IMES DISCUSSION PAPER SERIES

IMS DISCUSSION PPR SRIS Rsk Managemen for quy Porfolos of Japanese Banks kra ID and Toshkazu OHB Dscusson Paper No. 98--9 INSTITUT FOR MONTRY ND CONOMIC STUDIS BNK OF JPN C.P.O BOX 23 TOKYO 1-863 JPN

NOT: IMS Dscusson Paper Seres s crculaed n order o smulae dscusson and commens. Vews expressed n he Dscusson Paper Seres are hose of he auhors and do no necessarly reflec hose of he Bank of Japan or he Insue for Moneary and conomc Sudes.

IMS Dscusson Paper Seres 98--9 Ocober 1998 RISK MNGMNT FOR QUITY PORTFOLIOS OF JPNS BNKS kra Ieda* and Toshkazu Ohba** BSTRCT Ths paper verfes he mpac of equy porfolo on bank managemen, underscorng he mporance of managng he rsks nvolved and suggesng managemen of sensvy agans equy prce rsk as one rsk managemen echnque ha akes no accoun he correlaon beween equy prce rsk and cred rsk. To do hs, he paper focuses on he hgh correlaon beween expeced defaul probably esmaed by he oponapproach (Meron mehod) usng equy prce nformaon and spread over Lbor observed n he bond marke. Ths s used o calculae sensvy (dela and vega) o changes n equy prce and s volaly. ccordng o calculaons for a sample porfolo, hese wo sensves have a degree of uly n measurng he dsrbuon of rsk exposure and n usng equy prce ndex fuures and opons as hedges. In he hedgng of vega rsk (whch ends o reflec cred rsk) n parcular, long pu posons n equy prce ndex opons are shown o be poenally effecve. Keywords: equy porfolo, loan, expeced defaul probably, spread over Lbor, equy prce rsk, cred rsk, sensvy JL classfcaon: G14, G21 * Research Dvson 1, Insue for Moneary and conomc Sudes, Bank of Japan (-mal: akra.eda@boj.or.jp) ** Rsk Managemen Deparmen, The Long-Term Cred Bank of Japan, Lmed (-mal: ohba1998@aol.com) 1

TBL OF CONTNTS 1. PRFC 3 2. IMPCT OF QUITY PORTFOLIO ON BNK MNGMNT 4 2 1 Impac on corporae value and accounng prof or loss 4 2 2 Impac on BIS capal adequacy sandards 8 2 3 Implcaons 11 3. CORRLTION BTWN QUITY PRIC RISK ND CRDIT RISK 11 3 1 xpeced defaul probably calculaed by he opon-approach 13 3 2 Spread of bond yeld 16 3 3 Daa used 17 3 4 nalyss of expeced defaul probably and Spread of bond yeld 18 4. RISK MNGMNT TCHNIQUS WITH MPHSIS ON SNSITIVITY TO QUITY PRIC FLUCTUTIONS 19 4 1 Measurng and managng sensvy 19 4 2 sses and sensves o be managed 2 4 3 Calculang dela and vega 22 4 4 Rsk managemen usng dela and vega 24 5. CONCLUSIONS 29 2

1. PRFC The Japanese banks have long acknowledged he prce rsks n her equy porfolos, bu have done lle o manage or conrol hose rsks. The prmary reasons nvolved n hs are: 1) he fac ha he eques have been pu n her porfolos for he sraegc purpose of mananng busness relaonshp wh her clens; 2) he fac ha hgh raes of reurn on nvesmens n he lae 198s gave porfolos large unrealzed profs ha provded fnancal sably wh he banks; and 3) he fac ha here were few ools wh whch o hedge rsks even he banks had waned o do so for he eques n her porfolos. However, he prolonged slump n Japanese equy marke has caused hese same eques o become a facor for nsably n he banks fnancal healh, and he banks are now beng forced o reconsder her purposes for holdng he eques n her porfolos. Indeed, emergency relef measures had o be brough n for he fscal year endng March 1998. The measures provded banks wh he choce of valung her sock porfolos a cos and also allowed hem o coun unrealzed gans on real esae owards her capal. These measures are, however, nohng more han emporary accounng manpulaons and he banks wll probably fnd hemselves pressed o manage and conrol her exposure o equy prce rsks from now on. Furhermore, he ancpaed expanson n he secures dervaves marke, whch wll provde more hedgng ools, can drve hs rend. I s from hese perspecves ha hs paper sudes some mehods of equy prce rsk managemen. One pon gven parcular emphass n hs sudy s he relaonshp beween equy prce rsk and cred rsk. The banks have for many years boh held ssued by her clens for sraegc purposes and also loaned money o hose same clens. There s a posve correlaon beween equy prce rsk and cred rsk, and boh end o emerge n mes of economc downurn. From he perspecve of bank managemen, herefore, would be beer for he banks o consder her busness relaonshp wh her clens n such a way as o measure and manage boh he rsk and he profably of her clens, negrang cred rsk and equy prce rsk, raher han merely measurng and managng boh rsks separaely. Ths paper s as follows: In Chaper 2, we use accounng daa dsclosed by large banks o quanfy her rsk exposure and esmae s mpac on bank managemen. Ths s done o demonsrae how mporan s for banks ha hey manage he rsks n her equy porfolos. In Chaper 3, we perform an emprcal analyss ha demonsraes he hgh correlaon beween equy prce rsk and cred rsk. In Chaper 4, usng he relaonshps demonsraed n he prevous chaper, we show some echnques ha can be used o manage rsks n porfolo comprsng eques and loans. In Chaper 5, he concludng chaper n hs paper, we brefly summarze our fndngs and sugges fuure drecons n our research. 3

2. IMPCT OF QUITY PORTFOLIO ON BNK MNGMNT Ths chaper uses accounng daa dsclosed by he Japanese major banks (cy banks and long-erm cred banks 1 ) o quanfy her rsk exposures and llusrae he mpac ha hs rsk has on bank managemen. In Secon 1 we consder he mpac on corporae value and accounng prof or loss. In Secon 2, we consder he mpac on he BIS capal adequacy sandards. We begn by esmang rsk exposures a he end of he nex half accounng erm (sx monhs hence). In he formula for dong hs (shown below), sands for he lengh of he erm, K for book value a he end of he precedng erm, S for prevalng marke prce a he end of he precedng erm, S for prevalng marke prces a he end of hs erm, r for reurn on equy, and σ for equy prce volaly. S 2 σ = S exp r + σ ε as ε~φ(,1) (1) 2 The dsclosure documens furnshed by he banks do no provde deals on he specfc ssues n her equy porfolos or he amouns nvesed n each. For he purpose of smplcy, herefore, we have assumed ha each bank had a porfolo whch srucure was he equvalen of he TOPIX ndex. We consder he TOPIX ndex o be a good approxmaon because he equy porfolos of cy banks and long-erm cred banks are generally made up of eques of lsed medum and large-sze companes wh whom hese banks have enered no cross-shareholdng relaons as an ougrowh of lendng ransacons. To demonsrae he ncrease n rsk exposures o equy wre-offs, we have compared ndexes calculaed for wo perods: he end of March 1992, whch marked he begnnng of full-fledged effors o clean up bad loans afer crash of bubble economy, and he end of March 1997, whch was he mos recen me a whch he banks were no gven he opon of accounng for eques a cos. 2 1 Impac on corporae value and accounng prof or loss (1) Value a rsk (VaR) We wll begn by consderng he mpac on corporae value by calculang VaR (holdng perod s a half-year, confdence nerval s 99% le) as shown n quaon (2). 1 We have excluded from hs sudy Hokkado Takushoku Bank (whch faled las year) and Japan Cred Bank (whch moved o domesc sandards for capal adequacy n March 1998). For he pre-merger Bank of Tokyo-Msubsh we use smple oals from he fnancal sascs of Msubsh Bank and he Bank of Tokyo. 4

VaR = 2. 33 σ (2) Noe: σ TOPIX TOPIX S sands for he daly volaly of TOPIX (calculaed usng wo years of hsorcal daa). Fgure 1 conans he resuls for he calculaons. Noe ha VaR (average per bank) has declned from 1,174 bllon a he end of March 1992 o 778 bllon a he end of March 1997 because of a declne n volaly. 2 he same me, he rao of VaR o unrealzed gans on eques (VaR o URG rao) rose from 97% a he end of March 1992 o 142% a he end of March 1997 because of he need o ake profs on eques n order o wre off bad loans, whch consequenly rased book values. 3 Indvdually, he VaR o URG rao (a he end of March 1997) was parcularly hgh for Bank G (496%) and Bank (34%), whch were h harder han oher banks by he declne n unrealzed gans over recen years. Only Bank had unrealzed gans on eques n excess of VaR (8%). [Fgure1] VaR (bllon yen) nd of Mar. 1992 nd of Mar. 1997 VaR VaR o URG rao VaR VaR o URG rao Bank 571 93.2% 382 34.7% Bank B 128 129.3% 837 249.8% Bank C 95 98.4% 65 128.9% Bank D 125 14.4% 877 137.4% Bank 1838 11.7% 1251 8.% Bank F 1547 94.5% 121 15.7% Bank G 16 88.% 546 496.7% Bank H 1367 8.5% 748 229.8% Bank I 1325 98.6% 859 114.3% Bank J 788 83.3% 567 167.5% Bank K 1148 16.3% 819 125.1% verage 1174 97.2% 778 142.4% 2 The daly volaly of he TOPIX declned from 1.39% a he end of March 1992 o.94% a he end of March 1997. 3 verage book value was 2,2 bllon yen a he end of March 1992 (agans marke value of 3,23 bllon yen), bu had rsen o 2,63 bllon yen a he end of March 1997 (agans marke value of 2,18 bllon yen). 5

(2) xpeced wre-off of eques In hs subsecon we seek he expeced wre-off of eques (W) a he end of he erm (sx monhs hence). For he wre-off, we posed he dfference beween he erm-end marke prce and he book value a he end of he prevous erm as a loss f he marke prce was less han he book value. Therefore, f he marke prce was approachng he book value a he end of he prevous erm, here was a hgher lkelhood ha a wre-off would be seen a he end of hs erm. Workng from hs mechansm, s possble o calculae W as a fuure value of a pu opon wh a srke prce of K, whch s he book value a he end of he prevous erm. Ths s done n quaon (3). 4 = Max( K S,) f ( S ds W ) Where, r = KΦ( d + σ ) S e Φ( d) (3) S σ ln + r K + d = 2 σ 2 f : Probably densy funcon of lognormal dsrbuon Φ: Cumulave densy funcon of sandard normal dsrbuon Fgure 2 conans he resuls of he calculaon. 5 he end of March 1992, W (average per bank) was ny, and W o URG rao was.%, bu he rse n book values caused o ncrease o 2.2% a he end of March 1997 (n moneary erms, abou a 3-fold ncrease from he end of March 1992). Lookng a ndvdual banks, W o URG rao was parcularly hgh for Bank G (39%) and Bank (18%), whch corresponds o he large VaR values calculaed n Subsecon (1). 4 There wll probably be some dspue over wheher o use he expeced rae of reurn r or he rsk-free rae r n calculang he W. We have decded o use he rsk-free rae r (whch was assumed o be 1%). 5 In performng hese calculaons, we assumed, as noed above, ha each bank had a porfolo srucured o be he equvalen of he TOPIX ndex, so TOPIX was he only probably varable. However, s ordnary for ndvdual socks o declne even f he ndex self s rsng, so our W s probably undersaed. 6

[Fgure 2] xpeced Wre-Off (bllon yen) nd of Mar. 1992 nd of Mar. 1997 W W o URG rao W W o URG rao Bank..% 2.4 18.2% Bank B 2.5.3% 26.8 8.% Bank C.1.% 1.8.4% Bank D.3.% 3.6.6% Bank.4.%..% Bank F.1.% 6.7 1.% Bank G..% 43.1 39.2% Bank H..% 2. 6.1% Bank I.2.% 1.1.1% Bank J..% 5.8 1.7% Bank K.4.% 1.9.3% verage.4.% 12. 2.2% (3) 99% le pon of he equy wre-off Ths subsecon calculaes he 99% le pon of he equy wre-off (99%W); he resuls wll be found n Fgure 3. The amoun of 99%W (average for per bank) was neglgble a he end of March 1992 (3% of he unrealzed gans on eques), bu had rsen o 47% a he end of March 1997. In moneary erms, was on he order of several hundred bllon yen for all excep Bank, whch s an ndcaon ha he rse n book values has weakened bank s prof srucures. [Fgure 3] 99%W (bllon yen) nd of Mar. 1992 nd of Mar. 1997 99%W 99%W o URG rao 99%W 99%W o URG rao Bank.% 27 24.7% Bank B 273 29.3% 52 149.8% Bank C.% 145 28.9% Bank D 51 4.4% 238 37.4% Bank 3 1.7%.% Bank F.% 343 5.7% Bank G.% 436 396.7% Bank H.% 422 129.8% Bank I.% 17 14.3% Bank J.% 228 67.5% Bank K 67 6.3% 164 25.1% verage 38 3.2% 26 47.6% 7

2 2 Impac on BIS capal adequacy sandards Ths secon consders he mpac of equy porfolo on he BIS capal adequacy sandard rao (BIS rao). Unrealzed gans on equy porfolo (URG) are, for he BIS purposes, couned no Ter II capal (whch allows 45% of unrealzed gans on secures, up o he amoun of Ter I capal). Uncerany over erm-end equy prce herefore ranslaes drecly no uncerany over BIS rao. erm: quaon (4) calculaes URG o be couned owards Ter II a he end of he ( S K UL) URG = Mn, Where, ( UL ( S K),) = UL Max (4) UL : Upper lm of unrealzed gans on eques ha can be couned Noe ha he second erm n quaon (4) s a pu opon ha uses marke prce a he end of he erm ( S ) as he underlyng asse prce and he sum of he upper lm and book value a he end of he prevous erm ( UL + K ) as he srke prce. The expeced URG can herefore be sough as he value of hs opon. From hs s possble o seek 1) he expeced BIS rao, and 2) he 99% le pon of BIS rao a he end of he erm sx monhs hence (99% BIS rao). The resuls are found n Fgure 4 and Fgure 5. In performng hese calculaons, we assumed ha all condons excep hose specfcally relaed o eques were unchanged from he end of he prevous erm. In oher words, he only nfluence assumed for Ter I was from equy wre-offs, and he only nfluence on Ter II from changes n URG. Rsk asse was assumed o be unchanged. These resuls pon o he followng characerscs. 8

[Fgure 4] xpeced BIS Rao and 99% BIS Rao (end of Mar.1992) BIS rao xpeced dfference 99% dfference BIS rao BIS rao Bank 8.28% 9.61% + 1.33% 6.38% - 1.9% Bank B 8.4% 9.17% + 1.12% 6.37% - 1.67% Bank C 8.39% 9.23% +.84% 6.79% - 1.6% Bank D 8.1% 9.47% + 1.37% 6.71% - 1.4% Bank 8.18% 9.12% +.94% 6.82% - 1.35% Bank F 7.93% 8.85% +.92% 6.34% - 1.59% Bank G 8.27% 9.55% + 1.28% 6.43% - 1.84% Bank H 8.33% 9.28% +.94% 6.45% - 1.88% Bank I 8.25% 9.62% + 1.37% 6.87% - 1.38% Bank J 8.3% 9.92% + 1.62% 6.71% - 1.59% Bank K 8.43% 9.74% + 1.31% 7.2% - 1.24% verage 8.23% 9.41% + 1.19% 6.64% - 1.59% [Fgure 5] xpeced BIS Rao and 99% BIS Rao (end of Mar.1997) BIS rao xpeced Dfference 99% dfference BIS rao BIS rao Bank 9.2% 8.82% -.2% 5.4% - 3.99% Bank B 9.23% 9.24% +.1% 7.12% - 2.1% Bank C 9.9% 9.3% -.6% 7.73% - 1.36% Bank D 9.11% 9.5% -.6% 7.93% - 1.18% Bank 9.28% 9.87% +.58% 8.35% -.93% Bank F 8.93% 8.85% -.8% 7.26% - 1.67% Bank G 9.22% 8.8% -.42% 5.4% - 3.83% Bank H 9.4% 9.19% +.15% 7.% - 2.5% Bank I 8.76% 8.74% -.2% 7.98% -.78% Bank J 8.7% 8.69% -.1% 6.8% - 1.9% Bank K 8.75% 8.9% +.15% 7.71% - 1.4% verage 9.1% 9.2% +.% 7.12% - 1.89% (1) xpeced BIS raos a he end of he erm he end of March 1992, he expeced BIS raos a he end of he erm were generally abou one percenage pon hgher for all banks, whle a he end of March 1997 he rae of ncrease was wdely dfferen for ndvdual banks and had declned generally, rangng anywhere from.58% pon gan for Bank o.42% pon loss for Bank G. 6 6 Rsk asse a he end of March 1997 (average for all banks) was abou 34.8 rllon yen, so one percenage pon rse n he BIS rao would requre an addonal 35 bllon yen n capal assumng he amoun of rsk asse dd no change. 9

The reason for lower growh a he end of March 1997 compared o he end of March 1992 was ha Ter I declned whle Ter II rose, brngng he wo closer ogeher, whch resuled n a declne n he upper lm of URG ha could be couned no Ter II. lso a work was he rse n book values (K). These facors had he effec of reducng he value of he pu opon n he second erm of quaon (4). In pon of fac, comparsons of he dfference beween Ter I and Ter II (average per bank) show a dfference of abou 65 bllon yen a he end of March 1992, whch had declned o less han 6 bllon yen no even a enh hose levels by he end of March 1997. work n hs was an ncrease n hybrd capal nsrumen (specfcally, subordnaed deb and he lke), whch s a Ter II em (see Fgure 6). [Fgure 6] TerⅠCapal and TerⅡ Capal(average, bllon yen) nd of Mar.1992 nd of Mar.1997 dfference TerⅠ 1798 1612-185 TerⅡ 115 1554 + 44 Unrealzed gan on secures.45 Hybrd capal 55 288-262 43 1154 + 723 nsrumen Ⅰ-Ⅱ 648 58-589 quaon (4) ndcaes ha he expeced value of URG couned no Ter II a he end of he erm wll be larger f UL s gven and S K s larger han UL ( K [book value a he end of he prevous erm] s suffcenly small). (2) 99% BIS raos a he end of he erm he end of March 1992, 99% BIS raos were abou 1.5 percenage pons lower for all banks, bu a he end of March 1997 here were subsanal dfferences from bank o bank n he amoun of declne (he smalles declne was for Bank I a.78% pons; he larges, for Bank a 3.99% pons). he end of March 1997, 99% BIS raos had declned o he 5% level for Bank (5.4%) and Bank G (5.4%). mong he oher banks, he only one ha was sll above 8% was Bank (8.35%). The reason for he dfferences among banks n 99% BIS raos sems from he dfferences n he rao of wre-offs o URG (from % o almos 4%) ha was seen n Secon 1. In oher words, he larger he wre-off, he more of a declne here wll be on Ter I, whch has he effec of reducng he upper lm for Ter II (because 1

Ter II capal can be couned only up o he amoun of Ter I capal) and leads o a subsanal drop n BIS raos. 2 3 Implcaons One mgh be able o conclude ha equy porfolo n he pas had a posve effec on bank managemen by provdng he banks wh unrealzed gans, hough hs sably assumed ha equy prces would connue o grow. From a rsk managemen perspecve as well, one could be emped o beleve ha here was lle need o pay aenon o he rsk n equy porfolo as long as book values were low and equy prces were growng seadly. However, as we have seen, equy prces have slumped and repeaed prof akng has rased book values, and hs has ncreased he possbly ha equy porfolo wll have large negave mpacs on accounng prof and loss, corporae value, and BIS rao. These nsghs lead us o conclude ha equy prce rsk can no longer be gnored n bank managemen, and herefore ha a process mus be developed for measurng and dealng wh rsk exposure n oher words, ha rsk managemen needs o be pracced. Indeed, as referred by Yoshfuj[1997], now s he me ha bank managemen mus reconsder her own phlosophy of managemen he sgnfcance of holdng eques n bank s porfolo. 3. CORRLTION BTWN QUITY PRIC RISK ND CRDIT RISK In Chaper 2 we examned he mpac on bank managemen of he equy prce rsk n equy porfolo. However, we mus underscore ha hese eques are held for sraegc purposes, ha s, banks hold he eques because hey have longerm lendng relaonshp wh hese clens, and hs urges us o consder he magnude of he cred rsk exposure from hese loans as well. Ths chaper looks a he correlaon beween equy prce rsk and cred rsk, hereby seng he groundwork for comprehensve managemen of rsks from boh eques and loans. The hgh correlaon beween he wo can be seen from a cursory examnaon for he equy prce ndex and he defaul probably, 7 bu n hs paper we use as 7 For he perod 1986 o 1997, he correlaon coeffcen beween he equy prce ndex (TOPIX) and he defaul probably (calculaed by Tekoku Daa Bank) was.829, whch as large n comparson o oher facors. < Correlaon Coeffcens > TOPIX Defaul probably Yen/dollar rae 1yr JGB TOPIX 1. Defaul probably -.829 1. Yen/dollar rae.433 -.337 1. 1yr JGB.523 -.778.668 1. Unforunaely, here are few emprcal sudes of he correlaon beween equy prce rsk and cred rsk n Japan. One recen sudy, Suzuk [1998], provded an emprcal analyss of he relaonshp beween bond rangs and equy reurns, and found rangs o be a sascally sgnfcan facor n explanng equy reurns. 11

our measures of equy prce rsk and cred rsk: (1) he defaul probably as calculaed from equy prce nformaon and (2) he spread calculaed from bond prce nformaon. The specfc mechansms nvolved are oulned n Fgure 7: 1) he expeced defaul probably (DP) esmaed by he opon-approach s defned, and DP s consdered a funcon of equy prce nformaon (equy prce S, rae of reurn r, volaly σ ) (quaon (5)); 2) he spread over Lbor of corporae bond (LS) 8 s used o seek he relaonshp beween DP and LS n erms of acual equy prce and bond prce (quaon (6)); and as he resul from he frs wo seps, 3) LS s assumed o be a funcon of equy prce nformaon (quaon (7)). DP = f ( S, r, σ ) Defnon (5) LS g(dp) mprcal analyss (6) LS = g f ( S,, σ )) Hypohess (7) ( r [Fgure 7] Relaonshp beween Cred Rsk and quy Prce Rsk quy and Loan Porfolos quy Prce Rsk Prce S Volaly σ Rae of Reurn r 3) Hypohess from 1) and 2) LS= g( f ( S, r, σ )) Cred Rsk Spread of Corporae Bond (Spread over Lbor) LS 1) Defnon 2) mprcal analyss DP= f ( S, r, σ ) expeced defaul probably esmaed by he oponapproach DP LS g(dp ) 8 Lbor s he neres rae for Iner-Bank money ransacons beween banks and s herefore calculaed as he rsk-free rae plus a spread commensurae o he cred rsk of he bank nvolved. When handlng cred rsks of bonds from he perspecve of spreads, s essenally beer o do so n erms of spread over he rsk-free rae (.e., spread over governmen bonds). We have chosen o use he spread over Lbor n hs paper because of yeld curve dsorons caused by he naure of ndvdual ssues among Japanese governmen bonds yeld. s wll be dscussed n more deal n Chaper 4, hs paper s more concerned wh he change n spread ( dls ) raher han he absolue value of he spread, so we recognze here are no parcular problems wh no usng spread over governmen bonds yeld. 12

3 1 xpeced defaul probably calculaed by he opon-approach The expeced defaul probably calculaed by he opon-approach deems a company o be defaul when he value of s asse falls below he value of s lably. I can herefore be defned as an n he money (ITM) rae for a pu opon usng corporae asse as he underlyng asse and lably value as he srke prce. 9 The KMV model s one well-known use of hs expeced defaul probably. Kealhofer [1995] dscusses he conceps nvolved, and Mordara [1997] examnes problem pons and observaon parameer esmaon mehods. Sao and Mordara [1998] calculae and analyze recen DPs for Japanese banks and fnd ha DP s a suffcenly useful measure of he sae of corporae healh. In hs paper, we use he Meron [1974] mehod o calculae DP and bascally follow he Sao-Mordara [1998] mehod for esmang parameers. Below s an oulne of he calculaons nvolved. 9 The opon-approach was frs developed as a heory for valung bonds. In he early 197s, Meron [1974], Black and Scholes worked from he dea ha bonds are a conngen clam agans corporae asses o develop a heory for valung bonds assumng seady neres raes. More recenly, Duffe-Sngleon [1994], Jarrow-Turnbull [1995], Jarrow-Lando-Turnbull [1997], and Longsaff-Schwarz [1995], among ohers, have added neres rae flucuaon and defaul probably pahs o hs model o creae a valuaon model for dscoun bonds wh defaul rsk ha mee he no-arbrage condon. In he Longsaff-Schwarz model, whch s an exenson of he Meron model, he prce of a dscoun bond wh defaul rsk s as follows (deals omed): P( X, r, T ) = D( r, T ) wd( r, T ) Q( X, r, T ) (a) Where, P: Prce of dscoun bond wh defaul rsk D: Prce of dscoun bond wh no defaul rsk w: Wre-off rae Q: xpeced value for he cumulave defaul rae unl T V: Value of ne asse K: Defaul hreshold value X: V/K r: Shor-erm neres rae T: Tme o maury of bond Defnng he bond spread (= SP) as he dfference beween he yeld on he bond n queson and he yeld on a rsk-free dscoun bond (n hs case, he spread s he dfference beween bond yeld and he rsk-free rae, whch dffers from LS defned above), hen follows: SP ( X, r, T ) = ln(1 wq( X, r, T )) / T (b) If we hen use equy prce nformaon o esmae Q ( X, r, T ), whch s an expresson of he expeced defaul rae, hen s possble o use he heorecal spread calculaed wh quaon (b) and he acual spread observed n he bond marke o analyze he relaonshp beween equy prce nformaon and spreads. However, quaon (a) says ha he heorecal spread s a funcon of he bond s erm o maury T, so he lengh of he erm o maury wll have an mpac on he heorecal spread. Bu he erm srucure of spreads observed n he curren Japanese bond marke s almos fla (see Ieda and Ohba [1998]), so we can expec some dvergence from heorecal spreads. From hese consderaons, hs paper calculaes DP for ndvdual ssues and hen seeks he relaonshp beween DP and LS hrough drec emprcal analyss whou resorng o quaon (a). 13

(1) ssumpons The balance shee of a company a me s comprsed of asse, one knd of fxed-neres lably B and equy on he bass of marke value (presen me s me, maury s me T ). = B + ( =,, T ) (8) We assume ha asse follow he sochasc process below ( ~ ). ~ d = rd + σ dz ~ (9) Where, r : xpeced growh rae for asse σ : Volaly of he asse growh rae d ~ : Wener process z hs pon, he logarhm of asse a maury T s normally dsrbued 2 2 wh mean ln + ( r / 2 T and varance σ T. σ ) ~ ln = ln d~ z (1) T 2 + ( r σ / 2) T + σ (2) Calculaon of he expeced defaul probably DP Defaul s defned as he value of asse s less han he value of lably a ~ maury T (n oher words, T < BT ). In equaon form, he expeced defaul probably(dp) s expressed as: ~ DP = Pr( < T BT ) = ~ Pr(ln < T ln BT ln ) ln B = Φ T 2 [ ln + ( r σ / 2) T ] σ T (11) (3) smaon of parameers 1 quaon (11) conans fve parameers ( B T,T,, σ, r ). We wll assume ha maury of lably (T) s one year and B T s he book value of he neres-bearng 1 See Mordara [1997] for a dscusson of he problems nheren n esmaon. 14

lably 11 repored for he mos recen accounng erm. The oher hree parameers (curren value of asse, volaly of asse σ and expeced growh rae of asse r ) are calculaed from he followng smulaneous equaons (quaon (12), quaon (13), and quaon (14)): 12 ~ ~ ( T BT,) f ( T ) dt r T ~ e Max = = Φ ( d1) rt B e Φ T ( d 2 ) (12) Where, ln( / BT ) + ( r + σ d1 = σ T d = d σ T 2 1 2 / 2) T f : Probably densy funcon of lognormal dsrbuon Φ: Cumulave densy funcon of sandard normal dsrbuon σ = σ (13) Φ( d 1 ) r = r + 1 rb (14) Where, σ : quy prce volaly : quy r : xpeced growh rae of equy r : xpeced growh rae of marke value of lably B 11 We assumed here would be lle change n he book value of lably over he relavely shor perod of one year. Ineres-bearng lables were defned as he oal long and shor-erm borrowngs, bonds, converble bonds, employee deposs and blls dscounable shown on he fnancal saemens. 12 quaon (12) uses opon heory o value from quaon (8). 15

To solve hese smulaneous equaons, we used equy prce nformaon observed n he marke for he followng consans: quy : Number of socks ssued N Sock prce S ( N s assumed o be consan) quy prce volaly σ : nnualzed weekly hsorcal volaly (observaon perod of one year) xpeced growh rae of equy r : nnualzed average value (observaon perod of one year) for weekly raes of reurn xpeced growh rae of marke value of lably rb : ssumed o be zero. 13 If, as we have done above, he only DP varables are 3 2 Spread of bond yeld B T, N, and r B are assumed o be consan, hen S, r and σ, as seen n quaon (5). 14 The spread of domesc sragh bond yeld used n hs analyss s he spread over Lbor. The spread over Lbor s defned as LS n quaon (15) when he cash flow from he bond s swapped for floang neres rae (Lbor + LS ), and can be calculaed by valung dscoun facors sough from he swap. LS m Cp Sw n j (1 V ) + D( j= 1 = 2 365 m n j ( V + I) D( j ) 36 j= 1 j ) I (15) Where, V :Secondary marke value of he bond (per 1 par value) Cp :Coupon rae on he bond Sw :Swap rae for he same erm o maury as he bond 15 j :Dae of he j-h paymen on he bond D( j ) :The j dscoun facor 13 I s bascally mpossble o oban nformaon from he markes on he marke value of lably, whch makes mpossble o esmae s growh rae eher. Ths wll have an mpac on he expeced growh rae of asse hrough quaon (14), bu he expeced growh rae of asse self does no have ha much nfluence on he valuaon of DP n quaon (11), so we have assumed ha he expeced growh rae of lably was zero. 14 Ths corresponds o 1) of Fgure 7. 16

3 3 Daa used n j :Number of days beween j 1 and j m :Number of paymens unl maury I :ccrued neres For equy prces, we used closng prces from he Frs Secon of eher he Tokyo Sock xchange or he Osaka Secures xchange; for bond prces, we used he OTC (Over-he-Couner) sandard bond quoaons publshed by he Japan Secures Dealers ssocaon; 15 for fnancal daa, he daa publshed n fnancal repors. The bond ssues n our analyss me hree condons: 1) had bond prce quoe and closng equy prce hroughou he perod analyzed (see below), 2) had a erm o maury of less han 1 years, and 3) had ssung values of more han 1 bllon each (oal of 735 ssues). We analyzed he perod May 1997 o March 1998, usng daa from he fnal radng day of each week (48 weeks). 3 4 nalyss of expeced defaul probably and bond spreads quaon (16) conans a regresson analyss ha uses a me seres of 48 weeks worh of poolng daa for a cross secon of 735 ssues. Ths regresson llusraes he relaonshp beween DP and LS. 15 The OTC sandard bond quoaons sysem (revsed prl 1997) s summarzed as follows. Types of ssues: governmen bonds, muncpal bonds, governmen-guaraneed bonds, bank debenures, corporae bonds, and yen-denomnaed foregn bonds. Sandard bond quoaon ssues: In prncple, all ssues ha mee all of he followng condons (a) unlsed, domesc, publcly offered publc and corporae bond ssues (wh a remanng maury of a leas one year), (b) ssues wh a fxed neres rae from ssuance hrough redempon, and (c) ssues wh lump-sum redempon upon maury. (Under he revsed sysem, he number of ssues covered by he OTC sandard bond quoaons ncreased by approxmaely hree mes.) Calculaon mehod for he OTC sandard bond quoaons: arhmec mean of he quoaons receved from he reporng companes (hese quoaons represen yeld ndcaors for ransacons wh a face value of approxmaely 5 mllon yen as of 3: PM on he busness day before publc release). --- The OTC sandard bond quoaons are no necessarly based on acual ransacons (one of he reasons s ha he ousandng volume of ceran ssues s nsgnfcan), so here are problems wh he relably of he daa. Neverheless, he OTC sandard bond quoaons have he wdes coverage of any publc daa n Japan, and hey are consdered o be opmal daa for he analyses. Prce un nervals:.1 yen per 1 yen par value. Publc release of he OTC sandard bond quoaons: Daly (excludng holdays). Number of companes reporng quoaons: 28 companes as of prl 1997 (prevously 15 companes). 17

LS j = α + α1dp j + ε j (16) Where, LS : LS of ssue a pon n me j (n percenage uns) j DPj ε j α : DP of ssue a pon n me j (n percenage uns) : rror erm, α1 : Consans The resuls (Fgure 8) show DP o have a generally hgh explanaory power. The DP coeffcen ndcaes ha one percenage pon rse n DP wll produce 14 bass pon expanson n LS. [Fgure 8] Regresson Resuls (lower row : -value) djused-r 2 Inercep DP.7.22 1.4 3.53 286.32 To examne he changes n he relaonshp beween LS and DP durng he perod analyzed, we performed he regresson n quaon (16) for each cross secon n he 48-week perod. Fgure 9 conans he coeffcens of deermnans and he coeffcens of DP for he perod. [Fgure 9]djused-R 2 and Coeffcens of DP( α 1) 3.5 1 3 2.5 2 djused-r2 (R-axs).8.6 1.5 1.5 Coeffcen of DP (L-axs).4.2 97/5 97/5 97/6 97/6 97/7 97/7 97/8 97/8 97/9 97/9 97/1 97/1 97/1 97/11 97/11 97/12 97/12 98/1 98/1 98/2 98/2 98/3 98/3 Snce Sepember 1997 he adjused-r 2 has been a generally hgh levels, usually around.8. Ths ndcaes ha LS was more lkely o be deermned by DP. Noe also ha he coeffcen of DP has flucuaed beween.8 and 2. snce summer of 1997 (hough sablzed n 1998). 18

The resuls from hs analyss ndcae ha n a relavely shor perod of me, s possble o assume ha LS flucuaon wll be proporonal o DP 16,17 flucuaon, as shown n quaon (17). dls ddp = α 1 The nex chaper assumes ha he consan relaonshp shown n quaon (17) s observable n he equy and bond markes, and herefore ha LS s a funcon of equy prce nformaon. 18 4. RISK MNGMNT TCHNIQUS WITH MPHSIS ON SNSITIVITY TO QUITY PRIC FLUCTUTIONS Ths chaper assumes he relaonshp beween he expeced defaul probably and he spread over Lbor explored n Chaper 3 o be gven, and works from here o examne echnques for comprehensvely managng he bank porfolo, whch comprses loans o he clens and eques ssued by he same clens. Secon 1 explans he mporance of measurng and managng sensvy. Secon 2 dscusses he ypes of asses and sensves o be managed. Secon 3 looks a dela and vega, whch are wo conceps of sensvy. The fnal Secon 4 creaes an sample porfolo and calculaes acual rsk exposure, analyzng he effecs of hedge operaons n he process. 4 1 Measurng and managng sensvy One mehod of managng he rsks n a porfolo ha conans boh equy prce rsk and cred rsk s o calculae an negraed rsk exposure (VaR) adjused for he correlaon beween hem. rsk exposure calculaed n hs manner could become an mporan measure n he process of deermnng approprae level of capal for he operaon of he bank. Bu porfolo managemen requres more han jus a measuremen of rsk exposure. One mus also be aware of he porfolo s sensvy o dfferen rsk facors so ha when bases are found one s able o selec he exposure o be ncreased or no and deermne he specfc conrol echnques ha wll be used o do hs. In oher words, measurng and managng sensvy o rsk facors s an exremely basc process n dynamcally managng a porfolo. In Chaper 2, we observed ha equy prce flucuaons had a large mpac on he corporae value of bank, and hs, combned wh he hgh posve correlaon quanfably observed beween equy prce rsk and cred rsk, (17) 16 Corresponds o quaon (6) and 2) of Fgure 7. 17 I would be concevable o esmae a nonlnear funcon ha would provde a more sable relaonshp. 18 Corresponds o quaon (7) and 3) of Fgure 7. 19

ndcaes ha he basc objecves n managng a bank s equy and loan porfolo should be, 1) o conrol sensvy o equy prce flucuaons, and 2) o conrol sensvy o neres rae flucuaons. In addon, he dea ha sensvy o equy prce flucuaons s cenral o rsk managemen has oher major advanages, snce can also be expeced o produce a wder varey of hedge ools 19 and provdes managers wh a very easly undersandable measure. Once we have posed our wo basc objecves n porfolo managemen o conrol sensvy o equy prce flucuaon and o conrol sensvy o neres rae flucuaon he queson urns o he specfc managemen echnques o be used. In recen years here has been he emergence of many echnques for managng sensvy o neres rae flucuaon, bu here do no appear o be any specfc mehodologes esablshed for managng sensvy o equy prce flucuaon n relaon o cred rsk. We herefore focus on hs laer as we examne specfc managemen echnques ha mgh be used. Ths paper assumes ha asses are valued n erms of presen value and ha porfolos are managed for he shor erm based on hs valuaon. Orgnally, nvesmen horzon s long for porfolos of eques and loans, bu gven he magnude of he rsk observed n Chaper 2, we consder here o be a hgh need for shor-erm rsk conrol (radng and hedgng) based on presen value. 4 2 sses and sensves o be managed (1) sses The asses o be managed n hs dscusson are loans and eques. Managemen wll requre he wn perspecves of fnancal nsrumens and clen companes. The loans and eques n bank porfolo are no nvesed wh separae, ndvdual decsons. Raher, hey are generally conrolled by he exen of he relaonshp wh he clen companes. Fgure 1 caegorzes he clen companes of banks n erms of wheher companes wen publc and wheher bonds were ssued. The banks generally have busness relaonshp wh companes n all four caegores. nd here are hree forms ha ndvdual relaonshp aken: lendng only, equy-holdng only and boh. The sensvy managemen dscussed n hs paper observes he relaonshp beween DP and LS (quaon (16)) n he marke for companes n Caegory 1), and hen apples hs relaonshp o companes n oher caegores as well. Therefore, he focus of managemen wll be on companes n Caegory 1) for whch nformaon on equy prces and oher facors can be observed n he marke; managemen of companes n Caegores 2)-4) wll requre separae esmaon from such equy prce and oher avalable nformaon. 19 Secures dervaves wll be fully lberalzed n Japan n December 1998. 2

[Fgure 1] Caegorzaon of Clen Companes Bond ssuance (2) Sensves Yes Gong-publc No Yes 1) 3) No 2) 4) Our approach n hs subsecon s o measure he degree of sensvy o equy prce flucuaons for each clen company, and o add hese up o ge a oal sensvy for he porfolo. We wll begn by examnng he degree of sensvy o equy prce nformaon of dfferen classes of asses. For loans, we assume ha DP s nfluenced by hree varables, ncludng equy prce (quaon (18)). Therefore, DP has hree forms of sensvy, bu gven he fac ha DP s calculaed by he opon-approach, specal aenon mus be pad o sensvy owards equy prce and s volaly. DP = f S,, σ ) (18) ( r Where, S : quy prce r : xpeced equy prce growh rae σ : quy prce volaly quy s sensve o equy prce S and s volaly σ (sensvy o equy prce flucuaons s a funcon of he number of eques held 2 ). We are now able o defne wo sensves o equy prce flucuaons for a porfolo of loans and eques: 1) Dela: Percenage change n asse prce for a un change n equy prce S. 2) Vega: Percenage change n asse prce for a un change n equy prce volaly σ. 2 Takng he number of eques held as N, he marke value s NS. When hs s dfferenaed for S (when solved for sensvy), he resul s N. 21

4 3 Calculang dela and vega (1) Dela and vega for specfc clen companes DLT wll sand for he dela of loan and equy abou he -h company, whch can be expressed as follows: DLT = Loan + quy DLT = DLT ( deb) + DLT( sock) (19) dls ( deb) = m( deb) Du (2) ddp ds ddp Where, m deb) : Toal prncpal len o he -h company 22 Du ( : Duraon of he above LS : LS of he above DP : DP of he above dls = α 1 : esmaed from he emprcal analyss n quaon (16) ddp DLT ( sock) = (21) N Where, N : Number of he -h company s eques held If we lkewse use VG o sand for he vega of dealngs wh he -h company, hen he followng equaons wll hold: VG = Loan + quy VG = VG ( deb) + VG( sock) (22) dls ddp ( deb) = m( deb) Du (23) ddp dσ VG ( sock) = (24) (2) Dela and vega for he porfolo as a whole Le us consder dela and vega for a porfolo comprsng loans and eques from n clen companes (expressed as DLT ( porfolo) and VG ( porfolo) ). If one 22

consders sensvy o be he degree ha he marke prces and volales of ndvdual eques wll move n he same drecon, hen he sensvy of he porfolo as a whole wll be a smple oal of he sensvy of ndvdual eques. I would probably be approprae, however, o hnk n erms of sensvy o a equy prce ndex n lgh of he correlaons beween movemens of ndvdual eques and he resulng dversfcaon effecs. We wll assume ha he rae of reurn on equy of he -h company R can be expressed n he form of he followng sngle facor model. 21 R = β + β1 RM + ε (25) 2 2 1 2 M 2 ε σ = β σ + σ (26) Where, R σ, : Rae of reurn and s volaly of he -h company s equy RM, σ M : Rae of reurn and volaly of equy prce ndex ε, σ ε : rror erm and s volaly β β : Consans DLT VG, 1 dr ( ndex) = DLT (27) drm dσ ( ndex) = VG (28) dσ M Noe, dr = β 1 (From quaon (25)) (29) drm dσ 2 σ M = β1 (From quaon (26)) (3) dσ σ M Ths allows us o express he sensvy o he equy prce ndex of he porfolo as follows: DLT( porfolo) = n = 1 DLT ( ndex) 21 There have been many sudes of facor models ha explan he rae of reurn on ndvdual eques, and hey have progressed o he pon ha he fndngs may be of praccal uly. However, we have used he smples model avalable n order o avod needless complexy n our dscusson here. 23

= n = 1 DLT β (31) 1 VG( porfolo) = n = 1 VG ( ndex) = n = 1 VG 2 σ M β 1 (32) σ 4 4 Rsk managemen usng dela and vega In hs secon, we creae a smple sample porfolo and apply a rsk managemen echnque based on sensvy (as dscussed above) o demonsrae he specfc effecs ha can be acheved wh hs echnque. (1) Creaon of a sample porfolo and assumpons underlyng rsk exposure calculaons We seleced one ssue a random from among he ssues for each deb rang, as shown n Fgure 11. We hen creaed a sample porfolo comprsng loans and eques for fve clens. [Fgure 11] Deals of he Sample Porfolo Company Rang March 27 h,1998 Loan (bllon yen) quy (bllon yen) LS(bps) DP(%) Book value Book value Marke value a 27.3.2 1 1 12.5 b 51..69 1 1 12.5 c 97.7.97 1 1 12.5 d BBB 294.2 2.34 1 1 12.5 e BB 2,894.2 13.5 1 1 12.5 Toal 5 5 62.5 The followng assumpons underle our sensvy calculaons: 22 1) Rao of loans and eques We se he raos for marke values and book values wh reference o averages for cy banks and long-erm cred banks a he fscal year o March 1997. 23 22 The suffx n he formulas ndcaes he clen. 24

2) Calculaon of dfferenal coeffcens dls / ddp ( = α1) : Calculaed from he regresson analyss n quaon (16) (we use 1.4 from Fgure 8, whch conans he resuls of regresson analyss n he Chaper 3). ddp/ ds 3) Ohers, ddp / dσ : Calculaed from he amoun of change n presen value when S andσ are moved one un. Duraon Du : Se a one year hroughou. Bea of ndvdual socks β1 : Calculaed from weekly daa for he year o March 27, 1998. For sensvy, we have used sensvy o he ndex as was done n quaon (27) and quaon (28). To faclae measuremen n moneary erms, we have made he followng measuremens. quy prce 1% value (Prce1%v) = Change n presen value from a 1% rse n TOPIX = DLT TOPIX value a he me 1% Volaly 1% value (Volaly1%v) = Change n presen value from a 1% rse n TOPIX volaly σ 2 M = VG 1% β1 σ (2) Measuremen of exposure dsrbuon Fgure 12 conans he resuls of porfolo sensvy as defned above when measured for ndvdual clens. Noe ha s long for Prce1%v and shor for Volaly1%v, whch means ha presen value wll declne agans declnes n TOPIX or rses n TOPIX volaly. In hs case, here are few dfferences n Prce1%v among clens, hough here are wde dscrepances n Volaly1%v. Noe, for example, he relavely large exposure owards BB-raed Company e, and he fac ha exposure o Company b ( rang) s larger han ha o Company c ( rang). [Fgure 12] Sensvy by Clen: 1%v (.1 bllon yen) Company Rang Prce1%v Volaly 1%v a 1.21 -.7 β 23 Loans 27.4 rllon yen, book value of eques 2.5 rllon yen, marke value of eques 3 rllon yen. 25

b 1.34 -.73 c 1.27 -.47 d BBB 1.57 -.76 e BB 1.42-2.91 Toal 6.8-4.94 Fgure 13 and Fgure 14 conan he resuls of clen-by-clen smulaons of he change (hese are defned as dela rsk and vega rsk ) n presen value (PV) when TOPIX and s volaly are allowed o flucuae over a farly broad range (respecve rangs are shown n he able). These resuls also show a relavely hgh degree of unevenness for vega rsk. Noe also ha vega rsk s more nonlnear han dela rsk. [Fgure 13] Smulaon of Dela Rsk 6 4 Change n PV(.1 bllon yen) 2-2 -4-6 BB BBB -8-4 -3-2 -1 1 2 3 4 Change n TOPIX(%) 26

[Fgure 14] Smulaon of Vega Rsk 3 2 Change n PV (.1 bllon yen) 1-1 -2-3 -4-5 BB BBB -6-14 -1-7 -3 3 7 1 14 Change n TOPIX volaly (%) Fgure 15 conans approxmaons 24 of rsk exposure akng accoun of he degree of change n rsk facors. Ths shows he change n presen value from a change of one sandard devaon 25 n TOPIX and s volaly. comparson of dela rsk and vega rsk shows he laer o be larger (n absolue numbers) for all excep Company a (raed ). I s possble o make quanfable comparsons beween neres raes and oher rsk exposures f we use rsk exposures ha ake accoun of hese degrees of change n rsk facors. (3) Hedgng [Fgure 15] Sensvy by Clen:σ%v (.1 bllon yen) Company Rang Prceσ%v Volalyσ%v a 1.21 -.6 b 1.34-6.22 c 1.27-3.96 d BBB 1.57-6.5 e BB 1.42-24.7 Toal 6.8-41.97 In hs subsecon we examne hedgng ransacons ha can be used o conrol he rsk exposure of he porfolo whou changng busness relaonshp 24 Calculaed lnearly from 1%v whou usng smulaons. 25 We have calculaed TOPIX and s mpled volaly from he daly volaly found n hsorcal daa (one year). Ths was calculaed a σ (prce) = 1. %, σ(volaly) = 8.5 %. 27

wh clens (.e. whou changng he book values of loans and eques). 26 We envson TOPIX fuures and opon 27 as hedgng ools, and we assume ha was possble o make he followng hedges under he followng condons on March 27, 1998. 1) TOPIX ndex fuures Prce change s same as for spo ransacon, wh coss assumed o be zeros. 2) TOPIX ndex opon 28 Form: uropean pu opon xercse prce: 11 (he underlyng asse prce was 1258.55 on March 27, 1998) Term o maury: 12 days Cos: Premum pad a me of conrac ssumng, for example, ha one hrd of he rsk exposure n he porfolo were o be hedged, he objecve could be almos acheved by 6 conracs of shor fuures and 15,5 conracs of long pu opons, as shown n Fgure 16. [Fgure 16] Hedge Operaon (.1 bllon yen) Before Hedge Transacon fer Hedge Hedge Pu opon Fuures Hedge Rao (155 long) (6 shor) Prce1%v 6.8-1.51 -.76 4.53 33.3% Vol1%v - 4.94 1.63-3.3 33.1% Cos 7.2 In Fgure 17 and Fgure 18, we have allowed TOPIX and s volaly o flucuae over a comparavely broad range and observed he resuls for a one hrd hedge on he porfolo n erms of he change n presen value. The Fgures ndcae ha for dela rsk he hedged porfolo s over-hedged for a farly large declne n TOPIX. Ths s because of he non-lneary of he opons, and pons o he need for dynamc adjusmens n he hedges. For vega rsk, shows ha a farly hgh hedge effec can be expeced. 26 One concep for deermnng he amoun of he hedge would be o se objecves for measures of busness performance as dscussed n Chaper 2 and hen fnd an opmum hedge o acheve hs. Raher han deepen hs dscusson here, however, we have oped o provde hedge echnques ha reflec he correlaon beween equy prce rsk and cred rsk. 27 In lgh of he acual deph of marke radng, would be more realsc o use opons on he Nkke 225 raher han opons on TOPIX. We have used TOPIX here merely as a maer of convenence. 28 For prcng, we used a smple Black-Scholes model wh no dvdend paymens. 28

[Fgure 17] Dela Rsk and Hedge Operaon 4 35 Change n PV (.1bllon yen) 3 25 2 15 1 5-5 -1 Hedge operaon Dela rsk -3-2 -1 1 2 3 4 Change n TOPIX(%) [Fgure 18] Vega Rsk and Hedge Operaon 2 Change n PV(.1 bllon yen) 1-1 -2-3 Hedge operaon Vega rsk -4-14 -1-7 -3 3 7 1 14 Change n TOPIX volaly(%) 5. CONCLUSIONS Ths paper has verfed he mpac of equy porfolo on bank managemen, underscorng he mporance of managng he rsks nvolved and suggesng managemen of sensvy o equy prce rsk as a rsk managemen echnque ha akes no accoun he correlaon beween equy prce rsk and cred rsk. We verfed ha eques have a large mpac on measures of busness performance, specfcally accounng prof or loss and BIS capal adequacy raos. ssumng ha here wll be no reason o expec conssen ncrease n equy prces n he fuure, s dffcul o see how he holdng of eques for he purpose of mananng busness relaonshps would gve he bank a sronger fnancal foong or conrbue o s sably. We herefore see he need for banks o appropraely 29

manage he equy prce rsk for her enre porfolo, ncludng loans, and o ake seps o acvely conrol ha rsk. s a specfc means for dong so, we have dscussed he managemen of porfolos based on a degree of sensvy ha akes accoun of he correlaon beween equy prce rsk and cred rsk. In dong hs, we focused on he hgh correlaon beween he expeced defaul probably calculaed usng equy prce nformaon, and spread over Lbor whch s observed n he bond marke. Ths enabled us o calculae sensvy (dela and vega) o changes n equy prce and s volaly whch was defned as rsk facors. The frs of hese wo sensves s an ndcaon of he equy prce rsk for eques, he second of cred rsk for loans. ccordng o esmaons for our sample porfolo, hese wo sensves have a degree of uly n measurng he dsrbuon of exposure and n usng equy prce ndex fuures and opons as hedge ools. In he hedgng of vega rsk whch ends o reflec cred rsk n parcular, long pu posons n he equy prce ndex opons were shown o be poenally very effecve. We ancpae ha he lberalzaon of secures dervaves n December 1998 wll furher mprove he avalably of hedges n Japan. Below are some of he quesons o be resolved n subsequen research. 1) Correlaon beween equy prce rsk and cred rsk Daa consrans forced us o esmae he correlaon beween equy prce rsk and cred rsk usng equy prce daa and bond prce daa for a very lmed perod of me (fscal year 1997). Ths was a somewha pecular perod, however, snce was a hs me ha he slumpng economy caused cred rsks o begn o emerge n he markes. On-gong rsk managemen wll requre furher analyss of he relaonshp beween he wo rsks n oher economc envronmens. s a measure of cred rsk, we used he spread over Lbor of corporae bonds, bu we would noe ha he secondary marke for bonds s sll developng n Japan, and here wll herefore need o be furher sudy of measuremen selecon and analycal mehods as cred rsk-relaed markes develop, ncludng he expeced expanson n he marke for lqudaed creds. Fnally, addonal sudy wll be needed no he accepably of he varous assumpons underlyng our esmae of expeced defaul probably, and he handlng of clens for whom here s no equy prce or bond prce nformaon observable n he markes. 2) nalyss of erm prof or loss sensvy Ths paper dscussed a sensvy analyss echnque ha focused on shorerm changes n asse value. However, from he perspecve of rsk managemen n medum and long-erm bank operaons, here wll also need o be sensvy analyss ha focuses on accounng prof or loss for he erm. One example of an approach ha mgh be aken would be o pos asse and lably change scenaros ha ake accoun of fundng coss of eques, reserves and wre-offs of loans for he erm. One could hen creae scenaros n whch rsk facors change based on he 3

correlaon beween equy prce flucuaons and defaul probably, and work from here o esmae erm prof or loss sensvy. There have been few examples n Japan of oher sudes n rsk managemen echnques ha lnk equy prce nformaon and bond prce nformaon. We look forward o addonal heorecal and quanfable sudes on he ssues we have suggesed and on oher quesons n hs feld. 31

RFRNCS [1] Ieda,. and Ohba, T.: Kokuna Fuu Shasa no Ryuu Shjo n okeru Lbor supureddo no Sakn no Doko [ Recen Trends n he Spread over Lbor on he Domesc Sragh Bond Tradng Marke n Japan ], IMS Dscusson Paper Seres 96-J-13, Bank of Japan, 1998. [2] Sao, H. and Mordara, S.: Gnko no Samu Choka (Tosan) Kakursu: opushon apuroch n yoru Sue [ Defaul Probably of Japanese Banks: smaon by he Opon-approach ], Nhon Knyu Shoken Keryo Kogaku Gakka 1998 Kak Taka Yokoshu, 1998. [3] Suzuk, M.: Saken Kakuduke o Kabuka (reurn) n Kansuru Kousau [ Sudy of Bond Rang and Rae of Reurn on quy ], Shoken nalys Journal, prl 1998. [4] Mordara, S.: Tosan Kakursu Sue no opushon apuroch [ The Opon-approach for smang Defaul Probably ], Shoken nalys Journal, Ocober 1997. [5] Yoshfuj, S.: Sesakukabu Tosh ga kakaeru Makeo Rsuku Ryo no Shsan: ar moderu o Tekyo she [ The Tral Calculaon of Marke Rsk ssocaed wh quy Invesmen by Banks: n pplcaon of ar model ], Kn yu Kenkyu (Moneary and conomc Sudes), 16 (3), Bank of Japan, 1997. [6] Duffe, Darrell and Kenneh J. Sngleon: conomerc Modelng of Term Srucures of Defaulable Bonds, Workng Paper, Graduae School of Busness, Sanford Unversy, 1994. [7] Jarrow, Rober. and Suar M. Turnbull: Prcng Opons on Fnancal Secures Subjec o Cred Rsk, Journal of Fnance 5(1), 1995, pp.53-86. [8], Davd Lando and Suar M. Turnbull: Markov Model for he Term Srucure of Cred Rsk Spreads, Revew of Fnancal Sudes 1(2), 1997, pp.481-523. [9] Kealhofer, Sephen: Managng of Defaul Rsk n Porfolo of Dervaves, Rsk, (ugus,1995), 49-63. [1] Longsaff, Francs. and duardo S. Schwarz: Smple pproach o Valung Rsky Fxed and Floang Rae Deb, Journal of Fnance 5(3), July, 1995, pp.789-819. [11] Meron, Rober C.: On he Prcng of Corporae Deb : The Rsk Srucure of Ineres Raes, Journal of Fnance 29, 1974, pp.449-7. 32