We begin our evaluation of total trade analysis by comparing the results of two systems. Superficially, both systems in Table 9.5 appear to be the same, with identical figures for net profit, total number of trades, and average profit per trade. Beneath the surface, however, lies a different story.

The numbers in Table 9.5 measure the volatility of the average trade. The greater the volatility the less stable the average. Both systems have the same average $2,000 profit per trade. The trades associated with System A fluctuate in a tight range around its average. Range is measured here by the standard deviation of the trades profits. Based on its standard deviation of $714, the profit range for System A is from $1,286 ($2,000 - $714) to $2,714 ($2,000 + $714). System on the other hand has a standard deviation of $5,335, which translates into an average trade that ranges between $7,335 and ($3,335). These are dramatically different numbers for systems that appear to be the same. The net result: System A is the more stable system.

The systems can also be evaluated based on their coefficient of variations. This statistical measure is similar to standard deviation; the smaller the figure, the more stable the trades. Coefficient of variation (CV) is calculated in a percentage format allowing for easy interpretation between systems. CV is the standard deviation of a variable (e.g., profit per trade) divided by the average value of the variable:

CV= 100% x Standard Deviation/Simple Average

Look for systems with coefficient of variations of 200 percent or less. Numbers larger than this indicate instability and should raise your concern.

It is easy to get lost in these numbers. Sometimes it is best to review these statistical results in a graphic format. Figure 9.6 plots individual profits per trade from a new hypothetical system. Notice the clustering of data points as trades deviate little from the average. The only exceptions were trades 92, 93, and 94. These trades are considered to be outliers, to be discussed in greater detail in the next section. Despite these outlier trades, the standard deviation and coefficient of variation for this trading system were $8,761.50 and 162.30 percent respectively (see Table 9.6). These low values reflect a system that is extremely stable in relation to its average. This high degree of stability breeds trading confidence.

table 9.5 total trade comparison

System A System

1 qNSP 460000-Daily (08/19/85-07/18/97)

Table 9.6 total trade analysis

Total Trade Analysis

Number of total trades

Average trade

1 Std. Deviation (STDEV)

Run-up

Maximum Run-up

Average Run-up

1 Std. Deviation (STDEV)

Drawdown

Maximum Drawdown

Average Drawdown

1 Std. Deviation (STDEV)

Reward/Risk Ratios

Largest Loss Ratio Adj. Largest Loss Ratio

$5,398.49 $8,761.50

$46,464.67 $9,079.35 $9,036.06

($23,614.63) ($4,544.12) $4,527.92

52.73 44.67

Total stopped trades Avg. trade ± 1 STDEV Coefficient of variation

Max. Run-up Date Avg. trade ± 1 STDEV Coefficient of variation

Max. Drawdown Date Avg. trade ± 1 STDEV Coefficient of variation

Max. Drawdown Ratio Adj. Max. Drawdown Ratio

$14,159.99 / ($3,31 162.30%

5/15/97 $18,115.44 / $43.2 99.52%

7/16/96 ($16.19) / 99.64%

21.72 18.40

System

figure 9.6 profits per trade.

Table 9.6 also lists the standard deviation and coefficient of variation values for the systems run-up and drawdown calculation, to be explained in greater detail in the next few sections.

Oudier Trades

This section centers on outlier trades. Outliers have some unusual property, such as excessive profit or loss (see Box 5). The amount of excess is measured by the number of standard deviations away from the typical (average) value. For example, if a systems average profit is $200 per trade and the standard deviation is $50, then a trade that produces $400 profit would be ((400 - 200)/ 50) or 4 standard deviations from average.

Outliers are usually considered to be 3 or more standard deviations from average. Essentially, they are aberrations that cause system results to be unfairly positively or negatively biased. By removing outlier trades from the evaluation process, a new net profit figure can be calculated. This new select net profit figure, devoid of all aberrations, may offer a cleaner, more realistic trading perspective. Obviously, trend-following systems designed to accept numerous small losses to capture the infrequent big move rely on outliers to be profitable. Therefore, whether or not it is better to remove outliers requires some thought.

In general, systems that are heavily dependent on outlier trades have artificially inflated or deflated net profit results. Since outlier trades generally do not reoccur on a regular basis, they should be removed to present a more realistic trading perspective. The goal is to find a system with a select (nonoutlier) net profit figure worthy of trading.

A trading system with a few outlier trades is shown in Table 9.7. In this example, the system had a few positive outlier trades that boosted system profits. Although the systems select net profit figure is still presentable, it does make a trader think twice about the system. Is the system worth trading if it only generates $408,635 in profit without outlier trades as compared with its original $526,610? Only the individual trader can answer that question.

BOX 5

OUTLIER TRADES Select net profit: Net profit minus outlier trades.

Posidve oudiers: Trade values that exceed the average trade by plus three (3) standard deviations.

Negative oudiers: Trade values that are less than the average trade by three (3) standard deviations.