STATISTICAL ARBITRAGE MODELS OF THE FTSE 100

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1、STATISTICALARBITRAGEMODELSOFTHEFTSE100A.N.BURGESSDepartmentofDecisionScienceLondonBusinessSchoolSussexPlace,RegentsPark,London,NW14SA,UKE-mail:N.Burgess@lbs.ac.ukInthispaperwedescribeasetofstatisticalarbitragemodelswhichexploitrelativevaluerelationshipsamongsttheconstituentsoftheFTSE100.Ratherthane

2、stimatingcointegrationvectorsofhighdimensionality,astepwiseregressionapproachisusedtoidentifythemostappropriatesubspaceforthestochasticdetrendingofeachindividualequityprice.AMonteCarlosimulationisusedtoidentifytheempiricaldistributionoftheVarianceRatioprofileoftheregressionresiduals,underthenullhyp

3、othesisofrandomwalkbehaviour.Bothachi-squaredtestonthejointdistributionoftheVarianceRatioprofile,andadditionaltestsbasedonitseigenvectors,indicatethatasawholethestochasticallydetrendedstockpricesdeviatesignificantlyfromrandomwalkbehaviourandhencemaycontainpredictablecomponents.Acombinedcross-sectio

4、nalandtime-seriesmodelindicatesthattherelative“mispricing”oftheequitiestendstotrendintheshort-termandrevertinthelongerterm.Theout-of-sampleperformanceofthemodelsisconsistentlyprofitableusingasimpletradingrule,withthecombinedportfoliosuggestingapossibleannualisedSharpeRatioofover7foratraderwithcosts

5、of50basispoints.Furthermore,informationderivedfromthein-samplevarianceratioprofileisshowntobesignificantlycorrelatedwiththeout-of-sampleprofitabilityoftheindividualmodels–suggestingthattheperformancemaybeimprovedfurtherbymodellingthetime-seriespropertiesconditionallyonsuchinformation.1IntroductionI

6、nmanycasesthevolatilityinassetreturnsislargelyduetomovementswhicharemarket-wideorevenworld-wideinnatureratherthanspecificcharacteristicsoftheparticularasset;consequentlythereisariskthatthis“marketnoise”willovershadowanypredictablecomponentofassetreturns.Anumberofauthorshaverecentlysuggestedapproach

7、eswhichattempttoreducethiseffectbysuitablytransformingthefinancialtime-series.LoandMacKinley(1995)create“maximallypredictable”portfoliosofassets,withrespecttoaparticularinformationset.Bentzetal(1996),useamo