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such guestimate may be obtained by computing a simple lag/lead serial correlation: A correlation is computed between the profit and loss for Trade i and the profit and loss for Trade i + I, with i ranging from 1 to n - 1 In the example, the serial correlation was 02120, not very high, but a lower number would be preferable An associated t-statistic may then be calculated along with a statistical significance for the correlation In the current case, these statistics reveal that if there really were no serial correlation in the population, a correlation as large as the one obtained from the sample would only occur in about 16% of such tests Serial dependence is a serious problem If there is a substantial amount of it, it would need to be compensated for by treating the sample as if it were smaller than it actually is.

Let s see what would happen to a cataloger if it were to adopt the database initiatives proposed in this chapter. To understand the change, let s start with a traditional successful cataloger. This company has already put its catalog on the Web. It sends out 2,000,000 books every 6 months, at an in-the-mail cost of $2 per book. The company gets an

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Another way to deal with the effect of serial dependence is to draw a random sample of trades from a larger sample of trades computed over a longer period of time This would also tend to make the sample of trades more representative of the population, What ifthe Markets Change When developing trading systems, a third assumption of the t-test may be inadvertently violated There are no precautions that can be taken to prevent it from happening or to compensate for its occurrence The reason is that the population from which the development or verification sample was drawn may be different from the population from which future trades may be taken This would happen if the market underwent some real structural or other change.

overall response rate of 4 percent. Included in the mailing are 500,000 new names. These produce responses from 20,000 rst-time buyers. We are going to trace the lifetime value of these 20,000 rst-time buyers over four rounds (2 years). The average order size on the rst buy is $120, of which the product and ful llment costs are 40 percent. In the second-round mailing 6 months later to these 20,000 rst-time buyers, the purchase rate is 40 percent and the average order size is $130. This rises over the next year to $150, and the purchase rate rises to 50 percent. Of the original 20,000 rst-time buyers in round 1, there are 1800 who are still buying 2 years later. Meanwhile, of course, the company has proceeded with additional prospect mailings that are producing identical charts every 6 months. The lifetime value of the original 20,000 rst-time buyers after the fourth round is $67.68, as shown in Table 12-1. Let us now assume that the cataloger has adopted many of the recommendations made in this chapter. The company has spent $1,200,000 on software for its Web site that does several signi cant things: Asks for customer pro les, capturing email names and customer preferences and demographics. This reaches 20 percent on the rst round and an additional 20 percent on each additional round. Table 12-1 LTV of Catalog First-Time Buyers

As mentioned before, the population of trades of a system operating on the S&P 500 before 1983 would be different from the population after that year since, in 1983, the options and futures started trading on the S&P 500 and the market changed This sort of thing can devastate any method of evaluating a trading system No matter how much a system is back-tested, if the market changes before trading begins, the trades will not be taken from the same market for which the system was developed and tested; the system will fall apart All systems, even currently profitable ones, will eventually succumb to market change Regardless of the market, change is inevitable It is just a question of when it will happen.

Despite this grim fact, the use of statistics to evaluate systems remains essential, because if the market does not change substantially shortly after trading of the system commences, or if the change is not sufficient to grossly affect the system s performance, then a reasonable estimate of expected probabilities and returns can be calculated,.