dividend policy irrelevance and eigenvalue location

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1、DividendPolicyIrrelevanceandEigenvalueLocationA.J.OstaszewskiMathematicsDepartment,LondonSchoolofEconomics.CDAMResearchReportLSE-CDAM-2005-8.pdfMay9,2005AbstractThisnotegivesaquali…eda¢rmativeanswertoanaturalquestion,askedbyOhlsonandmotivatedbysomeearlierwork,concernin

2、gtheirrelevanceofdividendpolicytothecalculationofequityinthecontextofanOhlsonstylegenerallinearaccountingdynamic.DoesDividendIrrelevanceoccurwhendiscountingatarateofinterestRifandonlyifRissetequaluniquelytothedominanteigenvalueoftheprincipalsubmatrix?Thelattersubmatrix

3、relatestheaccountingvariablestoeachotherintheabsenceofanydividendpayout.Thequestionreducestotheassertionthatthemaximumeigenvaluemaxofthefollowing‘bordereddiagonalmatrix’23100166021776:::7:67400n15!1!2!n+1liesbetweenthe…rstlargestandsecondlargestamongj1j;:::;jnj.A

4、na¢rmativeanswernecessarilyrestrictsthedividendpolicyvector(!1;:::;!n+1).Theresultsshowthatanalgebraicconditionequivalenttodividendirrelevancederivedpreviouslyisnotvacuous.Keywords:Dividendirrelevance,dominanteigenvalue,bordereddiagonalmatrix.1.IntroductionConsiderthef

5、ollowing…rst-orderrecurrence,whichwetermtheOhlsonaccountingdynamics.9zt+1=Azt+bdt+avt;=dt+1=wzt+dt+vt;();vt+1=+ vt;with0 <1:Herez=(z1;:::;zn)2Rn;iscalledtheaccountingstatevector,whiledandvarerealstttttde…nedfort=0;1;2;::;representingrespectivelythedividendandtheinfo

6、rmationvariable(aproxyforun-accountedvalue);thevalueofthelatterisassumedtodwindleintoinsigni…canceovertime.Thevector!div=(w;;)isthedividendpolicyvector.Aisarealmatrixofsizenn;calledthereducedmatrixofthesystem().Itseigenvalues1;2;:::;narelistedinorderofdecreasingm

7、odulus,i.e.j1jj2j:::jnj:TheaugmentedmatrixisgivenbyA=A(w;)=Ab;wregardedasafunctionof(w;):Itseigenvalueswilllikewiseberegardedasfunctionsof(w;)andreferredtoas1;2;:::;n+1;identi…edthroughtheconditioni(0;:::;0;)=ifori=1;:::;n;andn+1(0;:::;0;)=:(1.1)

8、WewillbeworkingforthemostpartinanequivalentcanonicalsettingwhereAisreplacedby23100166022776:::7;(1.2)67400nn5!