Genetic Algorithms and Investment Strategy Development

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)


IV. EmergingMarketsExperiment:ChinaASharesMarket (15)


V. GasolinePredictionExperiment (19)


VI. Conclusions (24)

Experimentresultdiscussion SuggestedFutureExperimentsandSpeculations


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.


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)



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.


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.


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.


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.


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


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+


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.



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:


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.



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.


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.


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


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.


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.



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


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


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.


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.


WorksCited

Allen, Franklin, Risto Karjalainen. "Using genetic algorithms to find technical trading rules." Journal ofFinancialEconomics51(1999):245271.

Buffett,Warren,multipleletterstoBerkshireHathawayshareholdersandvariousinterviews.

FernnndezRodriguez, Fernando, Christian GonzlezMartel, Simn SosvillaRivero. "Optimization oftechnicalrulesbygeneticalgorithms:evidencefromtheMadridStockMarket."AppliedFinancialEconomics15(2005):773775.

Hsieh,Tingya,HsinLungYu."GeneticAlgorithmforOptimizationofInfrastructureInvestmentUnderTimeResourceConstraints."ComputerAidedCivilandInfrastructureEngineering19(2004):203212.

Tong, Tam and Chan. Genetic Algorithm Optimization in Building Portfolio Management. ConstructionManagementandEconomics19,(2001):601609.

Wang, K.J., S.H Lin. "Capacity Expansion and Allocation for a Semiconductor Testing Facility underConstrainedBudget."ProductionPlanning&Control13(2002):429437.

Whitman,MartinJ.,andMartinShubik.TheAggressiveConservativeInvestor.Wiley,1979.

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Genetic Algorithms and Investment Strategy Development