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1、Monte-CarloEvaluationofTradingSystemsThisdocumentiscopyright2006TimothyMasters.Reproductioninanyformisforbiddenunlesswrittenpermissionisobtainedfromtheauthor.Thealgorithmsandcomputercodepresentedinthisdocumentareprovidedwithoutwarrantyofanysort.Errorsandomissionsareposs
2、ible,andtheauthordoesnotacceptliabilityforconsequencesrelatedtoerrorsoromissions.Anyoneusingthecontentsofthisdocumentdoessoathisorherownrisk.Beforeemployinganyofthisinformationinasituationinwhichriskoflossisinvolved,theusershouldconfirmtohisorherownsatisfactionthatsuchu
3、seisappropriate.Therearefewthingsthatatraderenjoysmorethandesigninganautomatedtradingsystem,backtestingit,andwatchingitperformwellonthebacktest.Thedreamsofrichestocomearedelightful.Unfortunately,itisalwayspossiblethatluckplayedmoreofaroleinthesystem’sperformancethaninhe
4、rentquality.Evenatrulyworthlesssystem,onethatmakesitspositiondecisionsbasedonrulesthatarelittlemorethanrollsofcelestialdice,canexperiencefortuitouspairingofpositionswithmarketmoves.Thisisespeciallytrueifthetraderhasexperimentedwithseveralcompetingsystemsandchosenthebest
5、.Itisvitalthatthetraderestimatetheprobabilitythataworthlesssystemcouldperformaswellasthecandidateperformed.Unlessonefindsthatthisprobabilityisverysmall,oneshouldbesuspiciousofthesystem.Onemethodoftestingtheperformanceistoassumethatthehypotheticalpopulationfromwhichthehi
6、storicalreturnsweredrawnhasatruemeanofzero,andthencomputetheprobabilitythatresultsasgoodasthoseobservedcouldhavearisenbyluck.Ifoneiswillingtoassumethatthereturnsareindependentdrawsfromanormaldistribution,theordinarysingle-samplet-testisappropriate.If,asismorereasonable,
7、normalitycannotbesafelyassumed,abootstraptestwilldoafairlydecentjobatestimatingthisprobability.Thereisasecond,oftensuperiorapproachtohandlingtheconceptofworthlessnessinatradingsystem.Ratherthandefiningworthlessnessasthereturnsbeingdrawnfromapopulationhavingameanreturnof
8、zero,wedefineworthlessnessasthesystem’spositiondecisionsbeingrandomlyplaced,unrelatedtosubsequentmarketmoves.T
