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AnAlternativeViewofRiskandReturn:TheArbitragePricingTheoryChapter12Copyright?2010bytheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinKeyConceptsandSkillsDiscusstherelativeimportanceofsystematicandunsystematicriskindeterminingaportfolio’sreturnCompareandcontrasttheCAPMandArbitragePricingTheoryChapterOutline12.1Introduction12.2 SystematicRiskandBetas12.3 PortfoliosandFactorModels12.4 BetasandExpectedReturns12.5 TheCapitalAssetPricingModelandtheArbitragePricingTheory12.6 EmpiricalApproachestoAssetPricing12.1Introduction
ArbitragePricingTheoryArbitragearisesifaninvestorcanconstructazeroinvestmentportfoliowithasureprofit.Sincenoinvestmentisrequired,aninvestorcancreatelargepositionstosecurelargelevelsofprofit.Inefficientmarkets,profitablearbitrageopportunitieswillquicklydisappear.TotalRiskTotalrisk=systematicrisk+unsystematicriskThestandarddeviationofreturnsisameasureoftotalrisk.Forwell-diversifiedportfolios,unsystematicriskisverysmall.Consequently,thetotalriskforadiversifiedportfolioisessentiallyequivalenttothesystematicrisk.Risk:SystematicandUnsystematicSystematicRisk:m
NonsystematicRisk:n2Totalrisk
Wecanbreakdownthetotalriskofholdingastockintotwocomponents:systematicriskandunsystematicrisk:12.2SystematicRiskandBetasThebetacoefficient,b,tellsustheresponseofthestock’sreturntoasystematicrisk.IntheCAPM,bmeasurestheresponsivenessofasecurity’sreturntoaspecificriskfactor,thereturnonthemarketportfolio.Weshallnowconsiderothertypesofsystematicrisk.SystematicRiskandBetasForexample,supposewehaveidentifiedthreesystematicrisks:inflation,GNPgrowth,andthedollar-eurospotexchangerate,S($,€).Ourmodelis:SystematicRiskandBetas:ExampleSupposewehavemadethefollowingestimates:bI=-2.30bGNP=1.50bS=0.50Finally,thefirmwasabletoattracta“superstar”CEO,andthisunanticipateddevelopmentcontributes1%tothereturn.SystematicRiskandBetas:ExampleWemustdecidewhatsurprisestookplaceinthesystematicfactors.Ifitwerethecasethattheinflationratewasexpectedtobe3%,butinfactwas8%duringthetimeperiod,then:FI=Surpriseintheinflationrate=actual–expected=8%–3%=5%SystematicRiskandBetas:ExampleIfitwerethecasethattherateofGNPgrowthwasexpectedtobe4%,butinfactwas1%,then:FGNP=SurpriseintherateofGNPgrowth =actual–expected=1%–4%=–3%SystematicRiskandBetas:ExampleIfitwerethecasethatthedollar-eurospotexchangerate,S($,€),wasexpectedtoincreaseby10%,butinfactremainedstableduringthetimeperiod,then:FS=Surpriseintheexchangerate =actual–expected=0%–10%=–10%SystematicRiskandBetas:ExampleFinally,ifitwerethecasethattheexpectedreturnonthestockwas8%,then:12.3PortfoliosandFactorModelsNowletusconsiderwhathappenstoportfoliosofstockswheneachofthestocksfollowsaone-factormodel.WewillcreateportfoliosfromalistofNstocksandwillcapturethesystematicriskwitha1-factormodel.Theithstockinthelisthasreturn:RelationshipBetweentheReturnontheCommonFactor&ExcessReturnExcessreturnThereturnonthefactorFIfweassumethatthereisnounsystematicrisk,thenei=0.Re悼la廉ti初on崖sh撿ip醉B臭et蠢we后en墊t鑄he芬R獄et齒ur摘n決on劃t銀he咱C稼om脫mo寫n此Fa傷ct秤or釀&池E般xc瀉es塑s科Re精tu通rnEx往ce意ss渴r挑et透ur而nTh頸e察re具tu隔rn挖o弊n灰th踏e柳fa巨ct碗orFIf咱w斃e眾as拒su頑me緩t臂ha羅t符th霜er紅e廣is鈴n彼o騙un甲sy便st插e(cuò)m嚇at倡ic扔r螺is才k,叉t梳he早nei=等0.Re掌la炭ti婚on扯sh脅ip溝B拍et臉we豎en廣t障he熊R侵et舟ur最n卡on鋸t浪he岔C董om輸mo畜n壞Fa趕ct助or尚&功E棗xc耀es輪s總Re茄tu傳rnEx犧ce活ss抖r請(qǐng)et郵ur務(wù)nTh炸e贏re敘tu苗rn遠(yuǎn)o買n廚th艦e棉fa這ct身orFDi笨ff莖er升en意t堵se撥cu義ri吊ti繭es平w坐il亮l栗ha眼ve撞d誦if而fe戴re客nt柴b評(píng)et痕as喘.Po糕rt潔fo無li素os侮a蛇nd舟D辰iv調(diào)er難si較fi精ca度ti和onWe映k捆no翼w寇th紐奉at濤t葬he蘋p誕or俗tf饅ol求io墨r亂et繼ur猶n鋤is劍t蠶he闖w鮮ei破gh莖te飾d驅(qū)av嶼er束ag督e毛of富t檢he義r乎et婦ur倘ns事o魂n賺th駝e綢in趕di頸vi架du袖al膚a艦ss過et決s亞in汪t沈he規(guī)p確or罵tf餡ol錘io堅(jiān):Po滿rt來fo會(huì)li炊os幅a標(biāo)nd撞D虛iv尺er帽si宮fi如ca浙ti獅onTh才e城re澆tu酸rn鵲o殖nan朋ypo拼rt裁fo閃li嶺o提is園d換et樓er泳mi宅ne團(tuán)d救by野t番hr公ee務(wù)s屠et乘s竹of腦p頁ar層am狀et叮er偉s:In榮a軋l簡(jiǎn)ar桿ge捉p瓣or蠻tf精ol旅io到,黎th泥e虎th蘋ir濕d銀ro吃w劍of稅t些hi撈s盞eq戒ua非ti船on錘d層is棕ap銅pe腳ar擇s翅as課t奸he就u呀ns屯ys屠te抖ma點(diǎn)ti滔c遞ri討sk秧i爬s泉di恩ve耗rs梯if杯ie宅d涼aw堆a(bǔ)y談.Theweightedaverageofexpectedreturns.Theweightedaverageofthebetastimesthefactor.Theweightedaverageoftheunsystematicrisks.Po屬rt往fo柜li牽os渠a殊nd結(jié)D壞iv字er邪si寄fi捆ca辱ti選onSo突t之he搞r俊et糧ur厘n宵on唉adi塑ve顏rs敢if化ie穴dpo薪rt肌fo叨li近o且is盒d喝et吃er賊mi制ne渡d抱by嶼t恢wo閥s旗et研s旬of吼p閱ar乏am饑et磚er雅s:Th評(píng)e擊we哥ig宿ht喊ed奸a汽ve陪ra紡ge尖o葛f算ex淺pe勾ct鉗ed乘r潮et退ur芹ns撞.Th絹e姜we嚴(yán)ig莊ht嗽ed裳a(bǔ)揭ve喉ra扛ge跪o岡f耀th宗e角be辛ta盜s程ti守me爆s歪t(yī)h傲e病fa赴ct吼orF.In或a醬l爺ar討ge卸p股or說tf握ol絨io天,版th脈e離on善ly椅s裂ou螺rc膨e留of引u遙nc炎er敞ta象in們ty飲i寸s教th屆e媽po孝rt鏡fo些li借o’烤s靠se響ns優(yōu)it夾iv示it妄y滔to鬼t泳he鉗f蘋ac逐to導(dǎo)r.12任.4寄B座et歡as垃a日nd笛E坦xp私ec澆te撿d紹Re把tu吸rn充sTh繼e吐re盤tu簽rn飾o漢n稠a攔di瓣ve孤rs桐if泛ie登d客po豎rt做fo哄li灣o淘is旅t鍵he飲s熄um油o冤f詢th蔥e型ex叮pe匆ct紛ed段r答et著ur雄n傍pl客us蛛t叛he惠s弱en臺(tái)si綿ti具vi擇ty尾o身f帳th首e陜po恭rt中fo肢li妹o犯to沫t弄he抹f扮ac醒to抱r.Re益la態(tài)ti愉on宣sh寸ip匹B瓦et泄we氧enb&際Ex儲(chǔ)pe僻ct魄ed蛇R紹et噸ur況nIf允s秧ha行re譜ho恭ld賞er拔s韻ar諷e匯ig殖no栗ri密ng劫u罪ns員ys梨te烈ma艱ti酸c滔ri產(chǎn)sk包,累on母ly膛t曬he洞s低ys最te奮ma點(diǎn)ti漫c主ri煩sk儲(chǔ)o申f杯a堡st怨oc修k雹ca青n申be激r檢el宣at顆ed條t徒o蘋it購sex數(shù)pe尸ct復(fù)edre斯tu筑rn咱.Re恰la茂ti乏on問sh餅ip狐B宣et竹we系enb&劈燕Ex蘭pe扒ct晶ed容R屯et燒ur安nEx閉pe尖ct頁ed雅r栗et免ur幫nbABCDSM驚L12幼.5根T謙he稱C間ap潑it狼al潑A唯ss離et增P拍ri晉ci儀ng筋M渾od塘el皮a起nd粘t沫h(huán)e植A怒rb讀it蝕ra范ge懶P躁ri每ci鏈ng樓T懶he顯or趨yAP艇T禁ap浙pl辦ie獻(xiàn)s蹲to聚w業(yè)el富l大di幼ve小rs攜if柄ie激d泥po剝r(jià)t勒fo覽li刊os糊a踏nd滑n己ot樹n坑ec陶es糊sa乳ri澆ly首t償o撿in弦di扶vi坦du巷al腥s頑to唐ck堅(jiān)s.Wi等th牢A蜘PT拍i災(zāi)t奪is徒p鈔os范si依bl租e航fo腳r鏡so幣me疾i枕nd改iv幅id竄ua遷l肯st趟oc輕ks疤t侍o困be眠m唯is謠pr凝ic槽ed滾-侄n吃ot鉤l奸ie胖o洪n丈th育e脹SM醉L.AP佩T造is皆m罩or滾e荒ge竿ne離ra圣l接in膚t徑ha跟t允it乖g去et陷s怒to柄a鬧n民ex用pe農(nóng)ct搬ed頑r脹et拘ur絲式n吃an沸d襲be老ta華r捷el去at伏io鼻ns確hi干p觸wi太th成ou答t數(shù)th足e帶as底su刺mp碌ti筆on豎o州f財(cái)th運(yùn)e口ma辛rk詢et乘p青or哀tf過ol欣io科.AP裂T槳ca夏n計(jì)be暢e稠xt交en母de競(jìng)d棵to稱m攏ul況ti蝴fa傾ct帝or域m輪od垮e(cuò)l速s.12歡.6煩E焦mp縮慧ir什ic模al民A適pp沫ro鬧ac妄he幸s沙to萬A漫ss聰et鄙P譜ri躺ci塊ngBo是th繳t絡(luò)he企C傻A(chǔ)P平M均an愚d遣AP乎T誰ar處e紗ri博sk卡-b吹as劃ed路m埋od句el辭s.Em乳pi忠ri公ca斗l恢me塞th櫻od晃s宏ar穗e牧ba賄se似d泉le蒼ss隸o掙n瘋th豬eo宵ry徹a坦nd裹m沫or匙e暑on迫l凳oo肝ki棄ng溫f紫or及s航om運(yùn)e史re脂gu銳la銅ri撓ti座es條i鄰n酒th拉e哲hi融st戲or封ic跳al齡r猛ec抬or致d.Be漂a晃wa欠re永t充ha盜t嗎co卸rr鋪el莊at渡io往n店do勻es暫n辜o(jì)t若i則mp脅ly希c抄au純sa各li次ty姑.Re枕la斑te叉d邀to受e熔mp惠ir傍ic返al倉m而et英ho職ds賢i蘿s劍th瀉e匹pr邊ac儀ti堪ce讀o軍f福cl吊as講si企fy跡in眨g窗po使rt杠fo莫li蝴os咸b裹y剪st饞yl意e,e.愈g.艘,Va種lu拜e引po忙rt冶fo等li腔oGr殿ow霜th槽p掘or它tf卷ol頁ioQu銹ic文k碎Qu步izDi授ff累er片en球ti醫(yī)at怠e浪sy做st課em愁at犁ic菜r嚼is膚k逼fr錢om昏u當(dāng)ns席ys否te仰ma蛛ti驅(qū)c角ri鈴sk責(zé).郊Wh杏ic吩h姓ty追pe野i群s境es肥se稻nt伯ia榴ll捉y(tǒng)竿el拒im音in諸at飼ed挺w刺it拾h浙we曠ll客d程iv湯er看si咬fi瘋ed鍵p單or趨tf丙ol需io價(jià)s?De崇fi謹(jǐn)ne底a鏟rb狠it仔ra鹽ge勉.Ex誼pl華ai嶼n刺ho甜w梳t(yī)h憲e拋CA完P(guān)M貝b真e突co仙ns恰id垃er賴ed亂a軟s刮pe蠟ci府a(chǎn)l各c康as階e陸of真A抽rb舅it毀ra遲ge撇P躺ri密ci帝ng富T貌he屆or眾y?1.Supposeafactormodelisappropriatetodescribethereturnsonastock.Informationaboutthosefactorsispresentedinthefollowingchart.BetaofExpectedActualFactorFactorValue(%)Value(%)GrowthinGNP2.043.5%4.8%Interestrates-1.9014.0%15.2%Stockreturn10.0%a.Whatisthesystematicriskofthestockreturn?b.Thefirmannouncedthatitsmarketsharehadunexpectedlyincreasedfrom23percentto27percent.Investorsknowfromtheirpastexperiencethatthestockreturnswillincreaseby.36percentperanincreaseof1percentinitsmarketshare.Whatistheunsystematicriskofthestock?c.Whatisthetotalreturnofth
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