Channels

The next model relies on trends but are very different from the moving averages used in the previous optimizations. Originally called a price channel, it is now more familiar as an N-day breakout, the penetration of the high and low of the past M dajs. The pendration, which causes a buj or sell signal, occurs if the closing price penetrates the high-low band.

Table 21-8 shows the results of the interday test. A common variation of this method is to buy when the intraday high penetrates the upper band; however, this can cause ambiguities when both the high and low of the daj exceed both bands. It is not possible to know which one occurred first. Intuitively, the closing price is expected to be a more reliable indicator of direction than the intraday high or low.

TABLE21 -7 Results of a Two-Moving Average Crossover Model (1986-1996), $50 Transaaion Costs*

TABLE 21-8 Results of Interday Closing Price Channel

In the original tests shown in Table 21-8, the channel method has much lower profits and proportionally greater risk than the crossovers; results tend to be more erratic as well This method is clearly better than the single moving average, with more consistent profits, fewer trades, greater reliability, and even smaller drawdowns.

Testing the breakout shategj for 1986 to 1996 (Table 21-9), we see a different pattern than the update of the moving average method. The number of trades have dropped, the maximum drawdown has increased, while only one market showed all

TABLE21-9 Results of an N-Day Breakout (1986-1996 ),$50 Transaction Costs*

mStoiOOdinittpsoTS

Tescdmbnin 1987 or 1988

losses. Of the 300 total tests, 57°o were profitable, greater than either the moving average or crossover methods.

Modified Three-Crossover Model

The use of one or more slow-moving averages may result in a buy or sell signal at a time when the prices are actually moving opposite to the position that is about to be entered. This may happen when:

1. The rules consider the crossover of the moving average, rather than a penetration of the price.

2. The change in a simple moving average value based on the new price is less than the diange in the oldest price that was dropped.

For example, if a long signal occurs and the oldest price showed a decline of 50 points while todsys price declined 40 points, the new moving average value will rise by the difference, +10, divided by the number of dsjs in the moving average. This may also occur using exponential smoothing under the apecial conditions

By using a third, fester-moving average, the slope can be used as a confirmation of direction to avoid entry into a trade that is going the wrong way. This filter can be added to any moving average or multiple moving average sjstem with the following rule:

Do not enter a new long (or short) position unless the slope of the confirming moving average (the change in the moving average value from the prior dsy to todsy) was up (or down).

The speed of this third, confirming moving average only makes sense if it is equal to or fester than the fester of the frends used in the Crossover Sjstem.

Test Results

Fortunately, the results of both the Crossover Sjstem as well as the Modified ThreeCrossover Sjstem were available for the same commodities and the same years. Because the crossovers used in the latter model are exactly those of the first sjstem, the comparison will show whether the confirming feature improved overall results. From the 22 markets tested, plj-wood was removed because its poor results on both sjstems tended to distort the comparison. The important statistics are shown in Table 21-10.

The difference in using the Modified Three-Crossover Sjstem versus the simpler

Crossover System are:

Average change in profits -15.3%

Average change in equity drop -15.5%

Average change in percentage of profitable trades .9%

Average change in number of trades -26.1%

A dechne in profits equal to a decline in equity drop (or risk) is the same as using the original Crossover Sjstem with a 15.4>o smaller investment. The percentage of profitable trades increased negligibly, indicating that the confirmation filter did not eliminate more losing trades as was expected. The last point, however, shows a larger decline in the total number of trades, indicating that the profit per trade has increased. The new filter appears to catch the entries at a better point, and eliminate some trades with smaller profits. This tjpe of improvement means that there is more latitude for trading error,

TABLE21-10 Comparison of Sjstans 1970-1979

such as slippage. Although the overall profile of the Modified Three-Crossover is not much better than the Crossover Sjstem, it would be the preferred choice based on this information

4-9-18 Crossover Model Results

This model, using the same rules as the Modified Three-Crossover Sjstem, was well known before Hochheimers studies. It can be assumed that the selection of 4, 9, and 18 dsjs was a conscious effort to be slightly shead of the 5, 10, and 20 dsjs frequently used in moving average sjstems. it is likely that the sjstem was not developed by extensive testing, since all maricets are traded with these same apeeds. As simple as it seems, there are a few very sound conc ts in this approach:

1. Each moving average is twice the speed of the prior, enhancing their independence in recognizing different trends.

2. They are slightly faster than the conventional 5-, 10-, and 20-dsy moving averages.