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The store gains a mailing list, and hopefully an email list, that has real value As we know from this book, the store can calculate the value of each customer who gets a card and determine whether this covers the cost of issuing the cards Surveys by the Carlson Marketing Group have shown consistently that while only 40 percent of consumers participate in loyalty programs, those who do participate have higher-than-average incomes, and, once they are involved, their behavior is affected by the cards Let s see what a loyalty program could do for a retail store chain Table 10-7 gives the picture of customers before the program is introduced It costs $32 to acquire a new customer who makes an average of 14 visits per year and spends $50 per visit The modest lifetime value of $300 in the rst year rises to $29.

The techniques of linear programming are designed for optimization problems involving linear cost or fitness functions, and linear constraints on the parameters

42 in the third year Let s now plan a loyalty program We are giving on-the-spot bene ts to members in order to modify their behavior We are seeking to Increase the number of visits per year Increase the spending per visit Increase the overall retention rate To get these bene ts, we are prepared to spend $5 per customer in the first year, with the amount increasing to $10 per customer for loyalists who have been with us into the third year Table 10-8 shows what could.

or input variables Linear programming is typically used to solve resource allocation problems In the world of trading, one use of linear programming might be to allocate capital among a set of investments to maximize net profit If riskadjusted profit is to be optimized, linear programming methods cannot be used: Risk-adjusted profit is not a linear function of the amount of capital allocated to each of the investments; in such instances, other techniques (eg, genetic algorithms) must be employed Linear programming methods are rarely useful in the development of trading systems They are mentioned here only to inform readers of their existence HOW TO FAIL WITH OPTIMIZATION Most traders do not seek failure, at least not consciously However, knowledge of the way failure is achieved can be of great benefit when seeking to avoid it.

Failure with an optimizer is easy to accomplish by following a few key rules First, be sure to use a small data sample when running sirindations: The smaller the sample, the greater the likelihood it will poorly represent the data on which the trading model will actually be traded Next, make sure the trading system has a large number of parameters and rules to optimize: For a given data sample, the greater the number of variables that must be estimated, the easier it will be to obtain spurious results It would also be beneficial to employ only a single sample on which to run tests; annoying out-of-sample data sets have no place in the rose-colored world of the ardent loser Finally, do avoid the headache of inferential statistics Follow these rules and failure is guaranteed.

Figure 11-4

What shape will failure take Most likely, system performance will look great in tests, but terrible in real-time trading Neural network developers call this phenomenon poor generalization ; traders are acquainted with it through the experience of margin calls and a serious loss of trading capital One consequence of such a failure-laden outcome is the formation of a popular misconception: that all optimization is dangerous and to be feared In actual fact, optimizers are not dangerous and not all optimization should be feared Only bad optimization is dangerous and frightening Optimization of large parameter sets on small samples, without out-of-sample tests or inferential statistics, is simply a bad practice that invites unhappy results for a variety of reasons Small Samples Consider the impact of small samples on the optimization process.

Skin cancer is the most common type of cancer in both men and women with approximately 12 million cases in the year 2001 Prostate cancer is the second most common in men (198,000), and breast cancer is the second in women (194,000) Lung cancer is still the leading cause of cancer deaths in both men and women in the United States Brain cancer and leukemia are the most common cancers in children and young adults Cancer development is usually a very slow process that often takes place over a period of years or even decades The length of time (latency) to cancer formation depends on a number of factors such as genetics; the amount, type, and length of time of carcinogenic exposure; detoxification capabilities; DNA repair capacity; immune system strength; as well as diet, lifestyle, and age.