Insurance. By Mark Dorfman, Alexander Kling, and Jochen Russ. Abstract

Transcription

1 he Impac Of Deflaon On Insurance Companes Offerng Parcpang fe Insurance y Mar Dorfman, lexander Klng, and Jochen Russ bsrac We presen a smple model n whch he mpac of a deflaonary economy on lfe nsurers offerng parcpang conracs can be analyzed. Deflaon s smply modeled by assumng ha some fla neres rae drops o a lower level and says here for a ceran perod of me. We fnd ha a deflaon would have srong negave effecs on nsurers offerng parcpang conracs. hs s alarmng snce such conracs accoun for he larges poron of lfe nsurers lables n many counres. Numerous numercal resuls show ha he number of years of deflaon ha can be endured by an nsurer depends on many facors such as he level of reserves ha are presen a ouse and he relaon beween he level of neres raes before, durng and afer he deflaon. One of he mos mporan facors s he relaon beween he guaranee erm,.e. he erm durng whch a ceran neres rae s guaraneed whn he nsurance conracs, and he asse erm,.e. he erm o maury of he bonds purchased by he nsurer. We propose offerng conracs wh revewable neres rae guaranees o reduce he rss resulng from a deflaon.

2 . Inroducon Ever snce he raumac experence of nflaon afer WWI, whch produced he noorous pcures of wheel barrows of money beng exchanged for bread, economc polcy n many counres has been orened o preven a repeon of hs caasrophe. Cenral baners of all ndusralzed counres clearly consder he poenal for nflaon a reason o ae correcve acon. herefore, he recen appearance of dsnflaon, or deflaon, n Japan, and he poenal for hs phenomenon n e.g. Germany and he U.S. presens cenral baners and managers of fnancal servce companes an unusual, and equally nsdous, economc problem o confron and manage. Dsnflaon, or a downward spral of prces, s usually measured by comparng he cos of a sandard mare base of goods and fndng lower from one perod o he nex. perod of dsnflaon would also see declnng nomnal neres raes and pressure o lower worers wages. Deflaon also can be seen n a reducon of a counry s Gross Domesc Produc GDP. he causes and poenal cures for hs complex problem have been dscussed e.g. n Kumar e al. 23 or Svensson 23, and he problems caused by he decade-long dsnflaon n Japan are now well documened, cf. e.g. Hosh and Kashyap 24. hs paper addresses he mpac of dsnflaon on one of he pllars of he fnancal servce secor, lfe nsurance companes. I aes a frs sep owards undersandng he poenal problems dsnflaon poses for lfe nsurance companes. he paper analyses he hypohecal mpac of dsnflaon on he asses and lables of lfe nsurance companes ha manly sold so-called parcpang lfe nsurance conracs. hese are polces, where he polcy holder receves some guaraneed neres rae and some surplus parcpaon. Such polces have sgnfcan mare shares n many European counres, e.g. Germany or he UK. lso many non-varable Unversal fe polces sold n he US have smlar feaures. Usually, he guaraneed neres rae s fxed for he whole erm of he nsurance conrac, so when he fnancal mares n parcular neres raes ndcae ha he guaraneed rae may 2

3 be oo hgh, can only be reduced for fuure conracs bu no for exsng conracs usually no even for fuure premums n exsng conracs. Snce hese guaranees are ofen no adequaely hedged, hey pose a poenally hgh rs on nsurance companes. Problems arse n parcular n a deflaonary envronmen when real neres raes are closed o or even negave and nomnal neres raes are low. In order o focus on he basc effecs, we use a raher smple model for our analyss boh n descrbng asses and lables. Snce he model s raher generc, he lessons learned from hs analyss can be appled o lfe nsurers n many counres, e.g. Germany, UK or U.S. where requred afer modfcaon for counry-dsnc polcy desgn and asse-allocaon ssues. fer World War 2 here was some concern ha he U.S. economy would rever o he dsnflaonary mes ha preceded he war years. hs concern, whch proved unfounded, was aen que serously for a whle because he Grea Depresson lef a raumac memory. hus, acman and Gansbrugh s 946 analyss of he prospecs for and he poenal consequences of dsnflaon provdes a summary of economc hnng abou he problem sx decades ago, when he wors perod of U.S. dsnflaon was sll a farly recen phenomenon. ferwards, hs opc appears o have been negleced for over 5 decades unl Sellon, 23 presens a recen analyss from a cenral baner s vewpon. However, neher he older nor he newer leraure presens much nsgh no he specfc problems faced by he lfe nsurance ndusry. oh Sellon s 23 arcle and a laer paper by Clar 24 were publshed by he Federal Reserve an of Kansas Cy ndcang ha a leas one branch of he U.S. cenral ban was aendng o he dsnflaon poenal. Oher leraure on he opc ncludes a popular press boo by Shllng 999, a global focus on he problem by he Inernaonal Moneary Fund [Kumar 23], and a suggesed soluon for he problem by Svensson 23. ll of hs U.S. leraure serves o hghlgh he fac ha he poenal for dsnflaon 3

4 has been aen serously by a number of analyss. Hosh and Kashyap 24 devoe hree pages of her paper o an analyss of dsnflaon on Japanese lfe nsurance companes. hs paper ends wh a subsanal Reference secon cng leraure analyzng he Japanese economc problems of he 99s and hereafer. he maory of Hosh and Kashyap s paper s devoed o analyzng governmenal and banng problems posed by Japan s decade long sruggle wh a deflang economy. quoaon from hese auhors provdes nsgh no he experence of he Japanese lfe nsurance mare and he governmen s response o he poenal for banrupcy when lfe nsurers guaranee more neres hen hey can earn. he maor par of he losses a faled nsurers was born by he polcyholders n he form of reducons n promsed yelds. he aforemenoned revson of he Insurance c n ugus 23 has made possble for roubled nsurers o cu promsed yelds whou gong hrough he formal banrupcy process. p. 2. he remander of hs paper s organzed as follows: In Secon 2 we wll develop a model ha allows us o analyze he mpac of deflaon on lfe nsurance companes sellng parcpang conracs wh some guaraneed rae of neres. We ry o eep he model as smple as possble. Neverheless, s necessary o nclude a rudmenary model for he developmen of an nsurer s balance shee over me, a model for he nsurer s asse allocaon, he developmen of neres raes, he relevan nsurance conracs and hus he developmen of he lables,.e. he accoun values of he nsurance conracs. he ranson from a non-deflaonary o a deflaonary envronmen and bac s smply modeled by a parallel shf of he fla erm srucure of neres raes. Secon 3 gves a varey of resuls, analyzng whch combnaons of parameers mae an nsurer parcularly vulnerable or mmune agans he mpacs of deflaon. I urns ou ha as expeced he hghes rs les n a dvergence of he developmen of asses and lables ha occurs whenever long erm guaranees are no adequaely hedged by suable asses. Secon 4 closes wh a summary of 4

5 he mos mporan resuls and an ouloo for furher research. 2. he model framewor In hs Secon, we nroduce our model for he nsurance company s balance shee and asse allocaon and for he developmen of he lables. 2. he nsurer s fnancal suaon Followng Klng, Rcher and Russ 26, we use he followng smplfed llusraon of he nsurer s fnancal suaon a me gven n fgure. sses ables R Fgure Model of he nsurer s fnancal suaon Here, denoes he mare value of he nsurer s asses a me ; s he me boo value of he polcyholder s accoun or, n oher words, he polcy reserve whch also concdes wh he boo value of he asses; R s he reserve accoun whch s gven by R. lhough mgh conss of oher componens as well, e.g. equy, we refer o R as he asse valuaon reserves or hdden reserves. 2.2 he nsurer s asse porfolo In many counres, a huge poron of he asses bacng lfe nsurance conracs wh a guaraneed rae of neres are nvesed n neres bearng secures. In our model, we use a smplfed approach, assumng ha he nsurer s asses are nvesed n a porfolo conanng coupon bearng bonds only. any pon n me any free asses are nvesed n bonds wh a maury of years a he mare rae of neres. We call he erm o maury of he asses or us he asse erm. We assume a fla erm srucure of neres where he neres rae a me s denoed by. We assume ha he annual coupon of a bond purchased a me 5

6 6 concdes wh he mare neres rae, hus he mare value of he bond a me of purchase s he face value. If s he amoun of money ha s nvesed n a bond a me, hen fuure coupon paymens of * are earned a mes,, K and a fnal payoff of s provded a me. any neger pon of me beween purchase and maury, he mare value of he bond purchased a depends on he acual neres rae and s gven by. hus, he oal value of he asses a me s gven by. he amoun nvesed a me depends on he developmen of he lables. I wll be specfed n Secon he developmen of he nsurance lables For he sae of smplcy and n order o focus on he basc effecs, we consder a smple lfe nsurance conrac, a regular-premum endowmen conrac and gnore any charges. he premum P s pad annually. he benefcary receves a deah benef f he nsured des or some survval benef f he nsured s sll alve a maury of he conrac. he me o maury of any nsurance conrac sold s assumed o equal, whch s also called lably erm. oh, deah and survval benef are assumed o equal he curren boo value of he lables of he conrac. hus, he benefs depend heavly on he so-called oal rae of neres ha s creded annually o he nsurance conrac. For parcpang lfe nsurance conracs, hs oal rae of neres consss of he guaraneed rae of neres and some annual surplus. he guaraneed rae of neres s usually specfed for he whole erm of he conrac.

7 However, our model also allows for revewable guaranees,.e. guaranees ha may be adused every g years. We call g he guaranee erm. he surplus may change annually and s deermned by he nsurance company dependng on he reurn on asses earned n he correspondng year. Noe ha he deals of hs mechansm vary from counry o counry and somemes from nsurance company o nsurance company. he wo maor models ha can be found are so-called pon o pon guaranees and clque syle guaranees. In he pon-o-pon model, he polcyholder s guaraneed a maury of he conrac he amoun equvalen o he resul of a process whch creds a ceran mnmum neres rae o he nsured s accoun n every sngle year. In he case of a so-called clque-syle guaranee, as, e.g., mplcly requred by he German regulaory framewor, he guaraneed reurn mus be creded o he polcyholder s accoun each year. In wha follows, we focus on he laer ype. For conracs ha are sold a me, he annual guaraneed neres rae ha has o be creded n year s denoed by g,. Noe ha he guaraneed rae g, may no change durng he guaranee perod, even f he guaraneed neres rae s changed for new busness. hus, f guaraneed raes are decreased for new busness, e.g. n a deflaonary envronmen, all polces ha have been sold prevously are enled o her prevous guaraneed rae unl he end of he curren guaranee perod. If he guaranee perod concdes wh he erm of he conrac as s usually he case, he guaraneed rae for exsng conracs wll no be changed a all. y,, we denoe he oal rae of neres ha s creded a me o conracs aen ou a me. Obvously, has o be greaer or equal o he guaranee rae g,. We assume ha n every year a ceran amoun of new regular-premum conracs wh a oal annual premum amoun P are sold. For he sae of smplcy, all nsured are assumed o be male and of he same age x when he conrac s sold. he boo value of hese conracs afer years before payng he s premum s hen gven by 7

8 8 m m n x n P p,, where x p denoes he probably of a man aged x years o survve for years. he oal value of he lables a me s hen gven by, m m n x n P p. hs equaon compleely deermnes he developmen of he lables n our model. 2.4 Cash flows and renvesmens any pon n me, coupon paymens and maurng bonds provde an ncome of C. In addon, premums are colleced. he sum of premums colleced n year s gven by x P p P. he nsurance company uses coupon paymens and colleced premums o pay he nsurance benefs resulng from maurng conracs aen ou years ago, and he deah benefs D a year, gven by, m m n x x x n P q p q D, where q x denoes he probably ha a man aged x years des whn he nex year. he res of he money s nvesed n bonds a me,.e. D P C. Of course, hs changes asses and lables by he same amoun of money. 2.5 he nsurer s nal suaon Whn he model descrbed n he prevous Secons, we sar our analyss of he lfe

9 9 nsurance company a me. In order o have some busness n force,.e. a porfolo of nsurance conracs and asses, we assume, ha he suaon was sable n he pas,.e. ha every year conracs wh a consan annual premum amoun of P have been aen ou. P P and ha a consan rae of neres was provded o he nsurance lables n every year. hus, a, he value of he lables s hen gven by m m x P p. Furhermore, we assume ha he nsurer has some nal reserves R - cf. fgure mmedaely before some possble neres change ha mgh ae place a. y r we denoe he nsurer s nal reserve quoa a - :. R r hus, we have r. ssumng 2 K, we have and hus, r whch deermnes he asse porfolo a. From hs we calculae D P C and sar our proecon of he nsurer s fnancal suaon. 2.6 Modelng deflaon We assume he fnancal mares o ener a deflaonary envronmen a, he sar of our

10 analyss. hs s modeled as follows:. Mare neres raes drop mmedaely o some value. hus, he mare value of he nsurer s asses changes mmedaely o 2. he guaraneed rae of neres g, for new busness s reduced o mare raes. 3. For all conracs where he curren guaranee perod ends a, he guaraneed rae of neres s adused o mare raes. 4. In he fuure, no more surplus s creded,.e. for, all conracs receve us her guaraneed rae of neres. Furhermore, each year, he guaraneed rae of neres s adused o mare raes for all conracs where he correspondng guaranee perod ends. 3. Resuls. 3. ase case resuls In hs Secon, we analyze he mpac of deflaon on a lfe nsurance company. We parcularly focus on dfferen combnaons of and g, snce here appears o be a sgnfcan msmach beween asse and guaranee erm for ypcal nsurance companes n many counres. We sar wh a base scenaro ha assumes he followng parameers: Mare neres raes were sable a 5% for <, neres creded was also 5% for <, he guaraneed rae for old conracs s 3.5%., mare raes drop o %, he guaraneed raes g, are also reduced o % for and. he annual premum was P for < and says he same for. he nal reserve quoa before neres rae shf s r %. Noe ha he reserve

11 quoa r mmedaely afer he neres rae shf exceeds r snce he mare value of he asses ncreases due o he reducon of neres raes whle he value of he lables s a boo value ha remans unchanged. g We sar our analyss wh, 3, and 3. hese are ypcal values, e.g. for Germany, where usually conracs wh long-erm guaranees are sold ha are baced wh bonds wh a erm o maury of up o years. Fgure 2 dsplays he developmen of he asses and lables n uns of currency, lef axs as well as he developmen of he reserve quoa n percen, rgh axs for he base case scenaro wh r % rgh pcure and for an nsurer wh a lower nal reserve quoa of r 5% lef pcure..2 4%.2 4%. 3%. 3% 2% 2% sses & ables % % -% -2% Reserves sses & ables % % -% -2% Reserves 2-3% 2-3% -4% sses ables Reserves -4% sses ables Reserves Fgure 2: Developmen of asses, lables and reserve quoa n he base scenaro for an nal reserve quoa of 5% lef and % rgh I s noeworhy ha a, he neres rae drop leads o a dramac ncrease of he reserve quoa from % o almos 3% 5% o almos 25% respecvely snce he mare value of he old bonds ncreases whls he boo value of he lables remans unchanged. hen, however, he reserves sar decreasng, snce a raher hgh guaraneed rae sll has o be creded o old conracs. hese conracs maure sgnfcanly afer he correspondng asses yeldng hgh coupons. frs glance, however, he developmen of he asses and lables dsplayed n fgure 2 does no seem oo dramac, snce aes 5 years n he base case scenaro wh an nal reserve quoa of % unl he lables exceed he asses. Even f nal reserves only amoun o 5% of he boo value of lables, aes years unl

12 reserves become negave. Of course, he resuls also depend on oher parameers such as he level of neres raes durng he deflaon and he company s new busness volume. able shows sensvy analyses. We dsplay he number of years unl a shorfall occurs.e. reserves become negave for dfferen nal reserve quoas, dfferen values of he neres rae durng he deflaonary perod and dfferen volumes of new busness afer he neres rae shoc. Whle n he base case scenaro he nal reserve quoa s %, he deflaonary neres rae s % and he new busness does no change, we provde sensves for nal reserves r %, r 5%, and r 2% of and wce as much as n he pas. ase case No reserves %, a deflaonary neres rae of % and 2%, and new busness volume ow reserves 5% Hgh reserves 2% Ineres rae % Ineres rae 2% New busness % New busness 2% able Number of years unl shorfall under dfferen nal reserve suaons, dfferen neres raes and dfferen new busness volumes able shows ha even f he company does no have any nal reserves before he change n neres raes, aes 8 years unl reserves become negave. hus, he ncrease n reserves due o declnng neres raes a s enough o provde he guaranees on he lables for seven years. If nal reserves are 2%, no shorfall occurs whn he 3-year perod of our analyss. Snce afer 3 years, all he old conracs have maured and lower guaranees are gven for new busness, he company wh hgh reserves wll no go no a shorfall f neres raes reman low. he same observaon can be made f he level of neres raes durng he low neres rae perod s 2% nsead of %. If neres raes go down o %, aes 2 years unl he mare value of he asses falls below he nsurer s lables,.e. hree years earler as n he case of a % deflaonary neres rae. New busness seems o have very lle mpac on he number of years unl shorfall. 2

13 hs s no surprsng snce premums for new conracs are nvesed n asses ha mach he lables as long as here s no second change n mare raes. he resuls presened so far seem very encouragng a frs glance: If he economy eners a deflaonary sae, nsurers can mmedaely benef from ncreasng mare value of asses caused by fallng neres raes. hs creaes reserves ha enable hem o survve raher long n a deflaonary envronmen. However, ncreasng neres raes a he end of a deflaonary perod wll decrease he mare value of he asses. hs consues a maor rs n ha has no been aen no accoun n he analyses above. hus, we loo a a slgh varaon of he base scenaro: ll parameers are as dsplayed above, only afer a few years, mare raes go bac o he pre-deflaonary value. Fgure 3 shows he developmen of he asses and lables n uns of currency, lef axs as well as he developmen of he reserve quoa n percen, rgh axs for he base case scenaro under he assumpon ha neres raes go bac up o 5% afer 5 years lef pcure and years rgh pcure..2 3%.2 3%. 25% 2%. 25% 2% sses & ables % % 5% % Reserves sses & ables % % 5% % Reserves 2-5% -% 2-5% -% -5% sses ables Reserves -5% sses ables Reserves Fgure 3: Developmen of asses, lables and reserve quoa under he assumpon ha neres raes reurn o pre-deflaon level afer 5 years lef and years rgh for an nal reserve quoa of % In boh pcures, he developmen of asses and lables s he same as n he scenaro shown above for he frs four years. If neres raes go up agan a 5, he mare value of he asses drops and herefore reserves rapdly decrease. I can be seen from he lef pcure ha n he base case scenaro, a 5-year deflaonary envronmen can be survved wh posve reserves. However, reserves afer hs 5-year low neres perod are closed o. hs shows 3

14 ha f lables are calculaed on a boo value bass whle asses are subec o mare flucuaons, a scenaro of ncreasng neres raes can be very dangerous o he companes. hs s especally relevan f he conracs have guaraneed surrender values ha are close o he echncal reserves. I can be seen from he rgh pcure n Fgure 3 ha f neres rae reman a % for en years and hen go bac o he pre-deflaonary level, he nsurer ends up wh reserves of -5%,.e. a shorfall occurs. Obvously, he level of reserves afer a perod of low neres raes hghly depends on he duraon of hs perod. Fgure 4 shows he reserve quoa of he nsurance company afer a n-year perod of low neres raes as a funcon of n. Here, we assume ha afer n years, neres raes go bac o he pre-deflaonary level. reserve quoa afer a low neres rae perod 2% % reserve quoa % -% -2% -3% % -5% perod of low neres raes r5% r% Fgure 4 Reserve quoa of low neres raes r afer a perod of low neres as a funcon of he duraon of he perod In our base scenaro, he reserve quoa s a decreasng funcon of he duraon of he low neres rae perod. If he nal reserve quoa s %, a 6-year perod of low neres raes 4

15 can be survved whle for any low neres rae perod of 7 years or more, reserves become negave f neres raes sar o ncrease agan. Naurally, he problem ncreases, for lower nal reserves. For r 5%, all oher hngs equal, reserves are negave f neres raes ncrease afer a four year perod of deflaon. gan, we provde sensves for nal reserves r %, r 5%, and r 2%, a deflaonary neres rae of % and 2%, and a new busness volume of and wce as much as n he pas. able 2 shows he duraon of he longes deflaon perod ha can be survved wh posve reserves. ase case No reserves % ow reserves 5% Hgh reserves 2% Ineres rae % Ineres rae 2% New busness % New busness 2% able 2 Duraon of a deflaon perod ha can be survved under dfferen nal reserve suaons, dfferen neres raes and dfferen new busness volume s saed above, a 6-year perod of deflaon can be survved by an nsurance company wh % nal reserves whls only a 3-year perod can be survved f nal reserves equal 5%. able 2 also shows ha nal reserves are necessary o survve any perod of low neres raes. If he mare value of he asses a ncepon exacly mees he lables, any decrease n neres raes followed by an ncrease bac o he orgnal level leads o nvesmens a a low coupon rae whle hardly changes he nsurance company s lables. hs leads o negave reserves and hus o a shorfall. In he case of raher hgh nal reserves r 2%, any perod of deflaon of up o 4 years can be survved wh posve reserves. hs also holds for a company wh % nal reserves f he neres rae durng he deflaon perod equals 2% nsead of %. he same company can only survve a 4-year perod f neres raes even drop o %. gan, new busness volume seems o have only mnor mpac on he number of years a deflaonary envronmen can be survved. Ineresngly, a hgh ncrease n new busness 5

16 volume leads o a slgh reducon of he number of years for he base case company. More sensvy analyses wll be provded n he nex Secon. 3.2 Changng he erm of asses and lables he man reason why lfe nsurance companes would suffer very hard from a emporary deflaonary envronmen seems o be he sgnfcan msmach beween asse and lably erm. Fgure 5 dsplays anoher varaon of he base case, where he asse erm has been ncreased o 3 years and hus concdes wh he lably erm..6 8%.4 7% sses & ables % 5% 4% 3% 2% Reserves 2 % % sses ables Reserves Fgure 5: Developmen of asses, lables and reserve quoa for an ncreased asse erm. Snce n hs scenaro he asse erm and hus he asse duraon s longer, he ncrease of he reserve quoa a ouse s even bgger han before. he reserve margn s comforable over he whole perod of our analyss. However, alhough ncreasng he asse erm gves some mmunzaon agans he rs of deflaon, carres oher problems: If neres raes rse, aes a long me unl an nsurer wh a long asse erm can sgnfcanly rase he surplus creded o conracs. Clens would expec hgher surplus raes when neres raes are hgh. If nsurers have loced n lower raes for a long me, hs could resul n hgh lapse raes 6

17 n phases of hgh neres raes, as happened e.g. n he US n he 98es. hs s parcularly dangerous f he nsurance conracs have guaraneed mnmum surrender values, snce hgh surrender raes may force nsurers o sell her bonds a low mare values afer an ncrease of neres raes. Furhermore, may be dffcul and somemes mpossble o fnd a suffcen amoun and dversy of long erm bonds n he mare. We herefore now loo a a dfferen sraegy o reduce he rs resulng from a low-neres envronmen: reducon of he guaranee erm. Of course, s no desred o abolsh long-erm conracs, snce many parcpang polces are used for old-age provson. I would however be possble, o revew he guaraneed rae of neres n a lfe nsurance conrac on a regular bass, e.g. every years. In such revewable conracs, afer, 2, 3, years, he guaraneed rae of he conrac s adused o he rae ha s also appled o new conracs a ha me. hs rae s hen guaraneed for he nex years. Fgure 6 shows he resuls for an nsurer sellng such revewable guaranees. 7

18 .2 4%. 35% sses & ables % 25% 2% 5% % 5% Reserves % sses ables Reserves Fgure 6: Developmen of asses, lables and reserve quoa for a reduced guaranee erm revewable guaraneed raes. s n Fgure 5, he reserve margn s comforable over he whole perod consdered. However n hs scenaro, nsurers can ncrease surplus raher qucly f neres raes rse. herefore from a rs managemen pon of vew, offerng revewable guaraneed raes seems o be a preferable sraegy. We have seen so far, ha n he base case, a shorfall occurs afer 5 years whle no shorfall occurs f he asse erm s enlarged o 3 years or he guaranee erm s reduced o years,.e. revewable guaranees are sold. he same resul holds f boh, asse em and guaranee erm, are 5 years or 2 years. In he followng able 3, we provde more sensvy analyses wh respec o he asse and guaranee erms as well as for he nal reserve quoa r % no reserves, r 5% low reserves, r 2% hgh reserves, he deflaonary neres rae % and 2%, and new busness volume new busness % and new busness 2%. / g ase no ow Hgh Ineres Ineres New New 8

19 case reserves reserves reserves rae % rae 2% busness % busness 2% 5 / / / / / / / / / / able 3 Year of shorfall under dfferen nal reserve suaons, dfferen neres raes and dfferen new busness volumes for dfferen combnaons of asse and guaranee erm able 3 shows ha no shorfall occurs for companes nvesng n bonds wh a erm o maury equalng he guaranee erm of he lables. If he asse erm s slghly lower han he guaranee erm, e.g. for an asse erm of 5 years and a guaranee erm of years, companes wh no reserves wll suffer from a shorfall afer 5 years. For hgher nal reserve quoas, e.g. r % or r 2%, no shorfall occurs, no even f he deflaonary neres rae s %. If he asse erm s years and he guaranee erm s 2 years, no shorfall occurs for any of he parameer combnaons shown. If he asse erm s sgnfcanly lower han he guaranee erm such as n he base case or n he case where 5 year bonds are bough whle 3 year guaranees are sold, long perods of low neres raes canno no be susaned. shorfall occurs earler, f nal reserves or he deflaonary neres raes are lower. If nal reserves are hgh r 2% or he deflaonary 9

20 neres rae s 2%, only n he exreme case wh asse erm 5 years and guaranee erm 3 years, a shorfall occurs whn our consdered me horzon.. New busness volume has no nfluence on he year of shorfall for any combnaon of asse and guaranee erm shown. s menoned above, an ncrease of neres afer a low-neres phase wll have a negave mpac on he value of he asses and hus he reserves. herefore, we agan loo a a slgh varaon of he deflaon scenaro: ll parameers are as n he scenaro above, only afer a ceran number of years, mare raes go bac o 5%. able 4 shows he number of years ha can be survved n a low neres envronmen f neres raes go up agan a he end of he deflaon perod. g / ase No ow Hgh Ineres Ineres New New case reserves reserves reserves rae % rae 2% busness busness % 2% 5 / / / / / / / / / / able 4 Duraon of a deflaon perod ha can be survved under dfferen nal reserve suaons, dfferen neres raes and dfferen new busness volume for dfferen combnaons of asse and guaranee erm In he base case scenaro, where he nal reserve quoa s r %, he asse erm s years and he guaranee erm s 3 years, an ncrease n neres raes afer sx years of 2

21 deflaon sll leads o slghly posve reserves whle reserves become negave f neres raes ncrease afer seven years of deflaon. If for he same asse erm, revewable guaranees are sold, none of he deflaon perods modeled leads o a shorfall. For any asse erm, he number of years of low neres raes ha can be survved wh posve reserves can be ncreased by ncreasng he asse erm. However, a shorfall can only be avoded f revewable guaranees are sold,.e. f he guaranee erm s reduced. company whou any nal reserves, wll suffer from a shorfall, even f a perod of low neres raes of us one year occurs. hs holds for any combnaon of asse and guaranee erm shown. If he company has low nal reserves r 5%, shor perods of a low neres envronmen can be survved for every combnaon of asse and guaranee erm shown. If, e.g., a 5-year asse erm s combned wh long erm guaranees years and more on he lably sde, a leas a 2-year perod of deflaon can be endured. ny perod of low neres raes longer han 3 years would however resul n a shorfall as soon as neres raes rse agan. If he company nvess n 3-year bonds and sells 3-year conracual guaranees, 6 years of low neres raes can be survved. For a company wh hgh reserves r 2%, besdes he base case only he case where he asse erm s 5 years and he guaranee erm s 3 years leads o a shorfall afer a perod of low neres raes. ssumng a deflaonary neres rae of % nsead of %, has a smlar effec as a reducon of he nal reserves from % o 5%. Shor perods of deflaon can be survved whle f he guaranee erm s longer han he asse erm any long deflaon perod leads o a shorfall as soon as neres raes rse agan. If he deflaonary neres rae s 2%, agan only he combnaons of asse erm and guaranee erm wh a sgnfcan msmach, such as 5 / 3 or / 3, lead o a shorfall afer more han en years. In he scenaro where neres raes go down and up agan afer several years of 2

22 deflaon, he amoun of new busness does have a sgnfcan nfluence. If no new busness s assumed, he number of years ha can be survved s ncreased for any combnaon of asse and guaranee erm shown. In he case where boh, asse erm and guaranee erm are 3 years, any deflaon perod can be survved whle wh consan premum nflow a shorfall would occur afer several years of deflaon. n ncrease n new busness, e.g. a doublng of new busness premum nflows, slghly reduces he company s ably o endure perods of deflaon. hs s especally rue f 3-year guaranees are sold. Whle wh unchanged new busness 3 years can be survved n a low neres envronmen f he correspondng asse erm s 3, any deflaon perod of 9 years or more leads o a shorfall f he new busness volume s doubled. 4. Conclusons In he presen paper, we have presened a smple model n whch he mpac of a deflaonary economy on lfe nsurers offerng parcpang conracs can be analyzed. Deflaon s smply modeled by assumng ha some fla neres rae drops o a lower level and says here for a ceran perod of me. Snce he boo value of lables s calculaed by accrung pas premums wh he hsorc raes guaraneed rae of reurn plus surplus ha have been creded o he polces, hs boo value does no change when neres raes move. hus, he ranson o a deflaonary envronmen creaes valuaon reserves, snce he mare value of he nsurer s asses ncreases. Our analyses show ha hese reserves are suffcen o preven a shorfall for a sgnfcan amoun of me. However, when neres raes rse agan a he end of a deflaonary perod, he mare value of he nsurer s asses s decreased, whch may cause a shorfall. In parcular, we have seen ha a deflaon would have srong negave effecs on nsurers offerng parcpang conracs. hs s alarmng snce such conracs accoun for he larges poron of lfe nsurers lables n many counres. Ofen, such conracs are sold 22