as long as the signal condition persists for 2 additional days (buj if averages cross moving down, sell if up).

2. Liquidate positions when the 3-day average reverses its direction through the pricemean as long as it continues for 1 additional day.

3. No fixed stops are used.

The best profits in the 3- factor sjstem required both a 5-day average-modified and a lO-day weighted average to move across the price-mean, provided the 5-day average lagged behind the lOday. The current position was liquidated when the shorter-term average crossed the longer term. No fixed stops were used

Ma-xwells shidy represents a great amount of work and some simple and sound philosophy, but does not covei an adequate sampling of data to justify most of his conclusions. Conclusions were drawn based on a selected 50-day test period using May 72 pork bellies, leaving many questions regarding the success of this sjstem or any other sjstem when applied to this short test interval. Ma.xwell does test four other selected 50-day periods, but the reader cannoi know how these periods were chosen. Considering the effort in outlining a testing program and establishing rules, the extent of the sjstem testing is disappointing.

Comparing Methods of Calculation

Hochheimer:7 performs two interesting shidies: a comparison of three tjpes of moving average calculations and a test of the use of channels and crossovers. In the first analjsis, Hochheimer compares simple, exponentially

smoothed, and linearly weighted moving averages, tested on a good sampling of maricets (without financials and currencies, which did not exist during the 1970 through 1976 test period). The simple moving average and exponentially smoothed calculations are covered in Chapter 4 ("Trend Calculations"), and the linearly weighted refers to st -weigllting, in which integer values are used and each successive dsy is incremented by one, the most recent day having the highest weighting factor.

The rules that apply regardless of which calculation was performed, were:

1 . The trend calculation used the closing price only.

2. A buy signal occurred on an upward penetration of the moving average by the closing price; a sell signal occurred under the opposite conditions.

3. The model is alwajs in the maricet.

4. A trade cannot be executed when the days high and low prices are the same. It is assimied to be a locked-limil day

The test covered 7 years of data from 1970 through 1976 and moving average dajs (or equivalent smoothing constant converted as 2(dajs + 1)), which appear to range from 2 to 70. The results shown in Table 21-2 are interesting and logical, considering the rules. The longer frends (using more dajs) were consistently better than shorter ones, regardless of which technique was used. This would imply that the longer frends are more reliable. With a few exceptions, the best selection of dajs ranged from 40 to ""O.

A more carefiil look at the results proves interesting. During the 7 years of test data, soy-, beans had 728 trades using a 55-day simple moving average. That is more than lOO frades each year, one every 2 or 3 dajs. Hogs had 1,093 trades during the same period, and other commodities were similarly high. That seems to be an unusually large number of frades for the time interval used, indicating that there must have been many false frends that resulted in small losses; This is confirmed by the very low percentage of profitable trades, only 2l>o for soybeans. Nothing is indicated aboul transaction costs, and 728 trades costing $50 per trade in commissions and slippage would generate $36,400 in costs, about 1500 of the Net

Frank Hochheimer, "iVIoving Averages," and "Channels and Crossovers," in Technical Analjsis in Comjmodities J. Kauffiian (ed.) (John Wiley & Sons, NewYork, NY 1980).

TABLE21-2 Results of a Simple Moving Average Model

P/L shown m the table. The total soybean profit of $222,195 was equal to $305 per frade profit over the test period, a very good net retum and one that might have been unusual because of the exceptional volatility of the agricultural markets during the early 1970s

Comparing the Hochheimer results with the same sjstem applied to the 10 years fran 1986 to 1996, we see a very different picture (see Table 21-3). Many of the markets that produced laige profits now show losses. The currencies stand out as uniformly successfiiL however, the time periods for calculations varj from 40 to 75 dajs. The appearance of large calculation periods for the "Best Day- column indicates either a very successful long frend. as in the T-bonds. or an attempt to minimize the losses of markets without profitable frends.