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countertrend models, a stop sometimes provides an extra edge. This tendency might result from trend-following models already having a trend detection element: Adding another detection or verification element (such as an entry on a stop) is redundant, offering no significant benefit; however, the addition of a limit order provides a countertrend element and a cheaper entry, thus enhancing performance. With countertrend models, the addition of a trend verification element provides something new to the system and, therefore, improves the results. Sometimes it is so beneficial that it compensates for the less favorable entry prices that normally occur when using stops. On a market-by-market basis, model-order combinations that were strongly profitable in both samples could be found for T-Bonds, JO-Year Notes, Japanese

Year 1 Customers Retention rate 312,886 Year 2 219,445

Summary of Countertrend Moving Average Entry M o d e l s B r o k e n Down by Order, Moving Average Type, Model, and Sample

Year 3 188,994

Yen, Deutschemark, Swiss Franc, Light Crude, Unleaded Gasoline, Coffee, Orange Juice, and Pork Bellies. Figure 6-2 depicts equity curves broken down by model and moving average combination; equity was averaged over order type. The best two models were the front-weighted triangular average support/resistance and the simple average support/resistance. The best support/resistance models performed remarkably better than any of the contrarian crossover models. There were three eras of distinct behavior: the beginning of the sample until October 1987, October 1987 until June 1991, and June 1991 through December 1998, the end of the sample. The worst performance was in the last period.

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On the basis of the equity curves in Figure 6-2, as well as others not shown, it is evident that the countertrend models were better in the past, while the trend-following models performed better in recent times. In-sample, the stop order was best for every model-average combination, and, out-of-sample, for three of the six (two combinations had no trades so were not considered); entry at the open was worst in all but two cases. The stop was generally superior to the limit order, in-sample; out-of-sample, the limit was only marginally better than the stop. CONCLUSION In general, the trend-following models in Tests 1 through 24 performed better than the countertrend models in Tests 25 through 48, with a number of exceptions discussed above. The best models apparently are those that combine both countertrend and trend-following elements. For example, attempting to buy on a retracement with a limit, after a moving average crossover or breakout, provides better results than other combinations. In the countertrend moving average models, those that have

7. (d ) The one with the highest value to the company, which is determined by multiplying the probability of purchase and the pro tability if purchased 8. (a) Revise your marketing program. 9. (a) Work to retain segment B and increase the LTV of segment A.

a trend-following element (eg. a stop) perform better Pure countertrend models and pure trend-following models do not fare as well Moreover, adding a trendfollowing filter to an already trend-following system does not seem beneficial, but may instead increase entry cost Traders should try combining one of these countertrend models with something like the ADX trend filter Although the ADX filter may not have helped breakouts (because, liethe stop, it represents another trend-following element added to an already trend-following model), in a countertrend model such an element may provide an edge As true with break outs, the limit order performed best, except when the stop was beneficial due to its trend filtering characteristics, The results suggest certain generalizations Sometimes a stop can provide enough benefit to overcome the extra transaction costs associated with it, although a limit order generally performs best because of its ability to reduce costs.

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While such a generalization might help guide a trader s choices, one has to watch for potential interactions within the moving average type-model-order combinations that may cause these generalizations to fail The variables interact: Although each variable may have its own characteristic effect, when put in combination with other variables, these effects may not maintain their integrity, but may change due to the coupling; this is demonstrated in the tests above Sometimes variables do maintain their integrity, but not always WHAT HAVE WE LEARNED When designing an entry model, try to effectively combine a countertrend element with a trend-following one This may be done in any number of ways, eg, buy on a short-term countertrend move when a longer-term trend is in progress; look for a breakout when a countertrend move is in progress; or apply a trend-following filter to a countertrend model.

Year 1 Customers Retention rate Spending rate Revenue Cost rate Costs Acquisition cost ($140) Total costs Pro t Discount rate NPV of pro t Cumulative NPV of pro t Lifetime value 400,000 62% $320 $128,000,000 65% $ 83,200,000 $ 56,000,000 $139,200,000 $11,200,000 1 $11,200,000 $11,200,000 $28 Year 2 248,000 70% $340 $84,320,000 63% $53,121,600 $53,121,600 $31,198,400 1.22 $25,572,459 $14,372,459 $35.93 Year 3 173,600 74% $350 $60,760,000 62% $37,671,200 $37,671,200 $23,088,800 1.35 $17,102,815 $31,475,274 $78.69