Post on 18-Dec-2015
description
GeneticAlgorithmsandInvestmentStrategyDevelopment
MichaelDworkis,DarienHuang
FacultyMentor:Dr.FranklinAllen
May12,2008
WhartonResearchScholars
TheWhartonSchool,UniversityofPennsylvania
Abstract:Theaimof thispaper is to investigate theuseofgeneticalgorithms in investment strategydevelopment.Thiswork followsandsupportsFranklinAllenandRistoKarljalainenspreviouswork1 inthe field, aswell adding new insight into further applications of themethodology. The paper firstexamines the capabilitiesof thealgorithmdesigned inAllenandKarjalainensworkbyusinghumandeveloped (rather than markethistorical) datasets to determine whether the algorithm can detectsimplesignals; theresultsshow that thealgorithm isquitecapableofsuchbasic tasks.Next, theS&P500 test performed inAllen and Karjalainens originalworkwas confirmed. Then, experimentswereconductedinemergingequitymarkets,aswellascommoditiesmarketswitharangeoffundamentalaswellas technical indicators. The resultsgenerallyshownosignificantpositiveexcess returnsaboveabuyandhold strategy; speculations for possible reasons are discussed. In addition, suggestions forfutureresearchendeavorsarepresented.WewouldliketothankDr.FranklinAllenandDr.RistoKarjalainenfortheirimmensehelpandguidancethroughoutourresearchprocess.WethankDr.MartinAsherandtheWhartonResearchScholarsprogramforhelpingtomakethisresearchpossible.Alltheviewsexpressedinthispaperaresolelyattributedtotheauthorsanddonotinanywayrepresentanyauthorscitedoranyemployersoftheauthors.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,2
OutlineI. Motivation&IntroductiontoGA (p.3)
ExperimentMotivation Investmentanalysisprocess Limitationsintraditionalinvestmentstrategydevelopmentprocess IntroductiontoGeneticAlgorithmsandimplementationininvestmentstrategydevelopment PotentialstrengthsandweaknessesofGeneticAlgorithmsforinvestmentstrategydevelopment Investing:ArtorScience? Programminglanguagechoice Previousworkongeneticalgorithmuseinfinance
II. Perfectforesightexperiment (9)
ExperimentMotivation Inputselection Implementation Results&Discussion
III. S&P500experiment (13)
ExperimentMotivation Inputselection Implementation Results&Discussion
IV. EmergingMarketsExperiment:ChinaASharesMarket (15)
ExperimentMotivation Inputselection Implementation Results&Discussion
V. GasolinePredictionExperiment (19)
ExperimentMotivation Inputselection Implementation Results&Discussion
VI. Conclusions (24)
Experimentresultdiscussion SuggestedFutureExperimentsandSpeculations
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,3
I. Motivation&IntroductiontoGeneticAlgorithms
ExperimentMotivation:Marketparticipantsareconstantlysearchingfornew investmentstrategiesto
earnexcessreturns (definedasreturnsaboveabenchmarkmeasure) infinancialmarkets. Investment
strategies can be based onmodels as simple as buying stockswith low price/earnings ratios, or as
complex as trading a levered derivatives portfolio based on the historical correlations between a
portfoliooffixedincomesecurities,whiledynamicallyhedging.Strategiesproventoyieldexcessreturns
can be exploited in the market to earn money. The development of new successful investment
strategies,orthe improvementofmethodologiestoproducenewsuccessful investmentstrategiescan
beaprofitablebusinessventure.
Howare investment strategiesdeveloped?The answer can vary across asset classes. In the caseof
stocks and corporate bonds, traditional fundamental analysis entails analyzing the corporation, the
quality of the assets, and the specifics of the securities issued2. Such analysis is usually carried out
through the study of traditional quantitative indicators emphasizing value (various price/earnings
metrics), financial stability (liquidity ratios), andqualitativeopinions such asmanagementdepth and
expertiseandmarketdominance.Thegoalof suchanalysis is todeterminewhat is the real, intrinsic
valueofasecurity,andtothencomparethatvaluetothepricebeingofferedinthemarket.Traditional
analysis tools includediscountedcash flowmodeling,multiplesanalysis,andcomparable transactions
analysis.Whenadiscrepancybetweenthe intrinsicvalueandmarketpriceexists,there isachanceto
profitbybuyingsecuritiesbelievedtobeundervaluedandsellingsecuritiesbelievedtobeovervalued.
Other typesof analysis tools include technical analysis, inwhich an analyst studies variables such as
currentprice,historicalprice,volume,andmoretopredictfutureprices,andinvestsaccordingly.
Investment strategiescanbebasedonqualitative factors such investing ingreencompanieswitha
superior focusoncorporatesocial relationsandalternativeenergy,oronquantitative factorssuchas
trading futuresbasedonabelief that the relationshipbetween theS&P500and the JapaneseNikkei
index is meanreverting over a 6month horizon. Often investment strategies are based on both
qualitative and quantitative factors, specializing in a specific market niche (e.g. Asian smallcap
1Allen,Franklin,RistoKarjalainen."Usinggeneticalgorithmstofindtechnicaltradingrules."JournalofFinancialEconomics51(1999):245271.
2Whitman,MartinJ.,andMartinShubik.TheAggressiveConservativeInvestor.Wiley,1979.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,4
industrial) and then analyzing specific securities based on both quantitative financial and qualitative
managerialvariables.
New investmentstrategiesaregenerallydevelopedbyacombinationof innovativehypothesizingand
empirical research. Generally a human uses various financial analysis tools to discover a repeated
discrepancybetween intrinsicvalueandmarketprice,and then formulatesan investmentstrategy to
takeadvantageofthisperceiveddiscrepancy.Thesearchfornewinvestmentstrategiesiscarriedoutby
thousands of finance professionals around the world, and has the potential to yield huge profits if
found. For this reason, it isworth thinking not just about individual potential strategies, but about
refiningtheprocessthroughwhichnewstrategiesaredeveloped.
Limitations intraditional investmentstrategydevelopmentprocess:Twoprimarybottlenecksexist in
theprocessofhumansdevelopingnew investment strategies.Firstly,human thoughtprocessesmust
choosewhatvariablesaresignificantandworthspending time toanalyze.Thisprocesscanbebiased
bothbytraditionalinvestingphilosophy(e.g.thatlowP/Eratiosoftenpresentabettervaluethanhigh
P/E ratios) and by the lack of human conceptualization of potential relationships among variables.
Secondly,thereexistsabottleneck inhumanabilitytoprocessandanalyze largedatasets.Ananalyst
mightbe interested inpotentially investing inthousandsofpublicly listedcompanies,butwouldnever
havetimetothoroughlyanalyzealloftheirpublicstatements.
Inanattempttoalleviatebothofthesepotentialbottlenecks,thispaperexplorestheuseofagenetic
algorithm to optimize the analysis process in the development of investment strategies. Genetic
algorithmswere first recognized as a promising tool for financial researchbecauseof theirprevious
successinsolvingvariousNPhardandcomplexproblemsinengineering.
IntroductiontoGeneticAlgorithmsandimplementationininvestmentstrategydevelopment:Genetic
algorithmsareatypeofevolutionaryalgorithm,whichreferstoagroupofsearchheuristicsinspiredby
evolutionaryprocesses found inbiology.Theseevolutionarysearchheuristicsattempt to findoptimal
solutionstoproblemsbycreatingsolutionpopulationswhicharethenevolvedovertimeaccordingto
fitnesscriteriapertainingtothespecificproblem.
Thegeneticalgorithmused in thispaper is implemented in theMathematicaenvironment,using the
model developed in the original Allen and Karjalainen paper. Specifically, solution candidates are
representedinMathematicaasnestedtreefunctions,whichreturnasignaltobuyorsell.Inthecontext
ofthefollowingexperiments,allofthesolutioncandidatesreturnBooleanfunctions,becausethesignal
iseithertobuyornottobuy.However,othertemplatescouldbestructuredtoallowforbuying,short
selling,orneutralpositions,ortradingmultipleassetswithinastrategy.Eachnodeinthesolutiontree
canbeafunction,variable,orvalue.Solutioncandidatesareinitiallyrandomlygeneratedaccordingtoa
predefined template, which contains the available potential functions and variables. Values are
generated through a randomizing function. Basic functions included in all experiments with the
algorithm include arithmetic operators, absolute difference, and a moving average function. More
functionscanandshouldbedevelopedtosuitindividualmodels.
Sampletradingrule.(Inputs:Price.S&P500close,3monthgasolinefuturescontract)
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,5
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,6
First,apopulationofindividualsolutioncandidatesisgeneratedaccordingtothesolutiontemplate,and
is then evaluated by the fitness function. In the case of investment strategies, the fitness function
measuresexcess returnaboveabuyandhold strategy.The individualsare then rankedaccording to
their fitness, and then randomlymutated and recombinedwith each other (similar to the biological
processwithrecombinationandmutationofDNAduringthereproductionprocess),withabiastowards
themostfitindividualspassingontheirtraits.Next,thebestrulefromeachgenerationistestedagainst
arangeofdatacalledtheselectionperiod. Iftheruleappliedtotheselectionperiodoutperformsthe
previousrulesappliedtotheselectionperiod,itisthensavedasthebestruledevelopedsofar.Thebest
ruleisthenappliedtotheoutsampletestperiod,anditsfitnessisagainevaluated.
Thisprocessofevaluatingthefitnessofthecurrentgenerationandthencreatinganewgenerationof
solutioncandidatesbasedonthetraitsoftheparentgeneration isthencontinueduntilatermination
criterion is reached.Generally inexperimentswith investmentstrategydevelopment, the termination
criteria includereachingamaximumnumberofgenerations,orreachingaplateauoffitnesswhereno
progressisbeingmadeacrosssubsequentgenerations.
Potential strengths and weaknesses of Genetic Algorithms for investment strategy development:
Genetic algorithms help address the two aforementioned bottlenecks in the investment strategy
development process, but also come with their own limitations. Firstly, there is still an element of
humanchoicewithrespect toevenhypothesizingwhichvariablesshouldbepassedon to thegenetic
algorithmbasedprocess.Ifahumancannotconceiveoforfindaquantifiablevariabletoanalyze,there
isnowayforittobefedintothegeneticalgorithmbasedmodel.Withmanymodelingtechniques,the
traditional adage of junk in, junk out applies, implying that the results of amodel can only be as
quality as the data fed into it.With genetic algorithms, because of their unique ability to evolve a
solutiontoaproblem,junkin,junkoutisnotentirelythecase.Evenifjustsomeoftheinputdatais
relevanttotheproblemathand,thegeneticalgorithmshouldbeabletofilterouttheuselessdatafrom
thatwithsomedegreeofpredictivemerit,anddevelopaninvestmentstrategybasedsolelyonthedata
withpredictivemerit,essentiallyignoringthejunkdata,findingonlythediamondintherough.
The human bottleneck of choosing where to spend time searching for potentially profitable
relationshipscanbegreatlyaidedwithageneticalgorithm.Becauseof itssheercomputationalpower
advantageoverahuman, itcan lookatvastlymorepotentialrelationships thanahumanwouldhave
timetoanalyze,andthecostofdoingsoisminimalintermsofcomputationalpowerandmemory.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,7
Further,geneticalgorithmsapproachproblemswithoutpreviouslyexistingbiases.Ageneticalgorithm
wouldbejustaslikelytoinitiallyconsiderstrategiesinvestinginequitieswithhighprice/bookvaluesas
thosewith lowprice/bookvalues,asthealgorithm isuninhibitedbyconventionalwisdom. Thiscan
add significant valuewhen searching fornew relationships todevelop investment strategies yielding
aboveaveragereturns.
Investing:ArtorScience?Bysolelyrelyingonanyquantitative,blackbox investmentmethodology,
one ismaking tosomedegreeanassumption that investing isaquantifiablescience.Some investors,
including legends like Warren Buffet3 would likely argue that investing is more of an art, in which
financial statement analysis, innovative thinking and gut feeling are the primary components in
success,ratherthanascience,inwhichcompanies,securities,andmarketscanbequantified,analyzed,
and successfully predicted. With respect to a genetic algorithmgenerated investment strategy, one
mustanalyzewhetherthestrategymakesanyeconomicorintuitivesense,orifitisjustasemirandom
combinationofvariablesthatperfectlypredictedthepast,butoffer limited insight intopredictingthe
futureofthemarkets.However,theredoesnothavetobecompletedisconnectbetweentheartand
scienceapproachestoinvesting.Algorithmbasedmodelscanbeusedasscreens,toweedoutpotential
investmentopportunitieswhichmightyieldanaboveaverageexpectedprofit ifanalyzedusingsound
fundamentalanalysistechniques.
Programming language choice: The genetic algorithm was implemented in Mathematica, using the
model developed in 1999 by Franklin Allen and Risto Karjalainen. Mathematica is a popular
mathematicalsymbolicmanipulationsoftwarewhichiscommonlyusedinscience,engineering,aswell
as in finance;however, itsuse in finance ismainly limited toacademic research. Practitioners in the
financial industry (with a strong computing background) generally prefer other packages (such as
MATLAB) and programming languages (such as C++), because of their computational efficiency.
Mathematicaiscomparativelyslowtorun,andalsohasasteeperlearningcurvethanothercomparable
packages. However, it isworthmentioning that especially for finance professionalswhomay not
necessarily have the background in computer science Mathematica is much easier to grasp than
programminginC++.ForsomeonewithpriorexposuretomodernprogramminglanguagessuchasJava
andPython,MATLABprogrammingisrelativelyeasytopickup;Mathematica,however,generallytakes
3WarrenBuffett,multipleletterstoBerkshireHathawayshareholdersandvariousinterviews.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,8
longertomaster.Forcomputationalspeed,directlyprogramminginC++asopposedtousingasoftware
packageisgenerallythemethodofchoice.
Forthispaper,Mathematicawasusedbecauseitwasusedtobuildtheoriginalgeneticalgorithmmodel
inAllen,Karjalainen.Due to the long calculation times, thismethod isnot feasible for tradingonan
intradaylevel(tickbytick,withineachtradingday),sincesomeofthecalculationstakeseveraldaysof
computingtime.Thisproblem isexacerbatedwhenmany indicatorvariablesareconsidered). Genetic
algorithmsdefinitelymayhaveuse in intradaytrading,and futureapplicationscouldconsiderwriting
suchprogramsinC++forcomputationalspeed.Whileithasitsflaws,Mathematicaisstillawidelyused
softwarepackagewithverydetaileduserdocumentationandalargecommunityofusers.
Previousworkongeneticalgorithms in finance:Allen&Karlajainens1999workandensuingnotyet
publishedwork is thebasis for thispaperandseveralof itsexperiments.The1999paper found that:
Aftertransactioncosts,therules[foundbythegeneticalgorithm]donotearnconsistentexcessreturns
overasimplebuyandholdstrategy intheoutofsampletestperiods.Thepaperwentontosuggest
several topics for future research, including applying the genetic algorithm to futures markets, and
expandinginputstothemodeltoincludefundamentalvariables.
FernnndezRodriguez,GonzlezMartel,andSosvillaRivero(2005)4foundthatusinggeneticalgorithms
tooptimizemovingaveragetradingrules,excessprofitsaboveabuyandholdstrategywereachieved
fortheGeneralIndexoftheMadridStockMarket.
Several papers have been published examining the potential for genetic algorithms to add value in
project finance applications. In particular, constrained optimization models solved using genetic
algorithms have yielded beneficial results in building portfolio management5 maintenance and
4FernnndezRodriguez,Fernando,ChristianGonzlezMartel,SimnSosvillaRivero."Optimizationoftechnicalrulesbygeneticalgorithms:evidencefromtheMadridStockMarket."AppliedFinancialEconomics15(2005):773775.
5Tong,TamandChan.GeneticAlgorithmOptimizationinBuildingPortfolioManagement.ConstructionManagementandEconomics19,(2001):601609.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,9
replacement planning, semiconductor capital expenditure budgeting6, and public infrastructure
investment7.
In addition to published research, it is believed that numerous hedge funds and private investment
vehiclesareusinggeneticalgorithms,neuralnetworks,andothermethodsofevolutionarycomputation
as parts of their quantitative trading strategies. Algorithmic trading by hedge funds and investment
banksnowaccountsforasignificantamountofmarketvolume.
I. PerfectForesightExperiment;AbilitiesofGeneticAlgorithm
ExperimentMotivation:Tostartoffdemonstratingwhatthegeneticalgorithmiscapableof,practice
datawasused.Thismeansthatthedatahasbeenmanipulatedwithcertainprofitabletrendstosee
if the algorithm can identify the trends and formulate profitable trading strategies under these
environments. Theexperiment iscalledPerfectForesight thealgorithm isgiven theability tosee
onedayaheadby includingasecondvariablecalledtmr(fortomorrow)which istheclosingpriceof
thenextday. If thisexperiment fails, themodelmustbeadjustedbeforegoing forwardwithother,
moresophisticatedexperiments.Resultsindicatethatthealgorithmperformsquitewell.
InputSelection&Data:2variableswerechoseninadditiontoageneric(nonvarying)interestrateset
arbitrarilylowandconstantfortheentiredurationofthedata.Whileitmayseemextraneoustoexplain
the variables (they are indeed, quite simple in this basic experiment), the paper will adopt this
conventionofexplaining thesetupofeachexperiment forall themoresophisticatedexperiments to
follow.
1. Price:1monthgasoline futurespricesareusedasa realisticproxy,althoughany liquidasset
couldhavebeenused.
2. TomorrowsPrice:This is thepriceat thecloseof thenextday,given to thealgorithm today.
Theobjectiveisforthealgorithmtolearnthattomorrowspriceisaprofitableindicator.
6Wang,K.J.,S.HLin."CapacityExpansionandAllocationforaSemiconductorTestingFacilityunderConstrainedBudget."ProductionPlanning&Control13(2002):429437.
7Hsieh,Tingya,HsinLungYu."GeneticAlgorithmforOptimizationofInfrastructureInvestmentUnderTimeResourceConstraints."ComputerAidedCivilandInfrastructureEngineering19(2004):203212.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,10
3. Rate:This is aproxy interest rate, to calculate returns to stayingoutof stockmarket (and
being in cashmarket). While this is not necessary here, this is used because the algorithm
expectstotake incashrates,soforsimplicitya1%constant interestratevalue isused. Note
that thisdoesnotmean rate is in the setofconsiderationvariables,so thereneeds tobeno
worryabout caseswhere the stock tomorrow closes less than1%higher than todaybut still
higher.
Implementation:Forthisexperiment,apopulationsizeof100wasusedfor10generations. Thiswas
chosenbecauseofcomputationalefficiency,and itwouldbemore interesting ifthegeneticalgorithm
could find the signalmorequickly. Fitness isdefinedas cumulativeexcess returnoverbuyandhold
strategy. Transactioncostsweresetto0% (sinceactualperformance isnotwhat isofconcernhere).
Thetrainingperiodwas5yearsandtheoutsamplewasrunforapproximately10years.
Results&Discussion:Recallfromtheearlierdiscussionthatonedrawbackofthealgorithmisthatitis
notpossible to shortsell securitiesdirectly in thealgorithm (although this isaddressed somewhat,
through a manual trick using spreadsheet programming; this technique is reserved for more
sophisticatedexperiments). Therefore,given this feature, themostprofitable tradingstrategyshould
bethesimplesignal:
tmr>Price //Long stock if tomorrows closing price greater than todays, hold cash
otherwise.
Anyothersignalcapturesnoiseandwillnotbeasprofitableasthis. Usingpopulationsize100,for10
generations,thealgorithmfinds:
Bestsolutioncandidate:
Price > tmr //Long stock if tomorrows price > todays price. Most trials found this to be the best
solutioncandidate;thosethatdidnotfoundverysimilarstrategies.Givenlargertrialsizes(500/50,for
example),itislikelythatallbestsolutionswillhavethisform.
This signalwill recommend a longposition if tomorrows stockprice is greater than todays. This is
exactlywhatthealgorithmshouldhavefound!Thiswasfoundintherelativelysmallexperimentsizeof
100/10,withgreatspeed (computing timewas23seconds). While thisseemsquiteobvious (anyone
wouldknowtobuystocksthataresuretoincreaseinpricethenextday),theabilityoftheprogramto
finditisaminimumnecessaryconditiontoshowthatalgorithmmightpotentiallybecapableoffinding
excessreturnsinrealmarketenvironments.
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
1000%
GasolineBuy&Hold GAStrategy
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,11
Thisstrategyisquitesuccessfulingeneratingexcessreturnsaswouldbeexpected.Theexcessreturns
here represent the maximum possible excess returns over the time period in consideration, in the
absenceofshortselling.Onceagain,thisresultonlydemonstratesthatthegeneticalgorithmisableto
quickly pick up simple patterns and there is potential for it to find excess returns in real market
conditions.
Note:(Thedatesare justusedasplaceholders,sincethetemplatefromanotherexperiment isused) This isthe
outsampleexcessreturnsforarepresentativecandidateamongthemanyrunthroughs.
The tableabovewillbepresented throughout thepaper, so it isworthwhile todiscusswhatvarious
columnsmean.Insampleshowstheyearsthatwereusedasinsampletogeneratestrategycandidates.
Kisthenumberofprofitablestrategiesfoundinsample,Excessistheaverageannuallogreturn,andK+
is the number of profitable strategies in the outsample period (K+
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,13
II. S&P500Experiment
Experiment Motivation: The goal for this experiment was to try to obtain the results in Allen,
Karjalainen (1999)basedon theirexperimentswith theS&P500. Theexperimentwasundertaken to
makesure thatthealgorithmwasworkingproperly,andto learnhowtosetupexperiments for later
use. Essentially, the experiment hoped to achieve the same noexcess returns above buy and hold
result.Allthevariablesusedarepubliclyavailable.
Input Selection & Data: 2 variables were chosen: S&P 500 closing price and interest rates. The
experimentwassetupexactlyasinAllen,Karjalainen(1999).
1. S&P500:ThisisthedailyclosingpricefortheS&P500index,normalizedbydividingbya250day
movingaverage.
2. Interest Rates: 1month Treasury bill yields at first until 1992, then rolls over to Eurodollar
depositratesthereafter.Notethatratesherearenotincludedasanindicator,butonlyasthe
returnsforholdingcash.Thismeansthatthemodel,withtheonlyindicatorbeingprice,would
neverdevelopa strategywhich staysoutof stockmarket if returns to cash in the treasuries
marketarehigh.Rather,thestrategydevelopedwillbebasedsolelyonfunctionsderivedfrom
pastprices,andrateswillonlymeasurereturnswhileholdingcash.
Experimentsetup:Forthisexperimentapopulationofsize500and50generationswasused.Fitness
wasdefinedascumulativeexcessreturnoverbuyandholdstrategy.Transactioncostsof0.1%,0.25%,
and 0.5%. The training periodwas calculation deserves discussion. The data started in 1954, and
trainingperiodsbeganevery5years,until1979. Whatthismeans isthefirsttrainingsetconsistedof
datafrom1954toendof1958,and1959to1963isanothertrainingset,andsoon.Theyearfollowing
trainingistheselectionperiod,whereprofitablestrategiesfromthetrainingperiodarekeptifandonly
if they perform even better in the selection period, otherwise they are discarded. The outsample
evaluationperiodwasalltheyearsfromoneyearaftertheselectionperiod(ortwoyearsaftertheend
of the training period), until 2002. Each training set essentially leads to a new experiment; this is
valuable toavoidoverfitting thealgorithm toevents thatarespecific toacertainperiodof time (for
example,asuddenmarketcrash,etc).
Results & Discussion: It can be seen from the following table that under low transaction cost
environment, theexcess returnsareessentially0 (meanapproximately0,withslightvariation),while
excess returns become increasingly negative on average as transaction costs increase (which is
expected).ThisisinlinewiththeresultsofAllen,Karjalainenaswellasgenerallyacceptedtheory:the
S&P500 isoneofthemostefficientmarkets,andanystrategythatconsidersonlytechnicalpricedata
(withoutevenconsiderationforothertoolsoftechnicalanalysis,suchasvolume)cannotmakereturns
in excess of a buyandhold strategy, according to even the weakest forms of efficient market
hypothesis.
Primarily,thisexperimentwasusedtogainabetterunderstandingofthealgorithmandhow itworks.
HavingconfirmedtheresultsofAllen,Karjalainen(1999),thenexttest involvesusingthealgorithmto
searchfortradingstrategiesonanewsetofdata.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,14
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,15
III. EmergingMarketsExperiment:ChinaASharesMarket
ExperimentMotivation:PerhapstheS&P500issimplytooefficienttoallowtechnicalstrategiestoearn
excessreturns.Ifthatisthecase,wouldtherebegainsfromapplyingthealgorithmtopotentiallyless
efficientemergingmarkets? TheChinaAShares (opentopurchasebyChinese investorsandselected
qualifiedforeigninstitutions)marketisinterestingandrelevantforseveralreasons.Firstandforemost,
up until December 2007, China was experiencing an enormous bull market. At the same time,
institutional rules forChinese financialmarketswere favorable for the algorithm: shortselling isnot
permitted(ascurrentlysetup,thealgorithmcannotidentifyshortsellopportunities),andsharescannot
be soldon the samedatepurchased (thealgorithmperforms calculationsonan interdaybasis,and
doesnotgenerate intradaytradingstrategies). Finally,thepresenceofa largemassofretail investors
potentiallyincreasesthelikelihoodofpotentialopportunities,comparedagainstthemoresophisticated
hedgefunds,institutionalinvestors,etcthataredominantplayersinmoredevelopedmarkets.
InputSelection&Data: Thisexperimentwas runanalogous to theS&P500experimentabove. The
pricedata isChinaShanghaiAComposite Index closingpricesnormalizedbydividingby the250day
movingaverage,andtheinterestratedatawasgovernmentmandatedChineseCentralBankOvernight
rate.
Experimentsetup: Theexperimentwassetupusingapopulationsizeof500,and50generations.
Fitnessisdefinedascumulativeexcessreturnoverbuyandholdstrategy.Transactioncostswere0.1%,
0.25%,and0.5%. The trainingperiodwas1998 to2002,selection2003 to2004,outsample2005 to
2007. Note that recently the Chinesemarket has fallen quite dramatically,whichwould lower the
returns tobuyandholdstrategy (andmake thealgorithmstrategy lookmore favorable) thesedata
pointswerenotincorporatedintheexperiment.
Results&Discussion:
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,16
Themosteyecatchingfeatureofthetableonthepreviouspagemustbethesignificantnegativeexcess
return,varyingfrom 22%to 30%. Note,howeverthattheTtestofoutsamplereturnsvs. insample
returnsareessentiallyzero,sothestrategyisnotnecessarilyjustoverfittinginsampleandfailingout
sample. Inavolatilemarket likeChina,amoreappropriatemeasureof return should indicate some
measureofvolatilitysuchasaSharpeRatioorSortinoRatiowhichthebuyandholdbenchmarkdoes
notaccountfor.Ifthetimeserieswasendedearlierforthisexperiment,thesenegativeexcessreturns
wouldbemuchsmaller.
Inthedevelopmentoftradingstrategies,negativeexcessreturnsarenot inherentlybad.Ifreturnsare
significantlynegativewithahighstatisticalconfidencelevel,thenonecanprofitfromtakingtheinverse
ofthesuggestedtradingrule.Ifhowever,returnsarejustslightlynegative,thereisnoclearstrategyto
achieveprofit.However,becauseofChinas institutionalconstraintspreventing shortselling,evenan
strongexcessnegativereturndoesnotallowforasuccessfultradingstrategy.
Thereareseveralpossiblereasonswhyexcessreturnsweresignificantlynegative.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,17
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,18
In theoutsampleperiod,Chinaexperiencedof the largestbullmarkets inhistorysimplybuying the
stockat the startofoutsampleandholding ituntil2007producesannualgainsof40%+. As theA
Shares indexclimbedto its2007peak, itoccasionallyexperiencedsmalldipsalongtheway.Any long
only strategycompetingwithabuyandholdwouldneed to time thosedipsexactly right inorder to
exhibitsignificantoutsampleperformanceinsuchabullmarket.However,thetradingstrategieswhich
performed best in the insample period often stayed out of theA Sharesmarket and held cash for
varying lengthsof timeduring the insample.While innormalmarkets thiswouldbeconsideredan
essential part of a strategy in terms of riskmanagement, these strategies could be characterized as
overly cautious in thismassivebullChineseoutsamplebullmarket .Byholding cash for even small
periodsoftimebeforecomingbackintotheequitymarket,largeportionsofthebullrunweremissed.
Theabovegraphedstrategyhighlightsanextremeexampleofanoverlycautiousstrategymissingabull
market.
Whilereturnsagainstthebuyandholdarenegativeasmeasuredonthespecificdatesused,theyare
stillquitehigh inandofthemselves. Inthecontextofthehugebullmarketoftheoutsampleperiod,
the best performing strategy from the run still returned over 30% annualized,which is very strong
comparedtootherinternationalequitymarketreturnsoverthesameperiod.
Second,onceagain,onlytechnicalpricedatawasconsidered.EssentiallythisexperimentwastheAllen,
KarjalainenS&P500experiment,butdoneusingChinesemarketdata.
Finally, the time seriesbeingconsidered isvery short, seeingas theChinesemarket isquitenascent.
Thismeansthatthereisnotmuchtimeforthealgorithmtolearnduringthetrainingperiod,sinceitis
inevitable to make the training period short enough to have meaningful selection and outsample
evaluationperiods.Thedecisionwhethertouselargesamplesofdataandriskoverfittingversususing
smallsamplesofdataandfindinglimitedpredictivevalueisalwaysatradeoff,andhighlightselements
ofstrategydevelopmentthatarelargelyartratherthanscience.
The Chinese AShares experiment suggests that strategies which trade only on past price data are
generallynoteffectiveinthelongrun,evenwhenusedinalessefficientemergingmarket.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,19
IV. GasolinePredictionExperiment
ExperimentMotivation:Thegoalforthisexperimentwastodevelopamodelthroughuseofthegenetic
algorithm topredictgasoline futuresprices.Predicting thegasoline futures contractpricepresents a
particularlyrelevantandinterestingchallenge:thecommoditiesmarketsareinthemidstofahugebull
run,andenergy issuesaretakingaprominentplaceonthemacroeconomicscene,both intheireffect
oninflationandnationalsecurity.Withoilpricesover$100/bbl,thereisbothincreasingattentionpaid
toandspeculation intheenergyfuturesmarkets.AlthoughthefrontmonthCushingcrudecontract is
theworldsmostheavilytradedfuturescontract,thechoiceofadownstreamdistilledproduct(gasoline)
rather than crude oil enables the algorithm to develop a model a model incorporating more
fundamental data gathered from throughout the energy value chain. This was a new test for the
algorithm, on nonfinancial, industry specific data being used to predict the gasoline futures price.
Additionally,alldatausedinthisexperimentweregatheredfromfreepubliclyavailablesources,notably
theUSEnergyInformationAdministration8,andtheInternationalEnergyAgency9.
InputSelection&Data:14variableswerechosen,fromallalongthegasolinevaluechain,aswellasa
select fewmacroeconomic,marketwidevariables.Thedataspans fromMay1985 throughDecember
2007, which was chosen as the endpoint because of the lagged release of several of the variable
indicatorseventhoughpricedataforthegasolinecontractwasavailablethroughtoday.
1. Normalized (by 250day moving average) Front month gasoline future contract price: This
NYMEXtradedfuturescontractisthevariablethatthealgorithmisattemptingtopredict,butit
isalsoincludedasaninputvariable,sothatrelationshipsbetweenpastpricesandfutureprices
(technicalanalysis)canbediscovered.DatafromtheNewYorkharborgradecontractwasused
until2004,whenthemarketswitchedovertotheRBOB(reformulatedgasolineblendstockfor
oxygenblending)specification,whichwasusedforthedurationofthedata.
2. 3Monthgasolinefuturecontract:the3monthcontractisincludedinordertoprovidethestudy
oftheshapeofthefuturescurve.Commodityfuturespricesaredrivenbythespotprice,costof
storage,riskfreerate,andconvenienceyield,whichtakes intoaccountexpectationsofsupply
8Officialwebsite:http://www.eia.gov.
9Officialwebsite:http://iea.org.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,20
anddemand,includingseasonalvariance.Byincludingthe3monthcontract,thealgorithmhas
thepotentialtorecognizefuturescurveshapes,suchascontangoandbackwardation,which
arecommonlyassociatedwithbearishandbullishsignalsforthemarket.Withtheexceptionof
deliverydate,thesamecontractspecificationsasthefrontmonthcontractareused.
3. Frontmonthcrudeoilcontract:thisNYMEXtradedcontractforlightsweetcrudeoilforCushing,
Oklahomadeliveryisthemostheavilytradedfuturescontractintheworld.Crudeoilistheinput
commodity to be distilled into gasoline, and its price is a key factor in the price of distilled
products,includinggasoline.
4. 3 Month crude oil contract: with the exception of delivery date, this contract is the same
specification as the front month crude oil contract, and is included along the same line of
reasoningas the3monthgasoline future, inorder to facilitate thedevelopmentofa futures
curve.
5. Front month heating oil future contract: the No. 2 grade NYMEXtraded heating oil future
contractwaschosenbecauseofitsrelationshipwithgasolineasanothercrudeoilendproduct.
Crude oil is distilled into a variety of finished products. The differential between the
simultaneouspurchaseofcrudeoil futuresand the saleofvarious finishedproduct futures is
known as the crack spread, and isperceived as an approximationof refineryprofits.Chief
amongfinishedproductsaregasoline,heatingoilandjetfuel.Heatingoilisparticularlyrelated
togasolinebecauseof the relativeseasonaldemand foreachproduct:heatingoil is inhigher
demandinthewinterduringcoldweather,andgasolineisinhigherdemandinsummer,during
peakdrivingseason.
6. Thirdmonthheatingoilfuturecontract:withtheexceptionofdeliverydate,thiscontractisthe
samespecificationasthefrontmonthheatingoilcontract,and is includedalongthesame line
ofreasoningasthe3monthgasolinefuture,inordertofacilitatethedevelopmentofafutures
curve.
7. Percentagechange incrudeoilendingstocks:thisdata,gatheredmonthlyfromtheEIAwitha
onemonth lag in release time, represents thepercentagechange inUSheldcrudeoilstocks.
Sincecrudeistheinputforgasolineproduction,changeinavailablesupplywouldlogicallyhave
aneffectonoutputgasolineprices.AlthoughthisdataonlyreferstoUSsourcesandtheenergy
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,21
futurescontractsrepresentatrulyglobalmarket,itisstillworthincludingbecausetheUSholds
approximately20%ofglobalrefiningcapacity10,andthepredictedcontractvariablealsorefers
toaUSdeliverypoint.
8. U.S.percentutilizationofrefineryoperablecapacity:thisdata,gatheredmonthlyfromtheEIA
witha3month lag in release time,mightbehelpful indetermining the relativedemand for
distilledcrudeproducts.Averaging89.5%,periodsofextremehighorlowUScapacityutilization
might be correlatedwith periods of high or low gasoline demand, orwith outages in other
globalrefiningcapacity.
9. U.S.OperableCrudeOilDistillationCapacity(ThousandsofBarrelsperday):thisdata,gathered
monthlyfromtheEIAwitha3month lag inrelease,offers insight intothetotalUSdistillation
capacity.
10. U.S. Percentage Change FinishedMotorGasoline Stock: gatheredmonthly from the EIA and
releasedwith a 3month lag. This is ameasure of end supply ofUS gasoline, andwould be
expectedtocorrelatetosomedegreewithchangesinprice.
11. Worldwide Rig Count: This measure of global on and offshore rigs, gathered monthly and
releasedquarterlyfromBakerHughesInc.,isanindicatorofupstreamcrudesupplyandwidely
usedthroughouttheindustry.
12. CPIInflation:releasedmonthlybytheBureauofLaborStatistics,thisisanoncore(exfoodand
energy)measureof inflation.Unliketheothervariables included,therenoclearrationalewhy
CPIinflationwouldbealeadingindicatorforgasolineprices.However,oneoftheadvantagesof
usingageneticalgorithmtobuildamodelratherthanhuman intuition isthatsometimesnew
relationshipsarediscovered.
13. S&P500Close:althoughthere isnearlynocorrelationbetweentheS&P500dailyreturnsand
crude oil daily returns over the long run, theremight be an inverse relationship in times of
extremelyhighenergyprices,representingamarketconsensusconcernabout inflatedenergy
pricesslowingeconomicgrowth.
10Source:EnergyInformationAdministration,WorldCrudeOilDistillationCapacity,January1,1970January1,2008
14. 10year yield: collected daily, this was used as the return in the cash market when a long
positionwasnottakeninthefuturesmarket.Itwasalsoavailableforthealgorithmtouseasan
indicator, although logically it should have less predictive ability than other industryrelated
data.
Experimentsetup:Forthisexperiment,apopulationsizeof500wasusedfor50generations.Fitness
wasdefinedascumulativeexcessreturnoverabuyandholdstrategy.Transactioncostsweresetto0%.
Thetrainingperiodswere19862002,19911997,19962002,eachofwhichwasfollowedbyoneyear
selectionperiod,andoutsampleevaluationswerefromoneyearafterselectionperiodto2008.
Results&Discussion:Asthefollowingsummarytableshows,onaverage,slightnegativeexcessreturns
werefound.
Amongthevarioustradingrulesdevelopedthroughoutallthedifferent insampleperiods,onlytwoof
therulesyieldedexcessreturns, intheamountsof2.48%and6.87%.Ofthetworulesoneseemsnon
sensical,andtheotherisbasedonrelativechangeincrudestocks,gasolinestocksandheatingoilprices.
Thefollowinggraphshowsthethebestperformingtradingstrategydeveloped,versusabuyandhold
strategy.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,22
0%
100%
200%
300%
400%
500%
600%
GasolineBuy&Hold GAStrategy
Thebestrulefromthegasolineexperimentappearstobefairlyconservativeitstaysoutofthemarket
forlongperiodsoftime(upto5years)duringperiodsoflowervolatility.However,itismorelikelyto
enterthemarketduringperiodsofhighvolatility,ascanbeseenfromthetradesinthepastfewyears.
Examiningthegraphrevealsthatalthoughthebeststrategyunderperformedthebuyandholdduring
the total outsample as defined, during many parts of the outsample the strategy did indeed
outperform.Thishighlightsthenotionthatmultiplemeasuresofreturn(e.g.SharpeRatio,SortinoRatio,
etc.) should be examined before actually executing any strategy developed by this or any other
algorithm.
Thereareseveralpotentialreasonswhyexcessreturnsmightnothavebeenfound.First,thelengthof
trainingdatawasrelatively limited,comparedtotheS&P500experimentforexample.Althoughthere
were14differentpredictivevariablesincludedinthemodel,severaladditionalvariableswereunableto
beincludedbecauseeithertheywerenotavailableforalongenoughtimespan,ortheywerenotfreely
availableinthepublicdomain,forexampleDOEandEIAstatedpredictionsoffuturegasolineprices,or
any measure of future or options volatility. Second, the use of a population size of 500 and 50
generationsmighthavepossiblyoverfitthemodeltothepastdata,attheexpenseoffuturepredictive
ability.Third,themodelhasnowaytotake intoaccountnonquantifiableevents,suchasthespike in
gaspricescausedbyhurricaneKatrina in2005,oranyotherchange inpricecausedbythegeopolitical
economy.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,23
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,24
V. Conclusions:
Across all experiments, no significant excess returns were found by using the genetic algorithm to
developinvestmentstrategies.
1. ForesightExperiment:Passing thisexperiment (successfully identifying theprofitable strategy
thatwaspurposelyput into thedata)was theminimumnecessary condition for the genetic
algorithmtobeabletopotentiallygenerateprofitabletradingstrategies. Thenextdaysprice
wasgiventothealgorithm,and itwasabletosuccessfullydetectthisfacttogivethe intuitive
tradingstrategythatismostprofitable.
2. S&P 500 Experiment: This experiment recreates Allen and Karjalainens 1999 work, mostly
undertakenasa learningexercise,butalsotoshowconsistencyofresults. An interestingnote
here is inAllen andKarjalainensoriginalexperiment, the computational time requiredusing
preyear 2000 technology took over a days worth of computing time; by comparison,
approximatelythesameexperimenttookundertwohourstoprocesson2007hardware.
3. ChinaASharesExperiment:Onanelementarytechnicallevel,ChinaASharesmarketappearsto
besomewhatefficient,giveninstitutionalregulations.Resultsquestionvalidityofbuyandhold
asabenchmarkagainstwhichgeneticalgorithmgenerated strategiesare compared,because
buyandhold returnsare sensitive to the last fewdatapoints included in theexperiment. A
profitablestrategycanlooklesspromising(andviceversa)justduetohighorlowreturnsonthe
lastfewdays.Itisimportanttocompareexcessreturnsfrombuyandholdwithreturnsofout
sampleminusinsample,anditsassociatedstatisticalsignificance;profitablestrategieswillshow
significant positive (at least, nonnegative) difference between outsample and insample
returns. There appears to remainpotential forprofitable trading strategies that incorporate
additionalvariables,suchasfundamentals.
4. GasolinePredictionExperiment: Althoughnoexcess returnswere found, the results seem to
suggest that incorporatingadditional fundamentaldata into thegeneticalgorithmcan lead to
improvedresults.
Although no excess returns were found in these experiments, there are many ways to potentially
improveboththestructureanduseofthealgorithm,bothintermsofbuildingblocksthemodelhasto
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,25
workwith (greater sophisticationof solution templates), and choiceof inputs into themodel (wider
varietyofinputvariablespotentiallypreprocessedinlinewithfundamentalanalysis).Thereisroomto
improvethemodelbothontheartandsciencefront.
Theuseofgeneticalgorithmsforinvestmentstrategydevelopmentisanascentconceptwhichhasgreat
potential.
SuggestedFutureExperimentsandSpeculations:
Penaltiesagainstnonsensicalandovercomplexoutput:Whendevelopinginvestmentstrategieswitha
geneticalgorithm,thereisalwaystheriskofoverfittingthestrategytothepastdataset,attheexpense
oflosingpredictiveabilityforthefuture.Oftenoverfitinvestmentstrategiesuseanaboveaveragelevel
ofcomplexity,bothinvariablesusedandrandomnumbersgenerated.Onewaytoattempttocutdown
on thismightbe tochange the fitness function fromonlyaccounting forpositiveadditions toexcess
return to also incorporating a negative value, penalizing for excess levels of complexity. The new
function would be in the form of [Fitness = +F*excess_return P*complexity_factor]. This could
potentially reduce overfitting, and could alsomake execution easier, particularly in situationswhere
liquidityandtransactioncostsplaylargeroles.
Limitedsetoflinearbuildingblocks:Onepotentiallimitationofthealgorithmisthatallofthesolution
templatesworkedwithinthispaperwerecomprisedoflinearbuildingblocks.Giventhatthemaximum
possible branch depth of the solution candidateswas generally 6, it is possible to build polynomial
strategies from the linear building blocks, but unlikely to build a polynomial strategy that can
incorporateasignificantamountofvariables.
Startingwithahumandevelopedstrategy,then lettingthegeneticalgorithmtweakspecificvariable
levels: In addition to generating trading strategies from scratch, one potential use of the genetic
algorithmwouldbetooptimizepartsofatradingstrategyalreadycreatedbyahuman.Forexample,an
options trading strategy basedon a traderspersonalbelief about the volatility levels in themarket
mightbedynamicallyhedgedintheunderlyingassetsmarketwithassistancefromageneticalgorithm.
Another examplewould be if a fundmanager believes that an equity seems underpriced based on
fundamentalanalysis,andwantstopurchasea largequantityofthestockwithoutsignificantlymoving
the price. In this case, a genetic algorithm could be used in a constrained optimization model to
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,26
formulate thepurchaseof thepositionover a fixed amountof time,whileminimizing theeffectsof
tradingcostsandmarketmovements.
Purposelyoverfittingtothepastandthenadoptingtheinversestrategy:giventheriskofoverfitting
tothepast,howcanoneuseoverfittingpurposefullytoachievesuperiorreturns?Oneofthetraditional
beliefsofallvarietiesofefficientmarkettheoriesisthatstrategieswhichyieldaboveaveragereturnsin
thepastbasedonanalysisofhistoricalpriceswillnotbeabletoconsistentlyoutperforminthefuture,
becauseallpast informationbecomes incorporated intothemarket.Ifthis isthecase,one ideawould
be topurposefullyoverfit thedata to thepast to create a strategy that yields extraordinary excess
returnsonhistoricaldata,andtothentaketheinverseofthatstrategyasanewstrategygoingforward.
Theideabehindthis,broadlylabeledcontrarianism,wouldbethatanythingthathasworkedsowellin
thepastwouldunderperform inthefuturethankstotheinvisiblehandofthemarket,sotradingon
theinverseofthatstrategycouldpotentiallythereforeoutperforminthefuture.
Intradayconsiderations:Asmentionedearlier,thealgorithmisprogrammedinMathematica,whichis
abittooslowtobepracticalinintradaytradingeachruntakesupwardsofseveraldaysofcomputing
time (whendozensof indicatorsareused, forexample). However, itmaybepossible tousea small
assortment of technical indicators (price, volume, measures of momentum, etc) and generate
potentially profitable intraday trading strategies. For these applications, it may be preferable to
programasimilaralgorithminafasterlanguagesuchasC++.
Asset allocation experiment across multiple markets, asset classes: Genetic algorithms have been
proven to be successful heuristics in many examples of constrained optimization problems, both in
engineeringandinprojectfinance.Buildingonthisbodyofknowledge,oneareaforexperimentationis
foraconstrainedoptimizationmodel tobe setup todistributea largeamountof totalassetsacross
multipledifferentassets.Constraintscancomeintheformofminimuminvestmentineachassetgroup,
orinthefitnessfunctionofmaximizingreturnswhileminimizingrisk.Thissortofmodelcanbeusefulin
multiple scenarios, including global asset allocation among major asset management firms, risk
management fornational financial institutions,ora fundof fundsallocatingassets todifferenthedge
funds. This experiment could yield resultsbeneficial for investorsof all sizes, from sovereignwealth
fundsdiversifyingtheircountrysequitymarketexposureallthewaydowntoanindividualchoosingan
optimal401(k)allocation.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,27
Testing of optimaldistributionofdata among training, selection andoutsampleperiods: Taking a
quantitative approach to the issue of how to divide available data into training, selection and out
sampletestingperiods, itwouldbebeneficialforonetoexaminetheeffectsofdifferentdatadivision
strategies on the outsample returns of a common experiment. Although certain elements of data
divisionareuniquetoeachparticularexperiment,perhapsonecouldfindvariousheuristicstohelpwith
the process. Again, the need for this sort of experimentation highlights how the use of genetic
algorithmsininvestmentstrategydevelopmentisbothanartandascience.
Dworkis&Huang,GeneticAlgorithmsandInvestmentStrategyDevelopment,28
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