In most cases, you will find that the shorter trend periods are unstable. Because consistent short-term trends are rare over long test intervals, such as 10 years, profitable results for a l5-day moving average are usually caused by one or two very large profits, or a sustained move in one direction. The choice of a short-term trend rarely produces profits in the future

The ease of new computerized testing platforms allows a convenient look at robustness. For the single moving average, 20 periods from 5 to lOO dajs were tested in steps of 5 dajs. The last column of Table 21-3 gives the number of profitable tests. Six of the 15 markets tested had no profitable results using any calculation period. Overall, 45% of all tests were profitable. The interest rates show very erratic results with a wide range of best dajs. even for the T-notes and T-bonds, which had a large number of profitable combinations. Only the currencies appear to be robust within a framework of moderate performance.

Channels and Crossovers

This Hochheimer study consisted of two tests. The first is a crossover of two simple moving averages. The shortterm average (fast frend) ranged from 3 to 25 dajs and the longterm from 5 to 50 dajs. The objective was to eliminate the whipsaws that were evident in the first study. The rules for this sjstem were:

1. Each moving average used closing prices only; the long-term number of dajs was ahvajs greater than the shortterm dajs.

TABLE 21-3 Results of a Simple MovinzAverase Model (1986-1996). $50 Transaction Costs

2. A buy signal occurred when the short-term average moved above the long-term average; a sell signal occurred when the short-term average moved below the longterm average.

3. The model was ahvajs in the market.

4. if the high and low prices of the day were equal, a locked-limit day was assumed and no execution occurred.

The use of a longer and shorter frend infroduces the ability to identify a frend bias in the maiket and trade only in that direction. Theoretically, this should apply to the interest rates and to the index maikets, which have either sustained frends or an upward bias. During ttie period of the original tests, it may be the seasonality of the agricultural markets that dominate ttie frend. Using two moving averages, the faster one can be considered a timing mechanism, while the slower one tracks the underljing market direction. In Table 21-4, the number of trades are less than the simple movmg average model, and the percentage of profitable trades was increased, the tjpe of results that indicate a more robust method.

Retesting

The testing performed to find the best set of parameters is never the last test, it is ahvajs important to monitor performance and compare the out-of-sample results with a new optimization to determine the success of the sjstem

rules and the testing process. A 1982 publication of Hochiieimer" provides a rare opportunity to see how the original tests fared and how parameter selection would have changed based on both additional data and changes in price pattems. We can do ttiis ourselves by testing 5- or lO-year periods and comparing the results of the same portfolio, From these results we can visualize an overall change in

TraukL HocUieuuer and Richard J Vaughu. O.JUputenredTradlue Techui,jieE 1£ rnll Lyuch CuiuoditieE. NewYork, 19

TABLE21 -4 Results of Two Simple Moving Average Crossovers

which the maiket moves. We may find that noise has increased, causmg a shift to longer ttends, or that risk is much greater and the rehims are proportionally smaller.

Crossovers Retested

In the 1982 update of the Crossover Sjstem optimization using data through 1979, it is interesting to note that 11 out of P maikets selected two moving average speeds either identical (in sis cases) or nearly identical to the previous test. Five of the remaining six tests showed new selections that traded slower than the previous test. Only gold resulted in a faster selection, but the original test in 1976 couldhavehadonlyoneyear of data.

Because the results of using the parameters selected in 1976 were not shown in the new study, their performance could not be assessed. Eleven cases, however, in which the new parameters were either identic or had very small changes, can be used as a conservative estimate. Their out-of-sample performance is shown in Table 21-5. If the parameters are not identical, the 1979 test must show results that are higher than the actual out-of sample would have been.

The first reaction to the update of the 1976 crossover test should be very positive. Ahnost identical parameters for 11 out of 17 products originally tested were selected. This means that the ttaders who used this sjstem were using the optimum parameters during the 3-year period fran 1977 through 1979. How did they do?

Table 21-6 is a comparison of ttie out-of-sample period 1977 through 1979. In the cases in which the parameter selection was slightly different, it must be assumed that the total performance, 1970 through 1979, was better than the performance using the original parameters. Therefore, the out-of-sample period should be at least as good as the results actually achieved. Total profits were $201,649, ttading one contract of each market.

Two additional factors should be considered. Although only 3 of the 11 showed losses, the fast nature of this sjstem results in very low profits per ttade in 4 of the remaining 8 maikets. This may not seem serious until the realities of trading are considered, where the exact execution price is rarely achieved. A ttend-following sjstem, with orders entered as inttaday stops, must alwajs allow for slippage caused by lack of liquidity and directly related to the size of the order being executed (see the discussion of liquidity in Chapter 18). In a fast maiket, this slippage can be laige, often hundreds of dollars (in contraci

TABLE21-5 Retesting of ttie Crossover System

value) away from ttie intended price. Even Maifcet-on-Close orders are subject to slippage. A buyer using a Close-Only order should expect to get the high of the closing range; a seller will get the low. in Table 21 -6, the fiirthest right column assumes a conservative slippage, one that should be included in any test program. In some cases, such as copper and bellies, the slippage is small and does not seem to impact on profits; even the large profits of cotton survive well. But in the fastest frading commodities, even the smallest slippage will severely reduce large profits, frequently turning them into losses. The final total shows that those small costs, when applied to every product, were greater than the profits. Instead of making a killing in the market these fraders netted a loss.

T/iides

l-Way Slippage (5% Daily Rartge)

•Benoj* (could hive been «-. 5 worse).

Crossover Sjstem, 1986 to 1996

Bringing this technique forward to current markets, seen in Table 21-7, there is again a tendency to select longer calculation periods, especially for the short-term frend; therefore, there has been a shift from the optimum frend speeds of 5 to 10 years earlier. The number of total trades has dropped significantly aaoss all markets, and may be attributed to more market noise and less definitive frends. Because the use of two frends greatly increases the chance of overfilling the data, it should not be surprising that all of the markets show profits for some combination of fast and slow moving averages. The last column, indicating the number of profitable combinations, is needed to get a picture of the robustness.

Taking a closer look at Table 21-7, it appears at first ttiat ttie S&P would be highly profitable; however, ttie profit of $194,750, drawdown of $63,650, and profitable frades is deceiving because only 8 of 120 combinations were profitable. As a group, the currencies and interest rates performed well, and the total of all profitable combinations was 56° o, showing that the technique rf using two moving averages is likely to be more robust than the 45S* given by the simple moving average. When making these sjstem comparisons, you must be cautious that these tests represent a comparable range of test speeds.