STATISTICS
by Enrico Donner, Ph.D.

A continuous data series for modeling a futures trading system can be created in a number of ways. Here's a new method that uses a percentage-based back-adjusted technique to ensure that profits and losses from a trading system are equivalent over time on a percentage basis.
As a rule, the results of any trading system are evaluated in terms of dollar returns. This means that a \$10,000 loss on the Standard & Poor's 500 futures contract is considered simply to be a \$10,000 loss, without taking into account the period in which the loss has occurred. As an example, in August 1982, the S&P was trading around 110 points (Figure 1), at a face value amount of \$55,000. At that time, assuming a single point of the S&P contract was the equivalent of \$500, a \$10,000 loss meant an 18.18% loss expressed in terms of percentage returns. On the other hand, 15 years later, in August 1997, the same \$10,000 loss would have turned out to be a 2.10% loss (the S&P was trading around 950 points, or at a \$475,000 face value). The 20-point loss that would have been defined as just a bad trade in 1997 would have destroyed your trading career in 1982.

#### DATA SERIES

When we analyze futures contracts, we usually find four kinds of data series:
• Single data series
• Nearest futures data series
• Perpetual (constant-forward) data series
The single data series is the most common data format. The term refers to a certain expiration month, and start from the beginning (with usually low volumes) to the last trade's date (Figure 2).

The nearest future data is simply the union of several single data series, one after the other. The day before the expiration date of the current contract is usually chosen as the starting date for the following contract. Some providers (such as FutureSource) refer to this data format as perpetual. The major problem that may occur using the nearest future data while testing trading systems is that we may get false results because of the spread between the two following months (Figure 3).

FIGURE 1: S&P 500 FUTURES. From this chart on the S&P 500 future contract, you can see that the face value of the contract has been dramatically increasing through the years.

Enrico Donner is president of Wolf Group Ltd., a British Virgin Islands umbrella fund. As a professional trader, he is currently managing his portfolios through a systematic approach. He specializes in market neutral strategies and synthetic securities trading techniques. He may be reached at donner@wolfgroup.ch.