Security Analysts Journal Prize Factors Driving Correlations Between Fixed Income and Equity Returns Asset Allocation and ALM for Pension Funds

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1 ecui Analss Jounal epembe 5 ecui Analss Jounal ize 5 Facos Diving Coelaions eween Fixed Income and Equi Reuns Asse Allocaion and AM fo ension Funds Junichi Iwamoo CMA Chief Reseache ension Reseach Insiue The umiomo Tus & aning Co., d. Conens 1. Esimaion of Coelaion Coefficiens. Decomposiion of Expeced Rae of Reun b he Faco Model 3. Esimaion of and, and Faco Decomposiion of Fixed Income and Equi Reuns 4. Faco Decomposiion of Coelaion Coefficiens 5. Reseach Resuls 6. Influence of Coelaion Coefficiens on AM 7. Conclusion Absac Asse allocaion equies esimaing no onl euns bu also iss. In pacice, he volailiies of asses euns o he coelaion coefficiens beween hem is commonl esimaed b hisoical daa. Howeve, Ilmanen (3) and Asano (5) have poined ou ha he coelaion coefficien beween fixed income and equi euns have ecenl exhibied a significan shif. I is difficul o idenif impoan facos fo he coelaion coefficien inuiivel because he coelaion coefficien indicaes a elaive elaionship beween fixed income and equi. This aicle does no focus on he coelaion coefficien iself. Rahe, i alenaivel emplos a mehod o esimae he coelaion coefficien b decomposing expeced euns of equi and fixed income ino seveal facos. The esul of ou empiical sud poves ha he mos impoan facos ae eal inees aes and expeced dividends. Junichi Iwamoo, CMA: Gaduaed fom Keio Univesi, in 1987 and joined The umiomo Tus & aning, and hen assumed his cuen posiion in Apil 5. In 1994, he gaduaed fom he Gaduae chool of Inenaional Managemen, Inenaional Univesi of Japan and in 4 he Gaduae chool of Inenaional Copoae aeg (IC), Hiosubashi Univesi. His wiings include a pape eniled The Decision uppo Model fo Copoae ond Invesmen in The umiomo Tus (Jul 19,, Finance Fonie, The Niei Financial Dail) and Fixed-Income Fund Managemen le and efomance (Novembe 1, ecui Analss Jounal), and Asmmeic Infomaion concening epamens and Ris Managemen of M Invesmen co-auhoed, Mach 4, Financial Review. 1 The ecui Analss Associaion of Japan

2 ecui Analss Jounal epembe 5 1. Esimaion of Coelaion Coefficiens Recenl, he appopiae level of an equi is pemium o an expeced eun of equi is being discussed in Japan and he Unied aes. In pofolio heo o fund managemen, i is eviden ha expeced euns ae he impoan facos fo asse allocaion. Howeve, he acual esimaion mehod is no alwas obvious. The applicaion of pas is pemiums o he fuue b he hisoical appoach have been common among acuaies, consulans, and sponsos. Howeve, i has been poined ou ha his appoach ends o exaggeae expeced euns. Fo example, when Ano and ensein () decomposed hisoical daa of high equi euns ino seveal facos, he found ha escalaion in vaiaion levels and dividend ields explained he mos of euns, and equi is pemiums explained less. The claimed ha an expeced equi eun should eflec hese esuls. Coespondingl, Ibboson and Chen (3) have suggesed he suppl-side appoach whee an equi is pemium comes fom value added in he econom. Addiionall, he ied o esimae an expeced eun b assuming ha a change in he vaiaion level in he fuue could be ignoed. Influenced b heaed debaes in he Unied aes, uwabe (3), Mioshi (3), Yamaguchi (3) and ohes ae acivel conducing a vaie of sudies fo an expeced eun of equi b emploing he suppl-side appoach and he implied appoach fom an equi pice in Japan. I is obvious ha asse allocaion equies esimaion of no onl expeced eun bu also is. In pacice, he is of each asse o he coelaion coefficiens beween euns has been commonl esimaed based on hisoical daa, in he same wa as expeced euns have been esimaed. The iss (volaili) and he coelaion coefficiens ae assumed sable when compaed o expeced euns. Howeve, in ecen eas, eseaches b Ilmanen (3) and b Asano (5) has shown ha a ecen coelaion coefficien beween fixed income and equi euns have significanl vaied fom he pas levels, in boh Japan and he Unied aes. These eseaches indicaed ha whils coelaion coefficiens wee fomel high, he have since apidl deceased. Howeve, no consisen discussion of he bacgound, as has been he case fo expeced euns, has been conduced. Hence he bacgound o he shif in coelaion coefficiens sill emains unclea. A coelaion coefficien indicaes a elaive elaionship beween fixed income and equi, so i is difficul o inuiivel idenif wha facos have poenial influence on i. This aicle does no discuss he coelaion coefficien iself. Rahe, i adops a mehod o fis decompose expeced euns of equi and fixed income ino seveal facos, and esimaes coelaion coefficiens. The aicle hen claifies some facos ha consisenl influence he coelaion coefficien. Finall, he aicle emplos acual daa in ode o claif which faco is impoan. The ecui Analss Associaion of Japan

3 ecui Analss Jounal epembe 5 3 The ecui Analss Associaion of Japan. Decomposiion of Expeced Rae of Reun b he Faco Model efoe decomposing he coelaion coefficien ino seveal facos, his secion shows ha euns of fixed income and equi b faco models ae deived fom he following pice fomulas. In he fis fomula fo equi pice s, equi dividend fo peiod is denoed b D, expeced nominal gowh ae of a dividend b n g, expeced eal gowh ae b g and expeced equi is pemium b. In he second fomula fo a govenmen bond pice, he cash flow of fixed income fo peiod is denoed b CF, a coupon bc, nominal inees ae b n, eal inees ae b and expeced inflaion ae b l. n n n s g D E g D E D E 1 ) (1 (1) { } T T T n l l l C CF 1 ) (1 1 ) (1 1 ) (1 () Fom equaions 1 and, i is undesood ha he following facos ae impoan fo an equi pice: a eal inees ae, an expeced is pemium, and a dividend gowh ae. imulaneousl, a eal inees ae and an expeced inflaion ae ae supposed o be impoan facos fo a fixed income pice. Faco decomposiions of he euns can easil be done using he above equaions. These fomulas appoximae capial gains using Talo expansion ignoing ems exceeding he em o he second degee. Then, adding income gains, he faco decomposiions of a fixed income eun and an equi eun can be conduced as follows. Fis, equaion 3 expesses he decomposiion of a TOIX (including dividends) eun. The las em of D is impliedl esimaed b deducing each faco on he igh-hand side fom a ealized equi eun on he lef-hand side. s / and s /, which indicae capial gain o loss, ae obained b egession analsis wihou a consan em b TOIX (wihou dividends) euns fo he pas 1 monhs. ecion 3.1 will explain how o esimae and. D l D D g g l D D g g d s (3) 1 1 ased on g D d / and l g g n /. In addiion, D can be decomposed no ino a nominal value, bu ino a change in eal value and inflaion ae. u i seems unliel ha he upcoming dividend fo he nex peiod is significanl changed due o onl a change in he cuen inflaion

4 ecui Analss Jounal epembe 5 econdl, equaion 4 shows he faco decomposiion of a fixed income eun. ecion 3. will give he deailed explanaion of he specific esimaion mehod fo an expeced inflaion ae. / and / l ae esimaed fom he adjused duaion of NOMURA-I. c l l l l l (4) 3. Esimaion of and, and Faco Decomposiion of Fixed Income and Equi Reuns 3.1 Expeced Equi Ris emium I is impossible o obseve he expeced is pemium of equi diecl fom he mae. This aicle hus adops an appoach ha indiecl esimaes he expeced equi is pemium fom he fixed income is pemium. pecificall, he expeced equi is pemium can be obained using equaion 5 b assuming ha pemiums pe is conveges o he same value θ fo boh fixed income and equi, if he mae is efficien. The volailiies of fixed income and equi euns wee esimaed based on hisoical daa fo he las 1 monhs. n was esimaed b a cuen ield fom NOMURA-I, while f was esimaed b he ovenigh call ae (secued). σ ( ) n f θ, θ σ n f (5) σ σ Thee ae vaious mehods o esimae he expeced is pemium of equi. Fo example, uwabe (3) esimaed he expeced is pemium implied b an acual cash value a each ime using an equi pice model (a esidual pofi model). In his case, he eanings foecas fo all issues in TOIX (he dividend foecas, in he case of a dividend discoun model) is equied fo he ime peiods. This aicle does no emplo eanings foecas daa lie ha of Too Keizai because such daa do no cove all issues in TOIX 3. Howeve, he esimaion of he expeced is pemium seems o have coincidence wih he esul of uwabe (3). Figue 1 shows he esimaion, which sas a quie a low level duing he lae 198s and eal 199s, nown as he bubble eas. ubsequenl i euns o a sead level. ae. o i was assumed ha he effeciveness of a change in expeced inflaion aes could be ignoed. Hence, he dividend fo he nex peiod is analzed using D, based on a nominal base (eal basis). The eun on income was expessed as c / l, when assuming a consan ield. 3 elecing an appopiae esimaion mehod is difficul because he expeced is pemium canno be obseved in he mae. u secion 5 shows ha he expeced is pemium is no egaded as he impoan faco in he esimaion of coelaion coefficiens. 4 The ecui Analss Associaion of Japan

5 ecui Analss Jounal epembe 5 Figue 1: Esimaion of he Expeced Equi Ris emium 15 (%) Jan'88 Jan'89 Jan'9 Jan'91 Jan'9 Jan'93 Jan'94 Jan'95 Jan'96 Jan'97 Jan'98 Jan'99 Jan' Jan'1 Jan' Jan'3 Jan'4 3. Expeced Inflaion Raes ome sudies in he Unied aes o esimae an expeced inflaion ae fom he pice of an inflaion-lined bond. u in Japan, inflaion-lined bonds have onl been issued since Mach 4, so such bonds ae oall unavailable fo analzing he pas long peiods. Theefoe, anohe appoach is equied and he following mehods can be candidaes: one using such ime-seies models as ARIMA o mulivaiae AR o one esimaing he expeced inflaion ae fom a suve of people abou he expeced inflaion ae fo he fuue. As fo he fome mehod, a ime-seies model is difficul o consuc, paiculal in Japan whee he pices of goods have been declining ove 3 eas. The ARIMA model was examined fo his aicle. Howeve i was found a negaive expeced inflaion ae was unavoidable, so he model was unsuiable fo ou analsis. Kiagawa and Kawasai (1) have also ied o mae a mulivaiae AR model, bu he found i was difficul o fix he model b a popula saisical es lie AIC, and seleced explanao vaiables wee no sable as ime pogessed. Acnowledging ha ime-seies models ma be abia, he following mehod, efeed o as he Calson-ain Mehod (C mehod), was emploed. The C mehod obains he expecaion and he sandad deviaion of a populaion disibuion fom he esuls of hee quesionnaies fo he fuue condiions. As fo a consume pice foecas, he Cabine Office of Japan has been conducing a Diecion of ice suve (quae-cenu daa) included in he Consume ehavio Reseach quesionnaie (see Figue ). Quie a few analses ha emplo he esuls of his quesionnaie have been seen. ecause such quesionnaies abou economic end have some elaionship wih inflaion expecaions in he financial mae, his aicle emplos he esuls of hese quesionnaies. 5 The ecui Analss Associaion of Japan

6 ecui Analss Jounal epembe 5 Figue : Diecion of ice in Consume ehavio Reseach (%) Decease Unchanged Incease Alhough he C mehod has seveal vaiaions, his aicle emplos he adjused C mehod based on he aional expecaions hpohesis poposed b Ogawa (1991), Doi (1), and Hoi and Teai (4). The following is a bief descipion of he adjused C mehod. Assuming ha esponden i holds a heshold δ when he/she foecass a change in inflaion ae, he expeced inflaion ae l fomed b Jun-8 Jun-83 Jun-84 Jun-85 Jun-86 Jun-87 Jun-88 Jun-89 Jun-9 Jun-91 Jun-9 Jun-93 Jun-94 Jun-95 Jun-96 Jun-97 Jun-98 Jun-99 Jun- Jun-1 Jun- Jun-3 i him/he is compaed each ime, no simpl wih he las ealized inflaion ael,, bu wih he heshold l, δ. The esponden will answe, inceased if he ae exceeds he heshold. Convesel, he esponden will answe, deceased if he ae falls below answe, unchanged if he ae emains in [ l δ l δ ] Assume hee ha he expeced inflaion ae i,,,. l, δ. In addiion, he esponden will l follows he nomal disibuion N( δ ) µ. Equaion 6 can expess he quesionnaie esuls as follows: U as he pecenage of espondens ha answe he inflaion ae would incease, D as he pecenage of espondens ha answe decease. Φ means he disibuion funcion fo sandad nomal disibuion. Defining U D u and e ( l > l δ ) i, e li µ l > σ l µ l, δ µ l, δ µ Φ 1 σ σ δ µ l δ µ e e ( < ) Φ i <,, l l δ i, σ σ σ, d as follows. These values can be esimaed fom equaion 6 when calculaing (6) 6 The ecui Analss Associaion of Japan

7 ecui Analss Jounal epembe 5 Φ 1( 1 U ) u Φ especivel. D 1 and ( ) l δ µ,, σ d l δ µ, (7) σ If u and d ae idenified, µ and σ can finall be obained fom equaion 8. Then µ is he esimaion of expeced inflaion 4. In addiion, δ can be deived because he expeced inflaion l e i has he mean µ and he vaiance σ 5. u d l δ µ,, u d δ σ u d Figue 3 shows he esimaion of an expeced inflaion ae. The esul is eas o undesand when compaed wih he complicaed deivaion of he esimaion fomula. Figue and Figue 3 implies ha he expeced inflaion ae simpl eflecs he esuls of quesionnaies. Alhough hee is some flucuaion, hose who answeed, incease fom he cuen inflaion ae consisenl accoun fo he highe popoion of hose suveed. (8) 7 Figue 3: Expeced Inflaion Rae b he Adjused C Mehod (%) Inflaion Rae (Expeced) Inflaion Rae (Realized) - Ma-85 Ma-86 Ma-87 Ma-88 Ma-89 Ma-9 Ma-91 Ma-9 Ma-93 Ma-94 Ma-95 Ma-96 Ma-97 Ma-98 Ma-99 Ma- Ma-1 Ma- Ma-3 Ma-4 4 Quael daa is lineal complemened o conve ino monhl daa. Fuhemoe, i is believed ha he expeced inflaion ae has a em sucue; howeve, he aicle assumes ha he ae is sable duing he peiod. 5 Refe o Ogawa (1991), Doi (1), and Hoi and Teai (4) fo deails of he calculaions. 7 The ecui Analss Associaion of Japan

8 ecui Analss Jounal epembe 5 Figue 4: Nominal Inees Rae, Expeced Inflaion Rae, and Real Inees Rae (%) 1 Nominal Inees Rae 8 6 Expeced Inflaion Rae 4 Real Inees Rae - Jan-88 Jan-89 Jan-9 Jan-91 Jan-9 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan- Jan-1 Jan- Jan-3 Jan-4 Figue 4 shows a eal inees ae obained afe deducing he expeced inflaion ae l b he adjused C mehod fom he nominal inees ae n. The following poins ae noewoh in he Figue: (1) mos eal inees aes fall wihin he % o 6% ange and ae elaivel sable when compaed wih nominal inees aes, () eal inees aes become negaive beween 1997 and 1998 because of he ises in expeced inflaions, and (3) no much diffeence has been obseved beween nominal and eal inees aes since Faco Decomposiion Using Hisoical Daa he mehod explained in secions 3.1 and 3., an expeced equi is pemium and an expeced inflaion ae wee esimaed. Then, faco decomposiion of fixed income and equi euns is conduced using he pas daa of equi and fixed income euns. These daa epesened appoximael 16 eas of monhl daa fom Janua 1988 o Mach 4. 8 The ecui Analss Associaion of Japan

9 ecui Analss Jounal epembe 5 As fo equi, Figue 5 and Table 1 show he faco decomposiions fo TOIX euns s (wih dividends). Fis, he following componens showed a compaaivel sable pofi: eal inees ae, he pa of income gains, and inflaion ae l, he pa of is pemium and capial gains. upisingl expeienced an abnomal negaive siuaion duing 199 o eal 199, bu ecoveed and posed he highes accumulaed eun among all facos. On he ohe hand, eal inees has been boadl fla since econdl, he capials gains fom and flucuae moe han he income gains fom hose facos. In paicula, expeced equi is pemium flucuaed, which ma affec an oveall equi eun significanl. Addiionall, cumulaivel, he capial gains fom and ealized posiive pofis. Howeve, he fis and he second facos did no pla an impoan ole duing he peiod. The mos significan flucuaion is obviousl shown b he expeced dividend faco D (capial gain depends on changes in he dividend eal gowh ae g and expeced dividends D fo he nex peiod), he hid faco. The expeced dividend faco has consisenl been on a downwad end since 199. This is he onl faco ha has shown a negaive eun and he faco acuall dives ou all ohe facos. In ohe wods, a downun in an equi eun is aibued o a educion in he expeced fuue dividends. This fac is consisen wih he eseach esuls of uwabe (3) and ohes. Figue 5: Faco Decomposiion of Equi Reun (Accumulaed) 1 5 (%) Real Inees Rae (Capial) Ris emium (Income) Real Inees Rae (Income) Expeced Inflaion Rae (Capial) Ris emium (Capial) -5-1 Equi Reun Expeced Dividend (Capial) -5 Jan-88 Jan-89 Jan-9 Jan-91 Jan-9 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan- Jan-1 Jan- Jan-3 Jan-4 Equi Table 1: Faco Decomposiion of Equi Reun (Annual asis) Real Inees Rae (Income) Ris emium (Income) Expeced Inflaion (Capial) Real Inees Rae (Capial) Ris emium (Capial) Expeced Dividend (Capial) Mean 1.48% 3.49% 1.47% 1.7% 1.16% % andad Deviaion %.54% 6.5% 9.79% 18.49% 9 The ecui Analss Associaion of Japan

10 ecui Analss Jounal epembe 5 As fo fixed income, Figue 6 and Table show he faco decomposiion of NOMURA-I eun. Fis, eal inees ae and inflaion ae l, which ae he same as hose fo equi as income gain, poduce a sable pofi. econdl, he capial gains fom he flucuaion of and l ae volaile, also simila as in he case fo equi. Each has achieved eun of aound 1% cumulaivel. This is because, diffeen fom equi, he pice sensiiviies o he flucuaions of and l ae alwas negaive, and because and l ae coninuousl deceasing. Figue 6: Faco Decomposiion of Fixed Income Reun (Accumulaed) (%) 8 6 Fixed Income Reun 4 Expeced Inflaion Rae (Income) Real Inees Rae (Capial) Real Inees Rae (Income) - Expeced Inflaion Rae (Capial) -4 Jan-88 Jan-89 Jan-9 Jan-91 Jan-9 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan- Jan-1 Jan- Jan-3 Jan-4 Table : Faco Decomposiion of Fixed Income Reun (Annual asis) Fixed Income Real Inees Rae (Income) Expeced Inflaion (Income) Real Inees Rae (Capial) Expeced Inflaion (Capial) Mean 1.48% 1.47%.71%.51% andad Deviaion.35%.54% 5.44% 4.48% 1 The ecui Analss Associaion of Japan

11 ecui Analss Jounal epembe 5 4. Faco Decomposiion of Coelaion Coefficiens In secions and 3, fixed income and equi euns wee decomposed ino majo facos. Hee, he faco decomposiion of a coelaion coefficien beween fixed income and equi euns is conduced. The coelaion coefficien is given b equaion 9. cov(, ) ρ, (9) σ σ Afe appling equaions 3 and 4 o equaion 9, le us assume ha coelaions beween facos and hei diffeence can be ignoed. Then he numeao covaiance can be decomposed ino seven majo facos (13 facos as minimum uni) as follows: cov (, s ) cov l D, l l l va ( ) va ( ) cov (, ) cov (, ) cov ( D, ) cov ( D, ) (1) () ( ) ( ) ( ) ( ) ( ) ( ) va l cov, l cov, l cov, l cov, l cov D, l cov D, l l l l This equaion maes i possible o decompose he coelaion coefficien of equaion 9 ino seven facos. Moe pecisel, (1) he eal inees ae, () he expeced equi is pemium and he eal inees ae, (3) he expeced dividend faco and he eal inees ae, (4) he expeced inflaion ae, (5) he eal inees ae and he expeced inflaion ae, (6) he expeced equi is pemium and he expeced inflaion ae, and (7) he expeced dividend faco and he expeced inflaion ae. efoe examining each faco, hese facos will be gouped ino wo caegoies when we epiomizes hem ino he fome hee (1,, 3) and he lae fou (4, 5, 6, 7) in ode o obseve an oveall end. The fome goup ceainl has he vaiables elaed o he eal inees ae. o, he aggegaed impac of he eal inees ae on he coelaion coefficien beween fixed income and equi euns can be obseved. Meanwhile, he lae goup ceainl has he vaiables elaed o expeced inflaion ae l, so he aggegaed impac of he expeced inflaion ae on he coelaion coefficien can be obseved. The aicle efes o he fome goup as he boad eal inees ae faco and o he lae goup as he boad expeced inflaion faco. 11 The ecui Analss Associaion of Japan

12 ecui Analss Jounal epembe 5 5. Reseach Resuls 6 Figue 7 and Table 3 show he coelaion coefficien (ealized value), he coelaion coefficien (esimaion b seven facos), he boad eal inees ae faco and he boad expeced inflaion faco. As Asano (5) poined ou, he coelaion coefficien beween fixed income and equi euns, which had been posiive and high, apidl declined since The esimaed coelaion coefficien b he faco decomposiion mehod well descibes he ealized value, and shows paial divegence onl in eal 199 and oh he boad eal inees ae faco and he boad expeced inflaion faco show significan flucuaions and have peiodiciies. I is significan ha he move in opposie diecions. Addiionall, he coelaion coefficien, which moves beween boh facos, is obseved. Figue 7: Coelaion Coefficien (Realized), Coelaion Coefficien (Esimaed), oad Real Inees Rae Faco and oad Expeced Inflaion Faco (%) 3 oad Expeced Inflaion Faco 1 Coelaion Coefficien (Esimaed) -1 - Coelaion Coefficien (Realized) oad Expeced Real Inees Rae Faco -3 Jan-89 Jan-9 Jan-91 Jan-9 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan- Jan-1 Jan- Jan-3 Jan-4 Table 3: oad Real Inees Rae Faco and oad Expeced Inflaion Faco Faco 89/1 9/1 91/1 9/1 93/1 94/1 95/1 96/1 97/1 98/1 99/1 /1 1/1 /1 3/1 Real Inees Rae Expeced Inflaion Toal Coelaion coefficiens, covaiance, and vaiance ae calculaed using he 1 las monhs of daa. 1 The ecui Analss Associaion of Japan

13 ecui Analss Jounal epembe 5 To analze hese facos moe pecisel, le us examine each of he seven facos. Table 4 shows ha he each faco has a diffeen influence. Howeve, facos and D in equaion 3, and facos l and D in equaion 6 paiculal have bigge influences. Addiionall, Figue 8 shows he following covaiances: he covaiance of and D having a significan influence in faco (3), he covaiance of and D having a significan influence in faco (6). Consideing he elaion of hese covaiances and wo boad facos in Figue 7 maes i possible o undesand he specific ineacions wihin an econom, which dives he coelaion coefficien beween fixed income and equi euns. Fo example, he coelaion coefficien is boosed in a posiive diecion b an incease in he boad eal inees ae faco, when he coelaion beween and D declines jus as duing 1999 and lae 3. Convesel, when he coelaion beween l and D inceases jus as duing 1998 and, he coelaion coefficien is educed in a negaive diecion b a decease in he boad eal inees ae faco. imilal, when he coelaion beween l and D declines (duing 1998 and ), he coelaion coefficien is boosed in a posiive diecion b an incease in he boad expeced inflaion faco. On he cona, he coelaion coefficien declines b a decease in he boad expeced inflaion faco whee he coelaion beween l and D inceases. Table 4: even Facos Consiuing Coelaion Coefficien Faco 89/1 9/1 91/1 9/1 93/1 94/1 95/1 96/1 97/1 98/1 99/1 /1 1/1 /1 3/ Figue 8: Covaiance of (%).4 and D, Covaiance of l and D.3. Dividend Faco and Expeced Inflaion Rae (Diffeence) Dividend Faco and Real Inees Rae (Diffeence) -.4 Jan-89 Jan-9 Jan-91 Jan-9 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan- Jan-1 Jan- Jan-3 Jan-4 13 The ecui Analss Associaion of Japan

14 ecui Analss Jounal epembe 5 Wha do such movemens in each faco impl? As equaion 1 has shown, he coelaion signs beween and D, and also beween fixed income and equi euns ae opposie because cov ( D, ) is muliplied b /. Fo insance, le us conside he siuaion whee ises and D is impoved. Thus he coelaion beween hem inceases. The impovemen in D is diecl lined o he incease in equi euns, wheeas he incease in has a negaive effec on fixed income euns. As a esul, he coelaion beween fixed income and equi euns deceases. Fuhemoe, equaion 1 indicaes ha such pocesses can be obseved similal in l. Finall, he coelaion beween and D becomes he deemining faco fo he coelaion beween fixed income and equi euns because he influence of he boad eal inees ae faco exceeds ha of he boad expeced inflaion faco 7. In addiion, he eason wh coelaions of, D and l, D move in opposie diecions as in Figue 8 is he invese coelaion beween and l. Incidenall, he faco elaed o he expeced equi is pemium hadl has an influence on a coelaion coefficien. I can be explained b equaion 1. As Figue 5 and Table 1 show, D has moe significan flucuaion han ohe facos. Hence, he significanl flucuaing D and he vaiable ha foms covaiance wih D have a gea influence. Tha is he case fo he eal inees ae and he expeced inflaion ae l, which have covaiance wih D. Howeve, he expeced equi is pemium does no. Tha is wh he expeced is pemium is no an impoan faco fo he coelaion coefficien. Fom hose analses, eal inees ae and D have been confimed as he mos impoan facos affecing he coelaion coefficien beween fixed income and equi euns. To obain eal inees ae, he nominal inees ae n o he expeced inflaion ae l is equied. This aicle has emploed he adjused C mehod o esimae expeced inflaion aes bu anohe bee appoach migh be equied. Addiionall, alhough he aicle has impliedl calculaed he expeced dividend D as an ex-pos faco, ohe foecasing mehods should be consideed. Howeve, he mehod emploed in he aicle can be fa simple han meel acceping he calculaed coelaion coefficien fom hisoical daa, o han examining an enomous maco and mico facos one b one which become headlines of a newspape. 6. Influence of Coelaion Coefficiens on AM asl, le s discusses he influence of coelaion coefficiens on asses and suplus in he pension AM (Asse iabili Managemen). Given he fac ha a eal inees ae and an expeced inflaion ae ae he mos impoan facos affecing coelaion coefficiens as shown in secion 5, his secion also focuses on hese wo facos in conducing he analsis. This is because, founael, he inees ae and 7 Table 6 shows he sensiivi of he coelaion coefficien (bonds and equi) fo changes in he coelaion coefficien ( and D ). 14 The ecui Analss Associaion of Japan

15 ecui Analss Jounal epembe 5 he expeced inflaion ae ae also impoan facos fo a pension liabili euen. Fis of all, his secion defines he eun of pension liabiliies based on Yano (4). D ( D 1) is he adjused duaion of pension liabili, 1 is he eal inees ae on 1-ea govenmen bonds, φ ( φ 1) is he adjusing ae of benefi o inflaion, and is he eun of a nominal liabili. can be expessed b he following equaion: { 1 ( ) l} 1 φl D 1 φ (11) When equaion 11 fo a pension liabili eun is compaed wih equaion 3 fo equi eun and equaion 4 fo fixed income eun, he eal inees ae is found o be he common faco among he hee equaions in ems of boh income gain and capial gain. I implies ha he coelaions beween wo of hem ae high. Regadless of income gains and capial gains, he hid em of equaion 3, equaion 4, and he second em of equaion 11 show ha he inflaion ae is he common faco in he hee equaions wih a posiive conibuion. I should also be noed ha he inflaion ae is ealized in a pension liabili eun, while he ae is expeced in fixed income eun. Addiionall, no he enie ealized inflaion ae, onl some poion of i, is efleced in a pension liabili eun. On he cona, he fouh ems in equaion 11 fo a pension liabili and in equaion 4 fo fixed income show ha an incease in he expeced inflaion negaivel affecs euns. Howeve, he moe a pension benefi adjus o inflaion, he less a pension liabili eun flucuaes. 15 The ecui Analss Associaion of Japan

16 ecui Analss Jounal epembe 5 Figue 9 and Table 5 show faco decomposiion fo he cumulaive eun of a pension liabili 8. The eal inees ae 1 (income gains) and he ealized inflaion ae l geneae sable pofis. In oal, he ield aound 3% and 6% cumulaive euns especivel. Addiionall, he capial gains caused b he eal inees ae 1 and he ealized inflaion ae l flucuae significanl when compaed wih income gains, jus as in he cases of fixed income and equi. Each of he ems evenuall holds a posiive cumulaive eun. Howeve, he pofi caused b he expeced inflaion ae l is elaivel low compaed wih ha b he eal inees ae 1 duing he peiod. The eal inees ae 1 ielded appoximael 3% eun, while he expeced inflaion ae l ove 6% eun. Figue 9: Faco Decomposiion of ension iabili Reun (Accumulaed) (%) 1 8 ension iabili Reun 6 Real Inees Rae (Capial) 4 Real Inees Rae (Income) Realized Inflaion Rae (Income) - Expeced Inflaion Rae (Capial) -4 Jan-88 Jan-89 Jan-9 Jan-91 Jan-9 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan- Jan-1 Jan- Jan-3 Jan-4 Table 5: Faco Decomposiion of Reun of ension iabiliies (Annual asis) ension iabiliies Real Inees Rae (Income) Realized Inflaion (Income) Real Inees Rae (Capial) Expeced Inflaion (Capial) Mean 1.85%.38% 1.85%.4% andad Deviaion.37%.% 1.7% 5.5% 8 Figue 9 shows he case of.5% in adjusing he ae of inflaion. The naional bond ield applied in Equaion 11 was obained fom Facse. 1-ea daa was used as an alenaive because 1-ea daa was unavailable. 16 The ecui Analss Associaion of Japan

17 ecui Analss Jounal epembe 5 The suplus fomula can be given b asses and a pension liabili. When he diffeence beween asses ( as equi, as fixed income) and pension liabili is suplus Y, and a aio (funding aio) fo he pension liabili of asses is f, he fomula is expessed as follows: Y ( ), f When suplus eun Y is expessed as a ae of eun (sandadizing i wih pension liabili ) and w epesens he equi weigh in asses, suplus eun Y can be defined as follows: Y { w ( 1 w) } f (1) In addiion, suplus is σ Y can be obained b he following fomula: σ Y w w f σ ( 1 w) f σ σ ( 1 w) f cov(, ) ( 1 w) f cov(, ) wf cov(, ) f σ ( 1 w) f σ w( 1 w) f cov(, ) ( 1 w) f cov(, ) wf cov(, ) { w } { σ } Dopfel (3) has menioned ha a deceasing coelaion affecs he enie is diffeenl in he case of asses and he case of suplus including asses and debs. uch diffeence is easil undesood, because he fis em in equaion 13 is he is of asses and he second em added o he fis em means he suplus is 9. The decease in he coelaion beween fixed income and equi euns causes a educion in is of he hid faco of he fis em. On he cona, he coelaion decease in he hid faco of he second em ma incease is because equi is moe liel o have a diffeen feaue o a pension liabili, which is simila o fixed income. A suplus simulaion was conduced b changing coelaion coefficiens o he eun and he is of a suplus. aamees in he sandad model ae se as follows:.5 ( φ.5) as an adjusing ae o inflaion, 1 ( f 1) as he funding aio, and 6% fo equi weigh and 4% fo fixed income weigh ( w.6). aamees wee andoml changed fom hese fis seings. (13) 9 The fis em is efeed o as he is among asses and he second em as he is beween asses and pension liabiliies. 17 The ecui Analss Associaion of Japan

18 ecui Analss Jounal epembe 5 Table 6: Thee Diffeen Coelaion Coefficiens and ensiivi o Change in Coelaion Coefficien eween and D ensiivi fo Co (, D ) Mean Adjusing Rae Co, Co, Co, Co, Co, Co, -.319** -.191* ** ** ** * -.38** ** ** ** ** -.17 ** significan a he.5% level; *significan a he 5% level. The lef pa of Table 6 shows he sensiiviies of hee coelaion coefficiens fo a change in he coelaion coefficien beween and D, when adjusing aes of inflaion wee,.5, and 1. Fis, i was found ha he sensiivi of he coelaion coefficien ( and ) fo a change in he coelaion coefficien beween and D was negaive. This esul suppos secion 5, which shows ha he coelaion beween equi and fixed income euns deceases when he coelaion beween and D inceases. In addiion, because he coelaion coefficien is beween asses, i is cleal independen of he inflaion-adjusing ae. econdl, a song elaionship was no idenified in he coelaion coefficien ( and ) fo a change in he coelaion coefficien beween and D. Thus, he coelaion beween and is no much influenced b he movemen in he coelaion beween and D. Thidl, i was found ha he sensiivi of he coelaion beween and o a change in he coelaion beween and D, was negaive. Thus, he coelaion coefficien beween equi and pension liabiliies euns deceases as he coelaion coefficien beween equi and fixed income euns deceases. This esul showed ha he hedge efficienc of equi ha has some similai wih fixed income, deceased fo a pension liabilii, as Dopfel (3) has alead poined ou. Ineesingl, when inflaion ae φ inceased, i was obseved ha he negaive endenc of he coelaion beween equi and pension liabili euns was senghened, when he coelaion beween and D inceases. This phenomenon can similal be descibed in secion 5 whee he coelaion beween fixed income and equi inceases along wih inceases in and D. ecause he impovemen in D diecl inceases equi euns, he emaining elaionship beween and needs o be consideed. As shown in equaion 11, whee he adjusing ae of inflaion φ is, a capial gain is significanl influenced no onl b bu also b l. Howeve when φ is 1, he flucuaion is onl dicaed b, hus negaive elaionships cleal appea in. 18 The ecui Analss Associaion of Japan

19 ecui Analss Jounal epembe 5 Table 7: Reuns and Riss of upluses in ension AM (Consan Real Inees Rae Case) aamee Value Reun (Mean) Ris (andad Deviaion) Asse iabili uplus Inflaion Adjusing Rae Funding Raio Equi Weigh Assuming ha a eal inees ae emains consan, le us conside he change in he suplus is wih vaiousl changed paamees of a pension liabili and asses (Table 7). Fis, he suplus is inceases when he adjusing ae of inflaion φ ises. Along wih he incease in he adjusing ae, he coelaion beween and deceases eeping a posiive value, while he coelaion beween and deceases uning o a negaive value 1. Hence, he is beween asses and a pension liabili inceases because he second value of he second em in Fomula 13 deceases he negaive degee, while he hid value in he em also changes fom negaive o posiive. econdl, diffeen fom he adjusing ae of inflaion, when he funding aio changes, i causes no diec change in a pension liabili eun. Thus, he aio does no have an effec on each coelaion coefficien. Table 7 shows ha he is beween asses inceases wih incease in he funding aio, because he fis em depends eniel on he funding aio. Howeve no significan change is idenified in he is beween asses and a pension liabili. This is because he influences of he funding aio on he second and hid values in he second em ae cancelled ou because hese value signs ae opposie unde he condiions of he sandad model 11. Thidl, as he funding aio, he equi weigh does no have a diec effec on a coelaion coefficien. When he weigh of equi wih high is deceased, he is beween asses deceased in he aggegae. As fo he is beween asses and a pension liabili unde sandad condiions, he hid value in he second em becomes posiive, bu his poion educes wih he decease in equi weigh. Addiionall, because he second value of he second em becomes negaive, and because he weigh in his poion inceases in conas wih he educion in equi weigh, he value deceases fuhe. Finall, he is beween asses and pension liabiliies deceases. 1 ee he fis and second column fom he igh in Table ee he middle line of he fis and second column fom he igh in Table The ecui Analss Associaion of Japan

20 ecui Analss Jounal epembe 5 Howeve, i should be noed ha whee he coelaion beween and D changes, such a discussion based on he hisoical daa is no alwas conclusive. As explained ealie, his is because he values o signs of hee diffeen coelaion coefficiens (he igh side of Table 6) easil va because of he change in he coelaion beween and D. In he suplus is, he flucuaion of coelaion coefficiens beween fixed income and equi euns has he poenial fo consideable impac no onl on he is beween asses bu also on he is beween asses and liabiliies. 7. Conclusion This aicle emploed acual mae daa o conduc faco decomposiion of equi and fixed income euns. Then he aicle decomposed he coelaion coefficien beween fixed income and equi euns ino seveal facos and examined each. As a conclusion, he aicle confimed ha he coelaion beween eal inees aes and expeced dividends has he mos significan influence. Addiionall, as fo a pension liabili eun, he aicle emploed he suplus elaionship, whee a eal inees ae and an expeced inflaion ae ae impoan facos, o examine he following poins: how he coelaion coefficien among fixed income, equi, and a pension liabili vaies wih he change in he coelaion beween eal inees aes and expeced dividends and wha maes a coelaion coefficien which influences suplus is change. The mehod aemped in he aicle is he faco analsis of euns, bu his mehod involves some issues including he inepeaion of he eseach esul b hisoical daa. One is he esimaion mehod of expeced inflaion aes. The aicle emploed he adjused C mehod, because such an asse as inflaion-lined bonds, which allows us o now expeced inflaion aes diecl, is no available. Howeve, since hee is no appoach o confim he ue expeced inflaion ae fo now, moe eseach is equied. The ohe one is he sae of he econom. Accoding o Ilmanen (3) and Asano (5), he sae of he econom can be ecognized as an impoan faco affecing he coelaion coefficien beween fixed income and equi euns. The aicle used long-em daa fo ove 16 eas fo he analsis. Duing hese eas, excep fo a few eas a he beginning, nominal inees aes consanl declined and he Japanese econom emained sluggish. Hence, i is undeniable ha a diffeen esul ma be obained if hee is significan change in he econom in he fuue. Fuhe eseach and analsis ae equied, including compleel diffeen appoaches fom wha was adoped in he aicle. I would lie o expess m gaiude o Yuihio Asano (Yoohama Naional Univesi) who gave man useful commens. The auho is solel esponsible fo he conen of his pape, and an opinions expessed and eos ae his alone. The ecui Analss Associaion of Japan

21 ecui Analss Jounal epembe 5 Refeences: Ano, Robe D. and ee. ensein, Wha Ris emium Is Nomal? Financial Analss Jounal, Mach/Apil. Asano, Yuihio, The Coelaion beween Equi and Fixed Income, umiomo ension Jounal, Vol. 5 Ma 5 (in Japanese). Campbell, John Y. and Tuomo Vuoleenaho, Inflaion Illusion and oc ices, NER Woing apes 163, Naional ueau of Economic Reseach. Doi, Taeo, Incease in aving Rae and ecauiona aving Moive in Japan, ERI Discussion ape eies No.1, 1 (in Japanese). Dopfel, Fedeic E., Asse Allocaion in a owe oc-ond Coelaion Envionmen, The Jounal of ofolio Managemen, Fall 3. Hoi, Masahio and Nobou Teai, Applicaions of he Calson-ain Mehod o Japanese ice Expecaions, ERI Discussion ape eies No. 91, 4 (in Japanese). Ibboson, Roge G. and eng Chen, ong-run oc Reuns: aicipaing in he Real Econom, Financial Analss Jounal, Janua/Febua 3. Ilmanen, Ani, oc-ond Coelaions, The Jounal of Fixed Income, epembe 3. Kiagawa, Genshio, and Yoshinoi Kawasai, Analsis in edicion Eo of Inflaion b Time eies Model, an of Japan Woing ape 1-13, 1 (in Japanese). Mioshi, Yasuo, ong-tem Equi Reun Esimaion Consideing Changes in Valuaion, ecui Analss Jounal Vol.41, No.5, Ma 3 (in Japanese). Ogawa, Kazuo, Income Ris and ecauiona aving, The Economic Review Vol. 4, No., Apil 1991 (in Japanese). angong Joo, oc Reuns and Inflaion: A Covaiance Decomposiion, Applied Economics ees, Apil, Vol. 7, Issue 4. uwabe, Taashi, Global Convegence of Equi Ris emium, Ageing and ension Invesmen Vol. No. 4, Decembe 3 (in Japanese). Yano, Manabu, ension AM wih Inflaion-oeced onds, ecui Analss Jounal Vol.4, No7, Jul 4 (in Japanese). Yamaguchi, Kasunai, Yoshio Kanasai, Aio Maabe, and Tadaai Komasubaa, Equi Ris emium in Japan Empiical Evidence ove 5 eas fom a uppl-side especive, ape pesened a 11h Annual Confeence of Nippon Finance Associaion, June 3(in Japanese). 1 The ecui Analss Associaion of Japan