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1、Monte-CarloEvaluationofTradingSystemsThisdocumentiscopyright2006TimothyMasters.Reproductioninanyformisforbiddenunlesswrittenpermissionisobtainedfromtheauthor.Thealgorithmsandcomputercodepresentedinthisdocumentareprovidedwithoutwarrantyofanysort.Errorsandomissionsarepossible,andtheauthordoe
2、snotacceptliabilityforconsequencesrelatedtoerrorsoromissions.Anyoneusingthecontentsofthisdocumentdoessoathisorherownrisk.Beforeemployinganyofthisinformationinasituationinwhichriskoflossisinvolved,theusershouldconfirmtohisorherownsatisfactionthatsuchuseisappropriate.Therearefewthingsthatatr
3、aderenjoysmorethandesigninganautomatedtradingsystem,backtestingit,andwatchingitperformwellonthebacktest.Thedreamsofrichestocomearedelightful.Unfortunately,itisalwayspossiblethatluckplayedmoreofaroleinthesystem’sperformancethaninherentquality.Evenatrulyworthlesssystem,onethatmakesitspositio
4、ndecisionsbasedonrulesthatarelittlemorethanrollsofcelestialdice,canexperiencefortuitouspairingofpositionswithmarketmoves.Thisisespeciallytrueifthetraderhasexperimentedwithseveralcompetingsystemsandchosenthebest.Itisvitalthatthetraderestimatetheprobabilitythataworthlesssystemcouldperformasw
5、ellasthecandidateperformed.Unlessonefindsthatthisprobabilityisverysmall,oneshouldbesuspiciousofthesystem.Onemethodoftestingtheperformanceistoassumethatthehypotheticalpopulationfromwhichthehistoricalreturnsweredrawnhasatruemeanofzero,andthencomputetheprobabilitythatresultsasgoodasthoseobser
6、vedcouldhavearisenbyluck.Ifoneiswillingtoassumethatthereturnsareindependentdrawsfromanormaldistribution,theordinarysingle-samplet-testisappropriate.If,asismorereasonable,normalitycannotbesafelyassumed,abootstraptestwilldoafairlydecentjobatestimatingthisprobability.Thereisasecond,oftensuper
7、iorapproachtohandlingtheconceptofworthlessnessinatradingsystem.Ratherthandefiningworthlessnessasthereturnsbeingdrawnfromapopulationhavingameanreturnofzero,wedefineworthlessnessasthesystem’spositiondecisionsbeingrandomlyplaced,unrelatedtosubsequentmarketmoves.T
