[ ?) >---yJi Marginally successlul

This will give you a better understanding of how each value affects the total picture and allow you a way to visualize the robustness of each variable- Using a Invariable example, a range of fast and slow moving averages were tested for the Swiss franc based on a crossover strategj. The results of the slow moving averages are plotted for all combinations of the fast moving average in Figure 21-7; the fast average is shown in Figure 21,7b.

The individual test results are shown as circles above the slow or fast moving average period in Figure 21-7 For the slow moving average, it is clear that profits are greatest when 50 and 60 dajs are used for the calculation period; however, it is not as clear which of those two values is the best choice. The 60-day moving average posted profits higher than the 50-day average, but also showed profits below the lowest 50-day retums. A closer look shows that the average rdums of the moving averages over those periods is about the same, but the 60-day moving average has a higher variance. Normally, the best choice is the result that is most stable (the 50-day calculation), although in this example we must be cautious that the small number of tests do not make the 50-day, results look stable just by chance.

The results of the faster moving average, seen in Figure 2 1 ~b, show much greater variance. The ""-period results have a very wide range including the highest retums however, the averages of the th through 15th periods are very similar. With variance in mind, the 13-day calculation seems to be the best candidate. We can be confident that this method is robust, because nearly all combinations of fast and slow moving averages gave profitable returns, net of a $50 commission.

Standardizing Test Results

When testing a single sjstem, the results of one set of parameters can easily be compared with other sets because the test period, commissions, and other basic values are all the same. However, over time you will test many different sjstems and variations of those sjstems, and you will want to compare them to decide which strategj is best This requires some advanced planning.

Standardizing test results is the best way to increase the usefulness of extensive testing. This should include:

FIGURE 21-6 Three-dimensional map of crossover model

Swiss franc. 1986-1996

Slow moving average

1. Annualizing all values. Tests that you perfonn 6 months or 1 year apart are likely to use different time periods. Annualizing the results will make comparisons easier.

2. Rid; adjusting. A profit of $10,000 with a drawdown of $5,000 is effectively the same as a profit of $20,000 and a drawdown of $10,000, given adequate reserves. Expressing the results as profits divided by rid; can be useful.

3. Adjusting for standard error The important difference between two teds that yield the same results, one with 2 trades and one with 50 trades, is that the one with only 2 trades is a less reliable result. If both posted 50°o profitable trades, another losing trade would make the reliability of the second test drop to 49° o, while the firsl case would drop to . Instead, results should be presented at the same confidence level, which means subtracting the standard error from the current result. Analyds developing relatively slow trading sjstems will find that this procedure has a startling efiect on expectations.

Averaging the Results

Because the testing process is computer dependent, it is desirable to make the selection of the best parameters automatic. This can usually be done effectively by averaging either the profits or other results displayed in the test map In the case of a moving average sjstem first determine how broad the area of success must be so that it is not a spike, an anomaly in the results. For example, the results of a 3-, 4-, 5-, and 6-day test show profits of 1,000, 8,000, 3,000, and 4,000, respectively. The 4-day case is clearly a profit spike and could be minimized by replacing its value with the average of the three other values or by the inte olated value of the two adjacent points (Figure 21-8). In general, the substitution process in which PLi replaces PLi.

FIGURE2I- Visualizing the performance of multiple paramders. (a) The slow moving aver, age peaks at 50-60 dajs (b) The fast average may he best at any value fran 7 through 9 5.

Alternate ditplay of - !»

Swies franc 1986-1996

average

FIGURE 21-8 Replacing a spike with the average A or an interpolation 8. 9r-