The predictability of Zscore model on stock returns a perspective of US listed companies.docx
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ThepredictabilityofZscoremodelonstockreturnsaperspectiveofUSlistedcompanies
ThepredictabilityofZ-scoremodelonstockreturns:
aperspectiveofUSlistedcompanies
Content:
Abstract2
1.Introduction2
1.1ModelIntroduction2
1.2EssayStructure3
2.LiteratureReview3
3.DataandMethodology4
3.1Sampling4
3.2TheRelationshipBetweenZ-scoreandStockMarketReturn4
3.2.1TheDynamicPanelModel4
3.2.2TheRegressionResults6
3.3Z-score’sT-test10
4.Conclusions11
5.LimitationsandFurtherstudy11
Appendix12
Reference24
WordAccount:
1995
ThepredictabilityofZ-scoremodelonstockreturns:
aperspectiveofUSlistedcompanies
Abstract
Thoughdifferentextantmodelsintroducedtoforecastcorporates’financialstrength,themostprevalentoneisAltman’sclassicZ-scoremodel(Altman,1968)inpredictingfirms’financialdistresspossibilities.InordertogainanunbiasedinsightintotherelationshipbetweenAltmanZ-scoremodelandstockmarketreturns,thisstudyaimstoresearchthemodel’spredictabilitybySTATAbasedonadatasetof30listedindustrialcompaniesinUSfrom2000to2003.TheresearchoutcomesdemonstratethatAltmanZ-scoremodelworksefficientinevaluatingfirms’financialperformance.
Keywords:
AltmanZ-scoremodelPredictabilityMarketreturnSTATA
1.Introduction
1.1ModelIntroduction
Withanincreasingrateofcollapseinfinancialworldcurrently,investorshaveatendencytobemoreprudentialinmakingtheirinvestmentdecision.Dependingonthecompanies’balancesheet,differentmeasurementsareusedasproxiesforquantifyingfinancialstress,includingprice/bookvalue,ROE,debtratioetc.(Oberholzer,2010,AgarwalandTaffler,2007),alongwithseveralmodels,e.g.Boritz’sre-estimateModel,Taffler’sZ-scoreModel,Sandin’sModelandAltman’srevisedZ-scoreModel(Taffler,1983,SandinandPorporato,2007,Altman,2000),thoughthemostwell-acceptedmodelisstilltheonedevelopedbyAltmanin1968(Boritzetal.,2007).
Table1:
Differentmodels’notationandtheirvariabledefinitions
Itisnoticeablethatdifferentmodelshavetheirsuitableness.ThefirstZ-scoreisapplicabletolistedUSindustrialcompanies,whiletherevisedonein1995issuitableforthenon-manufacturingcorporates.Taffler’smodelissetuponthebasisofUKbusinesscontextandSandin’sisdesignedfortheemergingmarket.Hence,alltheseclaimsthatthemostadvisableoneforthispaperisthefirstmodelsinceoursampleisbasedon30USlistedairlinecompanies.
1.2EssayStructure
Theremainingtextconsistsof3parts.Thefirstpartintroducespioneers’studiesonthedevelopmentofZ-scoremodel,alongwithitsalternativemeasurementsandhowitpredictsthecorporates’financialperformance.ThenstatistictestswillbeconductedontherelationshipbetweenZ-scoreandfirms’stockmarketreturn.Aconclusion,limitationsaswellasfurtherresearchwillbepresentedinthethirdpart.
2.LiteratureReview
Theearliestbankruptcypredictionmodeldatesbackto1930s,publishedbyBBR(theBureauofBusinessResearch)(JodiBellovary,2007).Followingthat,FitzPatrick(1932)andSmith(1935)haveputforwarddifferentratiostomeasurefinancialstressbyunivariateanalyzing.ThoughChudson(1945)andBeaver(1966)havemaderespectivecontributionsinthisfield,thepath-breakingmultivariteresearchwasconductedbyAltman(1968),reputedasahighpredictivecapability(95%accuracy).Sincethat,thenumberoffinancialstrengthevaluationmodelhasincreasedconstantly,soaringto165inrecentfourdecades,e.g.WilcoxBinominalModel(1973),HanweckProbitAnalysis(1977),LevitanMDA(1985),AgarwalNeuralNetwork(1993),AnadarajanNNGeneticAlgorithmAnalysis(2004)etc.Somemodelshavenarrowapplicabilities,e.g.Meyer(1970),PettwayandSinkeyJr(1980)forbanks,(Taffler,1984)andMason(1978)forUKmanufacturingandconstructionfirms,Scaggs(1986)forairlines,WertheimandLynn(1993)forhospitalsetc.,whilesomemodelsaregenerallyused(e.g.Daniel(1968),Libby(1975),KarelsandPrakash(1987),Ward(1994)etc.).
3.DataandMethodology
3.1Sampling
Dataselectioncriterion:
(1)AllthecompanymustbeUSlistedones.
(2)Allthepublicinformation,includingbalancesheetsandothernon-financialdata,isavailableforalengthofthreeyearsatleast.
(3)Nospecialfinancialcrisishappenedduringthisselectedtimeslotandthesiftedtimeperiodshouldclosetothecurrenttimeasmuchaspossible.
Accordingtothat,asampleof30companies’fiscalannualdataduringthe2000-2003periodissiftedoutfromtheoriginalunbalancedpaneldataset.AlltherawdataappliedinthecalculateprocessareattachedintheAppendix1.
3.2TheRelationshipBetweenZ-scoreandStockMarketReturn
3.2.1TheDynamicPanelModel
ThoughtheaccuracyofAltman’sZ-scoremodel(1968)hasbeendemonstratedforseveralyearsandtheempiricalevidencehasalreadyproveditshigh-accuracy(EdwardI.Altman,2013),itisstillnecessarytodoapre-testtoensuretherelationshipbetweenZ-scoreandstockmarketreturninthispaperisexistedbyscattergraph(shownasbelow):
Graph1TherelationshipbetweenZ-scoreandstockreturn
Asthegraphdenotes,thereappearstobealinearrelationshipbetweenZ-scoreandfirms’stockmarketperformance,representingthattheresearchonZ-scoremodel’sforecastingabilityinthispaperisdoable.
Itisillustratedbyseveralliteracythatstockpricewouldbeinfluencedbyitspreviousposition(Poklepovicetal.,2013,Beneda,2006),that’sthereasonwhythispapersetupadynamicpanelmodel.Inaddition,consideringthatZ-scorehasadeferredimpactonstockmarketreturn,theDistributedLagModelshouldalsobeincluded.HencethedynamicpanelmodelisconstructedintoAutoregressiveDistributedLagModel(ARDLModel),DistributedLagModel(DLModel)andAutoregressiveModel(ARModel):
(3-1)
(3-2)
(3-3)
Where
denotesthestockmarketreturnforcompany
inthetimet,
standsfortheZscoreforcompany
inthetimet,
istheintercept,
isspecifictodifferentcompaniesand
istheresidualiteminnormaldistribution.
and
arethevector
ofallthevariables’coefficients.
Inordertoshowtheautoregressiveinfluence,therespectiveStaticModelshouldalsobebuiltasthecomparinggroup:
(3-3)
Intheabovemodels,theZ-scoreiscalculatedbyAltman’s1968formula(Appendix2):
(3-4)
Thestockmarketreturnconsistsoftwoparts:
thestockpriceandordinarydividend.
3.2.2TheRegressionResults
Table2presentstheregressionoutcomeofthestaticmodel:
Table2RegressionoutcomeofStatisticModel
Year
2000
2001
2002
2003
Totalreturn
Totalreturn
Totalreturn
Totalreturn
Z1
1.040
(2.924)
Z2
1.143
(1.309)
Z3
4.278*
(2.214)
Z4
0.141
(0.260)
Constant
24.809***
14.851***
6.983
21.203***
(8.758)
(3.436)
(4.656)
(3.869)
0.005
0.027
0.118
0.010
N
29
30
30
30
Notes:
duetoamissingvariablein2000’sdividend,sotheNin2000is29.
Inthistable,Z1,Z2,Z3andZ4standfordifferentZ-scorefrom2000to2003yearsrespectivelyandthetotalreturnistheindependentvariable,namely,thestockmarketreturn.Obviously,boththegoodnessoffitaswellasthestatisticalsignificanceforeachregressionarenotevident.AlltheseclaimthatthestaticmodelbetweenZ-scoreandstockmarketreturnisnotapplicableandmeaningless.Therefore,weruntheAR,DLandARDLModeltogainanunbiasedandefficientinsightintotherelationshipbetweenZ-scoreandmarketreturn(shownbelow):
Table3DLModelRegression
Regression
1
2
3
4
5
6
Year
2001
2002
2003
2002
2003
2003
Return
Return
Return
Return
Return
Return
Z1
0.254
-2.148
-1.529
(2.122)
(2.836)
(4.135)
Z2
0.886
-2.881
-0.347
-5.688
-3.888
(2.521)
(3.930)
(5.185)
(5.821)
(7.666)
Z3
7.569
4.721
7.045
11.434
11.067
(5.014)
(3.372)
(5.101)
(7.655)
(7.848)
Z4
0.031
-0.027
-0.028
(0.268)
(0.275)
(0.279)
Constant
14.740***
7.453
12.891*
8.509*
13.396*
14.144*
(3.619)
(4.739)
(7.051)
(4.976)
(7.076)
(7.476)
0.027
0.135
0.077
0.154
0.110
0.115
N
30
30
30
30
30
30
ThistablepresentsaregressionoutcomeinDL
(1),DL
(2)andDL(3)Model.Regression1to3aretheoutcomeofDL
(1)Model,showingthedeferredimpactonstockreturninoneunitvis-à-visZ-score.Regression4to5aretheoutcomeofDL
(2)Model,respectively,measuringtheZ-score’sdeferredimpactonstockreturnintwounitsandregression6testingthethreeunits’deferredinfluence.
ComparingtotheStaticModel,itisfoundthatthisDLmodelismorepersuasiveintermsofgoodness-of-fitthoughR-squarearestilllow.However,allthecoefficients’statisticsignificancelevelsarestillnotvalid,illustratingthatDLModelisnotefficientinquantifyingthelinearrelationshipbetweenZ-scoreandstockreturn.Therefore,itisnecessarytodetectdifferentkindsofARDLmodel’sexplainingpower.Theoutcomeofone-orderARDLregressionislistedbelow:
Table4one-orderARDLModelRegression
Regression
1
2
3
4
5
6
Year
2001
2002
2003
2002
2003
2003
Return
Return
Return
Return
Return
Return
Returnin2000
0.179**
(0.073)
Z1
-0.079
-2.444
1.439
(1.978)
(1.558)
(1.177)
Z2
1.986
-4.007*
-1.129
-1.339
-2.987
(2.306)
(2.241)
(2.849)
(1.703)
(2.159)
Returnin2001
1.089***
1.095***
(0.144)
(0.140)
Z3
7.399**
-1.326
6.803**
0.297
0.523
(2.853)
(1.029)
(2.802)