Managi ng Unknown Ri sks Vi e f ut ur e of gl obal r ei nsur ance. Gr aci el a Chi chi l ni sky and Geof f r ey Heal GRACI ELA CHI CHI LNI SKY i s UNESCO pr of essor of mat hemat i cs and economi cs, and di r ect or of t he Pr ogr am on I nf or mat i on and Resour ces at Col umbi a Uni ver si t y i n NewYor k ( 10027) . GEOFFREY HEAL i s t he Paul Gar r et t pr of es,; or of publ i c pol i t y and cor por at e r esponsi bi l i t y at t he Gr aduat e School of Busi ness at Col umbi a Uni ver si t y i n New Yor k ( 10027) . SUMMER 1998 t has been sai d t hat i nsur ance i s t he l ast of t he f i nanci al ser vi ces t o accept r adi cal change ( Denney [ 1995- 1996] ) . Yet t her e has been a f undament al shi f t i n t he geogr aphi c l ocat i on and i n t he or gani zat i on of t he r ei nsur ance i ndust r y i n t he l ast si x year s ( Chi chi l ni sky [ 19966] ) . Gl obal envi r onment al r i sks ar e par t l y r esponsi bl e f or t hi s change ; i ncr eased weat her vol at i l i t y and cat ast r ophi c r i sks ar e di f f i cul t t o di ver si f y usi ng t r adi t i onal i nsur ance pr act i ces . To pr ovi de a map t o t he f ut ur e, we need a r eal i st i c appr ai sal of how we got wher e we ar e. Thi s i s t he st or y of how humans have hedged r i sks . Ther e ar e t wo basi c and di st i nct appr oaches : st at i st i cal and economi c . The f or mer i s t ypi cal of t he i nsur ance i ndust r y ; t he l at t er t ypi f i es t he secur i t i es i ndust r y. Bot h ar e needed t o manage t oday' s cat ast r ophi c r i sks . Nei t her al one wi l l do. We show how a combi nat i on of bot h l eads t o ef f i ci ent out comes, and i s t he way t o t he f ut ur e ( Chi chi l ni sky [ 1996a, 1996b, 1996d] ) . The vol at i l i t y of weat her , t aken t oget her wi t h popul at i on movement t o war mcoast al ar eas and changi ng pr oper t y pr i ces, has made cat ast r ophi c r i sks hi ghl y unpr edi ct abl e. Many sci ent i st s bel i eve t hat cl i mat e change coul d be t he sour ce . A r ecent r epor t by t he I nt er gover nment al Panel on Cl i mat e Change ( I PCC) , char ged by gover nment s wi t h i nvest i gat i ng gl obal war mi ng, says t hat humans have a " di scer ni bl e" i nf l uence on gl obal cl i mat e . I n May 1996, i nsur ance execut i ves conf r ont ed t he ener gy i ndust r y over gl obal war mi ng, and t ook t hei r THE J OURNAL OF POKTFOLI O MANAGEMENT case t o t he Uni t ed Nat i ons Geneva meet i ng on cl i mat e change i n June 1996 ( Boul t on [ 1996] ) . Thei r case was hear d, and f or t he f i r st t i me t he Uni t ed St at es t ook a l eadi ng posi t i on i n suppor t i ng t he devel opi ng count r i es' cal l s f or har d t ar get s i n t he r educt i on of gr eenhouse gas emi ssi ons i n t he i ndust r i al count r i es. Envi r onment al mar ket s t hat t r ade count r i es' r i ght s t o emi t have been pr oposed and l oom l ar ge on t he hor i zon. 1 FI NANCI AL RI SKS Al t hough t he dat a on cl i mat e change ar e not concl usi ve, t he f i nanci al chal l enge i s al r eady r eal . I n t he l ast f ew year s t he pr oper t y/ casual t y i nsur ance i ndust r y has exper i enced r ecor d cl ai ms of about USS43 bi l l i on connect ed wi t h cl i mat e vol at i l i t y. I n t he Uni t ed St at es al one, t her e was t he 1988 Mi dwest dr ought , t he 1993 Mi dwest f l oods, and 1995 f l oodi ng al ong t he Cal i f or ni a coast . Hur r i cane Andr ew i n 1992 pr oduced about US318 bi l l i on of i nsur ed l osses and t ot al l osses gr eat er t han USS25 bi l l i on ( Chi chi l ni sky [ 1996a] ) . Andr ew was t he most devast at i ng nat ur al cat ast r ophe ever r ecor ded . I t al so l ed t o a wave of f i nanci al cat ast r ophe; t he hur r i cane af f ect ed al most ever y i nsur ance company i n t he Uni t ed St at es . Not knowi ng how t o hedge unpr edi ct abl e r i sks adds t he r i sk of f i nanci al cat ast r ophe on t op of t hat of t he nat ur al cat ast r ophe, a one- t wo punch t hat coul d l ead t o a soci et al di sast er . The year af t er Andr ew, t hi r t y- ei ght non- U. S. and ei ght U. S. r ei nsur er s, wi t h names as f ami l i ar as Cont i nent al Re and New Engl and Re, ei t her wi t hdr ew f r om t he busi ness or ceased under wr i t i ng cat ast r ophe r ei nsur ance ( Chi chi l ni sky [ 1996b] ) . Faci ng an i mpossi bl e chal l enge, many r ei nsur er s l ef t t he mar ket . Wor l dwi de r ei nsur ance capaci t y dr opped mor e t han 30%bet ween 1939 and 1993, and i t appear s t hat over 20%of t hat i s due t o Andr ew. Thi s nat ur al l y l ed t o changes i n t he mar ket pl ace . I nsur ance compani es coul d not buy enough cat ast r ophe r ei nsur ance, no mat t er how har d t hey t r i ed. As suppl y dr i ed up, pr i ces of cour se i ncr eased dr amat i cal l y ; t he r at e on l i ne went f r om 8 . 2% i n 1989 t o 21 . 4%i n 1994 . Hi gher pr i ces t hen at t r act ed new capi t al . Thi s l ed t o a maj or geogr aphi c shi f t of t he i ndust r y. Cont i nui ng doubt s about t he f ut ur e exi st ence of Ll oyd' s of London l ed t o a dr op i n t he U. K . mar ket shar e, f r om about 56%i n 1989 t o 23%1 i n 1995 . Si nce 1993 Ber muda' s r ei nsur ance i ndust r y evol ved f r om pr act i cal l y zer o t o i t s cur r ent posi t i on of 25% of t he MANAGI NG UNKNOW N RLSKS mar ket . I nvest ment banks ar e now bet t i ng heavi l y on t he r ei nsur ance mar ket . They ar e t he owner s of most of t he busi nesses cr eat ed si nce 1992 . REVOLUTI ON I N GLOBAL FI NANCE Toget her wi t h t he geogr aphi c shi f t , t her e has been a subst ant i al shi f t i n t he i ndust r y' s st r at egy. The i nsur ance der i vat i ves t hat have been r ecommended f or sever al year s ar e st ar t i ng t o pl ay a r ol e. I n 1992, we r ecommended t he cr eat i on of an i nst r ument t o bet on t he f r equenci es of cat ast r ophes, whi ch t he Chi cago Boar d of Tr ade ( CBOT) i nt r oduced under t he name Cat ast r ophe Fut ur es i n 1993 ( see Chi chi l ni sky and Heal [ 1993] ) . I n 1997, Mor gan St anl ey st ar t ed mar ket i ng a si mi l ar i nst r ument : a bond i ssue whose r et ur ns ar e l i nked t o hur r i cane f r equency ar i d sever i t y i n t he cur r ent US. season . Recent l y, Mer r i l l Lynch st r uct ur ed a t r ansact i on f or USAA, t he count r y' s l ar gest di r ect mar ket er of home and car i nsur ance, of f er i ng USS500 mi l l i on i n bonds on t he U. S. capi t al mar ket s t hat ar e t i ed t o t he company' s l osses f r omhur r i canes ( see Wat er s [ 1996] ) . Fi nanci al i nnovat i on i n r ei nsur ance mar ket s i s sl owl y devel opi ng, but t he under l yi ng pr essur e' i s r el ent l ess . Ever yone knows t hat access t o mor e l i qui d capi t al mar ket s i s essent i al t o t he r ei nsur ance i ndust r y. The der i vat i ves mar ket i s t he key t o l i qui d ar i d f l exi bl e t r adi ng of weat her r i sks . UNKNOW N RI SKS Unknown r i sks ar e r i sks whose f r equenci es we do r i ot know, and f or whi ch we ar e awar e of our i gno- r ance ( Chi chi l ni sky [ 19964] ) . You coul d t hi nk of t hese as r i sks f or whi ch we have mor e t han one act uar i al t abl e, each equal l y l i kel y. Ther e i s mor e t han one pr i or est i mat e of ' t he f r equency of t he event ( see Cass, Chi chi l ni sky, and Wt r [ 1996] ) . Exampl es of unknown r i sks ar e envi r onment al heal t h r i sks of new and l i t t l e known epi demi cs, or r i sks i nduced by sci ent i f i c uncer t ai nt y i n pr edi ct i ng t he f r e quency and sever i t y of cat ast r ophi c event s such as nucl ear r eact or and sat el l i t e r i sks . These r i sks ar e dr i vi ng maj or changes i n t he i nsur ance and r ei nsur ance i ndust r y t oday ( see Chi chi l ni sky and Heal [ 1998] ) . Take a si mpl e exampl e. One r el i abl e sour ce gi ves a 2%annual chance of t he occur r ence of a hur r i cane of a cer t ai n t ype, and anot her a 12%chance . Mont e Car l o SUMMER 1998 si mul at i ons and ot her pr ocedur es can he used t o at t empt t o t ease f r om al l model s a uni que st at i st i cal appr oxi mat i on t o t he t r ue f r equency. But what i f t her e i s no t r ue f r equency? How coul d t hi s be? Easi l y. Ther e nnay be t wo possi bl e cl i mat e pat t er ns, bot h equal l y l i kel y. Thi s i s t ypi cal of compl ex ar i d chaot i c syst ems such as t he cl i mat e ( see Chi chi l msky [ 1995] ) . Many cl i mat e exper t s vi ew cl i mat e as a f i ui da- must be known . Loss of l i f e ar i d car acci dent s ar e t ypi cal ex: unpl es . Her e t he l aw of l ar ge number s oper at es . Ther e i s saf et y i n number s ; wi t h a l ar ge enough popul at i on, t he number of t hose l i kel y t o be af f ect ed i s k nown wi t h consi der abl e accur acy. The sar r i pl e mean i s hi ghl y pr edi ct abl e i f t he di st r i but i on f or each per son or gr oup i s k nown . Thi s i s t he st andar d pr i nci pl e oi l whi ch i nsur ance oper at es . ment al l y non- l i near phenomenon i n whi ch chaot i c pat - Rei nsur ance i s si mpl y a way t o augment t he pool of t hose af f ect ed so t hat t he l aw of l ar ge number s t er ns emer ge easi l y. Such syst ems can have t wo " at t r ac oper at es bet t er . Al l t hat i s needed i s a r el i abl e act uar i al t or s, " or t wo di st i nct over al l pat t er ns of behavi or , each si gni f i cant l y l i kel y. Each of t hese at t r act or s descr i bes a weat her pat t er n, a r easonabl e st at i st i cal i nf er ence of t he t abl e descr i bi ng t he i nci dence per per son or gr oup, and a l ar ge pool of i nsur eds t o di st r i but e t he r i sk ( see Chi chi l r i i sky ar i d Heal [ 1993] ) . f r equenci es of a maj or event . I n such a chaot i c syst er n, I f t he number s ar e not l ar ge enough, i t i s st an- i t i s sci ent i f i cal l y i mpossi bl e t o pr edi ct f r om t he i ni t i al dar d t o spr ead r i sk t hr ough t i me . The number of peo- condi t i ons whi ch of t he t wo pat t er ns t he cl i mat e wi l l t ake : a pat t er n wi t h t wo hur r i canes a year , or t he ot her wi t h a dozen . Because we cannot pr edi ct , we f ace a r i sk . l east t en t i mes t hat af f ect ed i n one year . Thi s r equi r es We cal l i t a chaot i c r i sk because i t emer ges f r om t he chaot i c nat ur e of t he cl i mat e syst em. The f i r st st at i st i cal r eact i on i s t o const r uct a new act uar i al t abl e by t aki ng an aver age ; assur ni ng t he t wo st at es, 2% and 12%, ar e equal l y l i kel y, t hi s i s 7%. But t aki ng an aver age does not hel p. I t onl y ensur es t hat one i s wr ong 100% of t he t i me : 50% of t he t i me we ar e over i nsur ed ( t he pat t er n wi t h t wo hur r i canes per year ) , and t he ot her 50%we ar e under i nsur ed ( t he pat t er n wi t h a dozen a year ) . Bot h have maj or f i nanci al cost s. I f each hur r i cane l eads t o US$2 bi l l i on i n l osses, t he aver agi ng met hod l eads t o a US$10 bi l l i on shor t f al l 50% of t he t i me and US$10 bi l l i on over i nsur ance t he ot her 50%of t he t i me . Har dl y a measur ed way t o manage r i sks . I s t her e a sol ut i on t o t hi s pr obl em? The good news i s t hat t her e i s. I t i s possi bl e t o hedge such unknown r i sks successf ul l y and ef f i ci ent l y. To do so, however , one needs a car ef ul and cust omi zed appr oach t hat bl ends bot h i nsur ance and secur i t i es appr oaches t o hedgi ng r i sks . TW OW AYS TO HEDGE RI SK I nsur ance : The St at i st i cal Appr oach pl e af f ect ed by a hur r i cane over a t er n- year per i od i s at t hat t he r i sks be i ndependent t hr ough t i me, el i mi nat i ng i r r ever si bl e r i sks such as once- and- f or - al l shi f t s ar i si ng f r om gl obal war mi ng . Hur r i canes such as Andr ew ( 1992) and Opal ( 1995) , however , def y t he l aw of l ar ge number s . They af f ect l ar ge ar eas al l at once, bot h i n physi cal ar i d i n f i r i an" ci al t er ms, ar i d t hei r f r equency and sever i t y seem t o' be changi ng. The act uar i al t abl e i t sel f has become t he r i sk. I nsur ance does not wor k . What ar e t he al t er nat i ves? Der i vat i ves : The Ec onomi c Appr oach Ai l al t er nat i ve i s t he economi c appr oach . Thi s wor ks best f or cor r el at ed r i sks, i n whi ch t he same event occur s f or many peopl e al l at once . A dr op i l l t he val ue of t he dol l ar i s an exampl e ; t he event i s t he same f or ever yone i n t he US. economy. Ther e i s no way t o pool t hi s r i sk, al t hough, as we al l know, we can hedge i t by usi ng der i vat i ves ( cur r ency f ut ur es or opt i ons) . The pr i nci pl e used her e i s negat i ve cor r el at i on . One hedges by t aki ng a posi t i on t hat i s hi ghl y cor r el at ed wi t h t he r i sk, except wi t h t he opposi t e si gn . For exampl e, an i nvest or wi t h a dol l ar - based por t f ol i o who f ear s a dr op i n t he val ue of t he dol l ar can buy a f ut ur es cont r act i l l yen, or a dol l ar put . I f t he dol l ar dr ops i n val ue, t he i nvest or i s cover ed by t he i ncr ease i n t he val ue of t he der i vat i ve . Bear f unds have been The st at i st i cal appr oach t o hedgi ng r i sks, whi ch r el i es on t he l aw of l ar ge number s, i s t he t r adi t i onal f oundat i on of t he i nsur ance i ndust r y. const r uct ed on t hi s pr i nci pl e . The economi c pr ocedur e i s r adi cal l y di f f er ent f r om t he i nsur ance appr oach i n t hat i t does not r equi r e a For t hi s t o wor k, r i sks must be r easonabl y i nde- l ar ge number of peopl e. Nor does i t r equi r e knowi ng t he pendent acr oss i ndi vi dual s or gr oups, and t he f r equenci es f r equency of t he event or t he act uar i al t abl e . Thi s f r r r i da- SLI MMER 1998 THE J OURNAL OF PORTFOLI O MANAGEMENT ment al l y di f f er ent met hod i s t he way t he secur i t i es i ndust r y oper at es . I nst ead of pool i ng r i sks, one t r ades r i sks . Secur i t i es mar ket s ar e, however , not or i ousl y compl ex . For exampl e, t he pr ocedur e of t r adi ng r i sks j ust out l i ned makes no sense f or i ndi vi dual r i sks, such as deat h. Howwoul d we descr i be t he deat h of one si ngl e per son wi t hi n a l ar ge economy as one event on whi ch al l of us can t r ade? To do so woul d r equi r e an unr eal i st i cal l y hi gh number of secur i t i es, i ndeed 2' , wher e x i s t he number of peopl e i n t he economy. I n a wor l d wi t h f i ve bi l l i on peopl e, t he number of secur i t i es coul d exceed t he number of al l known par t i cl es i n t he uni ver se ( see Chi chi l r l i sky and Heal [ 1993] ) . I nsur ance, i nst ead, deal s wi t h such r i sks expedi t i ousl y. I f al l i ndi vi dual s ar e i n a si mi l ar r i sk cl ass, one i nsur ance cont r act woul d suf f i ce . The cont r ast i s st ar k, but i t makes a poi nt . I n a wor l d of unknown r i sks, nei t her secur i t i es nor i nsur ance r i l et hods wor k i n i sol at i on . THE I DEAL HEDGE: CATASTROPHE BUNDLES HOWDO CATASTROPHE BUNDLES WORK? Cat ast r ophe bundl es wor k best i n t he hands of an exper i enced r ei r l sur er or br oker who can cust omi ze t he i nst r ument t o t he cl i ent ' s needs . I l l a wi l y, t he r ei r l sur er i s sel l i ng a package t hat consi st s of i nsur ance, a secur i t y, and a r i sk manager ner i t / consul t i ng t ool . The br oker must f i r st i dent i f y wi t h t he cl i ent t he set of possi bl e descr i pt i ons of t he r i sk . Thi s cr uci al par t of t he pr ocess i nvol ves new t echni ques of r i sk manage r i l er l t . I t i s best handl ed on a f ace- t o- f ace and cust omi zed basi s . A mat hemat i cal f or mul a i s t hen br ought t o bear i n cust omi zi ng cat ast r ophe bundl es t o cust omer needs . Thi s f or mul a wor ks ver y wel l when t her e i s mor e t han one pat t er n of r i sk and t her ef or e mor e t han one " possi bl e" act uar i al t abl e, each t abl e bei ng subst ant i al l y l i kel y. Af t er t hi s i s achi eved, der i vat i ve secur i t i es whose payof f s depend on whi ch descr i pt i on of t he r i sk i s cor r ect ar e i nt r oduced . These secur i t i es ser ve t o hedge uncer t ai nt y about act uar i al t abl es . Fi nal l y, one st r uct ur es i nsur ance cont r act s t hat est abl i sh a compensat i on ar r angement i n a way t hat depends on whi ch descr i pt i on of t he r i sk i s cor r ect . Cat ast r ophe bundl es ar e pr opr i et ar y, and t hei r use i n a par t i cul ar l y si mpl e case i s i l l ust r at ed i n Exhi bi t 1 . We see t hat i nsur ance does not wor k when t he f r equency of a r i sk i s unknown, ar i d secur i t i es do not wor k when t he r i sks ar e i ndi vi dual . I f nei t her of t hese t wo appr oaches wor ks on i t s own, what does wor k? The i deal hedge i s a combi nat i on of i nsur ance PRI CI NG AND OPTI MAL PORTFOLI OS and secur i t i es ; t hi s ear l achi eve ef f i ci ent al l ocat i on of r i sk- bear i ng . We cal l t hi s a cat ast r ophe bundl e because i t Fund r nar l ager s ear l l ook at t he f l i p si de of t hi s bundl es t oget her t wo t ypes of i nst r ument s. I t consi st s of pi ct ur e and seek a combi nat i on of i nsur ance and secur i ai l i nsur ance i nst r ument wi t h a novel der i vat i ve secur i - t i es t hat of f er an opt i mal por t f ol i o i n i nsur ance and t y f or bet t i ng on t he f r equency i t sel f ( see Chi chi l r l i sky i nvest ment mar ket s . A par t of t hi s i nst r ument i s what and Heal [ 1993] ) . Mer r i l l Lynch and Mor gan St anl ey have f l oat ed r ecent l y. The l at t er t ype of secur i t y has emer ged and i s Secur i t i zi ng such i nst r ument s i s, of cour se, t he next st ep. now t r aded oi l t he CBOT As we have ment i oned, Thr ough t he use of cat ast r ophe bundl es, t he r el at ed secur i t i es have r ecent l y emer ged al so i n t he f or m r ei nsur ance br oker can access a l ar ge pool of managed of bonds f l oat ed by Mor gan St anl ey ar i d Mer r i l l Lynch. f i ends whi l e of f er i ng i t s cl i ent s a cust omi zed r ei nsur ance The combi nat i on of bot h i nst r ument s ensur es ser vi ce t hat manages r i sks opt i mal l y, and at ver y comt hat no f i nanci al cat ast r ophe wi l l occur , si nce t he r ei npet i t i ve pr i ces . sur er i s not exposed t o mor e r i sks t han i t can af f or d . At Pr i ci ng, of cour se, i s a cr uci al i ssue. What i s t he same t i me, t hi s appr oach can be used t o pr ovi de needed her e i s t o separ at e t wo par t s of t he r i sks and t o near l y f ul l cover age f or t he i nsur ed at a r ni ni r r l al cost . push each as f ar as i t wi l l go . The cont i ngent i nsur ance We show el sewher e t hat such i nst r ument s l ead t o par t of t he i nst r ument shoul d be appl i ed as f ar as possi an ef f i ci ent al l ocat i on of r i sk- bear i ng ( see Chi chi l ni sky bl e, cover i ng t he i ndependent par t of t he r i sk f or whi ch and Heal [ 1993, 1995] and Cass, Chi chl l i l l sky and Wu i t i s opt i mal l y sui t ed . Secur i t i es ar e t hen used f or t he [ 1996] ) . They r equi r e a car ef ul l y cust omi zed appr oach pur pose f or whi ch t hey ar e best : t he cor r el at ed par t of t o hedgi ng r i sk. Thi s gi ves t he t r adi t i onal f ace- t o- f ace t he r i sk . A mat hemat i cal f or mul a used t o const r uct t he i nsur ance appr oach an edge over r aw t echnol ogy. cat ast r ophe bundl e separ at es and pr i ces bot h par t s . MANAGI NG UNKNOW N RI SK SUMMER 1998 EXHI BI T 1 CATASTROPHE BUNDLE EXAMPLE Hur r i cane wor se t h .. an $3 bi l l i on once i n 15- year or once i n 5 : I nsur ance cover s i ndi vi dual pr oper t y r i sks Secur i t i es cover f r equency r i sk CONVERGENCE OF I NSURANCE AND SECURI TI ES MARKETS A t r adabl e ENSO i ndex i s a cont r act t hat pays an agr eed amount cont i ngent on t he val ue of a physi cal i ndex. I t i s si mi l ar i n concept t o t he cat ast r ophe f ut ur es i ng i nr oads i nt o t he r ei nsur ance busi ness . By i t sel f , I t i s no secr et t hat t he secur i t i es i ndust r y i s mak- t r aded on t he CBOT, and i s an exampl e of a secur i t y condi t i onal on t he i nci dence of t he i nsur ed per i l , t hat however , i t cannot succeed, because t he i ndi vi dual par t s i s, on whi ch r i sk descr i pt i on i s cor r ect . of t he r i sks cannot be handl ed ef f i ci ent l y by secur i t i es Ther e ar e t wo ext r eme st at es o£ t he ENSO k nown as El Ni f i o and La Ni na. I n El N1 4110 mar ket s ; t hey ar e t oo cumber some f or i ndi vi dual r i sks. cycl e, I nsur ance, based on t he l aw of l ar ge number s, has an year s, hur r i cane i nci dence i n t he sout heast er n US. i s i mpor t ant pl ace i n si mpl i f yi ng f i nanci al t r ansact i ons and bel ow aver age ; i n La Ni na year s, i t i s above . hedgi ng k nown i ndi vi dual r i sks. Exhi bi t Cat ast r ophe bundl es of f er one appr oach t o cor nput i ng t he l i mi t s of each i nst r ument , and bl endi ng 1 shows possi bl e pr obabi l i t y di st r i bu- t i ons of damage due t o hur r i canes condi t i onal on El Ni f o or La Ni na year s. t hemopt i mal l y t o achi eve t he most compet i t i ve pr i ci ng As an exampl e, assume t hat , i n an El Ni no year , of a cat ast r ophe r ei nsur ance por t f ol i o . The f ut ur e of t he i ndust r y i s i n t he hands of t hose who achi eve t he opt i mumbal ance, t hr ough i nt egr at i ng der i vat i ve secur i t i es wi t h cont i ngent i nsur ance t her e i s a 10% chance of a $5 bi l l i on l oss, a 20% chance of a $10 bi l l i on l oss, and a 10% chance of a $15 bi l l i on cont r act s, and i nt egr at i ng t echnol ogy wi t h cust omi zed Ni f i a year , t he pr obabi l i t i es ar e 20%, 30%, and 20%, r espect i vel y, gi vi ng an expect ed l oss of $7 bi l l i on . f ace- t o- f ace k now- how. l oss . The expect ed val ue of t he damage i s t her ef or e ( 0 . 1 x $5) + ( 0 . 2 x $10) +( 0. 1 x $15) = $4 bi l l i on. I n a La Assume t hat t her e i s a 40% chance of an El Ni no year , HURRI CANE RI SKS AND EL NI NO: AN EXAMPLE and a 60% chance of a La Ni f i a year . The t ot al val ue of i nsur ed pr oper t y i s t aken as $30 bi l l i on, so t hat i n a wor st case scenar i o - when t he hur r i cane damage i s at How exact l y woul d cat ast r ophe bundl es wor k? i t s max i mumof $15 bi l l i on - hal f of t hus val ue i s at r i sk . W e answer t hat quest i on wi t h a si mpl e but t ypi cal exampl e, dr awn f r om hur r i cane i nsur ance. Hur r i cane i nci dence i s condi t i oned by t he ENSO cycl e, so we I n an El Ni f o year , t he expect ed l oss i s 13 . 33% of t he i nsur ed r i sks, and i n a La Ni na year , i t i s 23 . 33%. I t f ol l ows t hat t he r at es on l i ne ( i . e . , pr emi ums as a per consi der , i nst ead of hur r i cane bonds of t he t ype t hat have r ecent l y been i ssued, a t r adabl e ENSOi ndex. 2 Thi s cent age of t he i nsur ed amount ) condi t i onal on bei ng i n El Ni f i o and La Ni na year s woul d need t o be at l east i ndex woul d achi eve ever yt hi ng one needs f r om hur r i cane bonds, but i n a mor e gener al and si mpl e f ashi on . 13 . 33% and 23 . 33%, expect ed val ue t er ms . SUMMER 1998 r espect i vel y, t o br eak even i n THEJ OURNAL OF PORTFOL10 MANAGEMENT I n t he f or mer case, t he i nsur er s ar e char gi ng pr emi ums i n excess EXHI BI T 2 HURRI CANE PROBABI LI TI ES AND THE ENSO SYSTEM Pr obabi l i t i es of l ouses i n El of expect ed l osses by $1 . 8 bi l l i on, har dl y a compet i t i ve st r at egy, and i n Ni no and La Ni na Year s t he l at t er case, f al l s shor t of expect ed cl ai ms by pr enr i uni i ncome $1 . 2 bi l l i on, cl ear l y a danger ous and unsust ai nabl e posi t i on . Nei t her case i s sat i sf act or y. To mat ch asset s t o l i abi l i t i es pr oper l y, i nsur er s need t o shi f t i ncome f r om El Ni f l o t o La Ni f i a year s . Thi s i s wher e secur i t i es condi t i onal on i nci dence, on descr i pt i on of t he r i sk, c ome i nt o t he pi cAs we have al r eady not ed, expect ed l osses ar e di f f er ent , dependi ng on what Bef or e we k now what t ype of year we ar e i n . ki nd of year wi l l occur , we t her ef or e have an expect ed l oss due t o El Ni f l o equal t o t he expect ed l oss i n an El Ni f l o year t i mes t he pr obabi l i t y of such a year , i . e . , ( 0 . 4 x $4) = $1 . 6 bi l l i on . For La Ni f i a, t he equi val ent cal cul at i on i s ( 0. 6 x $7) = $4 . 2 bi l l i on . Hence, ex ant e, bef or e we k now whi ch year we t ur e. They can be used t o t r ansf er i ncome bet ween El Ni f l o and La Ni f i a year s so t hat t he e sur pl us i n t he f or mer cover t he def i ci t i n t he l at t er . W need a secur i t y whose val ue depends on t he i nci dence of hur r i canes ; f or t he pur poses of t hi s exampl e, we t ake t hi s t o be a t r adabl e ENSO i ndex. Thi s woul d be a cont r act whose val ue depends on t he val ue of t he ar e or wi l l be i n, t he expect ed l osses i n El Ni f l o ar i d La ENSO i ndex and i n whi ch t r ader s can t ake l ong or shor t posi t i ons. By t r adi ng t hi s secur i t y, t he i nsur er i n Ni na year s ar e, r espect i vel y, $1 . 6 bi l l i on and $4 . 2 bi l - our exampl e can i n ef f ect t r ade i ncome i n El l i on, gi vi ng a t ot al of $5 . 8 bi l l i on as t he annual expect - year s f or i ncome i n La Ni f i a year s . A Ni f l o The odds wor k out ni cel y. The i nsur er want s t o ed l oss al t oget her . W e can now comput e t he pr el ni ur ne t hat woul d have t o be char ged f or cover i n each t ype of year bef or e t he t ype of year i s known, i n or der t o br eak sel l $1 . 8 bi l l i on i n an El Ni f r o year , i t s sur pl us of pr e- even on aver age . These woul d have t o be t he pr emi ums cont i ngent on bei ng i n each year - seen above t o bi l l i on of i ncome i n La Ni f i a year s, t o cover t he shor t f al l bet ween pr emi um i ncome and expect ed cl ai ms . I l l be 13 . 33% and 23 . 33% f or El Ni f i o ar i d La Ni f i a - our exampl e, t hi s happens 60%of t he t i me . The pr i ces f or ENSO i ndex cont r act s del i ver i ng mul t i pl i ed by t he pr obabi l i t i es of each t ype of year . Thus t he ex ant e r at es on l i ne ( bef or e i t i s k nown whet her we ar e i n an El Ni f l o or a La Ni f i a year ) have t o be at l east ( 0 . 4 x 13 . 33%) = 5 . 33% or ( 0. 6 x 23 . 33%) = 13 . 99%, r espect i vel y. I f i nsur er s f ol l ow ' t he obvi ous and t r adi t i onal pr ocedur e of char gi ng pr emi ur i L based on t he over al l expect ed l oss and not di st i ngui shi ng bet ween t he t wo cl i mat e pat t er ns, t hey wi l l char ge pr emi ums t hat wi l l br i ng i n t hei r over al l ex ant e expect ed l oss of $5 . 8 bi l l i on, i mpl yi ng a r at e on l i ne of 5 . 8/ 3( ) = 19. 33%. Thi s i s unsat i sf act or y because i n El Ni f l o year s t hey ar e over char gi ng ( expect ed cl ai ms ar e $4 bi l l i on ; t he r at e on mi umi ncome over expect ed cl ai ms, whi ch occur s wi t h a 40% chance . Cor r espondi ngl y, $1 i n El Ni f i o and La Ni f i a year s wi l l be pr opor t i onal t o t he pr obabi l i t i es of t hese event s, and so wi l l be i n t he r at i o of 0 . 4/ 0 . 6 or 2/ 3 . But $1 . 2 bi l l i on/ $1 . 8 bi l l i on = 2/ 3, so t hat at such pr i ces t he sal e of sur pl us i ncome i n El Ni f l o year s wi l l exact l y f i nance t he pur chase of i ncome t o cover t he def i ci t i n La Ni f i a year s . Over al l , t hen, we have a pat t er n of t r ansact i ons as f ol l ows : 1. I ssui ng i nsur ance cont r act s whi ch pr ovi de cover agai nst damage i n ei t her El Ni f l o or La Ni na year s. 2. Sel l i ng $1 . 8 bi l l i on of cont r act s cont i ngent on t he ENSOi ndex havi ng a val ue cor r espondi ng t o an El l i ne need be onl y 13 . 33%) ; La Ni f i a year s, t hey ar e under char gi ng ( expect ed cl ai ms ar e $7 bi l l i on ; a r at e oi l l i ne of 23 . 33% i s needed) . i t needs t o buy $1 . 2 3. Ni f l o year , at a pr i ce of $0 . 40 per dol l ar . Buyi ng $1 . 2 bi l l i on of cont r act s cont i ngent on t he ENSO i ndex havi ng a val ue cor r espondi ng t o a La Ni na year , at $0 . 60 per dol l ar . Thi s speci f i c combi nat i on of t r ades i n secur i t i es and i nsur ance pol i ci es descr i bed i n t hese st eps i s what we r ef er t o as " cat ast r ophe bundl es . " Thr ough t r adi ng cat ast r ophe bundl es, i nsur er s can ar r ange compl et e cover f or t hemsel ves and t hei r cl i ent s at mi ni mumcost , i n spi t e of not knowi ng what t he odds of l oss wi l l be . They achi eve t hi s by a speci f i c t ai l or - made combi nat i on of i nsur ance cont r act s and secur i t i es . Al l t hese cont r act s ar e condi t i onal on t he i nci dence of t he i nsur ed r i sk . Howdi f f er ent i s t hi s appr oach f r om t he pr act i ce t oday? The secur i t i es i ssued t oday secur i t i ee i nsur ance or r ei nsur ance r i sks, and t her ef or e br i ng mor e l i qui di t y t o t he r ei nsur ance mar ket . Thi s i s an i mpr ovement . But t hese secur i t i es st i l l l eave open t he possi bi l i t y t hat t he i nsur er i s ei t her of f er i ng non- compet i t i ve r at es or t aki ng on a danger ous exposur e . Today' s secur i t i es do not t ackl e t he essence of t he pr obl em. The key t o cat ast r ophe bundl es i s t o r ecogni ze t hat when t her e ar e sever al possi bl e act uar i al t abl es, al l r easonabl y l i kel y, we have t o suppl ement i nsur ance i nt r oduci ng and t r adi ng secur i t i es dependent on t hem. A speci f i c combi nat i on of i nsur ance and secur i t i es, and an equal l y speci f i c pr i ci ng pol i cy, ar e r equi r ed f or an opt i mal al l ocat i on of r i sks on compet i t i ve t er ms. - ENDNOTES ' Chi chi l ni sky [ 199( w] advances a pr oposal f or a gl obal r nar ket on gr eenl aousc g. Le emi ssi ons : and an I nt er nat i onal Bank f or Envi r or unent al Set t l ement s t o I nar adl e execut i ons, cl ear i ng, ar i l set t l ement s as wel l as r egul at e bor r owi ng and l endi ng r at es . ZENSO st ands f or t he El Ni i o- Soudaer n Osci l l at or , t he nar ne gi ven t o t } ne weat her pat t er n t hat or i gi nat es i s t he equat or i al Paci f i c and i nf l uences r ai nf al l and st or m i nci dence f r omAust r al i a t o sout her n Af r i ca . An i ndi cat or of di e st at e of t i r e ENSO cycl e i s a sea sur f ace t emper at ur e ( SST) i ndex f or t he equat or i al Paci f i c . SUMMER I " a 3Tl nas Ls a si napl ai cat i on . Ther e ar e al so year s t hat ar e nei t her , so- cal l ed neut r al year s . The number s we use i n t hi s exampl e ar e pur el y i l l ust r at i ve . REFERENCES Boul t on, L. " Debat e Wanws Up . " Fi nanci al Ti mes, May 29, 1996, P. 10 . Cass, Davi d, Gr a: i el a Chi chi l ni sky, anal Ho- Mou W u . " I ndi vi dual Ri sks anal Mut ual I nsur ance . " Economet r i ca, Vol . 64, No . 2 ( Mar ch 1996) , pp . 333- 341 . Chi cl ni l ni sky, Gr aci el a. " Cat ast r ophe Bundl es Can Deal Unknown Ri sks . " Best ' s Revi ew, Febr uar y 1996a, pp. 1- 3 . wi t h - . " Fi nanci al I nnovat i on i n Pr oper t y Cat ast r ophe Rei nsur ance : The Conver gence of I nsur ance ant i Capi t al Mar ket s . " Ri sk Fi nanci ng Neunl et t er , Vol . 13, No 2 Qune 1996b) , pp . 1- 7 . - . " The Gr eeni ng of Br et t on Woods . " Fi nanci al Ti mes, Januar y 2, 1996c. - . " Mar ket s wi t h Endogenous Uncer t ai nt y : Theor y and Pol i cy . " Ti eor y and Deci si on, Vol . 41 ( 19964) , pp . 99- 131 . - . " A Radi cal Shi f t i n Managi ng Ri sks: Pr act i cal Appl i cat i ons of Compl exi t y Theor y . " Cont i ngenci es, Amer i can Acader nyt of Act uar i es, Januar y- Febr uar y 1998, pp . 28- 32. Chi chi l ni sky, Gr aci cl a, and Geof f r ey M. Heal . " Fi nanci al Mar ket s f or Unknown Ri sks . " I n G. Chi chi l ni sky, G. M. Heal , and A. Ver cel l i , eds . , Sust ai nabi l i t y, Dynami cs and Uncer t ai nt y. At nst er dann : Kl uwer Acader ni c Publ i sher s, 1998, pp . 277- 294. - . " Gl obal Envi r onment al Per spect i ves, Fal l 1993, pp . 65- 86. Ri sks . " Jour nal of Economi c Denney, Val er i e . " Edi t or ' s Not e . " Gl obal Rei nsur ance, DScet nber 1995- Febr uar y 1996, p. 14 . Wat er s, R. " I nvest or s Get Chance t o Gambl e on Weat her. U. S. I nsur ance Gr oup Li nks Bonds t o Hur r i cane Losses . " Fi nanci al Ti mes, Jul y 30, 1996 . THE J OURNAL OF PORTFOLI O MANAGEMENT