Woing ap Sis Naional n of ompnc in sach Financial Valuaion and is Managmn Woing ap No. 37 anupcy law and fims' bhavio nn paulad ud omm Fis vsion: Jun 5 un vsion: Fbuay 6 his sach has bn caid ou wihin h N FNSK pojc on Maco is, Sysmic iss and nnaional Financ
- - anupcy law and fims' bhavio nn paulad and ud omm Fbuay 6 Fis daf, do no ci bsac h aim of his pap is o sudy h impac of banupcy law on financing, invsmn, dfaul and liquidaion dcisions of fims. W build a modl in which a fim can financ is invsmn by issuing db. h invsmn is isy. caus of is, h fim may dfaul. h fim manag as invsmn and dfaul dcisions in od o maximiz h valu of quiis. fo invsmn as plac, shaholds and bondholds bagain ov h sha of h invsmn ha is financd ough db and h annual coupon. f i occus, a dfaul h fim ns an obsvaion piod af which h dcision of liquidaion o coninuaion is an. h modl is solvd and calibad in od o poduc Fnch fims chaacisics. W hn sudy h ffc on financing, invsmn, dfaul and liquidaion dcisions of h fims, of changs in h paams ha summaiz h banupcy pocdu.. noducion Fnch fims sm o unda invsmn pojcs ha a lss isy han ha of S fims. Som popl agu ha his laiv shynss of Fnch fims suls fom banupcy law. oo hash amn of fims' financial disss would duc is aing. Such a laionship sms saighfowad; howv, in aliy i is much complx sinc h lin bwn h amn of financial disss and is aing involvs sval plays: h fim s shaholds, is cdios, is wos, is manags and h govnmn. h govnmn plays a ol ough h law on financial disss. hus, is aing dpnds on h whol s of nivsié ais auphin pmap, ann.paulad@dauphin.f nivsié d Lausann s, aud.pomm@hc.unil.f
- - conacual laionships bwn hs agns ha hav disinc objcivs. s a sul, h impac of banupcy law on is aing is no as inuiiv as i sms a fis sigh. chang in h law on fims' financial disss has a dic impac on dfaul and liquidaion dcisions. may affc as wll, all h dcisions h fims as upsam concning invsmn and is financing. hs dcisions a an by shaholds ha s o maximiz h valu of hi quiis. hy dpnd on financing conacs poposd by ponial cdios ha s o invs hi funds a is and un condiions simila o ha pvailing on financial mas. W consid a chang of h law on financial disss ha would ma h Fnch law bcom clos o h S on. Onc w a ino accoun h laionships bwn agns a sa, would such a chang ca incnivs fo h fim o ngag ino invsmns ha hav high is and uns? his pap poposs an answ o his qusion by concnaing on laionships bwn shaholds, cdios and h law. h law is summaizd by is majo chaacisics: h xisnc and h lngh of an obsvaion piod bwn dfaul and liquidaion o coninuaion dcisions, h chang in h fim duy o is cdios duing h obsvaion piod, as wll as h financial disss coss duing h obsvaion piod, and h dg of difficuly cdios fac cov hi funds in cas of liquidaion. o valua h ffcs of a chang in law, w consuc a modl of a fim bhavio. h fim w consid has h oppouniy financ pa of a isy invsmn ough db. Shaholds and cdios bagain ov h lvl and h a of h funds financing h invsmn. ncainy on h un on invsmn gnas a dfaul oppouniy. dfaul im, h fim ns h so-calld obsvaion piod duing which h coupon paid o h cdios is lighnd bu i has o pay financial disss coss. h la ncompasss vy diffn hings such as dic financial coss los of confidnc of supplis and of nw ponial cdios as wll as indic coss div ffo fom poduciv aciviy, sucuaion coss. h nd of h obsvaion piod, h fim coninus is aciviy if ma condiions impovd, if no, i is liquidad. n cas of liquidaion, cdios cov a facion of h n asss of h fim, which only paially covs h fac valu of h fim s db. his facion dpnds on liquidaion coss cos of sizu and of h slling of h maining asss. Of
- 3 - cous, h pobabiliy of dfaul and liquidaion, and h condiions und which hy occu affc h bagaining bwn cdios and shaholds a h im h invsmn is undan. W hn obain a lin bwn paams ha chaaciz h law and h fim dcisions: invsmn, financing sucu, loan as, dfaul, and liquidaion. Onc h modl is consucd and solvd, i is calibad o poduc Fnch fims financing chaacisics. W hn sudy h ffc of changs in h paams psning h law on financing, invsmn, and dfaul choics of fims. h main suls w obain a ha : a b pocion of cdios favos is aing by fims, h obsvaion piod is cosly fo all h agns and is no jusifid unlss fims us i o sucu fficinly. Moov, w also show ha i is no possibl o hav boh fims ha choos isi pojcs and a small dfaul a. Finally h sucu of h fims' financing and ins a spads a affcd by h whol s of paams chaacizing h law. Fo insanc, a b cdio pocion anslas ino a high db a simila o small as. h modl poposd h is lad o h liau ha consids dfaul as a dcision of h fim consisn wih h objciv of quiy valu maximizaion Lland994, Goldsin, Ju and Lland, Mollc, Mau and Saa 4. h conibuion of his liau is o consid h dfaul dcision as an ivsibl choic und uncainy ha can b modld as a al opion ixi and indyc, 994. Nvhlss, in his liau, dfaul lads o immdia liquidaion of h fim. h obsvaion piod is hfo no an ino accoun. Fw modls inoduc an obsvaion piod Fans and oous, 989, Longsaff, 99 bu only Fançois and Mollc 4 modls h dfaul dcision, an obsvaion piod, h liquidaion and financial dcisions. W a h famwo fom Fançois and Mollc 4 and inoduc upsam h invsmn dcision, which can b dal as a al opion as wll. Ou modl hfo mixs h appoachs of Fançois and Mollc 4 and Mau and Saa 4 fom which w a h modling of h invsmn dcision. Moov, in od o poduc a bs h obsvd suvival as of Fnch fims, as wll as h pobabiliy of liquidaion a h nd of h obsvaion piod, w modl uncainy by adding a jump pocss o h usually considd ownian moion fo h oupu pic of h fim. hans o his gnalizaion, w can a ino accoun sldom vns ha hav hug consquncs.
- 4 - h maining of his pap is as follows. Scion dals wih h dcisions of a fim ha is nily financd wih quiy. n scion w inoduc h possibiliy of ging ino db and a dfaul pocdu wih immdia liquidaion. n scion V h modl is xndd o h cas in which h xiss an obsvaion piod af h dfaul af which h fim is liquidad o gos on wih poducion dpnding on ma condiions. n ach scion h modl is solvd, calibad, and simulad. summay of h sul is finally givn in scion V.. nvsmn havio and cision o los of an nlvd Fim. n od o find h valu of h fim and o chaaciz is invsmn choics, w consid in a fis sp h cas in which h fim is only financd hough quiis. Of cous, in his cas h possibiliy of dfaul is of no lvanc. n a scond sp, w sudy h cas in which h fim can g ino db. h possibiliy of dfaul has o b an ino accoun.. asic ssumpions of h Modl W consid a fim whos sol ass is an opion o invs in a poducion pocss by paying a fixd cos. Onc his opion is xcisd, i poducd on uni of good p ya. h poducion cos is ; his cos is consan duing im. h im whn h good is poducd i is sold in a pfcly compiiv ma a a pic p uni. h pic voluion is sochasic. ncainy h pic voluion is givn by a gomic ownian moion combind wih a oisson pocss: d α d dz J dq
- 5 - h nd α and h volailiy a consan; dz is h incmn of a sandad Win pocss and dq is a oisson pocss: wih pobailiy λ d dq wih pobabiliy λ d Whn dq, h pocss followd by h pic jumps fom o J. W suppos ha h oisson pocss dq and h gomic ownian moion dz a indpndn. Gains o Losss of h civ Fim ofis of h fims a immdialy axd a a consan a. Moov, w assum ha h ax sysm is pfcly symmical wih h possibiliy of losss discoun. Onc opion has bn xcisd, h fim sas poducing bu a any im, i has h possibiliy o sop h poducion whnv i wishs. Financial nvionmn of h Fim W assum ha h xiss a is lss financial ass which povids a consan insananous un % p ya. W also suppos ha h pic of h poduc which is sold by h fim can b poducd using financial asss on h ma, li fo insanc fuu conacs. his assumpion allows us o appais h invsmn opion valu as wll as h valu of h aciv fim.
- 6 -. Opimal havio of h Fim h dcisions of an unlvd fim only concn h pic a which i should invs and ha a which i should sop poducing. Figu povids an xampl of h pic voluion of a fim which invss a im and sop poducing a im. Figu Valu of h Fim and hshold o Sop oducion W fis consid h valu of h fim onc h invsmn dcision has bn xcisd. h sandad agumn of is-nual valuaion imposs ha V which is h valu of h fim nily financd wih quiy saisfis h following diffnial quaion: [ λj ] V λ V λv J V, > wih h pic a which h fim dcids o sop poducion. h gnal soluion of quaion is givn by: V, > Wh and a consan o b dmind and and a soluions of h quaion: 3
- 7 - [ ] λ J λ λj. Wih > and <. Moov, h valu of h fim nily financd wih quiy quaion 3 has o saisfy: limv V V, 4.a 4.b 4.c ondiion 4.a xpsss h fac ha h valu of h oppouniy o sop poducion bcoms zo if h pic of h poduc bcoms lag. Such a condiion is saisfid only if. ondiion 4.b xpsss h fac ha a h im whn poducion is soppd, h valu of h fim is zo. ondiion 4.c nsus ha h pic which iggs poducion sopping is opimal. Subsiuing 3 in 4.a-4.c povids h valu of h unlvd fim: Wih V 5 Valu of h Opion o nvs and nvsmn cision W no F h valu of h opion o invs and w asily show ha F mus saisfy h following diffnial quaion: [ λj ] F λ F λf J F, < Wh is h pic a which h fim xciss h opion o invs. h gnal soluion has h fom: F < Ω Ω,,
- 8 - Moov, h valu of h opion o invs mus saisfy h bounday condiions. h fis condiion imposs ha h valu of h opion is clos o zo if h pic of h poduc nds o zo. implis. Ω W hn no h igg pic of h opion o invs of h fim nily financd wih quiy. h pic which iggs invsmn, shaholds a xacly indiffn bwn holding h opion o invs and xcising i. h hid condiion is a "smooh pasing" condiion which nsus ha h invsmn igg pic is opimal. V F, lim V F F Finally, h valu of h opion o invs can b win: [ ] V F nd h pic which iggs invsmn can b dmind wih h smooh pasing condiion: his quaion can b solvd numically bu no analyically Numical soluion and nalysis of h suls abl blow givs h numical suls concning h pics which igg invsmn and poducion sopping in h cas of an unlvd fim. aams of h modl hav bn chosn in od o poduc a bs availabl obsvaions on financing bhavio and on dfaul and liquidaion bhavio of fims cf. abl in appndix 3. Of cous, as in aliy fims g ino db and may fac an obsvaion piod, calibaion has bn mad using h compld modl psnd la in his pap cf. pa V.
- 9 - igg pics in h basic scnaio and vaians poposd dpnd on h chosn valus and canno b inpd conomically. Nvhlss, i is insing o obsv h way igg pics vay dpnding on h insiuional and conomic nvionmn of h fim. abl : nvsmn havio and poducion sopping fo an unlvd fim. asic scnaio Lss uncainy u in h ax a ncas in h ins a J λ nsiuional and conomic nvionmn of h fim 4% 4% 4% 4% 4% 5%.3.3.3.3..3 α λ J-.......8.6.8.8.8.8 λ....5.. J.8.8.9.8.8.8 havio of h fim 3. 4.7 9.9 3. 4.3 3...6.... h nd in h ownian moion α has bn fixd such ha h xpcd valu of h pic a any hoizon mus always b qual o h cun pic lvl. is simila o impos α λ J-, [ α λ J ]s sinc s. hfo, in h basic scnaio, in h absnc of shocs, h pic of h good poducd by h fim incass by % p ya, bu h fim has on chanc ov o ba a shoc ha would cu h pic of is good by J- %. Oh paams of h modl hav bn abiaily fixd o: 4,,.4. nvsmn iming is snsiiv o h insiuional and conomic nvionmn of h fim, whil poducion sopping is naly indpndn fom his nvionmn. hfo, a dcas in uncainy and a fall in h ax a always duc h hshold a which h fim invss whil an incas in h is lss ins a incass his hshold. h pic a which h fim sops poducing is naly insnsiiv o uncainy paams xcp ha of h gomic ownian moion. n h cas in which h fim is nily financd wih quiy, poducion sopping is a sldom vn. ndd, abl shows ha h discpancy bwn h pic which igg invsmn
- - and ha which sops poducion is such ha h fim dcids o sop poducing only if h pic bcoms 9% lss han h pic a which is has invsd and sad poducing.. Opimal havio of h lvd fim in h absnc of obsvaion piod onsid now h cas in which h cos of xcising h opion is a las paially financd wih db. fo xcising h opion o invs w suppos ha h fim finalizs an agmn wih h bondholds und which bondholds will pay h fim K whn h fim xciss h opion o invs, in un fo a coninuous coupon paymn of p ya h ins a a which h fim gs ino db is hn i /K. b has an infini mauiy baing dfaul. W assum ha h iming of h invsmn dcision is a h discion of h shaholds and canno b conacd in advanc by bondholds. Nvhlss, bondholds anicipa ha quiy holds choos an xcis sagy ha maximizs quiy valu. s such, bondholds will qui ha hi fuu commimn of K o financ h xcis of h invsmn opion b fai laiv o h agd coupon and h closing sagy. Finally, if h fim can g ino db, is dcisions concning pics a which i invss and liquidas and h conac wih bondholds which xpsss h amoun of db and h coupon.. Scuiy valus onsid fis and K as givn; ou objciv h is o compu h ma valus of quiy, of db and of h fim, onc h opion o invs has bn xcisd. h diffnial quaion which dscibs h lvd fim valu is h sam as quaion, xcp ha incom accuing o shaholds is now -- - p uni im. h analogous gnal soluion fo h lvd fim is:, > 6
- - Wh and a consan o b dmind, and a h sam as hos psnd jus blow quaion 3. is h pic a which shaholds dcid o dfaul. Moov, h gnal soluion 6 mus saisfy h following bounday condiions: lim, 7.a 7.b 7.c ondiion 7.a xpsss ha h valu of h opion o dfaul is zo whn h good pic bcoms lag. his condiion is m only if. ondiion 7.b xpsss ha a h im of dfaul, h fim valu is zo. ondiion 7.c nsus ha h pic igging dfaul is opimally chosn by shaholds. Subsiuing 6 in 7.a-7.c w g h valu of h lvd fim: Wih 8 No ha sinc.. Ma valu of h db of h fim Sinc db has an infini mauiy, h gnal soluion fo h db valu is: >,, Wh and a consan o b dmind and bounday condiions a: lim b V.a.b 9
- - ondiion.a implis, which xpsss ha if h dfaul pobabiliy dcass, h ma valu of db quals ha of a is lss ass infinily paying a coupon. ondiion.b xpsss ha a h im of dfaul, bondholds civ h unlvd valu of h fim lss h liquidaion coss. h la a assumd o b popoional o h fim valu b. Subsiuing 9 ino.a and.b, w g h ma valu of h isy db of h fim: b V Finally h oal valu of h lvd fim is h sum of h quiy valu quaion 8 and of h ma valu of h db quaion, ha is: L V V bv h ma valu of h lvd fim is qual o h valu of h unlvd fim plus h xpcd ax shild of db minus xpcd liquidaion coss.. nvsmn cision, ns a and Opimal Financing Sucu of h Fim his fim has an opion invs and a conac wih bondholds in which h la commi o povid K dollas o hlp h fim o financ is invsmn in xchang fo a coupon. Sinc h opion o invs is h sol ass of h fim, h cun valu of h fim is qual o h valu of his opion. Ou objciv h is o dmin h valu of h opion o invs and h pic which igg h xcis of his opion. Valu of h opion o invs W no F h valu of h opion o invs. W asily show ha F mus saisfy h following diffnial quaion:
- 3 - [ λj ] F λ F λf J F, < 3 Wh is h pic a which h fim xciss h opion o invs. h gnal soluion is of h fom: F < Ω Ω,, sids, h valu of h opion o invs mus chc h bounday condiions. ondiion 4.a imposs ha h opion valu bcoms clos o zo if h good pic nds o zo. implis Ω. o find h wo oh condiions, call ha h xcis iming is chosn by h shaholds. o do so, hy maximiz h quiy valu as opposd o h valu of h fim. W hn no h pic lvl ha iggs invsmn. ondiion 4.b xpsss ha a, shaholds a xacly indiffn bwn holding h opion o invs o xcis i. ondiion 4.c is a smooh pasing condiion nsuing ha h igg pic is opimal. lim F F F K, 4.a 4.b 4.c Finally, h opion o invs may b win: [ K ] F 5 h db lvl
- 4 - h appopia valu of K is asy o dmin. ondholds will no ag o giv K dollas o h fim whn quiy holds choos o invs, unlss K is a fai pic fo h db. Sinc hy now ha onc h conac is finalizd hy canno foc quiy holds o choos a fim-valu-maximizing xcis sagy, hy valu h db and hby dmin K und h assumpion ha shaholds will s o maximiz quiy valu and no fim valu. hfo, h incniv-compaibl K mus b qual o h ma valu of db a h invsmn igg. V b K 6 Subsiuing his K valu in quaion 5 and using h fac ha V, w g h opion valu o invs. [ ] L V F 7 nd h pic which iggs invsmn can b dmind using condiion 4.c: K 8 Wh K is givn by quaion 6. quaion 8 can b solvd numically bu no analyically. ns a a which h fim g ino db So fa, w hav considd a givn. quaion 8 povids h opimal financing sucu fo a givn. How o dmin h lvl o h ins a i /K ha a opimal fo h fim? Sinc and K a dcidd in advanc in h conac bwn shaholds and bondholds, w consid ha h fim slcs h ins a which maximizs h valu of h opion o
- 5 - invs among h conacs poposd by bondholds cf. figu.b blow. h cuv of h conacs poposd by h ban is such ha a any poin h ma valu of h db a h im of invsmn quals h fac valu of db.. Numical soluion and suls analysis suls of h numical soluions of h quaions dscibing h opimal bhavio of h fim a givn in abl. W focus on h ffc of h insiuional and conomic nvionmn of h fim on h invsmn, liquidaion, and financing ins a and lvag dcisions. Moov, by compaing h bhavio of h lvd fim abl wih ha of h unlvd fim abl on can appais wha changs if h fim can g ino db. h ffc of b on h nvsmn and faul cisions of h fim ompaing pics ha igg invsmn in abl and, on can no ha fims ha hav an accss o db invs ali han unlvd fims cf. figu.a. coms fom h fac ha sinc ins paymns can b dducd fom axabl bnfis, poducion bcoms mo pofiabl fom h poin of viw of h fim. ndd, w asily show ha if h ax a is zo, fims o no g ino db. h counpa o h possibiliy of db is ha fim can dfaul on hi db. h possibiliy o hav db hn mas invsmn asi bu also incass h pobabiliy of dfaul. n h basic scnaio, h suvival a a 5 yas of lvd fims is 75% agains 99% fo unlvd fims. h incas in dfaul is coms on h on hand fom h fac ha lvd fims hav an incniv o dfaul fo a pic high han h on a which unlvd fims sop poducing. On h oh hand, lvd fims invs fo a small pic lvl compad o wha unlvd fims do. Numical simulaions show ha h incas in dfaul is ssnially coms fom h high pic a which lvd fims dfaul.
- 6 - K/ uv of h conacs poposd by h ban F 3 F F /K* /K Figu.a Figu.b Opimal Financing Sucu and ns a lvd fim has a high dfaul is han an unlvd fim. h conac bwn h fim and h ban concns boh h financing sucu and h ins a as shown in bold in figu.b. h ban has o ma su ha a h im of invsmn h fac valu of h db quals is ma valu ; h la bing a dcasing funcion of h db a and an incasing funcion of h ins a. mong all h conacs financing sucu/ins a which mas h ban indiffn, h fim chooss h on which maximizs is quiy valu. n figu.b, i is h conac which achs h high "iso-opion valu" F. n h basic scnaio, fims choos a db a aound 8% fo a 3.4% ins a. Such financing sucu/ ins a combinaions suls fom a ad-off fo h fim: a h im of invsmn, i could choos a high lvl of db bu would hn incas is dfaul pobabiliy ha would lad h ban o qui a high ins a. On finally compus ha a h im of dfaul h ma valu of db is only 5% of h fac valu. ffc of h nsiuional and conomic nvionmn on h cision of h Fim
- 7 - Mo uncainy 3 incass h invsmn igg and dcass h dfaul igg. hs wo ffcs, joind wih high pic volailiy gna finally a high dfaul pobabiliy. s a consqunc, h fim has lss db and a high ins a. his suls on h on hand fom a chang in h slop of h cuv of h conacs poposd h ban and on h oh hand fom a chang in h shap of h "iso-opion valu" cuvs. n incas in h ax a has a dic ffc on h opimal lvl of db and on h ins a, which boh bcom high. ffcs on igg pics a simila o hos xhibid whn compaing unlvd and lvd fims: h invsmn igg is small whil h dfaul igg is high. Suvival as a slighly small. anupcy occus whn db has los a lag pa of is valu. n incas in h is lss ins a incass boh h invsmn igg and h dfaul on. h fim has a lil lss db and a high ins a. u dfaul occus whn h db has los lss of is iniial valu. Suvival as a naly insnsiiv o an incas in h is lss a. Fo high liquidaion coss, liquidaion occus fo a small pic. Suvival as a slighly high. faul occus whn db has los a lag facion of is iniial valu. h opion valu of invsmn gs small and invsmn is mad fo a high lvl of h pic. Opimal db is a lil small and h ins a is high. 3 W choos h h cas in which uncainy incass following an incas in h uncainy paam of h gomic ownian moion whil oh paams main unchangd.
- 8 - ablau : nvsmn and dfaul/liquidaion bhavio of a lvd fim in h absnc of banupcy pocdu. asic scnaio Mo uncainy ncas in h ax a ncas in h is lss ins a nsiuional and conomic nvionmn of h fim.4.4.4.6.4.3.3.4.3.3 λ..... J.8.8.8.8.8 αλj-......8.9.8.8.8.....3 havio of h fim 4. 6.3 3. 4.6 5. ncas in h liquidaion coss.83.78.85.86.8 b/quiy 8% 4% 36% 7% 5% Ma valu of h db a h im of 5.5% 4.7% 3.9% 6.5% % dfaul / fac valu of h db ns a coupon / fac valu of db 3.% 4.8% 3.7% 4.% 3.% Suvival a a ya % % % % % Suvival a a 3 ya s 9% 88% 9% 9% 9% Suvival a a 5 ya s 75% 69% 63% 75% 77% V. faul, Obsvaion iod, cision on oninuaion o Liquidaion W consid ha h fim can g ino db bu also ha h xiss a banupcy pocdu in wo sags. n a fis sag, h fim sas o b in dfaul and ns an obsvaion piod duing which h coupon i has o pay is ducd bu financial disss coss hav o b paid. n a scond sag, which sas a h nd of h fis on, h fim has o liquida o no.. faul, Obsvaion iod and banupcy igg h fim sas o b in dfaul whn h pic achs a lvl which will b dmind la on. h fim is hn und h pocion of h law duing an obsvaion piod. Fim's ash-flow duing h obsvaion piod
- 9 - uing h obsvaion piod, h fim pays financial disss coss ϕ and gos on wih poducion i hus pays h poducion coss bu i only pays a facion θ of h coupon. [ θ ϕ ] d anupcy igg h nd of h piod, if h pic is sill und h fim is liquidad. dios can g bac -bvu, and shaholds g nohing. h pobabiliy ha h fim is no liquidad a h nd of h obsvaion piod is qual o Φ, wih: Wh φ ν is h cumulaiv funcion of a nomal. disibuion wih Φ p λ φ ν v α ln J Figu 3 povids an xampl of h pic voluion fo a fim ha is liquidad af h obsvaion piod 3.a fo a fim ha gos on wih poducion af h obsvaion piod 3.b. Figu 3.a Figu 3.b Fim valu a h im of dfaul
- - h fim valu a h im of dfaul, V, is h discound sum of cash-flows duing h obsvaion piod plus h xpcd valu of h lvd fim a h nd of h obsvaion piod i may hn b liquidad: s s df V b df ds ds s V θ ϕ θ Fo cdios o accp h obsvaion piod ah han an immdia liquidaion, h obsvaion piod mus a las as pofiabl as immdia banupcy.. Solving h modl faul igg and quiy valu bfo dfaul Ousid h obsvaion piod, h quiy valu is sill givn by: > Wh is h dfaul opion. h im of dfaul, h quiy valu is such ha: df d ϕ θ ha can b win s appndix: Φ Φ Φ ϕ θ
- - Wh ln J Φ α p λ φ ν Wih α ln J v nd [ / ] ln J α Φ p λ φ ν Wih α ln J v h dfaul igg is dmind by shaholds who maximiz quiy valu. Opimaliy condiions a givn by: hs condiions dmin and s appndix. [ θ ϕ Φ ] Φ W show asily ha if gs clos o in h cas in which θ and ϕ h dfaul igg is high han h liquidaion igg in h absnc of obsvaion piod. noducing a dfaul pocdu ha would only b a dlay bfo banupcy incass h banupcy igg. his sul is qualiaivly simila o ha of Fançois and Mollc 4. Nvhlss, h mchanism gnaing his sul diffs fom h on invod by Fançois and Mollc 4 : i is no h possibiliy of ngoiaion bwn cdios and shaholds which gnas a high dfaul igg bu ah h fac ha an obsvaion piod of a givn siz mas i compulsoy fo h fim o anicipa h possibiliy of banupcy and povids hfo an incniv o dfaul bfo quiy valu is zo as i would b h cas wihou obsvaion piod ; h dfaul igg is hus high.
- - quiy valu of h fim may hn b win: Φ b valu wih a banupcy pocdu Φ Ousid h obsvaion piod, h db valu is sill givn by: >,, wh is h dfaul opion valu. h im of dfaul, i is such ha: s θ ds df b V df Whos xpssion af having compud h ingals is givn in appndix. h im of dfaul, w hav:. his quaion povids h paam valu s appndix. nvsmn cision and b Lvl o dmin h db lvl and h pic which igg invsmn, w us h mhod alady us o compu i h invsmn igg, ii h db lvl and iii h ins a ha has alady bn psnd in h cas of a lvd fim in absnc of dfaul pocdu.. Numical soluion, alibaion of h Modl and nalysis of h suls suls of h numical soluions of h modl fo sval ss of h insiuional and conomic paams a givn in abl 3. W analyz fis h abiliy of h calibad modl o poduc h obsvd bhavio of fims s appndix. W hn sudy h ffc of
- 3 - paams which chaaciz h banupcy pocdu: lngh of h obsvaion piod, financial disss coss, facion of h coupon ha is paid duing h obsvaion piod and liquidaion coss. alibaion of h Modl basic scnaio h liquidaion cos b has bn fixd o %, which is h upp bounday of h valuaion povidd by Maléco 995 fo Fnch fims. No nvhlss ha high liquidaion coss hav bn cnly obsvd in h cas of h banupcis of Moulinx and lsom. call ha -b may b inpd as h facion of h valu of h fim which non-pioiay cdios can g bac in cas of liquidaion. ndd, in ou modl all h poducion coss wags and mony du o supplis as wll as axs a paid a ach im and in paicula duing h obsvaion piod. aam b psns hn h liquidaion cos cos of sizu and of slling of h maining asss. W hav fw obsvaions on h financial disss coss duing h obsvaion piod. call ha in aliy hy ncompasss vy diffn hings such as dic financial coss, loss of confidnc of supplis and of nw ponial cdios, as wll as indic coss du o h divsion of ffo fom poduciv aciviy owads sucuing. his boad dfiniion is flcd in h boad ang of h valuaions xising in h liau: fom 3% of h fim valu o 57% of h claims. n ou scnaio, h coss of financial disss vay fom.5% basic scnaio o 5% of h ma valu of h db a dfaul im. W find again h sam poblm of lac of infomaion fo h paam θ which is h facion of h coupon which is paid duing h obsvaion piod. n abiay way, w ma i vay bwn 5% basic scnaio o 3%. ncainy paams of h gomic ownian moion and hos of h oisson pocss λ, J hav bn calibad in od o poduc a bs h suvival a of fims af invsmn, as wll as h facion of banupcy a h nd of h obsvaion piod fixd a ya as i is obsvd. W obain a suvival a a 5 yas 6% which cospond o h suvival a obsvd a 3 yas. No howv ha h obsvd a is h on pvailing
- 4 - fo all fims ha is fo boh lvd and unlvd fims, whil h modl fs o lvd fims. is qui inuiiv ha if sicing o lvd fims, h suvival a should b low. h facion of fims ha a liquidad a h nd of h obsvaion piod 66% is in h ang of h obsvd valus 6 7%. h db/quiy aio xpssd in ma valus is 7% a h im of invsmn. W do no hav obsvaions of his aio. ndd h sol availabl daa concn h db/quiy aio a any im of h fim lif af invsmn. his la aio is bwn 6% and 4% fo Fnch fims and 5% and 55% fo S fims. noducing an obsvaion piod. o g h ffcs of h xisnc of an obsvaion piod, on can sudy h fim bhavio whn inoducing an obsvaion piod wihou changing h financial budn of h fim no cu in h coupon paid o cdios no financial disss coss. W compa h bhavio of his fim fis column in abl 3 wih ha of a fim fo which h is no obsvaion piod fis column of abl. h xisnc of an obsvaion piod povids an incniv fo fims o g ino dfaul ali han hy do wih no obsvaion piod, which is consisn wih analyical suls. h dfaul igg is significanly affcd by h xisnc of an obsvaion piod whil h oh paams of h modl hav only a maginal ffc. Moov, h obsvaion piod povids incnivs fo fims o invs ali. small invsmn igg and a high dfaul and liquidaion igg hav h immdia ffc o duc h suvival a fom 75% o 6%. Sinc h fim gos banup fo a ah high pic, h aio bwn h ma valu of db and is fac valu is high a h im of dfaul which mans ha cdios can g bac a lag pa of hi claims. Fims can hn hav a lag db 3% a small as.7%. y fixing h financing sucu 8%, w show ha in h absnc of obsvaion piod, h ins a h fim facs would b vn small.3% ; nvhlss, his combinaion db-ins a would no b opimal fo shaholds s figu.b.
- 5 - h dfaul pocdu uing h obsvaion piod fims bnfi fom a cu in h coupon and mus pay a cos of financial disss. h inoducion of h cu in h coupon and of h cos of financial disss povids an incniv fo fims o invs la wihou affcing h dfaul igg. h suvival a a 5 yas is high. Sinc h coupon is no long fully paid duing h obsvaion piod, bans qui a high ins a fo h sam lvl of db. n abl 4, h whol s of vaians has bn don by fixing h financing sucu. W obsv ha a fall in h pa of h coupon ha is paid fom 5% o 3% fo a givn db 7% anslas ino ins as ha a significanly high 3.9% agains 3.4%. Finally, h opimal bhavio of h fim, whn h pa of h coupon i has o pay is cu, consiss ino ducing db whil h ins a bcoms high.
- 6 - abl 3: nvsmn bhavio, financing sucu, dfaul and liquidaion dcisions wih a banupcy pocdu. Obsvaion piod wih no financial consquncs asic scnaio Mo uncainy ncas in ax u in h pa paid of h coupon duing dfaul ncas in h coss of financial disss ncas in h liquidaion coss Lnghning of h obsvaion piod nsiuional and conomic nvionmn of h fim.4.4.4.4.4.4.4.4.3.3.3.4.3.3.3.3 λ........ J.8.8.8.8.8.8.8.8 αλj-.........8.8.9.8.8.8.8.8 θ.5.5.5.3.5.5.5 ϕ.... 3..........3. havio of h fim 3.6 4.4 6.8 3.5 4.8 5.3 5.4 4.7.63.63.65.67.63.66.59.9 / %.3% 9.8%.4% %.9%.3% 4.9% b/quiy a h im of invsmn 3% 7% 3% 34% 5% 7% 4% 6% Ma valu of db a h im of dfaul/fac valu of db 4.% 35.5% 35.5% 34.9% 3.6% 35.% 3.3% 43.7% ns a coupon / fac valu of h db.7% 3.4% 5.% 3.9% 3.6% 3.% 3.4% 3.5% Suvival a a ya 99% 99% 98% 99% 99% 99% 99% 98% Suvival a a 3 yas 8% 8% 76% 79% 8% 8% 83% 75% Suvival a a 5 yas 6% 6% 56% 6% 63% 63% 64% 56% % d liquidaion a h nd of h obsvaion piod 66% 66% 67% 66% 66% 66% 66% 7%
- 7 - abl 4: nvsmn bhavio, financing sucu, dfaul and liquidaion dcisions wih a banupcy pocdu fo a givn lvl of db. asic scnaio Mo uncainy ncas in ax u in h pa paid of h coupon duing dfaul ncas in h coss of financial disss ncas in h liquidaion coss nsiuional and conomic nvionmn of h fim.4.4.4.4.4.4.4.3.3.4.3.3.3.3 λ....... J.8.8.8.8.8.8.8 αλj-........8.9.8.8.8.8.8 θ.5.5.5.3.5.5.5 ϕ.... 3.........3. havio of h fim 4.4 5.6 5. 4.3 5.3 4.7 4.5.63.8.48.7.66.7.4 /.3%.6% 9.9%.8%.9%.5% 5.5% b/quiy a h im of invsmn 7% 7% 7% 7% 7% 7% 7% Ma valu of db a h im of dfaul/fac valu of db 35.5% 37.3% 3.6% 33.4% 35.% 33.4% 44.% ns a coupon / fac valu 3.4% 5.7% 3.% 3.9% 3.% 3.8% 3.6% of h db Suvival a a ya 99% 93% 99% 99% 99% 99% 99% Suvival a a 3 yas 8% 7% 83% 8% 8% 8% 76% Suvival a a 5 yas 6% 5% 65% 6% 63% 6% 56% Lnghning of h obsvaion piod
- 8 - h coss of financial disss do no affc ins cdios g duing h obsvaion piod; hfo, hy hav naly no ffc on h financing sucu and on h ins a. Nvhlss, hy affc h invsmn igg: fims dcid o invs la. f h obsvaion piod gs long, h fim invss la and dfaul ali which ducs suvival as. maginally affcs h opimal financing of h fim which ducs slighly is db a a lil high ins a. Liquidaion h nd of h obsvaion piod, h fim is liquidad if h pic is lss han h dfaul igg. Shaholds do no g anyhing and cdios g h valu of h fim lss h liquidaion coss. h high hs coss, h la boh invsmn and dfaul. hy hav h sam lvl of ins a bu fo small db lvls. Fo a sam financing sucu s abl 4, hy would fac a high ins a. Such a mchanism is no pfcly compaabl wih ha xhibid in h cas of a ducion of h pa paid of h coupon. n boh cass, cdios' pocion is small bu h nobody gs any bnfis fom an incas in h liquidaion coss whil a cu in h pa paid of h coupon bnfi o shaholds. V. Synhsis of h suls and conclusion dios pocion and is aing by fims his pap ss o appais whh a chang in h banupcy law could povid incniv fo fims o ngag ino isi bu mo pofiabl aciviis. H, a b cdio's pocion anslas ino ih a cu in liquidaion coss o by an incas in pa paid of h coupon duing h obsvaion piod. n boh cass indd, fo a givn pic lvl, fims accp o invs fo a high lvl of uncainy. W hav hfo shown ha an incas in cdio's pocion would ncouag fims o invs in isi
- 9 - invsmns. h b cdio's pocion givs hm h possibiliy o hav a high db a simila o small ins as. acically, i mans ha any policy ha mas i asi fo h cdio o aac h n asss of h fim in cas of liquidaion 4 would impov h laion ship bwn cdios and shaholds. No howv ha is also anslas ino a small suvival a: on h on hand fims ging involvd ino isi pojcs a dfauling mo; on h oh hand, dfaul and liquidaion a dcidd fo high pic lvls. h fficincy of such a policy canno only b masud hough h avag obsvd dfaul a bu also hough h iniial is aing. Sudying h lin bwn pa paid of h coupon duing h obsvaion piod and is aing w obain ha nay fall of his pa paid suls mus com wih an incas in h pa of h n asss of h fim h cdios g in cas of liquidaion o pvn fims o ngag ino vn lss isy pojcs. h ol of h obsvaion piod n impoan sul of ou modl is ha h xisnc of a dlay bwn dfaul and liquidaion o coninuaion povids h fims wih an incniv o in ino dfaul ali. his anslas ino a significan ducion of h suvival as. h obsvaion piod is hfo cosly and can only b jusifid if fims us i o oganiz fficinly. W ach a bounday of h modl dvlopd h which dos no a ino accoun h aciv bhavio of fims which oganiz duing h obsvaion piod. ansioy ffcs vsus long un ffcs 4 o ma i asi fo h cdio o aac h n asss of h fim can b an hamonizaion o a simplificaion of h collaal laws. f w only ca on claims hold by bans, i can also b h nunciaion by h sa o is pioiay claims, bu w hn igno h social cos of such a policy.
- 3 - So fa, w hav analyzd h long un ffcs of a chang of h law on fims' financial disss. Ou modl dscibs h ffcs of h law on h whol s of dcisions h fims as fom h bih of h fim. Wha would b h ffcs of a chang in h law on fims ha alady xis? f h ms of h conacs bwn cdios and shaholds a fixd, on shows asily ha any cdio pocion snghning would favo cdios wihou affcing shaholds. n paicula, h dfaul igg mains unchangd. f h ms of h conacs can b changd, fims should g small ins as. W ach h anoh bounday of ou modl in which a ngoiaion piod af piod of h conac bwn cdios and shaholds canno b considd.
- 3 - fncs ndad G., Kaplan S., 998, «How osly is financial no conomic disssµ? vidnc fom Highly Lvagd ansacions ha cam isssd», Jounal of Financ, 53, pp. 443-493. ldson M.,., 995, «Liquidaion oss and apial Sucu», Jounal of Financial conomics, 39, pp. 45-69.,., 997, «h dminisaiv os of b sucuings: Som cn vidnc», Financial Managmn, 6, pp. 56-68. lazy.,, La failli : élémns d analys économiqu, conomica, ais. lazy., ombi., 998, Ls défaillancs d npiss, ollcion Qu sais j? 33, sss nivsiais d Fanc, ais. uan., Giad., 4, «Quls indicaus pou la d ds npiss fançaiss?», nalyss conomiqus, 3, Févi 4 ul Hms SF, 4, «Ls éfaillanc d npiss n Fanc au mi Sms 4», L ullin conomiqu, 9. Fançois., Mollc., 4, «apial Sucu and ss ics: Som ffcs of anupcy ocdus, fohcoming in Jounal of usinss. Fans J., oous W., 989, «n mpiical nvsigaion of Fims in oganizaion», Jounal of Financ, 44, pp. 747-769.
- 3 - Gilson, S., 997 «ansacions oss and apial Sucu hoic: vidnc fom Financially isssd Fims», Jounal of Financ, 5, pp. 6-96. Goldsin., Ju N., Lland H., «n -asd Modl of ynamic apial Sucu», Jounal of usinss, 74, pp. 483-5. Hlwg, J., 999 «How Long o Jun onds Spnd in faul», Jounal of Financ, 54, pp.34-357. Koajczy., Lvy., 3, «apial Sucu hoic: Macoconomic ondiions and Financial onsains», Jounal of Financial conomics, 68, pp. 65-9. Lland H.., 994, «opoa b Valu, ond ovnans, and Opimal apial Sucu, Jounal of Financ, 49, pp. 3-5. Longsaff F., 99, «icing Opions wih xndibl Mauiis: nalysis and pplicaions», Jounal of Financ, 45, pp. 935-957. Maléco, J.F. 994, «h Ov and nd-nvsmn ncnivs und Fnch 985 anupcy Law», ahi d chch du G, 944, Juill. Mau. and Saa S., 4, «al Opions, gncy onflics, and Opimal apial Sucu, à paaî dans Jounal of aning and Financ. Mollc.,, «ss Liquidiy, apial Sucu and Scud b», Jounal of Financial conomics, 6, pp. 73-6. O, 4, L d l Obsvaoi onsulai ds npiss n ifficulé. Wan J., 977, «anupcy oss: Som vidnc», Jounal of Financ, 3, pp. 337-347.
- 33 - Wiss, L., 99, «anupcy soluion: ic oss and Violaion of ioiy of claims», Jounal of Financial conomics 7, pp. 85-34.
- 34 - ppndix : quiy valu a h im of dfaul h im h fim dfauls, is quiy valu is such ha: df d ϕ θ Wih df Φ Φ Φ Wh Φ ln J p ν φ λ α Wih J v α ln [ ] ln / J p ν φ λ α Φ Wih J v α ln nd ϕ θ ϕ θ ϕ θ d d W finally hav: Φ Φ Φ ϕ θ minaion of h dfaul igg
- 35 - h dfaul igg is dmind by shaholds ha maximiz quiy valu. Opimaliy condiions a: [ ] λ ϕ θ J Φ Φ Φ [ ] Φ Φ λ J h soluion of his quaions unnowns sysm is givn in h x. b valu wih a banupcy pocdu
- 36 - s df V b df ds θ Wih s ds θ θ Φ Φ df Φ Φ Φ Φ Φ Φ df df V Wih Φ ln J p ν φ λ α [ ] ln / J p ν φ λ α Φ Φ p ν φ λ Φ ln J p ν φ λ α Wih J v α ln ln ln
- 37 - [ ] ln / J p ν φ λ α Φ Wih J v α ln ln ln Φ p ν φ λ Wih J v α ln ln ln
- 38 - vailabl daa on fim financing, dfaul and liquidaion