The predictability of Zscore model on stock returns a perspective of US listed companies.docx

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）