Portfolio Diversification and Supporting Financial Institutions.docx
- 文档编号:9620147
- 上传时间:2023-02-05
- 格式:DOCX
- 页数:16
- 大小:28.42KB
Portfolio Diversification and Supporting Financial Institutions.docx
《Portfolio Diversification and Supporting Financial Institutions.docx》由会员分享,可在线阅读,更多相关《Portfolio Diversification and Supporting Financial Institutions.docx(16页珍藏版)》请在冰豆网上搜索。
PortfolioDiversificationandSupportingFinancialInstitutions
FinancialMarkets:
Lecture4Transcript
January28,2008
ProfessorRobertShiller:
Today'slectureisaboutportfoliodiversificationandaboutsupportingfinancialinstitutions,notablymutualfunds.It'sactuallykindofacrusadeofmine--Ibelievethattheworldneedsmoreportfoliodiversification.Thatmightsoundtoyoualittlebitodd,butIthinkit'sabsolutelytruethatthesamekindofcausethatEmmettThompsongoesthrough,whichistohelpthepoorpeopleoftheworld,canbeadvancedthroughportfoliodiversification--Iseriouslymeanthat.Therearealotofhumanhardshipsthatcanbesolvedbydiversifyingportfolios.WhatI'mgoingtotalkabouttodayappliesnotjusttocomfortablewealthypeople,butitappliestoeveryone.It'sreallyaboutrisk.Whenthere'sabadoutcomeforanyone,that'stheoutcomeofsomerandomdraw.Whenpeoplegetintorealtroubleintheirlives,it'sbecauseofasequenceofbadeventsthatpushthemintounfortunatepositionsand,veryoften,financialriskmanagementispartofthethingthatpreventsthatfromhappening.
Thefirst--letmego--Iwanttostartthislecturewithsomemathematics.It'sacontinuationofthesecondlecture,whereItalkedabouttheprincipleofdispersalofrisk.Iwantnowtocarrythatforwardintosomethingalittlebitmorefocusedontheportfolioproblem.I'mgoingtostartthislecturewithadiscussionofhowoneconstructsaportfolioandwhatarethemathematicsofit.Thatwillleadusintothecapitalassetpricingmodel,whichisthecornerstoneofalotofthinkinginfinance.I'mgoingtogothroughthisratherquicklybecausethereareothercoursesatYalethatwillcoverthismorethoroughly,notably,JohnGeanakoplos'sEcon251.Ithinkwecangetthebasicpointshere.
Let'sstartwiththebasicidea.Iwanttojustsayitinthesimplestpossibleterms.Whatisitthat--Firstofall,aportfolio,let'sdefinethat.Aportfolioisthecollectionofassetsthatyouhave--financialassets,tangibleassets--it'syourwealth.Thefirstandfundamentalprincipleis:
youcareonlyaboutthetotalportfolio.Youdon'twanttobesomeonelikethefishermanwhoboastsaboutonebigfishthathecaughtbecauseit'snot--we'retalkingaboutlivelihoods.It'sallthefishthatyoucaught,sothere'snothingtobeproudofifyouhadonebigsuccess.That'sthefirstverybasicprinciple.Doyouagreewithmeonthat?
So,whenwesayportfoliomanagement,wemeanmanagingeverythingthatgivesyoueconomicbenefit.
Now,underlyingourtheoryistheideathatwemeasuretheoutcomeofyourinvestmentinyourportfoliobythemeanofthereturnontheportfolioandthevarianceofthereturnontheportfolio.Thereturn,ofcourse,inanygiventimeperiodisthepercentageincreaseintheportfolio;or,itcouldbeanegativenumber,itcouldbeadecrease.Theprincipleisthatyouwanttheexpectedvalueofthereturntobeashighaspossiblegivenitsvarianceandyouwantthevarianceofthereturnontheportfoliotobeaslowaspossiblegiventhereturn,becausehighexpectedreturnisagoodthing.Youcouldsay,Ithinkmyportfoliohasanexpectedreturnof12%--thatwouldbebetterthanifithadanexpectedreturnof10%.But,ontheotherhand,youdon'twanthighvariancebecausethat'srisk;so,bothofthosematter.Infact,differentpeoplemightmakedifferentchoicesabouthowmuchriskthey'rewillingtobeartogetahigherexpectedreturn.Butultimately,everyoneagreesI--that'sthepremisehere,thatforthe--ifyou'recomparingtwoportfolioswiththesamevariance,thenyouwanttheonewiththehigherexpectedreturn.Ifyou'recomparingtwoportfolioswiththesameexpectedreturn,thenyouwanttheonewiththelowervariance.Allrightisthatclearand--okay.
Solet'stalkabout--whydon'tIjustgiveitinaveryintuitiveterm.Supposewehadalotofdifferentstocksthatwecouldputintoaportfolio,andsupposethey'reallindependentofeachother--thatmeansthere'snocorrelation.WetalkedaboutthatinLecture2.There'snocorrelationbetweenthemandthatmeansthatthevariance--andIwanttotalkaboutequally-weightedportfolio.So,we'regoingtohavenindependentassets;theycouldbestocks.Eachonehasastandarddeviationofreturn,callthatσ.Let'ssupposethatallofthemarethesame--theyallhavethesamestandarddeviation.We'regoingtocallrtheexpectedreturnoftheseassets.Then,wehavesomethingcalledthesquarerootrule,whichsaysthatthestandarddeviationoftheportfolioequalsthestandarddeviationofoneoftheassets,dividedbythesquarerootofn.Canyoureadthisintheback?
AmImakingthatbigenough?
Justbarely,okay.
Thisisaspecialcase,though,becauseI'veassumedthattheassetsareindependentofeachother,whichisn'tusuallythecase.It'slikeaninsurancewherepeopleimaginethey'reinsuringpeople'slivesandtheythinkthattheirdeathsareallindependent.I'mtransferringthistotheportfoliomanagementproblemandyoucanseeit'sthesameidea.I'vemadeaveryspecialcasethatthisisthecaseofanequally-weightedportfolio.It'saveryimportantpoint,ifyouseetheverysimplemaththatI'mshowinguphere.Thereturnontheportfolioisr,butthestandarddeviationoftheportfolioisσ/√(n).So,theoptimalthingtodoifyouliveinaworldlikethisistogetnaslargepossibleandyoucanreducethestandarddeviationoftheportfolioverymuchandthere'snocostintermsofexpectedreturn.Inthissimpleworld,you'dwanttomaken100or1,000orwhateveryoucould.Supposeyoucouldfind10,000independentassets,thenyoucoulddrivetheuncertaintyabouttheportfoliopracticallyto0.Becausethesquarerootof10,000is100,whateverthestandarddeviationoftheportfoliois,youwoulddivideitby100anditwouldbecomereallysmall.Ifyoucanfindassetsthatallhave--thatareallindependentofeachother,youcanreducethevarianceoftheportfolioveryfar.That'sthebasicprincipleofportfoliodiversification.That'swhatportfoliomanagersaresupposedtobedoingallthetime.
Now,Iwanttobemoregeneralthanthisandtalkabouttherealcase.Intherealworldwedon'thavetheproblemthatassetsareindependent.Thedifferentstockstendtomoveupanddowntogether.Wedon'thavetheidealworldthatIjustdescribed,buttosomeextentwedo,sowewanttothinkaboutdiversifyinginthisworld.Now,Iwanttotalkaboutformingaportfoliowheretheassetsarenotindependentofeachother,butarecorrelatedwitheachother.WhatI'mgoingtodonow--let'sstartoutwiththecasewhere--nowit'sgoingtogetalittlebitmorecomplicatedifwedroptheindependenceassumption.I'mgoingtodropmorethantheindependenceassumption,I'mgoingtoassumethattheassetsdon'thavethesameexpectedreturnandtheydon'thavethesameexpectedvariance.I'mgoingto--let'sdothetwo-assetcase.There'sn=2,butnotindependentornotnecessarilyindependent.Asset1hasexpectedreturnr1.Thisisdifferent--Iwasassumingaminuteagothatthey'reallthesame--ithasstandard--thisistheexpectationofthereturnofAsset1andr2istheexpectationofthereturn--I'msorry,σ1isthestandarddeviationofthereturnonAsset1.WehavethesameforAsset2;ithasanexpectedreturnofr2,ithasastandarddeviationofreturnofσ2.Thosearetheinputsintoouranalysis.Onemorething,Isaidthey'renotindependent,sowehavetotalkaboutthecovariancebetweenthereturns.So,we'regoingtohavethecovariancebetweenr1andr2,whichyoucanalsocallσ12andthosearetheinputstoouranalysis.
Whatwewanttodonowiscomputethemeanandvarianceoftheportfolio--orthemeanandstandarddeviation,sincestandarddeviationisthesquarerootofthevariance--fordifferentcombinationsoftheportfolios.I'mgoingtogeneralizefromoursimplestoryevenmorebysayingthat,let'snotassumethatwehaveequally-weighted.We'regoingtoputx1dollars--let'ssaywehave$1toinvest,wecanscaleitupanddown,itdoesn'tmatter.Let'ssayit's$1andwe'regoingtoputx1inasset1andthatleavesbehind1-x1inasset2,becausewehave$1total.We'renotgoingtorestrictx1tobeapositivenumberbecause,asyouknoworyoushouldknow,youcanholdnegativequantitiesofassets,that'scalledshortingthem.Youcancallyourbrokerandsay,I'dliketoshortstocknumberoneandwhatthebrokerwilldoisborrowthesharesonyourbehalfandsellthemandthenyouownnegativeshares.So,we'renotgoingto--x1canbeanythingandx--thisisx2=1-x1,sox1+x2=1.
Now,wejustwanttocomputewhatisthemeanandvarianceoftheportfolioandthat'ssimplearithmetic,basedonwhatwetalkedaboutbefore.I'mgoingtoerasethis.Theportfoliomeanvariancewilldependonx1inthewaythatifyouput--ifyoumadex1=1,itwouldbeasset1andifyoumadex1=0,thenitwouldbethesameasasset2returns.But,inbetween,ifsomeothernumber,it'llbesomeblendofthe--meanandvarianceof--theportfoliowillbesomeblendofthemeanandvarianceofthetwoassets.Theportfolioexpectedreturnisgoingtobegivenbythesummationi=1ton,ofxi*ri,.Inthiscase,sincen=2that'sx1r1+x2r2,orthat'sx1r1+(1-x1)r2;that'stheexpectedreturnontheportfolio.Thevarianceoftheportfolioσ²--thisistheportfoliovariance--isσ²=x1²σ1²+x2²σ2²+2x1x2σ12;that'sjusttheformulaforthevarianceoftheportfolioasafunctionof--Now,sincetheyhavetosumto1,Icanwritethisasx1²σ1²+(1-x1)²σ2²+2x1(1-x1)σ12andsothattogethertracesout--Icanchooseanyvalueofx1Iwant,itcanbenumberfromm
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- Portfolio Diversification and Supporting Financial Institutions
链接地址:https://www.bdocx.com/doc/9620147.html