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50 Markowitz and Xu discuss several other correction formulas for cases that have weaker restrictions. The procedure for estimating H is considerably more complicated. Conclusion This chapter has described three approaches to backtesting trading systems: 1. The standard in-sample/out-of-sample data set approach. 2. The leave-one-out technique. 3. The Markowitz/Xu correction formula. The purpose of a rigorous and intellectually honest backtesting procedure is to produce good estimates of future performance. Because intuitions about performance are likely to be poorly grounded and therefore incorrect, only a disinterested, objective approach will yield good estimates. Disciplined use of tools such as leave-one-out testing and the Markowitz/Xu data mining correction will, in the end, prevent false optimism and lead to higher profits. References Kaufmann, Perry and Schwager, Jack D., Smarter Trading: Improving Performance in Changing Markets, McGraw-Hill, 1995. Murphy, John J., Technical Analysis ofthe Futures Markets: A Comprehensive Guide to Trading Methods and Applications, Prentice Hall Trade, 1987. Rotella, Robert P., The Elements of Successful Trading: Developing Your Comprehensive Strategy Through Psychology, Money Management, and Trading Methods, Prentice Hall Trade, 1992. Schwager, Jack D., Technical Analysis, John Wiley & Sons, 1995. Endnotes 1. Two books published by the New York Institute of Finance, one by Robert P. Rotella titled The Elements ofSuccessful Trading and the other by John Murphy titled Technical Analysis ofFutures Markets, provide rudimentary information about backtesting. Many of the heuristics in these two books are formalized in this chapter. Perry Kaufmans Smarter Trading: Improving Performance in Changing Markets discusses the intuitions behind backtesting for the nonacademic reader. Jack Schwagers well-known Technical Analysis discusses some of the pitfalls that are associated with poor backtesting methodology. 2. The discussion of the Markowitz/Xu data mining correction in this chapter summarizes an original article by Harry M. Markowitz and Gan Lin Xu which was published in the Fall 1994 issue of the Journal ofPortfolio Management. This at tide contains the derivation for the data mining correction formula. In addition, it has an interesting discussion on holdout periods (a synonym for out-of-sample data sets).
Performance evaluation is critical to the design, development, and monitoring of a trading system. Traders and investors alike need to assess their systems true worth to build trading confidence. The tools presented in this chapter allow traders to implement a process that systematically and objectively evaluates trading performance. The rationale for a detailed evaluation is simple-every trader has his or her own idea as to what makes a great trading system. A system that fits one person may not be appropriate for another. It is not uncommon to hear two traders talk about the same trading system that one loves and the other hates. This difference in opinions is most likely attributed to their individual trading style. One trader may be aggressive, while the other is conservative. Just because a system is historically profitable, does not guarantee that every trader will follow the system. There are plenty of trading systems to choose from; the object is to find the one that best matches the personality of the trader. Only the individual trader can make the final decision as to the worth of a trading system. Does the trader have the reward/risk profile to trade the system? No matter how profitable a system appears, if a trader does not have the intestinal fortitude to follow it, he or she should look for another system to trade. Throughout this chapter, we will refer to various trading systems to help in the /evaluation process. A trading system is defined as a methodology that buys or sells a / commodity/security for a specific reason. It can be 100 percent mechanical or totally intuitive; as long as it generates buy and sell signals, there is enough information to 1 evaluate. A sample trade-by-trade report as outlined in Table 9.1 contains the key data \ necessary to perform a detailed evaluation. In general, the data consists of the entry \ and exit date/price information. The majority of popular technical analysis software \ packages as well as brokerage statements contain this information. With this basic xkta in hand, we are ready to evaluate the trading performance of a system. The Evaluation Process The evaluation process has several parts. Each part examines trading performance from a different perspective by using specific evaluation tools that are explained throughout Evaluating Trading Performance David Stendahl
Table 9.1 Trade-by-trade report  87 06/20/96 $670,390 1 $6,004,710 69.39% 07/03/96 $677.640 $3.505.750 0.68% ($2.649.280) 71.41% | 07/09/96 08/21/96 | $660,970 $670,670 | $4,698,900 | 0.92% | $6,194,640 ($23,614,630) | 20.78% 95.07% | | 07/18/96 08/21/96 | $641.430 $670,670 | $14,214,880 | 2.77% | $15,710,620 ($9,277,350) | 62.87% 94.11% | | 10/30/96 11/27/96 | $711,550 $762,160 | $24,622,070 | 4.80% | $29,146,950 ($2,576,230) | 91.88% 85.82% | | 12/10/96 01/23/97 | $759,720 $733,950 | $11,775,010 | 2.30% | $21,296,510 ($17,546,610) | 54.83% 75.55% | | 04/02/97 05/16/97 | $764,570 $838,270 | $35,866,900 | 6.99% | $42,812,170 ($11,751,310) | 78.46% 87.32% | | 04/15/97 05/16/97 | $757,070 $838,270 | $39,519,400 | 7.71% | $46,464,670 ($2,230,460) | 95 42% 85.79% | | 04/15/97 05/16/97 | $757,070 $838,270 | $39,519,400 | 7.71% | $46,464,670 ($2,230,460) | 95.42% 85.79% | 95 { t | 07/02/97 07/09/97 | $904,300 $920,980 | $8,098,160 | 1 58% | $14,955,770 ($1,120,100) | 93 03% 57 50% |
the chapter. Certain tools are easily calculated while others are more complex. The combination of all of these tools will provide for a complete and thorough system evaluation. To assist in the evaluation process, we will use evaluation software packages co-developed by RINA Systems, Inc. and Omega Research Portfolio Maximizer. An evaluation process begins with a general overview of your systems performance. Once complete we progressively work toward more specific evaluation tools to determine the systems true trading characteristics. The entire evaluation process comprises of the following separate procedures: System analysis. Profit ratios. Return figures. Sliding and rolling summaries. Equity curve analysis. Total trades. Outlier trades. Drawdown/run-up. Consecutive trades. Time analysis.
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