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.rer ry r{ c Q'---, fY*'i Risk, Retunm, amdthe CapitalAsset Pricing Model kill or luck?That'sthe questnn llc Wnll Sttut laurnnls Investment Dartboard Contcstsoughtb answcr hy comparing rh, a.tu,rl i,,ve{rrnr re-uh- ,'f profe*i,'rr.rl ,)r.,1)\1, dgdrr-t.,nr.,hurdnd rl.,rl lhros,r.. I Iere . l-,\\ the . onn .r worlFd frr.t, fl, t{drl Shce!Iourlnl (WSD pickcd forrr professional anal)'sts,and each of thosa pros formeci a porifolio b), picking four stocks.The stocks h.,.1orr.,.jc.r lr\ \Y<f A\41.\.or \.r-.i.r,t: have a market capitnlizationof .t least Xj50 rtlrlhon ,i -lo.L pn,e oi,r, IL'sr $2:.rrrd "r.l l\.'venver.rEd.ilv I'rd'* .l dl le.r.l'b'n0.rr' -. Sccond,nnrateurscould enicr ihe contestby L-rr.'ilirg thpu picl ,'t d .rnth .rocl ro th, WS, \ 'hich then pickcd four amntcursat random and combined thcir choicljs to makc a four siockportfolio.Third, a group of'di t,'rsform".l.r portLlotrv i-'.'$Int toLrrd.'rts .rr rl,. .rocl l.rbl"-.\r lhe o(qruning p.r.h ot curtesi, thc WS/ announcedtho bix resullnrg portfoltus,nnd at tht cnd oi six monihs, the paper announced fesults. the The lop tw'opros were invitcd back fof the ncxt contest. <in,F I".'0 lh(rc i{\e bpfl 142compk'r,'i The pros bo.t the daris 87 times and contesis. Iost55 fimcs.The pros nlsobeatthe Dowjones lndustrial ,^verateh 547' of ihc'contesis. The pro- h.rJ .rn nvern6e .i\-r,,'nrh portr..lro r.lum ul 10.'i. nr|rilrhr8h,r rl,rn eilh.r th, c.oo rlre{lJrl. DTI\ {r\ mon.h.r\, rdt. ',i ',r retum of only 3.57..Thc readers,|neartinl, l.n .rn ,\errdf nf 4', \!r-u. " -.l|r\. penod (30contests) itain of 7.2'l for the pros. D{r lhe\e r!\Lll\ mc.,n ll,al .lill ir Ino,( lh.rn rrrp,,rr,rnl lu.l whenrl ..nrc.lo r'\e,li rd in sk)cks? Not necessarily, accordingio Brirk)n Malkiel, arl ccononics plofessorat I'rincetor and the alrthor of ihe lr'idely read book, ,{ cin.( lF( nr 'Rn,t,l,qWal]. n,'.r.r tv,l/ qrr.1r. selcctcd portfoliosconsislof rarldonlly chosen rhulld h.,re .,\L-.rAe r.l "to.l', thev Horvever,thc pros havc consistentlypicked l,'tshri-k .1,\L:. BF. du., rh,rcr\.r-,,1.,,ll m.r tpr Llunngr1),*l ol lhe r,,rlci ,'n,. srJhl expecthigh-fiskshcks to outperfonn the average stock.According b Malkiel thc pros' peF formancecouid due io. risin8rnarketralher be than superior analyticil skills. Thc WS.l sloppedihat contcstin 2002, r,{ewon'i knor{ so \4dlU.l ,'., . rits\t,'r wrunts. ior.,,rL \vherh(r I hc h 5/ nnN run.., ruq . onlc-t prllmt cr\ .,mJteLrr..rd.,Ir..r -r\ d,rt- In lhe re.f nllv.or)r Conicst No. 21, ihc darts trounced the Pleicd r,'d, r-b\ t.llnrn820. \1 r.J.rhcrc.rdL,, (.-, of -1.1% (the Doi{ JoncsIndusrrial Average w.r' .rp 5.1 I. O\crrll. r..r,ier. ..'r1*t-. 'thiL. ll,e.l.rrl. h.r\e w,'rr I r. lf you +' vau' hl\rLi hke t,' vnler the.,'rrtp\1. sk)ckpick b 201 In ihis chapter, .e start from the basicpremisethat investorslike retums and dislike Iisk. Therelore,people $'ill invest in riskier assetsonly if they expect to rcceivehigher returns.We.tefhe precisel]r rvhat the term /isl meals as it re]ates to invesiments.We examineproceduresmanaters use to measue risk, and wc Thetextbook's Web sire discuss relationshipbetweenrisk and retum.In later chapters extendthesc c o n r o i i so n & c e / f e r h a r the \^re relationshipsto show how dsk and return interact b detcrminc sccufity prices. Managers must understandand apply theseconcepts thcyplan thc actionsthat as chapter's cu arlons co 'he The f e for ihii chapieris will shapetheir firms' futures. FMl2 Ch O6 lool Kt.xls, ro open the f e ond fol 6.1 lnvestmrentReturns With mosi investments, individual or bllshess spendsnoncy toclayivith thc an expectation earninjl even more money in the future. The conceptof /ctrl, proof f.ictes investors 'ith a convenient\^'ayto express financialperfornance of an the investment.To illustrate, supposeyou bu)' 10 sharesof a stock for 51,000. Tlle stockpays no dividends,but at the end of one vear,you sell thc sbck for' $1,100. What is the retum on your $1,{)(l{l investmcnt? One \,vayto expressan investmcntrcturn is in dolln/ irr'rs. Thc dollar reium is simply the total dollars receivedfrom thc invcstmcntlcss ihc amount invesicd: Dollar retum : Amount receivecl Amouni invcstcd : $1,100 $1,000 : 100. lf, at the end of the ycar, yor scll thc stock for only $900,your dollar reiurn lvill be $1i10. Althorgh cxprcssingrcturns in dollars is casy, t*,o problcms adse: (1) To makc a meaningtuljudgmcni about thc rctunl, you need to know the scale(size) of the ilvesiment; a $100return on a $100invesimentis a good return (assumhg thc invcshncntis hcld for l year),bui a 5100 reiun or a $j10,000 in\.estment rvould be a poor retu . (2)You also need to know the ttuing of the return; a $j100 return on a ljl00 inveshnerltis a very Boodreturn if it occrirsalter one trear but the same d.Jll.r',rurr ''t, r '0 ), .-i-,rut \,r);,od. The sduiior to the scaleand tjrnin8 problemsis !o express investmentresr ts as nfesalrctutn,nr Wtc.rtdSe /drl,rs. For example,the Iate of relurn on the 1 year stockinvestment,lvhen $j1,100 receir.ed is after 1 ]rear, 10%l is Amornt rcccivcd Rateof return : Dollar retuD Amount tuvested Amouni invcsicd ljl00 $1,000 Amount invested = 0.10 10%. The rate of reium calculation"slanctardizes" return bv considerinsthe annual the Irve. rnert Al Lougl' I'r.e'.rn'plel'."onh oneoutflo(.,nJone 'FtLrr'.perLrnilo low the annualizect rate of retun can easily be calculated situations 'here in rm tiple cashfloR'soccurover time by using tim value of money concepts. ofd Model Rsk, Reiurn, the CopllolA$et Prlclng shoud stive In Chopterl, we lold you lhol mo'rogers io mokeiheir firmsmorevolloble, ond lhol rhevolue of or r r s oele ri re d . b / rl e ' 7 e r:l i l g o rd i " k rl o w sl rl r]. n s how io meosurco flrm's risk ond the roie ol rel!,r expeciedby shoreholders, which o$ecislhe weighi ed overose cosr of copito (WACC). All ese hed equol, higher risk increoses the WACC, which reduces flrm'svolue. fie --- { . waccl {r wAccl' {r WACC)' {l wAcci StLi'tt5l Di{fefcntiotc bei.deen dolldr returnsand rolesof rctum. onC Why orc rqtesol returnsupedorio dolldr rerur.sin remrsof oc@unti.sfor fie lize of inveslment the iiininq of (osh{low5? Supposcyou poy 5500 for on inverheni rhor rerurns5600 ifl I yeoi Whoi i5 the onnudl rdte of rcturn? l2o%l iiisk 6.2 Sianei-A!{ine Thus, Risk is defined Wfl)silr'"a ha/ard; a peril; exposureto lossor Lnjlrr].." ihnt somc unfavorablevent will oc(ur. If you go sk)' risk refers to the chancii diving, yoLrarc iaking a chnncewith your life skydiving is risky. Ii you bet on thc horses,you arc riskhg youf moncl,. If )rou hi,est in speculntivesbcks (ot rcruy, ll|l1 stock), vou nrc tnking a risk in the hope of c.rrring.rn apprcciabte ,4n asset's risk can bc ilrulyzed in t ,o ways: (l) on a stnnd rlone basis,whcrc ihc assctis considercdin i$olrti(nl,and (2) on a portlolio basis,where ihe asseiis an stand-alonerisk he].l as one of a nrrnrbcrof assets a Porifolio. ThLrs, nssot's in would f.ce if he or she held only thjs ono isset. Obviousl),, is the risk an invesior lo ost assets held in pr)rtfolios,but it is necessarl' utrcl(rstandstand-alone are risk nr d portfolio context. risk in order to u)rd$staDd of To illustratethe risk of finincial assctr,s pposean invesk)rbuys 5100,000 rctufn of 5%. In this c.rse,the rate oi bills rvith an expected shori-tcrn TreasLrrl' and ihe investmeni rellrrn on the investment,5T,cnnbe estimaiedquite precisely, if the $100,000 \^,crcinvestedin is clefincdas benrgessenti,rlly ris(11.. Hoivcvct just being organizcclio prosper't ior oil in the mid the siock of a conpany Atlantic, then ihe invcshncnt's retlrrn could not be estiurntcclprcisely.One nriShtanalyzethe situationrnd concludethai ihe criry./r'ilrnic of rcturn, in a sta' tistical scnse,is 20'1, but tlrc nrvesior should recognize Lhnt Lhcd.trdl rate ot thcrc is a significani return could rante frorr, sav +1,000%to 100%.Becnuse return, the stock would dan8er of actually earning much lessthar the cxpectccl be r"l.r rrLl' )itt rto ,tlisnnenj sha ,l bt tu,lotnku lessltu ttp':ct,:,1 ol n ttnr ishighenotqh pocril'cdt isktrftht ifir',:stt'tr]tt our crnmple, it is In 1t, eiryot te the itLttstt fot tlk b buy the oil c(nnpnn),'s stock ii clear tlut fci{ if any invesiorsr{,()Lldbe rvilling T-bill. its expecicdretufn were thr s.rmcas ihai of the 203 Probobiliry Disribuiions Bosic for ond Foods Roieof Retu.n sl,ock on if This Demond Oc.urg Probdbi[ry This of Demond Oc< Sircng 0.3 o.4 0r t! 100% t5 17a) 4A% t5 lt 0 ) Risky assets rarely actually produce their xpectedratesof return, generali, risky assetsearn either more or less than 'as oritinally expectec]. Indeec:I, if assets always prodrced their expected returns, they would not be risky. lN'estment risk, then, is related to the probabiligr of actuall)' eamhg a low or ncgativerctun: The $cater the chanceof.t lo$/ or negativereturn, th(] riskier th(] invesimcnt. Howcver risk can bc dcfinccl morc prcciscly,an.l wc do so h thc Frobabitity Distributions An event's l'"lalUtrtl is c:lefined the chance that the event will occur. For as example,a weather forecaster might state,"There is a 40% chanceof rain toctay and a 60% chancethat it will not rain." If ail possibleevents,or outcomes,are listed, and if a probability is assigned to each event, the listnlt is called a probability distuibution. Keep in mind that the probabilities must sum to 1.0, cr 1007,. With ihis in mind, considcrthc possibleratesof return due to dividends and investmentin the stockpricc changcsthat yolr nighi cam ncxt year on a $1{1,000 an lntcrnct companyoffcris stockoJeither or it nrg deep discountson faciory sc.onds and ovcrstockcdmcrchandisc.Bccausc its nc{, scrviccslnay or may not bc compctitivc in thc faces intensccompetitbrl, markefplace, ib future ea.nilgs cannotbc prcdictcd vcrv wcll. lndccd, sor11c so Basic ner. conpary could developbettcr serlicesand litcrally bankrupt food staplcsto groccry siores,and Foods,on the other hand, disiributescssential its salesand prcIiis are relatively siablc and predictable. The rate oI rctum probability disttbutions for the iwo companies shown are in Table6 1. Thereis a 30'l' chanceof strong dcmand, in {.hich caseboth compades will have high earn gs, pay high dividerrds,and enjoy capital gains.There is a 40% probabiliiy of nomal demand and moderaierciurns, and thereis a 30% low probabilityoI weak demand,(.hich $.i11rnean carningsand dividends as well as capital losses.Notice, however, that's raie of refun could vary far more rridely than that of BasicFoods.Therc is a fairly high probability ihat the value of's stock will drop substanliaLly, resr.tin8 in a 70% loss, while thereis a much smaller possibleloss for BasicFoods. Note that the followinjl discussion dsk appliesto a[ random variables, of nol 20 Chopter 6 Ris[,Relum, ond ihe Copiro A$l Pricing Model Colculotion Expected of Rotes of e-Ies0uTce Demond t$e Prohobilir ol Roieof Return 6r Roieof Relurn Compony's Thk Demond if This Demcnd Product: if This Demond Product: (21x (31 Produd' oc(urins occur5 occurs l2l x (51 = t4) = (6) (21 (3} {lt {5) Srrong 0.3 o.4 0,3 IA I00% t5 170l 30% 6 (2 t ) 40% t5 (t0) 12./" 6 t9l Exoected of Return Rate If we multiply each possiblcoutcomeby its probability of occurrenceand then sun thcseproducis,as in Table6 2, we have a ?r.rSrled a|dl,rse outcomcs.The of weights are the probabilities,and the weighted averageis the xpectedrate of retuln, i, called"r hat."' Thc cxpected ratesof retum for both and Basic Foods arc shown in Table6-2 to be 15%.This iypc of iable is knorvn as a pdyof Thc c'xpected raie of return calculationcan also bc exprcssed an equation as that doqr thc same thinS as thc p.lyoff matrix table:'? Expectedrateofreturn = i = Prrr + Prr, + . . -r-Pirn: >PLrr. 16-l) Here ri is the ith possiblcoutcome,Pi is the probabjlity of the ith outcome,and n is the number of possiblcoutcomes. Thus, i is a wei8hied avemgcof ihe possible outcomes (the rr values), $'ith each outcome's r\'cight being its probability of occurrcnce. UsiIS the data for, obtain its expectedrate of rcturn as l\e i=PLG)+P,(r,)+Pdrt = 0.3(100%) 0.405%)+ 0.3(-70%) + = 15%. BasicFoods'cxpected rate of retum is also 15%: + + i = 0.3(40%) 0.4(15%) 0.3( 10%) = r5u/a. Wc can graph the raiesot rcturn to obtain a picturc of the va abilily ofpossible ouicomcs;this is shown in thc Fi8ure6-1bar charts.The height ofeach bar signifies lhc probability that a given outcome $'ill occur. The ranEjeof probable In lob' choprc6, E will u.e ir ond i. b rgn'ly fi reruh! oi bon& ond iocls, rc5pecriEly Howder, 6u dEinc ron n uniece$ary in rhis.hope,, s. c ilt u3e6 seneolrerm, i lo 3 sn t Ae 'pe.ied Gtum on oi ,Thr glorion svo d br ony rondomvdrdbe wfi o discrele probobiirydisr6uion, nor luifor sro.[ rtuns I 205 Probobility Distributions's of ond 30 60 40 20 0 20 40 60 I Erpecled Rare ot Beturn I is return of 15%.]I1e returnsfor fron 70 b +100%,with an expected BasicFoodsis also 1570, its nngc is much na o$,cr. but expected retun for Thus lar,rrc'haveasstrreLlthai onlv threesituationscanexist strong,normal, and weak demand.Aciually,of course,dcmand could rangc fronl a dccp .lepresin sionto a fantasticboo , and therearcunlimitcd possibilities bctwcen.Suppose pafienceto assign a probability to cach possiblc lcvcl of we had ihe lime and demand( 'iih the sum of ite probabililjesstill equaling 1.0)and to assigna ratc of return to eachstocklor eachler.elol demand.We would have a tablesinlilar to Table61, except it woulct have many more entries in each coiunnr. This table col d be used to calculaieexpeciedrates of relum as shohrr prcviously,and thc probabilities and outcomescould be approxjmatecl coniinuouscurvessuch as by thosepresentedin Figure 6 2. Llere il.e have changed ihe assunrpfions that so thereis essentiallyazero probabititythat Sale.conis rcluln willbeless rhan 70% or more than 100%,or that BasicFoods' retum will be less than 10% or more than40%,b t virtualy any return r.ithin theselinits is possible. 'l'heti.eJtter, nLorc peakcd, prcbdbililv Dr the dislriL)ution, morcLikL4t is that thc Llr it nct1tLll ollt.otIt: ruill be clase theeipected ta ulue, nni, cotgcquutlV, less the liklly it is thtltth! dctutllretut raillettLI l1t bdolD eryectd rc!urn.Thus,thelighterthefob Ip thc rbiliLy Llisttibliia ,thelauet ttu risknssigedta r sto.i. SinceBasicFoodshas a rela' tivcly tighi probability distributio& its a.tral ?"trlfl is likely to be closerto its '157. expcct rctur thai that l Measuring Risk: lleviaiion Stand-Alone ThcStandarrl hassurounded Riskis a difficult conceptto grasp,and a greatdeal of controvcrsv ittempts to define and measureit. Floweveaa commor dcfinition, and onc that is satisfactory many puryoses, slatedin iernrsofprobabiliti, disidbttbns such for is 206 R sk, Reiuh, ond the CopltolAs6t Prc ng Model as thosc prcsented in Figore 6-2: TII! tiglttcr th ptobnbilitv distribution of crpccted ttu fLnuft rtt nls,thc snlaller tiskoln Siren11orst c,rt.According to this definition, BasicFoodsis lessrisky than because thcre is a smaller cha)rcc that iis actualreturn will end up far below its expectccl rcturn. To bq mostmetul, any measure risk should hnvea definite valuc wc need of a measurcof the tightness the prcbability disiribution. One suchrncasurcis the oI standarddviation, the symbol for whjch is {r, pronounced"sigma." Thc snaller the standarddeviation,the tighter the probability djstribution, and, accordin8li,, the Iessrisky thc stock.To calculate standardde!'iation,we proceedns shou,n the in Table6-3,taking the followrng stepsil 1. Calcuiaiethe expected raic of retum: f\pec,(d r.rre o',.' urn i _ >rr. For, previously found i : 15%. lve 2. Subtract the cxpected rate of rcrum (i) from each possibleoutcomc (rr) to obtain a sei of deviationsabout i as shown in Column 1 of Table6 3: =r,-r' Deviationi 3. Sqlare eachdeviation, then muliiply ihe rcsult by the probability of occrr' rence for jis rc]atcd olrtcome,and then sunr ihcse products to oblain thc Continuous Probobility Disiributions's BosicFoods' of ond 0 15 t t%) -\o o$ no1o1 ,eoordns o p obob ol .o o o-.o-a- Fo/e beer ld q.o ,o{ rcse:1 ^ro'o ts e 6 l T ' - " l"p ,o b .h r yo'obb nr '"5 5'l .orl 0.r'6er \-..r beo\er\""o" ",o,l r -o4s m o 1 /o o r ,6 "o r o 1 p - "o d o r j^r'he"w | -on.i 1ourdd i :-o'B oppopri oreroo)r$hol rl"ep'obobil'rylolob'oris o' lc.r br ol,"tu,r o, ba,r who, l " p'oba6,l,\ ijolobbn e'r'ed ftrnricacour$3 ins exodly fiorrcb lhis bpi. is.ovo,od in debilin 'o'" jlhe5e aq!orions ore vo id hr ony rondomvor ob e nom. dh.rere probobil\, dnribufion, nar ur for returns 207 Siondard Deviotion Colcu's (Voluesfor r'ond i ore percentoges.) ( ll 100 15 = 85% 15 - t5: 0 70 t5 : -85 1., iF (21 7,225% 0 7,225 k,- il,P {3t .31 ,225lla - 2 , 1 6 7 . 5 % 17 = l0)(0.041 0 . 0 =2 ,22s)l0.31, 1 6 7 . 5 \7 2,335.0% = Srondord devioriono : \Gl : .,-t3SS:i.= Usm variance of the probability distributiol as showr in Columns 2 and 3 of the table: = varLance o- : f rr . z\t 16'21 4. Finallt finct the squareroot of the vadanceto obtain the standarddeviation: Standard deviafion = 0 - {6-31 Thus, thc standard deviation is essenfially \^'eightedaverageoI the deviaa tions 6om thc expectedvalue, and it providesan idea of how far aboveor belolv standarddeviaiiorl the expeciedvahe the actualvalue is likely io bc.'s we Using ihesesanc procedures, Iincl Basic is seenin Table6-3 to be o - 65.84%. has the larger Foods'standarddcviation to be 19.36%. that tior! rvhich indicatesa greatervariation of returns and thus a greaterchance ihe aciual rciuln ma), be substantiallylower ihan ihe expcctedreturn. Therefore, a iskicr investmentthan BasicFoodsrvhen held alone.a is If a probability d istribution is normal,the l?.irdlrefurn wili be within r 1 standard deviation of the eryc.tcdreturn 58.26percentof thc time. Figure 6 3 illustratesthis point, and it also shows the situationlor :t2 o and a3 o. For Salecom, for Foods.Thus, i = 15%and o = 65.84%, whercasi - 15%and o = 19.36% Basic if the tr.o distributions were normal, there .ot d be a 68.267'probabilitlr that or's actual retum would be in the ranee of 15 :t 65.84%, from 50.84to rangeis 15 :t 19.36%, irom 4.36to 34.36%. or 80.84%. BasicFoods,the 68.26% For o Forthe averasefilm listed ol thc Ne$, York StockExchange, hasgenerallybeen ln the ranse of 35 to 40%in reccntvearslMo, fnonc o c..u.bB hoveno builin lormulobr lhd is [e aipeded vo !e o, vofon.e lor di5.rcleprobobi iy p,.6.hllrl$ fof o olrcomes equo. The,erore, mrr so yo! o,e dirr 6dons, er.epr fo, $e speco .ose n wh ch 'he .o4op"or'P oo o .od. oc l" p o o - o ' d ' 1 4 . 1 . 6 . o rl qaB ' o'. 'qa , o , . o . . l . o ' ""Pr o o lo ,' o D - tsDo 6 o b l1o o,' 'a; p p 0 0 0o ,"ool a L ol od ob' o. , l.o b..mror-o o oo. "" ^ 1 e ,.0 0 d shbuliom,olhoush n po$i6e b f fd lree.dd inson the web $o1do $e.a tuLof.B fof d reE disr bufan: 208 Risl,Retum, ond rheCopirolAsser Pricing Model Probobiliiy Ronges o Norrnol for Distribuiion e- r es ouT c e pobobility diskiburions, e lt/ei 64 ol rheletb@k'sWebsire. o. Ihe o@ undd th normdl.!tu6 owdy! squos 1.0, o, 100%.Thus, ordsunderony oo r of iormo th6 oryes d.own on ihe som6roa, wh. ar ih.y 016p6dkedo, fldt, mu3r 6qudl. bo Holfof e areo!nde'o cuvo s b thelehof$e meoi,ifd.orns $oi$oro is o 50%pbbob ry thor ocruolourcomg wilb. ei! rhoi $e meoi,ondhoI is b ihe ,lshr ?, indicoriso 50%probobilry of fior 'he llbo d'6d1a, $. mdn lr w $on ol Ae oreou;derthocurye,68,26% w thn llo of $e meon, indicorns hB p.obob k 68.26% k hor liiy ifrot acruol ihe ourcome I bewiihii rhoonge i o 10i + d wi Usins Historical toMeasure Data Risk In the previous example,we describedthe procedurefor finding the mean and standarddeviation when the data are in the lorm oI a known probability distri bution. Supposeonly sample returns data over some past period arc available. The pasi realized rate of return in period t is denotedby ir ("r bar t"). Th aver ,rFe Jnnu.rl refu r ovLr Lhcldstn)pdr" i-r..ql (6-41 The standarddeviationofa sampleof retums canbe estimatd using this formula: Esfimateds = S - l6-5) When estimatedfrom past data, ihe standard deviation is often delroted by S. Here is an example:5 rBecouse o,e eimorins fia tondod devioroi l@m o 3ompe of obseNorois, rhedenominoiornEquorond5 we od o'rr L q r o ro a oJ o1d 6 ) o e b' 1oo l '1o1 o,o ro' e,ampe ror,i +e 'oo. bmpe danddJddc, e."|h6 !b. or 6r-'n 5" al Loo' ord p e,, \.ley -o'rd S to' S-) oser'he 'b \.dd'dd4,oion s*od rurordl,o, rou<okuLror enuol fordebih 2005 2006 2407 (15 5 + 20) 't5% 5 20 - 10.0%, r - i m a r " a u to rsr /1r5 1of+ trs:lotT(ro V , I f v2 Fxr= 73)% ln Er.el, tlle average can be found using a built-jn function: : =AVERAGE(0.15,-0.05,0.20) 10.0%.For the sarnple siandard deviation, thc = tunction is =STDEV(0.15,-0.05,0.20) 13.2%. pastvadof The historicals is often used as an estimate the future o. Because S good estimateoI future risk. ability is likely to be repeated, maybe a reasonably for of However,it is rsually incorrectto use aA,s somepast period as an estimate a ihe expectedtutlrre retum. For example,just because stockhad a 75%reium i in the past year,thereis no reasonto expecta 75%return this year. e T50uTc Measuring Stand-Alone The Risk: CoefficientVariation of If a choicehas io be made betweentwo investmentsthat have the sameexpected the retums but diffcrent standarddeviations,most peoplewould choose onewiih ihe lower standard deviation and, tllerefore, the lorrer risk. Snnilarlt given a choicebetweentlvo investnents yith the samerisk (standarddeviation)bui diffrent expected returns, investo$ would genenjly prefer the investment widr the higher expectedretum. To mosi people,this is corunon sense retum is "good." investorst'ant as much retum and as little dsk as risk is "bad," and consequently possible.But how do .e choosebetween t\^'o investmentsif one has a higher expectedreturn bui ihe other a lower standard deviation?To help answer this question,we o{tenuse anothermeasureof dsk, the coffi.ient oI vadation (CV), retum: which is the siandarddeviation divjded by the expected Coefficientof vaiation = f (6-61 dnd it prctides a lare The nefftcie ! ol'r)ariatiatl shousthe sk per nit of rct11rn, tuo nltet ndti'nes nal lhe dre meanh gful basis conparison whentheexpertutl rctwns on far return, the coeffi sdmc. SinceBasicFoods and tave ihe sameexpected cient of variation is not necessary this case.The firnt with the ]arger standard in deviation,, must have the lareer coeflicientofva ation when the means is are equal.In fact, the coefficientoI variation for 65.84/15: 4.39anc:t = 1.29. is more ihan threetimes as that for BasicFoodsis 19.36/15 Thus, thc ofvaria riskv as BasicFoodson the basisoI this cliiedon. Because coefficient is a better measurethan just tion capturesthe effectsof boih sk and return, it siandard deviation for evaluaiine stand-aloneIisk in situations where tt^'o or reilrrns. more investmentshave substantiallydifferent expected 2t0 RGk,Reium,ond ihe Cdp iol A$et P clng Model h T heiobe oc c om p o n y i n h i sb o x s !mmd ri z els e hi s is ror co irodeoff betweenrisk ond rer!'n Io' d f{ereni Those osseis rhorproduced ihe closses investmenls. of hlghesi overose relurnsdLsohod lhe highesl stoni o ,s p s o ,e rr F .Fol do, dder o. o. " r d | -* d 6 siocks hod the highest over exompe, smoll-compony of oge annuolr e i u ' n ,b u r l h e i r s b n d o rd d e v l a l i o n relurns wos oso lhe h ghesi. By corlrosl, U.S. devioiion,bur Treosury ls hod ihe owesl srondord b they olso hdd lhe lowesioverogerel!rn. Dls lr ibuiion R e o l i z e dR e tu rn s 1 9 2 6 -2 0 0 5 of , N ol e l hal o T-bi l l s ri skessi f you hol d untri ' notutiry, bat if yo! invesrin o rollng porifollo of T-bllhond ho d the po'ifolio for o numberof yeors, i w on youri i venmeni ncome i l l vorydependl ns w hoi hoppensto lhe eve of inierslroles ln eoch yeor Wh le you con be sureof rhe returnyou wi I eorr on o T-bi , you cannotbe sureofthe returnyoL:willeorn over o numberof yeors. on o po*{o io of Tbi Ls smoll Stock! Averogerellrn Ercessreilrn over Tbonds' l7.4% I 1.6 tong-Te.m tong-Term torge Compony Corpo.ote Bonds Bond5 Sto.ks 12.3% 20.2 6.5 6.2% 8.5 5.8% 9.2 u.5. Bills Inflotion 3.8% 3.1 3.1% 4.3 o.a ' ' I h e x . e $ , e i l r n c ve r T b o n d sn .o L lcd ' h e ' fr to r co d slp ' e mi l m'l fondonyi fnvesl orexP e.l rctu'i 5i rhedmarobesi mi orro rerum3 elrned in thc pon, rheex.e$ erufwi o s.6e $e cmrenrrisl p,emilm thol is rete.led ii Ja.mir) p,.es s.or.e, Bosed.i sb.(s, 3od5, Btlls anl tnllotlar \/oltntid aliti.r 2006 ve'.6ool ichicoso: bbohoi Aso.iote!, 20061 ,;r ilCiLf.l\ l i '.:.!. . ,:1 .11 ..,! { i!,ir eC Supposeyou llave $'orked hard and savcd 51 million, which )'ou now plfln io nrvcst.You can bulr a 5% U.S. Treasurvsccurity,and at the end oI 1 year yolr nl i{ill hdvc a s11le milion, il4lich is your original investmentplus $j50,000 $1.{15 nrtcrcst. Altcn.ttivel)', you cnn bu_v stock in Gcnctic Advances. If Genetic your sbck $'ill ircreasein value k) AdYnnccs' rcscarchprogramsare successtul, nrillion. Ho$,ever, the research a failurc, thc value of ),our stock rvi1lgo if is $2.1 You regard Ccnctic Advances'chanceoi'suc to /ero, an.l yorl ni]]be penniless. ccssor lailur(] as being 50 50, so lhe expcctcd value of the stock investment is : thc + SubtractnlB $1 milliotl cost of lhe siock 0.5(S0) 0.5($2,100,000)91,050,000. or teavesan (xpccicd profit of $50,000, all erpectcd (but dsky) s% rate of returN = o.os = s%. xj50,000/$jl,000,000 profit (rcprcsenting 5"/.raie a Thus,you halc a choicbeth'eena surc Xi50,000 profit (alsorepr ot reiuln) orr thc Trcasurysecuritvand a riskl' erpectcd$s0,0{10 senLnrg 5? cxpcctcdrate of return) on the Cendic Advancesstock.Whjch one a Mosl would you .h()osc? you dnasethc! tla:sht1cnt, vnu arc tisk n1'ercc. f is u,ith risk nillrse, d ccrhi V thc Ne Se ntL)ustor risk n1'ercc a ln.,.sfos rr" intl.et1 shnll ftprd lo his or hi "strio s na elt. Be1xsethis is tl1 l-lodLme11tcLl fa.t,11)e ba)k. irssrrierisk aversiontrro ghauttl| ntmindcr of Lhe of Wlut.rre lhe implicatn)l1s risk aversion for securif' priccs arld ratcs ot the returll? The answeris that, othcl.things held conslanir, highcr a securitl,'sdsk, the lo 'er iis pricc an.l ihc higher its requirectreturn. To scc hod risk avcrsbn SuPposeeach itfects secu iy priccs, considcr again BasicFoods and to stockis expected pny an ann al dividetld ofSl5 iorever.trndcr thcscconditions, Risk o Porfo Conlexr in io the price of eachstock is just the presentvalue of a perpetuity.If eachstock had an expected return of 15%,then eachstocks price would be P - $15/0.15= 9100. Investorsare averseto risk, so under theseconditionsthere would be a general preference BasicFoods it has the sameexpected for retum as less but risk. Peoplewith money to investwould bid for BasicFoodsrather than stock,and Salc.comstockholderswould start selling their stock and using the money to buy BasicFoods.Buying pressurewouid ddve up BasicFoods' stock, and selling pressurewould simultaneouslycauseSale.con'sprice to decline. Theseprice changes, trrn, would causechangesin tlle expectedrates of in retum on the two securities. for Suppose, example,that BasicFoods' stock price was bid rp from 9100to $150,'s stockprice declinedftom $100 to $75. This would cause Basic Foods' cxpccted return to fall to 107', wllile 's expectedreturn would rise to 20%.6 The differencein returns,20% ihe 10%: '10%, a dsk piemium/ RB {,hich iepresents additional compensation is ilvestors require for assumnlgthe addifional risk of siock. ]n Tlris exampledemonstrates very important ptlr..ciplet n narketdafli nted a ilvestots,riskietsccurities st have m hghet eryrcted rns,nsestitlldted ret h! riek-aTierse lf not bythefiaryinaL itrceitot,thanless ielq serrLrities.this sit ntiondoes e:dst,b ying nndseLLing thenarket u)iLl in it ta occur. We will considerthe questionof how t'orce much higher the retuns on dsky secu ties Dust be later irr the chapier,after we seehow diversification affcisthe way dsk should be measrired. Then, in later chapters, will seehow sk-adjusted we mtes of refum afleci the pricesinvestors are wiling io pay Ior bonds and stocks. SEIF'TEST Whdtdoes"inve5tment meqn? risk" Setup on illustrotive probobiliry dishibution on investment for Whoris o poyoffmohii? in WhLho{ lhe two stock, srophed risure6'2 i5 les rirky?Why? Howdoesonecolculoie slondord d,e deviorion? (l) hovedifferenr rerurnr: thesbndorddeviotion Whi.h is o bere neosure riskil ossets of expecred or 12) lhe.oeffi.ient ofvoriorion? Why? fxploinlhe{ollowins stotemenr ore "Mo'r inveslors ri'k averre." Howdoesriskoversion offect ror,es return? of An invostment d 30%chdn(e producing 25%return, 40%(hod of produc'ng l0% rehr.n, hos of o o o dndo 30%chonce producins 15% of o relurn. Wholi5il5expeded.etorn? Whotis il tondord I7%) deviation? {15.7%) relurn? A sb(k'sreturn, theposi3 yeors l0%, I5%,ond35%. for dre Whoiis lhe historicol overoge (top/d Whotk lhe historicol lomplesiondord deviotion? 1257d An inveshent on exDecled hos reiurn 15% of dndo ,tondord deviolion 25%. of Whotis its(oe{fi.ien' of vodotion? 12.01 6.3 Riskin Portfalio a Context In the precedingsectio&rve considered isk ofassets the held inisolation. Now we analyze risk ofassetsheld in portfolios.As we shall see, asset the ar held as part of a portfolio is less risky than the sameassetheld in isolation.Accord glt rnosi jRecorho tfiep Ese nrvo! s of ape@ ebr r i5P- Cr / r , wher eC F l s f i e c o i s r o n 'o m u o . d $ f o w o l $ e p e p e t u iry Solvins f, $e elpededretunlor Boscroo& s $15/$150- 010 - 1091 expedd lor The ,erurn h, irS l5/$ 75 =0 20 =2 0% . 212 Chopler 6 Risk, Rerurn, fte Copilol ond A$erPricing Model financialassets aieactuallyhelclas paris ofportfolios. Banks, pensionfunds,insur ancecompanies, mutual funds,and otherfinancialinstiiutionsarercquircd by law b hold diversified portfdn s. Even individual invesbrs-at least those rvhose sec rity holdingsconsitute a significantpart of their iotal $,ealth generallyhoLd portfolios,not the stock of only one firm. This being thc case, from nn irvcsbr's standpointthe Iact that a pariicular stockgoesup or down is not very inrln)rtant, u1l1tlt t'npD ntil is the rct is att his ot hcr portf io, and thc|onfolia's risk. Loiit-al\1, tht:n,tl:!|risknd rcturnafn ittlif idualsedtity shaltltl nl] te ns al holrlthnt I)? i st:uri1/ affrcts th( isk otrl r.t n' of the portlnto in iohich it is h(ld. To ilhLstrate, Pay Up hrc. is a collectknragency ihat operatesnatidlnidc thro gh 37 offices.The conrpiny is not h'ell known, jis sbck is not very ]iqui.l, its earningshave fluctuatedquitc a bit in the past,and jt dorjsn'tpay a dividend. All this suggests ihai Pav Up is risky and that the requiredraic of retum on its siock, should be relatively high. Howcver, Pa),Up's requirod rate of returr in 2006, t and all other years,!r'asqlritc lorv in relation to thoseof most othr companies. This irldicatesihat invesiorsrcSardPay Up as being a low{isk company in spile of iis unccrtrin profits. Therrcasonfor this counterbtuiiivc fact has to do \.i!h diversificationand its effeci on risk. Pay Up's earnnrilsrisc dudng recessions, i{hereas most other cornpanies'eamings tend to dechrc !\,hen the econonv slumps.It's like fire insurance-it pavs of{ when other things go badly.Therefore, adding Pay Up to a portiolio of "nomal" sbcks tends b stabilizercturns on the entire portfolio, thus making the portfolio lcssrisky. Portfolio Returns Thc expectedreturn on a portfolio, ip, is simplv the rvcighted averageof ihe cxpcctedreturls on the individual assets lhe portfolio, $/ith ihe weig]rtsbenrg in thc fractnrnof the total portfl)lio hvested in eachassct: ; =s , ; +v , ; + +, . ; 16-7) Hcrc the i's rre the expectcdrctun]s on the irdi\.idual sbcks, the \^,j'sare the rjcights,rncl thereaie n stocksnr the portfolio.Noie that (1)wi is the fractior of ihe portfolio'sdollar value invcstd in Stock i (that is, the vahrc of the investnrent nr Skrcki di!,id.d by the total vahc or ihe poftfolio) and (2) thc l\,'s must stlm to 1.0. Assume that in August 2002 a security analyst estimatcdthat the following retuDs couki be expected thc sbcks of four larte comp.nics: olr SouthwestAirlilcs Fcclilx Dell 150% 12.0 10.0 9.0 ff we fornred a 5100,000F)rtfolio, investnrg 525,000in cach stock, the expcdcd portfolio return lvould bc 11.5%i i,, = w,i, wri, + w1i1+ \,air : 0.25(1s%)0.2s(t/n,) 0.25(10%)0.25(9%) + + : 71.5%. in Risk o Porifo Conrext io 213 Olcourst, thc nclual.calizcd ratcsofrcturn willalDrostccrt.rinlybedifferentfrorn their cxptcL('Ll vilucs, so therealizedporifdio rc'tlrrD, lvill be differentfrom the it, expecLcd rctum. for examPlc,Starbucksrrighi cloublL'andprovide a return of + 100%, r\'hcreab De]] rnighi have a terriblc ycar,fill sharp\', and have a return of 7591. Noie, though, that ihose t!\,o cverris$'ould bo somcwhatoffsetting,so the portfolio's return night stil be closeio its c\pcciod rc'trrn, L'vcnthough the ind; vjclual sk)cks'aciualretums a'ere far from ihojl c'rpoctcdrcturtls. Porlfolin llisk As lve just sar\tihc cxpccted retum on a porttolio is simplv the rveighted average of the expoctcdfcturns on thc individual asscisLn ihc portfolio. Ilolvever uiike rtlrrns, fisk {)f a portfolio,of, is gcicrallv not thc w(.igLrted ihc average the stan oi dard dcviaft)ns of thc individul asseBh tl1. portfolio, the porifolio's risk .ill irlmostalwiysbcsrrallcr thanthcwcighiedavcraiac th(..rssets' In fact,it is ihe ol o's. orctically to cornbhcstocksthatarc in.liviclon quite risky asmeasured lly by Possiblc Lheir stnndarddcvinfionst.' form a portfohr that is completely riskless, r'ith c'p: 0. Toill sirak thc cffcctofcombining asscts, cons crth sjtuaiionin Figure6 4. TheboLkln1 sectiongives daia on ratcs ol rcturn f(,r Sk)cksW an(t M indif iduallv, aswell is for a portfolio invesied50%in cachsk)ck.l'ho threetraphs plot the data ir a ti e seriesfonrat. The iiro stockswould bo quito risky if they rvereheld in isol.rtn)\,but when lhe_v combincdto form I'ortf(tio h/M, thev are not risky at are all (Notc: Theseslocksarc calledW and M becausL' graphsof their returnsin thc Figure6-1 rcseDrble w and an M.) d TIle reason W Stocks and M cantre conbnrcd ki form n riskless portfoliois that ihrir fctlr.nsmole counte(_-vclically ioeachothi'f lr'her !v's rchrmsfal, thoseoi M dsc,nnctvic{ vers.l. The tendency tlvo variables nrov.'togcthcris called.onelaof k' tion,nnd ihc corelation oefiicientnle.sures this tfndcnc),.: svmbolfor thecor Thc nlathn cocfiicient the Crkletterrho, p (pronoundrd is roc).ln stafistical tefms,we sry tlut thc returnson Stocks Wand M arel)lr,4l rit{dlr?,.l/.d/,-.r]tcd, p = 1.0. l[/ with l hc estimateof correlationfrom a sampleol hisn) dntr is oftcn callcd "1t." H(rc is ihc formlrla to estimatethe correlatior bclwcen ltocks i and j (ii,i is thc actualrctum for Stock i in period t, an.:lti,^,His thc nvcra8c rchl.n durinB thc n?('rn)d srmplc, slmilar notation is used for Stockj): p Eslimnted =R : {6-Sl i ^-)'1i)tt' Irortunntclv, is easy to estimateth corrl.t()rr coelfi(ientswith a iinancial it .alclrlak)r. Simplv cnter the returns on the tl,vo st()cksand thcn prcss a key l.bcled "r"i In E:r..,/, use the CORRELirnction. SecFM12 Cn 06 Tool Kit.rls for thocalclrlatn)n correlationbeth'eenStocksW .rnd M. of Tho otlpositc of pcrfect netative correltrtidr,witl\ t, = 1.0,ts ttftrt positi|e ()rrrrli(r,, $,ith p = ltetums on two perlccLlyFosiLively correlatedstocks , o ,9 " o ooo's o . d , p o o ,. . , , pd 4 | " do"oo o n ra o O ! o, e o l o ob e o,r ' d 'o "l :z eoor n . l i . a r e r f o r fe r wo vo r r o-b e so e n .r r e a b / r o e o .,d fc,-i hol i ,.honssi norevdobeoe oi r 1 ' lnc o s d "" 'o1 idepdndenr o'.honqes n rheo$e, 'Seeod turo,io o, ir.ol.u rhe e'.d nepi A !o, Mre horrhe.oreloroi .oefi.ied : olbn olor -onuollo, , lenob d6 / r l r eb r m r ' w e u se Ih e r e r o o vo id co n ffio n w$ ,o !u lcd lodci orcce,areaf,etu,r NegolivelyCone oted Sroclslp Rores Relun for lwo Derlectly of ond for Portfolio WM w Sro<k (iw) PortiolioWM (ipl e' I e50uI c e Kirxli ot the lexrbool( 2003 2004 2005 2006 2047 CottelatedStocks(p : lor Roles Retufn Two Pe ectly Positively of MM' ond lor Portfolio sl,o.kM {-M) I:'Vil e-Ie50urce sro<kM'(iM) Por olio rr ' lrp) 2003 2004 2005 2006 2007 R i s [ i n o Porftoio Conreit 215 (M and M') would move up and down togethet and a portfolio consisiingoJ h4'o suchstockswould bc cxacily as risky as eachindividual stock-This poini is illustratcdin Figlrre6-5,where we seethai the portfolio's siandarddeviatidr is equal to thai of the indivjdual stocks.Thus,diaersit'bation nothitlgtu rctfu.eriskif the daes consists perfectL!positltel! corrclntedstocks. ol |ottfaLio Figures6-4 and 6-5demonstrate t when stocksarc perfectlynegativelycor tha rclaied(p = '1.0), risk can be diversilied arvay, all but when stocksare perlcily posidvelycorrelaied(p : +1.0),diversificatjondoesno good whatsoever. rcaL In itr virtually all stocksare positively conelaied,but not perfecily so. Paststudies haveesijnratedthat on averagethe correlationcoefficieni ihe monthly rcrums lor on iwo randomly selecied siocksis about 0.3.'Urder thisorndition, combining cks sk inloportlolios tduces risk bul doesnat cotrylclely ellmildfelt. Figure 6 6 illustrates thispoint with t'llrostockswhose correlationcoefficient p = -F0.35. portfo is The lio's averaSeretum is 15%,which is exactly the same as the average return for our oiher tvro ilustrati\.e po folios, but iis standard deviaiion is 18.6%,rvhich is bet('eenthe other lwo portfolios' standarddeviations. Theseexamplesdemonstrate that in one extremecase(p = 1.0), sk canbe completely eliminated, while in the other extreme case (p : .r 1.0), diversification doesno good whatsoever. The real 'orld lies beh{een theseextremes, com so binhg stocksinto portfolios reduces, but doesnot eliminate,the dsk inherent in theindividual stocks.Also, we should note that in the real world, it is iflpossible to find stocks like W and M, ('hose returns are expected to be perfectly negatively .atrclaIed. Thercfore, it is inLpassible t'orm conpletel! riskless stack pottfolios. to DiversiJication can reduce risk but not eliminate it, so the real world is similar to thesituationdepictedin Fiture 6 6. What would happenif we hcluded more than two stocksin the portfolio?,,1s r nlle,the riskof a pottfolia |dll decline the lttLher stocks thepottfalia as of in incrclises. If wc addcd enough partially conelated stocks,could we complctely elininatc risk?ln general,the answeris no, but tlle extentto which adding stocksto a portfolio reclrcesits risk depends o the Llqrcr af carrcldtio,among the stocks:The smallcrthc positivc corfclaiion cocfficicnts, lowcr thc risk in a lar8c portfolio. thc lf some stocks had correlationsof 1.0,all risl<could be eliminatcd. /rl trc rurl uorld,Irhercthe catrcldtions arc but amongtheirulhirltnLstocks getLenll!positilte less thatl+1.A some, fiot alL,riskcanheelilnindted. bLt , In general,therc are higher conelationsbetra'een returns on iwo compaihe jn nisin the sameindustry than for tu.o conrpanjes different industries.Th s, io nininize risk, po lolios should be diversifiedacross indushies. Diversifiable versus Risk llisk Market As noted above, ii is difficult if not inpossible to find stockswhose cxpected rctums arc negativelycorrelatcd-most stockstcnd io do {'cll whcn thc national is cconomy strongand badlywhen it is wcak. Thus,cven very largc portfoliosend rp with a slrbstaniial amo nt of risk, brt not as nl ch sk as if all thc money were invcstcdin only onc stock. 6aiven nud/ by Chon, ond averose corclorofcoeffclad llt99) sr mcred 'A recenl seleded Korcedi,23,Loloiishol 'hor$eenrbeteen No lorse{ompony toorondomly wos0 whie 6e ove,ole rieorion c. .oeltic iock .. ,\o. 100. , t"!o o p _ . .to o 3 o to o 3 o01.o -L oi o" n"p" odolrq ",,c rolon \ o t o p o , o o p .;.o 4. D .. "^ .r o. { .. ,s .o o o , e .,. . o. i ,q l e ri vod" findi.dl SJodier, Lehou, Moll e, ond X! lound VoL 12, No 5, Winrer 1999, pp 937 974 A sldy 6y CompbeLl, \o10 0b/t.o-tooo o "o",o9" o "oo,;t c- o o , i 0 . . n \" o . a 0 o t, --o,\. ' o'pbJV o ' ' - ! t B ' | o , M o l e o d ,e ' o o ' H..' d id J.) b !L ' B".. tnpiri.. Expororionot diosyncrottrP,s|'iaun.lofFinance Febrr.ty2OOl, pp ) 43. 216 Risk,Return,ond 'he CopiJo A$el PricingMode Roiesof Rerlrnfor Two PoaicllyCorreoted Siocks(p = +0.35) ond for Portfoio WY slockY (fr) 2003 2044 2005 2Aa6 2AO7 40.a% r5 . 0 {5.01 {10.0) 35.0 l!4% 22.6% To scc more preclsly how portfdio size affccis lnt ifolb risk, considcr by Figurc 6-7,lvhich showshow portirlb risk is affected torming lnrgerand largcr porifoliosof randomly selectccl , York StockExfh.nB('(NYSE) Nc stocks. Standard (leviatiorrs plotted lirr.rn irvcrn$c onc stockportiolio, . t$() sbck porlfoljo, and are of thai rlere listcd so on, up io a porttblio consisinrS all 2,000plus coDrnon skJcks thal, in gcnon the NYSEat the iime ihe diti \!clc graphed.The Braphilhrstrntes tL'n(ts c:tecline to and er.l,lhe fisk ol.r porttolxr.onsisinig ofiarge corrpan! skJcks to approa.h sonc li it ns lhf silc of the portfolio nrof.s(s Accor(ting to dnia deYi.lti.n of n ono skrckportfolio (or accunulaied nl rcccnt)'enrs,,rr,thc st.rndard of an average sbck), is appftixim.tely 35ta.A portfolio consisting nll stocks,r\.hich dcvixtion, ('M,of about 20%, is c.lLled market portfolio, ivould havc a standarcl the wLrich sholtr as thd 1l) izontil-d.rthd line in Fitufe 6 7. is '1'hs,rbtulfhrlfaftltutjsk,liii;.ii:iithtlnr)ernge i, i)rliritlr l!to&c lt.dit iuikd il tlx sk).lt htld tdrcrsn tlltltIt\Uliotfsit'itdp'rrtfLln,:|')htLltisortctlntLlnitlg10ot ir Somerjsk a]w.ys romains,horvever, nan sta.lis r itltn tcr t)fd;/lirlr/ l/,,1rrsttlrs. in so it is virlually impossiblc to cliYersifvai{ay the effects('i bro.r.]stock narkei nrovemenis ihai alfcci nlDrost slocks. all 'lhe part ol . stock'sisk that oir be eliminatcdis c.rlled,1tr'.fLtF,dl,n l\,hile risk, llrc thL'part that.d,rrr)i bc cliDrinniedis called ,,rt'i"t r'rs,t.!L' f,r(.tthnt a large palt ('l the risk ofanv indi\'idrr.l siock can be elimnlatc.l is !it.rllr iniP()rtant,bccause rntional m|estors n ill elinrin.rit it .rnd thus rendcr it irreleunl r Dve [ificb e r Glr .L $ li^ .wi.3 ..n p.i yrre.l i .,.r,xyren.r'.r5LMo,l d,+sosoknow nosnondttri ri ouq rynendtr, d bd., , sk, iris hc , sl rhor,emotu olier,live6if.orlon. Rsk n o Portfollo Context 217 Effects PoafolioSize on Portfoio Riskfor AvercgeSiocks of 35 25 ..,' 15 Sland- )rL:r' 10 5 *Tii,i""i:l:;il; Diversifiablc risk is cause(l by srch r.rndon cvents as la\^'suits, shikcs, slrccessfuland unslrc(csslul nurketing programs, the $,iuring or losing of a nriior .ontract, an.l othcr e\ cnts thnt.rre ulicluc h) a Parti.!l.rf lirm. llecausc thcsc event! lre ranLlom, thcir etlects on a porttblio can be rliminntcd bv c{n ersification-b,1d elents in onc firnr \ill be ofisei bv good c\ orts in nuother Market risk, on thc oiher h.rnd, stcDls fionl l.ctors that s)'stcrnati.ill), nffc.t Drost iirns: r'ar nlflrtion, re.essions, an.l high intL,rest rntes. S;1cc nrost st()('ks are rregatileh affcdcLl bl thesef.r.tors, markcl risk cinnot be elnninatcd b), divcr$lfication. Wc krllnd that invcsiors demand a prcmiunr f(n bclring risk thai is, thc hiith( r thc risk of a sccuiiy, Lhc highcf its cxpccicd return nrLrstbe to inducc invcsnns t!) blrv (or to hold) ii. Tjowcvcr', if invcst()s arc prinrafily co[cernccl lvith thc risk ol thcir port[lios rather Lh,1n isk of thc nrdividLral sc.Lrrities h thc portfolio, ho$, thc shoulcl the risk of an inc{i! idual sbck be rne.sured? One .rnst cr is provided bv ih'r Capital Asset P.icing Model (CAPM), an import.rnt tooLuscLl to annlvTc th( rrhibnshiP between risk .rnd ratcr of rcturn Th( lrrim.rrv conclusim of th( C?\l'VI is this: Irf rflr,iyt,tt jirk ot njt hldir.tdtnl :ir,{ t ,s ,is..),riftl,xtu,r, to ir. ,'tskofli n'tll-ti1'ersifid totlltio. i\ \to.k might bc.luile riskv if held by itsclf, bui if ha1l o{ its isk can be eliDrirrnt(.cl diyersificatior, ihen its relevnnt risk, {'hich is ils.or,by h ih"tiotl tu fh( tlotlloli.,s risl, i! much snrallcr Lhan ils sinnLl-.rlonc sk. f dec. l , t h c 1 9 9 0 N o b e P r ize wo l.q .r ld lr o lh e d e ve o p cr o fr h e cAP ^l ,P .e$.nH a,ryMo,l o{l zand Wl .n F Sli.lpe rfe CAPM s a rcdvey.omp er $eory rr b.sic. cmeft o,e pr8edad i rh s.hap rcr A more niepth presed.rof oppca15 Choprer in 7 I 214 Ris[,Relurn, rheCopiro A$el PricifgMode ond Figure6-7 showsihoi on investorcon 5ignificonly AhhoughU.S. investors hove r.odilionolly6een reduce podfolio rlsk by holdins o lorge numberor relo vely re uclonlto hold internolionol o$ets, ii E o slocks.The figure occomponyingrhis box sLrggesls sofebellhor in lhe yeorsoheodU.S.investors shifi wi +or i.vesor mo) b. ob e to .edrce r s[ erer r:nl'e' moreond moreoflheir o$eis lo overseos invesimenls. by holdingo lorge port{oliool stocks fromo I oround 50ur.e fo. tudher rdino see Kennefi Koso "M6suino a rhe word, becouse rerorns domestc ond inrer Goid: lrom hremdonol P; foio DiwAilcorion," fedeinei,", lhe of noriono tocks ore noi peffecilycorelored. Bdnl.l s.n Fftrcis.a Weeklyle,ter,fo 94-l4lAprII, I9t4) ('/.) U.S.and lnternalonal Siocks Number Stocks ol in pordo io . ..,. tlt .L.r,.Suppo- !,'ud,-^lfe,cd rr. .\.|nrl,l, \.rnrple\^rll lp m ,1" rhi, pornr h, chnnceto flip a coin once.lf it's hdads,you win ti20,000, t if jt's/tails,you losc b = TNs rctum is 0.5($20,{100)0.5( $16,000) r 1j16,000. is .r good bel-ihe expectcd Horvevrr it isa highly risky proposition, becausevou haYea 50%chance oi $2,(l(I). losinB516,000. Thus,yolr nright lvell refrsc to make the bct.Aitcrnativcly,slrppose you were offercdthe chincc h) flip a coin 100times,and yotr wolrld l\,nr $200tor eachhea.tbul k,sc$160for onchtail. It is thcoreticnlly possiblc' ihal ].ou would flip all hrads and win $20,000,nnd itisalso theoretically possiblc that vou i!,.'uld flip a tails nncl lose l;i6,000,bLLt chances very high thai you lvould actrrallyIlip the are trbort 50 headsand abotLt50 iails, lvinring a rlct ol about $2,(){)0. Although each irdividtal flip is a nsky bet, collectivc'ly you havc a lo propositid L'ccause I -isk r$st of ihe risk hasbccn dilersificd dway This is the idea bohind holdnr8 portlo lios ofsbcks r.rtherihanjost one sbck, exceptthat rvith stocLs of the risk cannot all be diminatdb),divc'rsificaiion-those risksrelatcdtobroad,systematjc chnn8esin thc s()ck narkct will remain. Arc all siocksequallyriskv iI the sclrse that acldnrg theD k, a neI divcrslfied porifoiio will have the sameelfecton the portfoli(ls riskiness?'lheansh'cr is no. Differentstockswill affcci the portfolio (tifierently,so differentsccuritieshnvc diiferellt lielrccs of relevantrisk. How c.n the relevanirisk ofan irrdividual stockbe me.rsured? r,e havc sc'c'n, Iisk oxceptthat rclated lo broad markct io\'e As al1 mentscan,and presumablv rvill, be dn,frsified away.Afterall, \\ty acceptrisk that can be easilyliminate.l?lh( riskthat roliitls nltu di'r)ersifVnrynnrket risk,ot tht is risklhnt is iitltrh,iLl that rrtul, and il ,:n benortrcd blt thcdt:lrccta uhitlt r ifi Risk o podfotio in Contexr stt)ckt ds ta noLte ot doro with themarket.Itrthe ncxr sccriur, devetop. mcas_ 4i ure of a stocks market sk, and then, in a later sectiolr, introducean cquaiidr wc Ior determnlhg the rquiredraie of rctum on a stock,given iis markerfisk. 219 Contribution toMarket Beta Risk: As we notedabovc,the primary conclusion the CAPM is thar the retevalt risk of of an individual stockis ihe amolurtof risk rhe srockcontribuies a welt-diversifid ro portfdio. The benchmnrkfor a well diversifiedstock portfolio is the market port folio, which is a portfotio containingatt stocks.Ttrerefore, relevanrrisk ;f an the indjviclual stock,which is called its beta coefficient,is defhcd urder ihe CAI,M as the amount of isk that the stockconfribulesto the markcr portfotio. In CAPM terfninology, is the correlaiionbet{,eenrhe irh stock,srehrm and the rerun on p,ru the market,oi is the starrdarcl deviation ofthe ith stock,s rctum, and oMis the sian dard deviation of the market'srerum. The betncoefficienr the ith stock,dcnorof ed by br, is defined as fouo$,,s: '-.-!.. (;)* r,' d' ^ l6-91 \-l This tells us that a stock with a high standarddeviation,oi, r.ill tend k) hrvc a hith bcta, which meansthat it cont butes a relativcly larse amount of risk k) a hcll-drv,1.ified porlrolio.lhr.m,rte-sen." U...'u'" .l sbck with high stand,aloncrisk will contribrte a lot 'i.'tt "1r,",lhjng.a,us(lu,rl ofrtsk to ttrepoitfolto. Notc r^o thri .r5to\|. { rlh n high(,'r'rl.,rion wrrhthFnr.,rk(.t, . x r dt.o ha\c., t.rr8e p.N beta,and hencebe risky. This also makessense, becalrsc hish corretation a mcans rh.rr erijica,roni. nol lx lpin; nru,h h"n,ct\csh,ct(onlrib te. i I,i ,,i nst r,, di\ r, Llrlp"'lrolio. l, ,. ,. ) A , "k - ,The cordriance betaecnstoc( i and dre m.rrket, COV,M, denn^d.,- : F COV;y - p,s o; oy. r', ;r--, .0, {6-10) SubstitutingEquation 6-10 into 6-9 providcs arrctherkequenttv used expression C OVIM ",M 6 0 $ 1 ,. 't=i r 16"ll l, -o y;_,, Calculatorsand sprcadshcets can calculaterhc componenrsof Eqnation G9 rt ,r,..tnd o\r).which(rn th(ir be usedto cnlcuLrt(,b(.l.r.Lut isnnorhLr rtrcre w.rv. ^r Suppose you plofte.l the sk)ck'sretums on thc y-axis of a graph and rhe market portfolio'sreturns on thc x-axis,as shown in Figurc 6-8.The formula for rhc slope rusins h todcaldoh, fie sampe covoronce cai be coclloiea ds >(r -' ^ \ ){ , , . , i' * , 1 Sompe.ovoion.elromhi5bri.o dob = cov! Col, uldnq tle .o@, | \om"$hor rhonrot, utohc rhc , o,,etoro. \o ,r hoF ot,{dy , o .utokd 'onrh F r I r 4 d 1c -a!a ' 'ou o .cl, o " \c. o a .,o F o r d rol <o._tore e onetor o. fi on 220 Risk,Rero.n.ond lhe Copilol Asel P.icingModel of a relfessio lirrc is exactly qual to the formula for beta in Equaiion 6-11. Therefore, estimaiebeta for a secuitt you can just esiimatea regressnnwith to the stok'sfeturnson the y .1xis and the market'sreturns on the x-axis. Intlividual Betas Stock The tendencyof a stock to move up and don'n \,vithihe market is reflectedin its /iststd.tis definedas one wiih a betaequalto 1.0.Such bctr coefdcicnt. d-rclir8c An $,ith thc market,rvhich a sbck's reLurns lend to nove up and.lown, on averagc, is neasuredby someindcx suchas the Do{ jones Lrdustrials,the S&P500,or the Now YorkSbck Exchangc Conposite lndex.Aportfolio ofsuch b = 1.0stocksrvill move up and .{owr lr,iih the broad market indexes,and it h'ill be just as risky as thc irdexes.A Portfolioof b = 0.5siockswjll bc half as risky as thc market.On thc oiher hand, a porlfdio of b = 2.0stocksivill be twice ns rjskv as thc market. Figure6-8 sholvsa graph of the historic.llrchrrnsof threestocksand the mnr ket.ThedatabeLow thegraph assumcth:t in Year1 the "mafket," deiinedas a pori capital plus Sanis fdn) consistnlg a[ stocl$, llad a toin] retum (dividend yielc:l of yickl) of iM = I {l'l and Shcks II, A, and L (for High, Average, and l-ow risk) alsoall had retuns of l0%. In Ycar 2, ihe markc'tivent up sharply,and the rcturt1on tlc nr.rkt portfdio was i = 207. Retumson the thrce stock also h'ent up: H soard Thc to 30o/.r .errtup to 20%,the sameas ihe market;and I- only $'ent Lrpb 15cl,. A The threestocks' m.rkei droppcd in Year3, allclthe nrarkctreturn nns rM = 1{l%retxrns also fell,H plunSj|tito 30?,A falling io 10ft,,andLgoir\SdowntorL= 0'/".Thus,the thrcestocksall tnovdh ihc samedircction thc mnrket,but H $'as as just bl, far ihe most volltile; A \^,as as volatiLe the narket; an.l L v!as lessvoLatil. as Bctameasurcs stock'svolatility rclniive io ihc market, which by dcfniLion a has b = 1.0.As we noted above,the slope of a regrc'ssion sho*'s how a stock linc Dx)\,c's response a movcment in thc generalmarkei. Mosi stockshave betas in to h thc rangeof 0.50to 1.50, an.l the avcragebeta for all stocksis 1.0by dcfinition. Thcoretically, is possiblcfor a sk)ck to have a ncgativebcta. In this casc,the it slock's returns urould tend b rise whcncver ihe rctLrrnson othcr stocks fall. In prncti.c,\'ery fl,w stockshavc a negalivobcia.Keepin mind that a stockiI a gi\'n period ma), novc counter k) the overall market, evcn though the stock's bcta is when positivc.lfa sbck hasa positivebeta,$,c lvould.rf..l itsreturn h mcreasc evcr thc o\.erallsbck markct rises.However,conrpanyspecjficfactorsmay cause the siocks realizcdreturn k) decline,evcn though thc lnarkei's rcturn is positil'e. Porllolio Bclas ,1 A ver), hportrni fcatureof bcta is that thclbetaof a portfolio is i weiilhted aver ageof its individual securitics'betas: b. = w.b, + w,b, + t6-r2l Herc bf is the bcta of the portfolio, and it shor^'sho$'volaijlo ihe portfolio is in relation to the ma.ket, w, is the fraction of thr portfoln) invested in the Riskin o Porr+o Conrext o 221 Reolive Volotiliiyof Stocks A, crnd H, Fellrn onrslocki, a H i ghR i skb= 20 2A 20 30 Belurn lhe Markel, (%) on iM 2A 2 3 Beld t0% 2A (t 0 ) Nore:The5e threeiock porexo.ry on rhenrcsresion lns This id.ob.rholrhey d,e eipoJed ony 1omorkelrisl Mdlolfunds $orcoi.enrrolo on sroclswi$ beb ol 2 0, I 0, cnd 05 wl hovepolrerns mlor lo rhos 5 sh.M n [e groph. lih stock; and bi is the beta coeflicient of the lth stock. For example, if an investor holds a $100,000 portfolio consisiinjl of S33,333.33 nrvestedin each of threestocks,and if eachof the stockshas a beta of 0.7, then ihe portfolio's beta wiu be bp = 0.7: : bp - 0.3333(0.7) 0.3333(0.7) 0.3333(0.7) 0.7. + + Sucha portfolio 'ill be less dsky than the market, so ii should expeience relatively nanowpdce s\^'ings and have relativelysmall rate-of-return fluctuations.ln tennsof Figure6-8,the slopeof its rctressionline would be 0.7,.lvhich lessthan is that for a portfolio of average sbcks. 222 Chopler 6 Reluri, theCapitolA$er ond Prlcing Model Risk, No$, supposc one d the exisftrg stocks is sold and rcplaced bl' a sh)ck with br = 2.0.This .rctionwill increascthe bcta oi thc portfolio fro]n bfr - 0.7 hl b,."- 1.13: + + blr = 0.3333(0.7) 0.3333(0.7) 0.3333(2.0) FIada sk)ckrvith b, = 0 2 bcenaddcd,the porttoliobcta uould havedeclinedfrcm (1.7 0.53. would redLrcc risk of ihe polt the to Adding a lolv-bct.1 sbck, therefore, folio. Consequcntl),, adding neN stocksb a porlf(tio carrchangethc riskbcss of lctn ,,.,rsr/,"s cantribu,]i)ii th'! riskaf i ponfa ;ts to ilrai portfolio. Tlr.s, srrcf, st(r.k's !i'..bcl ir$llu c.ttcct fieis t. of thr stt\ks risk- Points Kev Relaled lieta to The prcccding annlysisof risk in a portfolio context is p.rt of tho C.rpital Asset PricingModel (CAPM), and u,c can highlight tlrc key ponrts as follows: of L. A sk)ck'srisk consists two componcnts,marketrisk ind diversifiablerisk. b!' 2. Divcrsifiablcrisk carl bc ehn ateLl diversification,rnc:lmost investorsdo in irdocd djvcrsil', ejthcr by ho]ding largc portf(niosor by purchastugsharcs is a Drlrtualturn.l.We arc llt, thcn, rvi market risk, r^4rich Guscd by gc'ner al movementsin the stockmarket and which rcflectsthc fact that most stocks arc systematicnlll,affccled bv events like wat reccssions,and inflatbn Market risk is the only risk rclcvant to a ratiolral,diversifiednrvcstorbecatse suchan invesbr rvould climinatc diversifiablerisk. 3. Invcsbrs must be coDpensatcdfor bcadng risk-the grcaier thc risk of a is siock,ihe hjBhorits rcquired return. Howeler, compensation rcquired onll for risk that cannotbc cliNinatl'(i try diversification.lf risk premiums existcd risk, lvell-diversifidinvestors\,vouldstari brton sk)cksduo to dir.ersifiable ing ihose securities(r,hich would not be especiallyriskv to strch investors) and bidding up iheir prices.Thlr stocks'final (equilibiunl) e\pected relurns would reflectonty noncliversifiable market risk. lvhichis an irdex l . The nlarkei risk ofa stockismeasuredbyiis betacocfficieni, of thL'stock's rclaiive volaiility. Ifb equals1.0,ihen the stockis nbout as fisky as tlrr market,if held in n diversitiedporttulio.Ifb is lessthan 1.0,thc sbck is lessrisky than the narkci. If beta is grcnier than 1.0,the sbck is nlore risky. Thc bcta ofa portfolio is a weightcclaveragcof ihc hllividualsecurities'betas. l,cfil.oclr.iott defa. i)t$ha,lhcslockat'liclsthei.kolatiil,ctsificLl 6. Strrrd sio.l'.s pottlt bttnis the kst ttle.tat,tknsurcolavstocksisk. llo, SEI"F-TEST Explointhe followinsdotement "An ossetheldor pdrrofo portfolio;sgenerollylessrisky ron thc some os s et e l di . i s o l o l i o n ." h Whot i' meonr by perfert positive .orrelation, peie.t negonve <oteloion, ond *to .orclation? lD senerdl,con lhe rirk o{ a portfoliobe reducedto zero by ;ncreosing nunrberof siocksin e po.t. ifie folio? Fxplo;n. Whoi i5 the beto of o n4k ihdl is s5.irky o3 ihe norket? Why is betq the theo.eli(oliy conecl meosure o ,iock'srisk? of lf you plottcdthe returns o portkulor stnL versulthoseon the DowJoneshrdexover the posl5 yed*, on r hot w o : d th e ,l o o co f th e ,e o ,e ' i o n li nevou obroi l ed ndi coreobourrhestocksnrortetri :k? An invertor ho, o threeJtocl p".*of;o *iti 525,000 investedin Dell, 550,000 invesledin ford, ond in lo 525,000 invested Wql-Morr.Dell'sbeld i, erlimotcdlo be 1.20, Ford'sbelo is estimoted be 0.80, pordolio?{0.95) dnd Wol-Mo.t! beld is esrimdled be 1.0. Whdr i5 thc eslimoted to beto of $c inve5tor's Co cuollng BetoCoefflclenrs 223 ing 6.4 [alculal Br'1a Coeffirientr The CAI)M is an dr drrr modcl, which mear$ that all of the va ablesreprosc i before thc-fact,ejryecfcd (rs.In particular,the bcta cocfficient val usedby invcsiors should reflectthe expected volaiility of a gi\.enstock'sreturn veEus th reiurn c)n the n1arketduring soml'ri"ru period. Flowever,peoplegeneraly calculatobctas usinS data from some prsl pcriod, and then assumc that the stock's rclative \jolaiiliiy will be the samein the future as it ('as in thc past. Table r,4 sho('s the bct.s for some ('eI known cornpanies, provided by as tr\o diffcrcnt financial of8nnizalions, Zacksand YahoolFinance. Notice ihat thejr cstinatcs of beta usully diffcr becausethey calc late beta in slightly dilfcrent ways.Civen thesediffcrerices/ many analvstschooscto calcl ate thir own betas. from Figure 6-8 lrc$,betas are caiculatcd. The actualhistoricalreturns Recall fora company are plotted oIl the y-axisand then:rrki portfolio'sreturnsarlrplot ted on the x'axis. A regression line is then fittcd through the points,and thc slope regression ltuc provides an estimateof thc sk)ck'sbeta.Although it is pos of the with a calculatot ihey are usually calculated sible io calcuiatcbeta coefficients pro r.ith a conputcr either with a statisticalsoftrvarepro$am or a sprcadshcet filc IMt2 Cft 06 Tbol l(il.r/s sl'rows beta coefficicniis calcu cran1. Thc how CE's iated r.rsing E-tccltregression function.'3 The first stepin a regression analysisis coripiling the data.Most allalysisLrse monthly data, aliholrgh some use 52 \^,eeks ('eckly daia. We of 4 to 5 vears of lsc 4 yearsof monthly data, so s'e beganby downloading 49 tnonths decidecl to r/eb site. \4/euscd ihc S&P 500 of stock priccs for GE Iron thc YahoolFinance portfolio bccauseit is representative thc n.rket and of Index .s ihc markei Table6-5 shou,sa portidl of this datai the becausc man)' analystsuse this index. full d.rin sct is nr the file FM12 Ch 06ToolKit,rls, for A(tuolComponres BetoCoefficienrs Some Stocktlicker Symboll IAMZN) (CSCO) Cisco Sysiems (Ko) coco-colo DellComplier{DEtt) Eleciric Empire Dislricr {EDE) Enersen co'p. (EGN) HeiizIHNZ) MeffillLyn.h(MERI Microsoft Corp.(MSFT) Procrer Gqmbe (PG) & s@aer hr|P://yw.:cr5..or Zocks 2.53 L99 0.38 Lt6 o.45 o.57 0.90 o.32 t.68 L23 0.t0 2.93 1.56 4.82 I 05 4.75 o.93 To 5eeupdoleden noles, so b hnp://w.zo.ks .comond enler e icker Quoieslor beio. Or go .<on ond enler rhe ricker is symbol.When ihe 'esu Key Slol tcs lrom the eft o.a4 0.42 1.44 0.35 o.76 ond hip.//limr.Fh@rm. jt oron 6 / p l o n a r o i o f c o . u la r isL e ta w ,o ln o n co .a lcu o r o r se ew ebfx,E nri on6sorl hol sxrbook! Rck,Reiurn, rheCopllolA$et PrclngModel ond Stock Relurn Doio for Generol Electric Md*et tevel (s&P500 lndexl Morket Return GEAdiusted SbckPrke 34.33 34.59 34.74 32.87 GEReturn 0.8% 5.8 l.l Moy 2006 ApriL2006 Morch2006 FebrLrory 2006 1,280.16 1,3I0.61 ),294.87 1,2ao.66 1.2 l.l 0.0 A ugls l2002 )uly 20A2 .)une 2002 May 2AO2 Averosereiurn{onnla J Siondorddeviotionlonnuol) G E or d lhe m o rk e r 916.47 9l L62 989.82 1,467.14 0.5 7.9 7.2 ..!4 27.34 29.16 26.31 28 02 10.8 -6 I NA :4% 19.!% o.49 49% t9.t% chect our hip://finonce .yoh@.comfor Gene,o olso down ood doto for the saP 500 ndex !5in9 Th secondstep is io converi ihe sto(k pricesinto ratesof return. l"or exanr ple, h ihd thc \,la)' 2006rctun for CE, $,c fhd thc percenta8e changr fron tle = = prcviousmonih: (534.59 $34.33)/$34.59 0.000i1 -0.83%.ra also finctLhc We percentchangcof lhe S&l' lndex level,and use this as the Dlarketreiurn. As Table 6-5 shows, CE had an averageannual retunr of 6.97 cluring this 4-ycar period, lvhile thc ntrket hac{an avra8eannual ret rn of 5.4%.As lve noted before,it is Lrsually unreasonabl lhink thaLth(]futurc cvecied rcturn for to a stockr\iI equal its a\,erage hisioricnlreturn over a relatilel]' short period, such esti as I )'cars.Holvover,rve nliSht rvell cxpectpast volntility b be a reason.lble matc of futurc voiatiliq', at leasi cluring the rext couple of ycars.Notc iha]i!\e \'ersLrs 13.0% for stand.uddeviationfor CE's return dlrrins ihis period t'as 19.1% ihe narket. Thus, ihe markefs volatilitv is lcss iharl ihat of CE. This is what ll'e portfoli(rand thus nluch of Lts rvould expeci,sincethe market is a rvell-di\.crsified and risk hasbeendivrrsifieda$,ay. The correlatjN bct*'eerlGE'sstockretLrrns th markct returns is about 0.19,il.hich is a liltlc higher tharl the correlation for a tvpicnlstock. As Figure6 9 sho\^.s pbt ofGE's roturnsaganlstthe market feLurns. you r{ill a notice if vou look in tbe file -rM72 Ch 06 Tool Kit.rls, rve used the rjYrrl Chaft rrrhe p,i(er reponedin Yo[oo]F,n.n.eo,e adtuted lor di',dendsoDd no.l splih so we.oi .ocuiore rhe ,erumo: fie pc,.eirose.hon!. h rheolilied p,.e lfy.! usec sor.e thor.epon5ocrualnorlel pric6, fiei you hovaro mole rheo.l urmenry.uself when .ol.u olins ruri5 Fo, erompe, ruppo:e rh. t..l prce is $100 n J! y, rhe.on poiy ro5 a 2.ifl spli, ond $e adlolprce r fiei $d0 ir Alsui rhe,eponed oduied p,.e fo, Alssrwolld bs $60,6urrfe,epoied p..e lorllly wou d 6e loweredro $50 to rcfscl r,e no.[ sp ]r Thr s veson o.cuob no.l rhe,erlrn wo!d ,erurn 20'; l$60 or 2Ol, the 5ohe 03 il $ere hod iorbee" o rp r, i $50)/$50 h.v. beoi l5l 20 wor t50, $)O0l/$100 - 20", Or apporo rhea.rudipr.e h seprembe, rhe.omponypod c n od.befw o3 $60 S ho,eha,l e6 ho'e eomedo,eturnat {$60 $10 Sl0 d via e id ,o n n fie cd u .lp ,.e $50)/$50 - 40%. Yohoolrinon.e,epoir on adutad pri.c ol t60 fa',, oid oi od dbd price.f $,1235/ 1091 Ason, fie perce olc.honse in fis I!, sepiohber,wh.h sivcs a reilrn.f 1$60 $42 357)/$12 3sl .duned Dri.e d..u,orev rcle.h rrc odlolrctum Colcu aiing BeloCoefficienh 22s Colculotingo BetoCoefficient cenerol Elechlc lor 20% =07 243iM + 00025 Rr=0.2413 iaturc k) ndd n trend line and io display the equationaDd R: value on the chart itsclf. Altomativel)', we could have used the Er../ rcgrcssnD analjisis feature, rlhich $()uld have provided more dctailcd data. l-ig ro 6 9 showsthat GE'sbcta is about 0.72, showr b), th c slopecoefficient as h thc rc8rcssn ec:llration displavcdon the chari.This nlcansthat GE'sbetais less than thc 1.0 averagebeta. Thus, CE moves up and down lcss than tlle market. Notc,howqver,thtrt thepoints are not clusterecl very tightly around the regressn linc.Sonreiimes doesmuch beiter than the markci, $hilc at other times it docs GE much worse.The I* r'alue sho{.n nr the clurt measurcsthc decreeof disDersion .rb,,r.l rccrr.-ion line.\r, \ ,pe.rkinc. nr(.FUrr.t .p.r,.nr.g. or rhLh, rt lariancc ihat is explainedby ihe regression equ.riiolr.Ar Rr ot 1.0 indicatesthat aLlpoints lie exactlyon the line, hencethat all ol the varianceoi the v variableis txplaincd bv the x variable.CE's Rr is about 0.2,{,which is fairly i},pical for an mdividu.ll stock.This indicatesthat about 24% of thc varianceilr GE's returns is oxplained the market rcturns-If we had domea sinilar anal!,sis a portfolio b!, for of 40 ra domly selected stocks,then the points would probably have been clus' tercd tightly around thc rcgressionline, and thc R':uould have probably becn Fin.ll)', note that ihe intcrcepishown h ihe regrcssion cLlualion the chart is on Sincethe rcgrcssjonequalionis bascclon onLhlydata, this means about0.0025. thaiovcr this period GE'sstockeamedabout 0.25% moro pcr rlonih than an avcragestockas a result of factorsother than a gencyal incrcasc stockprices. in SEtF-TEST Wholypes of doto ore neededto cql(ulqtcq bctq (oefficienifor on o(tuol compony? Whdt doet lfie R'z medsure? Whot is the Rr for o rypicolcompony? 226 Risk, Rerurn, lhe CopilolAsser ond Picing Model 6.5 The Relationship betwecn Risk and Rates Returrr of In the precedilrgscction,we saw that under th CAPM theory bcta is the appro priate mcasureof a stock'srelevantrisk. Now we must specify th relationship betw\inrisk and retum: For a given level of risk as mcasuredby beta,i{hat rate of reiurr should investorsrequire to compensate them for bearint that risk? To begin,let us defirrlrthe follo\.ing termsl i = erpect:d rate of return on the ith stock. r = tEuired lale ol tetuin on the iih stock.This is the minimum expected return that is required to induce an averageinvestor to purchasethe i = raalized, after-the-fact retum. rRF = risk fiee rate of rctuln. In this context,rRFis generallymeasuredby the expected rctuln on long-termU.S.Trcasurybonds. bj = btacoefficient the ith stock. of rM = required rate of rchrm on a portfolio consisting of all stock, which is called t:henarket portfolb. Pv = risk prernium on "tlle market." RPM - (rv - rR is ihe additional retum over the sk-free rate required to induce an averag investor to invest in the markei portfolio. RPi = risk premium on the ith stock RPt = RPv)bt. The markt risk premium, RPM,shoh's the premium invesbrs requirc for beadng the risk of an averaSe stock,and it dcpends or1the degrecof risk aver sion thai investors on averagehavc. Let us assumelhai Trcasury bonds yield rff : 67,and themarket hasa requiredretufllof rw = i1%.Them.lrket riskpremium is 5%: = RPNj rM rRf = 71'h - 6% = 5%. We canmeasurc stock'srelativeriskiness its betacocfficient. a by The risk prcmium Risk premium for Stocki : RPr: (RPM)br. 3l t6-r Ifu'e know ihe market risk premiun, RPM, and the shck's risk as measuredbyits beta cocflicient,br, we can find the stock'srisk premium as the product (RPNrb,. For example,ifbr = 0.5a d RPM= 5%, then RPris 2.5%l RPi = (57r(0.5) = 2.5./a Thc rcquired rcturn for any inveshnentcan be exprcsscd generalteflns as in Reqlrired retrrn = Risk-free retorn + Pfemium for risk. Here the risk-free return includes a premium for expected inflation, and r'\'e un.ler .onsidcration have simjlar maturities and liquidigr assrme il'Iatihe assets Under theseconditions,the relaiionshipbetweenihe rcquired rcturn and risk is calledthe Se.urity Market Line (SML): TheRelotionship benveenskondRoies Reiurn R of 227 retum qN/r F.,,_H^^. Req,,rred Ri.k-free /Marter ri.t\/crock i.) rare - \ premrrm /\ ucr.r / ri = rRF+ GM rRr.)br t6"r4) = rru.+ (RPM)],r. The requiredrcturn for Stocki can be witten as lollowsl rr=6%+s%(0.s) =u.57a. If some other Stock j were riskier than Stock i and had bt : 2.0, thcn iis requiredraie of return lvould be 16%: Ii= 6% + l5c.)".0 = 16.1.. An averagestock,with b = 1.0,nould have a requiredreium of 11fi, the sane as the markct retufll: r,\ = 6% + (5%)1.{l= ll7' = rM As noted above,Equation6114 callecl SecurityMarket Lhe (SML)equa' is ihe tion,and it is often exptessec{ graph form, as in Figurc 610, whch shows thc in SMLwherl rRF: 6% anc{lu'M = 5%. Note the following points: 1. Requiredratcsof return are shown on the verticalaxis,whilc dskas measlrred by beta is shown o|r the horizontalaxis.This graph is quitc different from the one shoi{n in Figure6'8, wherc the returnson individual stockswere plotted on the vcrtical axis and returns on the rnarkel index w'ercshou'n on the horizontal axis. The sbpes of the ihree lines jrr Figure 6-ll trere used to calculatE the thrcc sbcks' belns,anLl those betas were then plotted as points on th horizontal axis of Figur all0. 2. Riskless have bi = 0; therefore, appcarsas thc verticalaxis interseclrriLies rff ceptin Figure6-10.If we could conshucta portfolio that had a beta ofzero, ii would hale a requirec{ retun equal to the risk-freeratc. 3. The slopeof the SML (5%in Figure6-10)reflctsthc dcgreeofrisk aversionin ihe economy th grcatcr the averageinvstor'saversic to risk, then (a) thc ste?er theslopeol thc linc, (b) the greaterthe risk prcrnium for all stocks, and (c) the higher the rcluircd rate of return on all sbcks.r5 Thesepoinis are cliscussedfudher in a laicr section. =1.0,andbr =2.0agrco 4. Thevalues workcci we out for stocks withbL= 0.5,br with the values shown on the graph for rL, rA, and rH. 5. Negative betas ar rarc but can occur.For examplc,some stocksassociatcd with gold, such as a rnining operation,occasiflrally have a negative bcta. Basedon the SML, a sk)ckwith a negativebetashould have a requiredreturn lessthan the risk-fr(r(r rate.In fact, a stockrvith a vcry largebut negativebcta mighi har.e negative rcquired return! This meaN that lvhen the markct is doing $'ell, this stock will do poorly. But it als(, inplies the opposite:Whcn the market is doing poorll,, a negati\,beta sbck should have a positivc return. In other words, the negativebetastockactsas insurance. Thercforc,an 'de.s o r " \"' M l . o n .bte TLe.l opeo o / ro'ql l '" o . r " b e b .il.+ e .lo p e o eqo _ o ' oL" d'.d.d6r'\c .iite l .p" .1 o f od bdo a.d 0l . . 90 " - m \ - o , , q , o b o o "e ,N) 6^ b., o"., 0, -" 1". - a to t".o p " -9..e610 Lpo r.b ' l." o p e o r r 6 v L sq .o o i, o', oo. .l\F - o r ' ' ncroore nr iinedeof6ebtom I 0 ro 2 0 woud prod!.e o 5 per.enroge nr po 224 R+ Rerun ond rhecop,ro A$er Pnc,ng Mode SecurilyMorkel - 6'/" + (5%)b 9r.11_EJr_allo-! irvestor rright be willhg io acccpta negativc' thc retun on the stock clLrring good tjmes if ii is likcll, to provide a positive retun m baclijnlcs. Lloththe ScclrriLy\,larket Linc ancl . compnnv'spositi(tl on ii changeovcr tjmc cllreto chnngesin intcrest ratcs, invesbrs' aversidl to risk, and jnciividual u comparries'bctas. Suchchanges discussed the Iollowing sections. are The lmpact lnflation of Inier$t is the saDrc "renl" on borro$cd mone]',or the prico of mone,v. as Thus,rnr is ihe price of nxmcy to a riskLess borro\^,erThe risk free rafu as measLrrcd the by rate on U.S.Treasury secrriLics calledthc rorrrrrl, or taol11,/irrc,anclit consists is oftr() eleme ts: (1)a /enlitfldtioil f( rdteaf tt rn,t",and(2) ainlflatiot t,rctn|rn. lP, e.lualto the anticipatedr.1tc inflation.r"Thus, r,,r = r* 1 lll The real rate or of long tcrm Treasufybonds has historicall), ranged from 2% k) 'l%, \^lth.1 ncan of about 3%. Thereforc,if no rnfLationwcrc expectcd,long tcrn Treaslrrybonds \^'ould ),icld about 3%.Howcvcr, as thc of inflaft)n hcreascs,a pr miuDr rnust be nddcd to thc rcal risk frcc rate of rcturn to compensate iiyestors for the lossof purchasingFoser that reslrltsfrom inflation. Therefofe,the 6% rRf sllown nr Fig re 610 night be thouiahtof as consistingof n 3% real risk-freerate : of rettrn plus a 37. inflation premium: rRF r* IP = 3% 3'/c: 601 . If thc cxpecte.l inflationratemseb-v27 , to 3'l r 27 = 59 , ihis \! oulll causc rrn to riseto 8%.SrLch change shovn h Figure6 11 Noticethat und.'r the C APtvl, is . th a dis.rson izL o n sr e .n ,e o su ,y 0 id ! d s..o doi i o moturi yr+ p,emi !m MR P N e,ew e rL!detheMR P n r'ro si mpLtrE r 6 see chopici 5 for morc on bond p,i.ins ond bond,D, I sn uN Tl-p R"lo on f,p bpv-- o t ord qo.ei or q- 229 Intlolion = S[41, 8o/" 5%(b + ) Sr'rq= 6%+ 5%(b) lncrease n AriicipaiedInilaton,A P = 2'l. O gin allP= 3% RealFisk-Free ol Return, Rate 05 thc becausc incrcase rRj.leads in toan c4rnlincreasc'jn raieol rcturn on ali dsky as$ets, thcsn)neinflation prcmiu m is built ilto thc rcquircd rate of retun1of both rjsklessand rM, i1rm 11 sky assets. (]xanrpk', drc rate of reiurn on an averagestocl<, increass For points. to l3%.Other dsky sccurities' rns alsoriseby 2 percentagc retu The discussion abovealsoappliesto any changin the noninal risk-freelntercstraie,lvhether it is causedby a chingc in expectedrnflaiion or in the real intcrcst rate. The ke), point lo rcmember js that a changc in rRr {'ill rol necessarily a calrse changein thc market risk pronrium, r\'hich is thc requircd retltrn on the market,rM,minus the risk freeratc, r{,. In other worcls,asrRF changes, nlay ure so requiredretum on Lhemarket,kecping the market risk premium stablc.Thhk of a sailboatfloating in a harbor Thc distancefrom the ocran lloor to th occansuriaceis like ihc risk-freerate, and it noves up and doanr with the tides.Thc di5from thc top of the ship's mnst to the oceanfloor is like lhe requircd market tance Ironl the masircturn:lt, too, moles up and down with the tides.llut thc distance thc oceansurfaceis like thc nrarket risk premium it genertrllystays the top to move thc ship up and dor{,n.ln other .ords,a changein sanc,cvcn though LiLles raie also causes .hange in the requircd market return, rM,resulting a thrisk-free risk premium, rv rRF in a rclaiively stablemarket in Risk Chanscs Aversion Thc slope oI the Sec(rity Market I-ine reflectsthc cxtent to which invcstors are the aversc risk the steepcrthe slopeof the line, thc Sreater averatc irvestor's to riskaversion. Supposcinvesiorswere indifferentb risk; thatis, they wcre not risk If L'ould alsoprovide an expecicdretum of avcrsc. rnFwere 6?, ihcn risky assets 6%,trccause therewcrc no risk aversior"there $ould be no risk promirim, and iJ so thcSMI- vrould be plottcd as a horizontal line. As rlsk aversionincreascs, does thc risk premium, ard ihis causes slopeof thc SML to becomestccpcr. the I 230 Choptd6 RGk, Reium, ond rheCopirolAserPricing Model shiti theSMLCoused Increosed Aversion Risk by SML,= 60/0 7.5o,6(b) + 1 72 5 sML, = 6% + 5%(b,) 9.75 6 .5 Premium,rM, rBF 7.5% - [. Premium,rM, raF= 5% 2.0 Fi8lre 612 illustratcsarr ilcrcasc in risk aversion.The markct risk prcmium riseshom 5 to 7-59,, causingrM to risc. from rMr = 117.k, rM, = 13.5%. The rc'turns on oiher risky assets also rise, and the effectof this shift in risk aversionis more pronounced riskier sec rities.For exaDrplc, requirdreturn on a stockwith on the bi = {1.5 increascs onlv 1.25perccniaBe points, flon 8.5 io 9.75%, by $'hercasthat onastockh,ithb,=l.5nrcreasesby3.75perccntagepoints,from13.5to17.25q,. ('oeflicienl [.hancliin a Slotk's Rcla As rve shrll seelatcr in the bd'k, a firm can influencc its markct risk, hcnceits bcta, through changcsin the compositionof its asseis its anclalso throLrgh Lrse oi debt. A company'sbata can also changeas a result of external factors such as increased competitionin its industry,the expirationof basicpatcnis,and the like. When soch changes o.cur, the reqriiredrate of rturn also changcs. SETF-TEST Differeniiote omong the expected rote of return (il, e requnedrote of retuin (r).ond the reolized,ofier the-fod return ltl on d stock.whkh wolld hoven be lorse. to set yo! to buy $e no(k, i or r? Wouldi for a ond i rypicollybe rhe someor dif{erent o given(ompdny? Whoi ore the differen.e5 betwee. the relorive volotil;tygroph {Figure 6-8), where "betosore mode," ond t he S M L ro p hl F i g u re l 0 l , w h e re' b etos u5ed" ? i ru* bo$ how thegroph5 constru.ted d g 6 orc D ore oi rhe informolionlhev .oovee Whot hoppens the SMt groph in Figure6-10 when inflqlionincreoses decreoses? to or Whol hoppensro rhe sML sroph when risl oversionincrmser or dsreoses?\r.60r would lfie SMt look w I ' k er f j n ' e rro rs e r" i n d ,ffe re n ' n !L rho.,5.hod /ero ri ,k ove4 on? 'o How con d firm influenreil, morketrisk o, rellected it5 beh? in A stdk hos o beidof 1.4. Arruhe fiolthe risk-fre rote i5 5.5%ond the morketriskDremium 5%. Whol ir s lhe sto.k! requiredrote of rerurn?(l?.5%] Ihe CAPM,Rkk ond Reiurn:s Somerhing ng? Miss 231 Risk. Return: 6.6 The CAPM. and lsSomething Missing? The Floly Crail of ftrance is the searchfor thc rclaiionship between risk and rcquiredratesofrcturn. This relationshipaffecisthc sccurities purchased and sdd by investors, strategies the chosenby portfolio nana8ers,and the projectssclcctcd by fact, most decisionsin financeboil down to the tradeoflbeiween risk and retum: Doesthe securityor projectill questionhave enough rehlrn to jusiify its risk? To answer this quesfion,you must be able to specify the relationshipbetwcen requiredreturn and risk. If the securityor projectprovides at leastthe requircd retum, then it is acceptablc'. The Capital nsset Pricing Model (CAPM) was the first theory of risk and reiurn to becomewidely used by analysts, invcstors,and corporations. Onc of its key contributions is the insight that requircd rcturns sl'rouldnot be affectcdby dn'ersifiabledsk and that only nondiversifiablcrisk matters.Indeed, invesbrs hai'e becomemorc diversified as the CAI'jM has bccomemore widelv known.r7 However,despitc the CAPM'S intuitive appeal,a number of studieshave rajsed concems about its validit). In parti.ular, a study by Eugene Fama of the University of ChicaSoand Kenneth Frenchof Yale castsdoubt on ihe Fama and Frcnch found two variablcs that are consisiently rclated to stock returns:(1) thc firm's size and (2) its market/book ratio. After adjustingfor other factors, they found that smaller firms havc providd relatively high retums and that rehrms are relatively high on stocks with bw market/book ratios. At the sametime, and contrary to the CAPM, they found no relationshipbeh{een a stock'sbeta and its return. As an alternatjveto the traditional CAPM, iesearchers practiiionelshave and begxnto look lt) more generalmuliifactor rnodelsthat expand on the CAPM and addrcss shortcomings. iis The multifactor model is an attractivcgeneElizationof the tfaditional CAPM model's insighi thai market rjsk, or the risk that cannoibe diversifiedawat underliesthe pricing oI assets. a multifactor model, market In riskis measured relativc to a setoFriskfactorsthat determinethebehaviorof asset reiums/ wherasthe CAPM gaugesnsk only relative to the market return. It is inrportantto note that thc risk factorsin the multifachr modelsare all nondivr sifiablesourcesof risk. Empincal research ilvestigating the relationshipbetwn economicrisk factors and sccurity rehmrs is onSonrg,but it has discovered several nsk factors including thc bond default premium, the bond term structurepre mium, and inflation-that affecimost securities. An underlying assurnpiionofihe CAPM (and most other isk retum models) is that investorsare raiional, or at leastthe large invesbrs whosebuying and sell ing actionsdeterminc sccurity pdces are rational. However, psychologists havc long known thai hunans aren't always mtional, and ihis has led to a new fild nl finance called behavn)ral fhance. Behavioral finince seeks to explain why investorsand managers)nake certain decisions, vcn if thosedecisionsseem io contradictrational pricing models such as the CAPM. We discussthe Fama-Frnch models,ihe mrLtifactormodels,and behavioral financein more detail in ChapterT.And as we will discussin Chapter 10,it is not lrhere r evrdence "Ihe Divesifcoron sussei ns rhor]nveno6 nilldo nor dveBiry enoush.SeeMe I Sroimon, Plzzle, EDoDcklAndly's )aunat,244.1, pp ESeeEugeie F fomo oid Kenne$R freich, "TheCro$ Sedof ol Erpeded tocl Rerums," ^a-53 /ourrol oI fjd,.e, *i , " ' o - d h s 6 1._ .' o r co ! { "1 ." ' q . o'-onqsL-o o.' 1 - 232 Chopler 6 Prlclng Model Rsk,Reium, iheCopiiolA$er ond always easy to estimatebeta or the markct risk prenium for ihe CAPM. Despite however,the CAPM is still the most u'idely used risk-return mo.lel theseissues, for corporatefinanceapplications. SELF.TEST lhe txploin. Ar ihere qfly .eoron! 10qt]eslion volidity of $e CAPM? Summary we In this chapter, describedthe trade{ff betweenrisk and retlrn. We beganby how to calculate risk and retun for both tudividual assets and portfo discussing risk and risk in a portfo lios. In particular we difierenijatedbeh{een siand-alone and h,c explaincdthebenefitsof di!.erification. Finally,r{'edevcloped lio context, explainsho$,risk affects ratesofrcturn. In the chaptersthat fol the CAPM, \ 41ich Iow we will give you the iools io estimatcthe required ratesof return for bonds, preferredstock, and comlnoll siock, and we will explaiu ho{,firms use these retums to .levebp their costsof capital.As you lrill sce,the cost of capital is an important element in the firm's capital budgeting process.The key concepts coveredin this chapterare listcd below as thai sone unfavorableer.entwill occrir Risk can be deFined ihe chance The dsk of an asset'scash flows can be consideredon a stand-alonebasis (ench asset by itself) or in .1 portfolio context, h,here the investnent is co bined with othe. assets and its risk is reducedthrouth diversifi.ation. and they aremore concened Most rationalinvesbrs hold portfolios of assets, lrith the riskinessof thejr portlolios ihan with the isk ol individual asseis. The expected retum on an investmeniis the mean value ofiis probabilittrdistribution of retun$. The greater the probability that the actual return $'iI be far below thc expected return, the gteater the stand'Alonedsk associaied 'ith an assei. The average invesior is risk averse, which meansthat he or shemusi be compensated for holdhg risky assets.Therefore, skier assets have highr requiredretums than lessdsky assets. An assct'srisk consistsof (l ) diversifiable risk which can be elimim ted b)' di!'ersiJicarion,plus (2) market risk, which cannoi be eliminated bv diversification. The relevant risk of an individual assetis its conidbuiion to the riskinessof a market risk. Sincemarket dsk welldiversified portfolio, which is the asset's cannotbc eliminaied by diversification,investorsmust be conpcnsated for bearingit. the Asiock's beta coefticient,b, is a measlre of its marketrisk. Betamcasures extentb which the sbck's returns move rclative to ihe market. A high-beta stock is more volatile than an averagestock,whilc a low-beta stock is lessvolatile ihan an alerage siock.An averagcstockhas b = 1.0. The beta of a portfolio is a weighted averageof the betasof the individual securities the portfolio. in The Security Market Line (SML) ecluation shows the relationshipbctweena security'snurket sk and its requireclrale of retu|n. The return required for any security i is equal io the iisk-free rate plus tlre market dsk premiun times thc securitys beta: ri = rRr + (ltPv)bi Even thouSh the expectedrate of return on a stock is Senerallyequal to its requiredreturn, a number of things can happcn to causethe requircd rate ol . return to clunge: (l ) th risk-(aeerate can changebecau o f changes either se in real rates or anticipaied inflatjon, (2) a stock's beta can change, ard {3) investo$' aversionto dsk can change. Because in returns orl assets different countriesare not perfectly conelated, global diverci{ication may result in lower risk {or mr. tinational companies and globally diversifiedportfolios. Questions (6'll DeIine the follo\ ring terms,ushg gnphs or equationsto illustrateyour ansrvers ra-here1'er feasible: a. Stand-alone risk, dsk; probability disidbution b- Expectedrate of retum, i c. Continuousprobabiliiy dist bution d. Standarddeviation,o; variance,o'z; coefficientof variation,CV e. Ri.l dver.ion re"h,,p,i r"re ol return,r t. Risk premium for Stocki, RPt,market risk premium, RPM g. Capiial AssetPdcing Model (CAPM) rr. t.pecte.l relurr on porltolio. m.rrket por.foho i!: i Conelrflon,oetfi, rert,p; (orrel.,hon j. Market dskr diversiJiable riskr relevantdsk k. Betacoefficieni, averagestock'sbeta,bA b, 1. SecurityMarket Line (SML);SML equation m. Slopeof SML as a measureof dsk aversron {6.21 The probability dist buiion of a lessrisky reiurn is more peaked than that of eriskier retum. What shape would the probability distribution have for (a) com pletely cefiain returns and (b) completely uncertain returns? {6-3) Secudty A has an expectedretum of 7%, a standard deviation of retuins of 35%, e co elation coefficientwith the market of 0.3,and abeta coefficient of 1.5.Scudt) B has alt expectedretum of 12%,a standard deviation of retums of 10%,a conelatior with fte market of 0.7,and a beta coefficient of 1.{1. Whch secudfr is riskier? Why? {6-a) Suppose yo11 owned a portfolio consisting of $250,000worth of long-te r U.S.governmentbonds. a. Wol d your portfolio be riskless? b. Now srppose you hold a portfolio consistingof $250,000 h'orth of 30-day Treasury bills. Every 30 days yourbills mature,and you reinvestthe principa: ($250,000) a new batch of bills. Assume that you live on the investmenl in income fron your portfolio and that you want to maintain a constantstandard of living. Is your portfolio truly riskless? Could someone c. Can vou think of any assetthat would be completelyriskless? developsuch an asset? Explain. (6-5) If investols' aversionto risk increased,r^'ouldthe dsk premium on a high-beta more or lessthan that on a low-betastock?Explain. stock increasc rcturn double? {6-61 If a companv'sbeta h'ere to double,ra'ouldits expected Chopler6 R i 3 kR 6 i u rn ,i d rh eC o p l o l A ssei rcng Model , o P (6-4 Is it possibleto constructa portfolio of st()cks which hasan expected return equa to the risk-freemte? Appeor A Self-TestProblenlS sorurion, inAppendix {sT-r StocksA and B havethe following historicalreturns: } Reoli4d Roi6 of Return Year Stock Retumr r^ StockB'sRtum9is A's 2003 2004 2005 2006 2DO7 |J8%) 44 \22) 22 34 Q4E) 24 (4) 8 56 a. Calculate the average rate oI retum for each stock duing the s-year period. Assume that someone held a pordolio consisting of 50% of Stock A and 50% of Stock B. What would have been the rcalized rate of rclum on the portfolio in each year? What would have been the average retum on the portfolio during this period? b. Now calculatethe standard deviation of returns lor each stock and for the portfolio. Use Equation6-5. c. tnoking at the annual returns data on the two stocks, would you guess that the corrlation coefficient tretween rctums on the two stock is cloGerto 0.8 or to -0.8? d. If you added more stocks at mndom to the portfolio, which of the followint is the most a..urat statement what would happnto op? of (1) o, would rcmain constant. (2) o" would dechre to somewhere in the vicinity of 207.. (3) op would decline to zero iJ enouth stocks were included. (SI-2) ECRI Corpomtion is a holdint company with four main subsidiaries. The per' Sero Rquned centate of its business comint ftom each of the subsidiaries, and their respctive ^ond xe,urn btas, are as fo ows: xo,. or Subsidiary Eleclric utility Per.ent.geof Business Beta lntmational/spcial projcts 60Eo 25 10 5 0.70 0.90 1_30 1.50 What is the holdint company'sbeta? b . A6sume that the dsk-fiee rate is 6% and the market risk premium is 5%. What is the holding company's required rate of return? ECRI is considering a change in its strategic focus: it will reduce its rcliance on the electric utility subsidiary, so the percentaSeof its brrsinessfrom this subsidiary will be 5()%.At the same time, ECRI will incrase its reliance on the intemational/special Fojects divisio& so the percentage of its business from that subsidiary will rise to 15%.What will be the shareholdeE' required rate of retum if they adopt ihesechanges? PfOblemS Answers Appeor Appendix in B 7: : ' Easy Problerns3 1 (6-11An individual has Xj35,000 irvcstcd h a stockwhich has a beta of 0.8and $40,000 Porrlolio Bero hvestc'd in a stock .ith a beta of 1-4.lf theseare the only h^.oinvestments hcr in portfolio, what is her portfolio's bcta? (6-21Assumethat the risk-freeraic is 6% and the expectedreturn on the markct is 13%. Requned ot Reru.n What is the required rate of rcturn on a stockihat has a betaof 0.7? Rore (6'31 Assume that the risk free raLeis 57, and the market risk premium is 6%. What is Epected ond Requi,ed Rotes Return of the expectedreturn for the ovcrall stock market? What is ihe requircd ratc of return on a stockthat hasa bL'ta 1.2? of (6-41A stock'sretum has the following distribution: ExpecbdReiumDiscrebDnhlbution I'rob.bility of This Conpany's Prcducts R i te of R etun i f Thi s (50%) 0.1 4.2 0.4 02 Strong (s) l6 25 60 !l 1! Calculatc the stock's expectedretun, standard deviatiol, and coefficie)li of (6-51The m,rrlcl and SlockI havethc follonirg probJbrlrty di\lrrbulron- 0.3 0.4 0.3 l5,tL 9 18 20c/,, 5 12 a. Calculatethe expected ratcs of rcturn for the market and StockJ. b. Calculatethe standarddeviationsfor the market and StockJ. c. Calculatethe cofficients variation for the market and StockJ. of Rquired ot Reru.n Rote 16-61 a. CaiculateStockA's beta. b. lf StockA s beia werc 2.0,what would be A s new requiredrate of return? Reouned Roreol Return rRl. {6-7) Suppose = 9%,rM = l4%, and br - 1.3. a. What is ri, the requiredrate of retum on Stocki? b. Now supposcrRr(1) increases 107.or (2) decreases 8%.The slopeof the to to SML remainsconstant.How would this affectrNland ri? 236 Chdpior6 Risk, Reiuh, lheCopilol ond Asst Pricins Model rRF to The c. Now assume remains 9%but rM (1)increases 16%or(2) fallsto 13%. ai slope of the SML dos not rernain onstant How would thesechangesaffetri? (6'81 Suppose you hold a diversified portlolio consisting of a $7J00 investment in each of 20 differcnt colnnlon stocks. The poftfolio beta is equal to 1.12. Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7,500 and to use these proceeds to buy another stock for your portfolio. Assumethe new stock'sbetais equalio 1.75. Calculateyoul poftfolio's new beta. 16_91Suppo6e you are the money manater of a $4 million investment fund. The ftlnd Podfolio Requied Retun consists of four stocks with the followine investments and betas: Stock Investment Beta Ll t'. ) ' B c D 600,000 1,000,000 2,000,m0 1.50 (0.50) 1.25 o_75 Challenging Prcblems 10-13 I{ the market rcquLd mte of rctum js 1476and the risk-free Ia te is 670,what is the ftmd's rcquired rate of reium? (6_t You have a $2 million porifolio consistingof a S100,000 investmentin each of 20 0l different stock. The portfolio has a beta equal to 1.1. You are considering selling $100,000worth of one stock which has a beta equal to 0.9 and using the proceeds to purchase another stock which has a beia equal to 1.4. What will be the new beta of your portfolio following this transaction? Requlred oi Relurn an average Rore stockis 13%,and the dsk Irce mte of return is 77,.By how much does r) t6"r rate of return on StockR has a betaof 1.5,StockS has a betaof 0.75,ihe expected the required return on the riskier stock exceedtl required retum on the less dsky stock? (6-12l Stock A and B have the following historical rctums: Year Slock As Retms, t^ Sto(k 8's Retums, lD 2003 2004 2005 2UX 2UJ7 (18.00%) 33.00 15.00 (050) 27.n Q4.5A%) 21.80 30.50 Q.60) 26.30 Calculatethe average rate of return for eachstockdudnt the s-yearpedod. b. Assumethat someone held a portfolio corgisting of 50% of StockA and 50% of StockB. What would have been the realizedrate o{ retun on the portfolio in each year? What would have ben the averate return on the portfolio during this period? Calculate the standard deviation of rtums for each stock and for the Dortfolio. d . Calculatelhe coeflicientof varialion for e.(h stocl and lor the portfolio. If you are a risk-averse investor,would you prefer to hold StockA, SiockB, or ihe Dortfolio? Whv? (6-r3)You have obseNed the follo\'vingreturns over time: Slo.k Y 14% Yed Market 12L IU 212 1 15 2003 2004 2005 2006 2007 13,h 7 2l ii 2a I l1 3 20 Assume ihat the risk frce rate is 6% and the arket risk premium is 5%. a. What arc the betasof StocksX and Y? b. What arc the requiredratesof rcturn for StocksX and Y? c. What is the reqlriredrate of return for a portlolio corsistinBof807' ofStock X and 20%of StockY? retum is 22%,is StockX under- or ovelvalt1ed? d. If StockX's eapected Problem Spreadsheet {6-14) Start\,viththe partial model in the file FM12 Cit 06 Pll Build a Model,xlsfron the siockprices textbook'sWebsite.BartmanIndust es'and ReynoldsIncorporated's and dividends, along r.ith the Market Index, are shown below Stockp ccs are reportedfor December 31ofeachyear,and dividendsreflectihosepaid during the The markei data are adjustedto include dividends. vear. @ i' 2007 2006 2005 2004 2003 2002 $17.250 r4 .7 5 0 16.500 10.750 11.375 7.625 Reynoldslncorporated Dividend Storl Price Dividend Markeilndex clude! Dive. $1.15 1.06 1.00 0.95 0.90 0.6.1 $18.750 52.100 46 750 57.254 60.000 55.750 $3.00 2.90 2.75 2.50 2.25 2.00 11,663.9E 6,785.70 8,679.9E 6,434.03 5,602.28 4,705.97 anntal returnsIor Bartmarl,Reynolds,and the Use the daia given to calculate Market Index, and then calculateaverageretums over ihe s-year period. (Hint: Remember, refluns are calculatedby slrbtraciingthe beghning price tuom the ending price to get the capital gain or loss,adding the dividend to the capital gain or loss, and dividing the rcsult by the beginning price. Assum that di\-idends are already included in the index. Also, )'ou cannot calculate rate of rctul'lr for 2002because the vou do not have 2001data.) ( dl, Uldlplhe Rel de\ idri!a. .l '\e r.,rrn. lor BJrtm.i,r, r o d-. rrd -..rnd.rd the Markei Index. (Hinr Use thc samplestandarddeviationformula given nt the chapter, which conespondsio the STDEVfunction in E cel.) Now calft ate the coe{ficients variation for Bariman, Reynolds,and the of Market Index. returns Constructa scatter diagramgraph tlut shoys Baftnan's anctReynolds's on the vertical axis and the Market Inde/s retums on the horizortal axis. 238 Chopler6 Risk, Relum, ond theCopito AsslPricing Model e. Estimate Bartman's and Reynolds s betas as the slope of a regression with stock retum on the vertical axis (y-axis) and market rcflrm on the ho zontal axis (x-axis).(Hinl use Elc?l's SLOPEfunciion.) Are thesebetas consistent with your graph? The risk-tuee rate on lont-tem Treasury bonds is 6.04%. Assumethat the mar' ket risk prcmium is 57d. What is th expected return on the market?Now us the SML equation to calculate the two companies' required returns. If you formed a portfolio that consisted of 5090of Bartman stock and 509dof c. Reynolds stock, what would be its beta and its required retum? h. Supposean investor wants io include Bartman Industries' stockin his or her portfolio. StocksA, B, and C are curendy in the portfolio, and iheir betas are 0.759, 0.985,and 1.423,respectively.Calculate the ner^,' pordolio's required reiurn if ii consistsof % oI Bariman, 15%of StockA, 40%of Stock 4 and 20% of StockC e-teS0Lltce @ Cyberproblem Pleasego to the textbook's Web site to accessany Cyberproblerns. ;:iiFtrEt Assume that you rccenily gaduated with a majo! in finance, and you just landed a job as a financial planner with Bamey Smith tnc., a large financial servicescorporation. Your first assignmentis to invest $100,0mfor a client. B':ause funds are to the be invested in a businessat the md of I year, you have ben instructd to plan for a l-year holdinS period. Futher, youl boss has reskicted you to the investment alterlMiives shown in the table with dir probabilities and associated outcoms. (DisregArdfor now the items at the bottom of $e data, you will fill in the blanks later.) Rtums AltErnative on lnvesinenls EllimoiednoiEof Return SE o, d|G tconomy kobottliry l-Billj In&sties Repo rnn 122.C/") 28.O% Americon Foom Porfolio 10.0%' ll3.o%) 2-Sto* Porl6lio 3.0% Recession 0.1 LO% Belo* ov er oge 0 .2 O.4 u/ 0.1 Lo 8.0 u\, 9! 0. 0 r 2or 2O.a J )u 50.0 1.7% 7.9 -0.86 ta./ 0.0 { r o.o1 7.o ro ls.O 10.0 t5.0 Averose ,Above overog Boom i o cv b 45o 29a ll0 0 l (?!!l 43.o 30.0 13.8% ts.O% 13.4 18.8 ls . 3 t.a 1.0 0.68 ofAnor coi foom do noi olwor movin ih.oms dnedion os $.v.rol ..oia 'Nor rhdl rh6esimoledreturns my. fofxomple, when rha{onomy i! b.l.w overase,consmeG pucho!6lswr moiie$es illon $gywoud f$a eco.omy rer 3horer Hower, if rh. 4oi6i,y is in o flot ur ree$ioi. o numb. of coism66 who re. plonniig lo prncho d m@ erpnri innd $ moliE$ noy p!rdor., in{od, o chgper f6m moiE$. U.dd 66e.ircunrbnes, re rcdd Aned@n r@m'5 s|ftk p.r6 b b. hisher il fiere is o lslsion fion E *onotiy Ks iusr bl@ owros.. Barney Smith's cconomic forecastin, staff has dcvcbpcd probabiliiy estimatesfor ihe state of the econony, and its security analystshavc devloped a sophisticaied conputer progran that was used to estirnatethc ratc of return on eachalternativeunder eachstateof the economy. Alta lndustriesis an electronics firm, Repo Men Irc. collectspasFdue debts;and Amerjcan Foanrman factures mattresses and various oiher foarn producis. Barney SDlith also majniains an "index fund" which owns a markei-weighted fraction of all publicly traded stocks, you can irvest ir ihai fund, and thus obtain averagestocknrarkctresults. Giventlle siiuation as describcd,answcr the followjng quesii(trs. a. What are invesimentrctunrs?What is the retum on an inveshncnttlni costs and is sold afier 1 year for $1,100? $1,000 Do b. (1) Why is the T bill's rctum independeniof the state of the econonry? T-bills pronise a completely risk.flcc rcturn? (2) Why are AIta lndustrics' rcturns expected move with the economywhereasRepoMer's areexpcctcd to to move counterto the econorny? and fill h thc blanks c. Calculatethe expectedrate of rcturn on cachalic'rnatjve in the roi{' for i in the table. d. You should recognizthat basnrSa dccision solely on expectedreturns is your client, like virtuappropriateonly for risk'nutral individuals. Bcause ally everyonc,is risk avrse,the riskinessof eachaltenmtive is an important One possiblemeasurcof risk is the standarddeviatiul aspectof thc decisionof returns-(1) Calculatethis value for eachaltcrnative,and fill in the blank in the row,for o in the table.(2) What typc of risk is mcasuredby the standard deviation?(3) Draw a graph that shows nt,8/r/y the shapeof the probability disrributions for Alta Industries,American Foam,and T-bills. e. Supposeyou suddenly rememberedthat the cocfficientof variation (CV) is risk than thestangenerallyregardedas being a bettermeasure stand-alone of dard deviarion when the alternatives being consideredhave widely diffring expected retums. Calculatethe missingCVs, and fill in the blanks in th row asthestandard for CV in the table.Doc.s theCV producethesamcrisk rankinSs deviation? f. Suppose you creatd 2-stockportfolio by investinS a Sso,fin in AIta Industries (l) r.rum (ir). the.tand.rrd .tnd$q0.000 RepoMerr. Calculate e\pected in the (o, r, alld (he coefdcrcnt varjrtion (CVF)f\,r thi. portfnLo,rrd fill in devialion of 12\ rhe.rpproprirLe bl.rnk- th( inblc. How doeslh( nlk.'f thrs2-sto.lpodorn in lio comparewith the risk of the individuaLstocksif thcy wcrc heLd isolation? g. Suppose hvestor startswith a portfolio consisting onc randomlyselected an of stock.What would happen(1) to the risk and (2) to thc expcctedreturn of the portfolio as mor and more randomly selected stockswcrc added to th porF folio? What is ih implication for investors? Draw a Sraphof the two portfolios io illustrate your answer. h. (1) Should port{olio effectsimpact thc rvay investorsthnlk about the risk oI ndividual stocks?(2) If you dccidcd to hold a 1-sbck portfoLio,ancl conseinvestors, could yolr expect quently were exposed morcrisk thancliversified to to be compensated all of yorir risk that ls, could you carn a risk prenium for on that part of your risk thai yor'lcould llave eliminatedby divrsifying? How are beta coeffii. How is market risk measued for individual securities? cientscalculated? j. Supposeyouhavethe following hi siorica returnsfor the sbck marketand for I how to calculatcbcta,and use the anoihcr conpant P Q. Unlimitcd. Explai1l historicalstock retunN to calculatcihc beta for PQU. lnierprci your results. 240 qnd Model Risk, Relurn, ihe CopitolAset Prlcing Market PQU 1 2 3 4 5 6 7 8 10 25.7T1 8.0 211.0 15.0 32.5 13.7 40.0 10.0 210.8 213.1 40.0c" 215.0 215.0 35.0 10.0 30.0 42.4 210.0 225.4 25.4 The expected rates of return and the beta coefficienis of the altematives as suppliedby BarneySmith'scomputerprogram are as follows: Secuity Altalndustiies Market AneicanFoan T-bills RepoMen Return d) 17.47' 15.0 13.8 8.0 1.7 Risk (Eeta) 1.29 1.00 0.68 0.00 (0.86) (1) Do the expectedreturns appeario be relatedto eachaltemative'smarket dsk? (2) Is it possibleto chooseamong the altematives on the basis oI the information developed thus far? (1) Write out the Security Market Line (SML) equation, use it to calculate the\. required rate of retun on each alternative, and ihen tTaph the relationship bet$'een the expected and rcquired mtes of rcturn. (2) How do the expected rates of retum compare with the required rates oI return? (3) Does the fact that RepoMen has all expectedretum that is lessihan the T-bill rate make any sense? (4) What would be the market rjsk and the required return of a 50 50 pofifolio of Alta Industries and Repo Men? Of Alta Indushies and Amencan Foam? (1) Suppose i 'estors raised thei inJ'lation expectaiions by 3 percentage points over current estnnates reflectedin the 8% T bill rate. What effect as would higher inflation have on the SML and on the retums required on lighand low-dsk securities?(2) Supposeinstead that investors' sk aveEion increased by enoughto causethe market dsk premium to increase 3 perceniWhat effectwol d this have on the age poirlts. (Inflation femains constant.) SML and on returns of hish- and low-risk secudtis? Additional Cases Selected The lallowing casesfoft Texichoice, Tftomso, Leilning's onlinelibrcry, corier finnl of lhe cancepf discussedin this chapter and arc awilable at ht tp Jhozu t ert.h oi ce2. on. 7u. c Klein-BrighamSeiesi Case2, "Peachfree Securities, Inc. (A)." B gham-Buzzard Sedes: Case 2, "Powerline Network Coryoration (Risk and Reium)." ... View Full Document

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