Adverse selection in the annuity market when payoffs vary over the time of retirement


 Roderick Randall
 1 years ago
 Views:
Transcription
1 Adverse selecton n the annuty market when payoffs vary over the tme of retrement by JOANN K. BRUNNER AND SUSANNE PEC * July 004 Revsed Verson of Workng Paper 0030, Department of Economcs, Unversty of nz. Abstract Ths study deals wth a specfc mplcaton of adverse selecton on annuty prcng. Varyng the tmepath of the payoffs over the retrement perods affects annuty demand and welfare of ndvduals wth low and hgh lfe expectancy n dfferent ways. Therefore they can be separated by nsurance frms through approprate contract offers. We show that n ths framework a NashCournot equlbrum may not exst; f one exsts, t wll be a separatng equlbrum. On the other hand, even f a separatng equlbrum does not exst, a Wlson poolng equlbrum exsts. (JE: D8, D9, G) * Address: Department of Economcs, Unversty of nz, Altenberger Straße 69, A4040 nz, Austra. Phone: , 8593, FAX: 98. Emal:
2 Introducton Prvate lfeannuty markets are frequently recognzed as beng weak. That s, less lfeannutes are demanded than one could expect, gven the need to nsure aganst uncertanty about the duraton of lfe, n order to smooth consumpton approprately over one's lfetme. Emprcal evdence for ths fact, whch s sometmes called the "annuty puzzle", has been establshed n varous studes for the US (see, e.g., MOORE AND MITCE [000], FRIEDMAN AND WARSAWSKY [990]), but also for the U.K., Canada and other countres (for an overvew see BROWN [00]). To the extent that the low demand s explaned by a bequest motve or by the exstence of a publc penson system, the weakness s not attrbuted to an ntrnsc problem of ths market. owever, there s a further reason put forward n the lterature, namely asymmetrc nformaton whch leads to adverse selecton: The fact that ndvduals have more nformaton about ther lfe expectancy than annuty companes leads to an overrepresentaton of persons wth a hgh survval probablty among the buyers of annuty contracts, whch n turn drves down the rate of return on annutes below the rate correspondng to the average probablty of survval. As a consequence of ths phenomenon, a loss of welfare arses for persons who cannot buy an approprate annuty contract. Ths shortcomng of the annuty market s supposed to become ncreasngly mportant, because n many countres the exstng publc penson system, organzed Emprcal evdence suggests that none of these three reasons alone, but only the nteracton of adverse selecton, publc penson system and bequest motves can explan the weakness of the market. See, e.g., FRIEDMAN AND WARSAWSKY [988, 990], WAISER [000], MITCE ET A. [999].
3 accordng to the payasyougo method, s expected to allow only a reduced replacementrato n the future, hence ncreased prvate nsurance wll be requred. In the present paper we focus on the fact that annuty contracts provde perodc payouts for the duraton of the annutants' lfe (or at least for a fxed number of years). We pont out a further consequence of the asymmetrc nformaton problem, n addton to the adverseselecton problem descrbed so far: The tme structure of the payoffs matters. Indvduals wth low lfe expectancy wll put less weght on the payment they may not receve n the last perod of lfe than ndvduals wth hgh lfe expectancy do. Ths fact can be used by frms to offer annuty contracts whch are favourable for lowrsk ndvduals but not for hghrsk ndvduals. Indeed, n two recent emprcal papers, FINKESTEIN AND POTERBA [00, 004] have found evdence for such selecton effects n the U.K. annutes market. They analyzed three types of annuty contracts, whch dffer n the tmepath of payoffs: constant nomnal payoffs, annually escalatng nomnal payoffs and nflatonndexed payoffs. They showed that for the latter two contracts the expected present value of the payoffs, based on the average populaton mortalty, s sgnfcantly lower than that for fxed nomnal annutes. Ths result suggests that those two contracts, whch provde the hgher payoffs n later years, are selected by ndvduals wth a hgh lfeexpectancy: Only these ndvduals have an ncentve to buy such contracts, because for them the expected present value of the payoffs, based on ther low mortalty rates, s hgher and may exceed that of annutes wth decreasng real (.e. fxed nomnal) payoffs; the latter
4 are favourable for ndvduals wth lower lfeexpectancy. In fact, estmatng a hazard model regardng the annutants' lfespans, FINKESTEIN AND POTERBA [004] found clear evdence for such an annutant selfselecton wth respect to the tme profle of payoffs. Moreover, the selecton effects turned out to be qute large. In the present contrbuton we provde a theoretcal analyss of the functonng of annuty markets, when selecton through the tmng of payoffs takes place. In partcular, we nvestgate the reacton of nsurance demand and the consequences for the exstence of equlbra, f nsurers offer contracts whch vary wth respect to the tmepath of the payoffs. In the model usually employed for the analyss of annuty markets (see PAUY [974], ABE [986] and WAISER [000]), there s one perod of retrement, and there are two groups of ndvduals wth dfferng lfe expectancy. Competton takes place va prces (.e. va the rate of return, that s the penson payment per unt of annuty), whch are fxed by the frms. Indvduals can buy as many annutes as they want. As s wellknown, n ths framework only a poolng equlbrum s possble, where all ndvduals receve the same rate of return. We extend ths model by ntroducng two perods of retrement, to whch the ndvduals may or may not survve, and by assumng that the payoffs need not be the same n both The lower expected present dscounted value of the real annuty, based on average mortalty, may partly also arse, because a premum for the nsurance aganst nflaton has to be pad. The market for real annutes s analyzed n BROWN, MITCE AND POTERBA [00], who study the role of governmentssued nflaton ndexed bonds and other securtes as nstruments, whch nsurance companes use to hedge prce level rsks (prmarly n the UK and US). owever, the authors do not consder selecton effects. 3
5 perods. Ths mples that contracts are characterzed by two prces, set by the frms. The mportant aspect n ths extended model s that  n accordance wth the observaton mentoned above  annuty demand as well as welfare of the ndvduals are senstve wth respect to the tme structure of the payoffs, and the possblty arses for frms to separate buyers accordng to ther survval probabltes. Ths addtonal separaton effect, whch was up to now neglected n the theoretcal lterature, may represent a further explanaton for the fact that annuty markets are not well developed. Indeed, t turns out that n such a market no NashCournot equlbrum may exst. If one exsts, t wll be a separatng equlbrum. The NashCournot equlbrum n nsurance markets was studed by ROTSCID AND STIGITZ [976]. In ther framework frms offer a number of dfferent contracts whch specfy both a prce and a quantty. Indvduals who prefer a hgher quantty are wllng to pay a hgher prce for t. A prerequste for the exstence of prce and quantty competton s that ndvduals can buy at most one contract, whch may be a reasonable assumpton for some nsurance markets, e.g. nsurance aganst accdents, but seems dffcult to apply to the annuty market. 3 Consequently, n our model ndvduals are free to buy as many annutes as they want. Separaton becomes possble because frms can fx two prces nstead of a prce and a quantty. As a potental answer to the queston of what happens n an nsurance market, f no NashCournotequlbrum exsts, WISON [977] ntroduced a dfferent equlbrum 3 ECKSTEIN, EICENBAUM AND PEED [985] make ndeed the assumpton of a prce and quantty competton for the annuty market wth one perod of retrement only. In ths framework they derve the same results as ROTSCID AND STIGITZ [976]. 4
6 concept, whch s based on specfc belefs of frms concernng the reacton of other frms to new contract offers. We show that a Wlson equlbrum always exsts n our model. Other studes whch qut the assumpton of a sngle perod of retrement are by TOWNEY AND BOADWAY [988] and FEDSTEIN [990]. Feldsten consders a publc penson system, organzed accordng to the payasyougo method, and dscusses the tme structure of the benefts. e assumes two perods of retrement, but only survval to the second s uncertan. In ths framework current populaton prefers to receve benefts ether n the frst or n the second perod of retrement, dependng on whether the return on socal securty s lower or hgher than the expected return on prvate savng. owever, steadystate welfare s maxmzed by payng benefts only n the frst retrement perod, snce ths ncreases savngs and therefore unntended bequests. The paper by TOWNEY AND BOADWAY [988] deals wth the market for prvate annutes and s, thus, more related to the present contrbuton. The authors model the lfespan from retrement to death n contnuous tme and consder termnsured annuty contracts,.e. contracts whch guarantee a stream of payoffs for a lmted tme, ether untl the nsured ndvdual des or untl the term of the annuty expres. In ther analyss of equlbra, Townley and Boadway take the stream of payoffs as constant over the whole duraton; hence the contracts are characterzed by two parameters: the term (duraton) and the payoff (per unt of money nvested). In contrast to our model, where frms can separate costumers through a varaton of the payment over tme, Townley and Boadway study separaton effects wth respect to the term of the annuty: 5
7 Indvduals wth longer expected lfespan estmate a contract wth a longer duraton hgher than ndvduals wth shorter expected lfespan. In the framework of ther model, wth asymmetrc nformaton concernng lfeexpectancy, no equlbrum may exst, f t exsts, t s ether a poolng equlbrum or a separatng equlbrum. In TOWNEY AND BOADWAY [988] ndvduals can make provson for the tme after expry of the annuty through prvate savngs only. In a related study (BRUNNER AND PEC [00]), we have consdered a model whch also takes the exstence of tmelmted annuty contracts nto account, but allows ndvduals to provde for the tme after expry of the annuty by purchasng another annuty. That s, ndvduals need not make ther decson concernng oldage provson for the whole tme of retrement at once, but can do so sequentally. In ths framework t turns out that only a stuaton, where all ndvduals decde sequentally, represents an equlbrum, whch s to the dsadvantage of the shortlvng ndvduals. The rest of our paper proceeds as follows: In Secton we ntroduce the basc model of consumpton behavour under asymmetrc nformaton wth two perods of retrement, where ndvduals provde for oldage by buyng annutes. We analyze the effect of a varaton n the tme structure of the payoffs on annuty demand and on welfare of an ndvdual under uncertan lfetme. In Secton 3 we turn to the nvestgaton of equlbra. Frst, we derve all results concernng the exstence and characterzaton of the equlbra n the basc model. Then we extend the model and allow ndvduals to save n rskless bonds n addton to annutes. Secton 4 contans concludng remarks. 6
8 Annuty demand n a model wth two perods of retrement. The basc model wth asymmetrc nformaton Consder an economy wth N ndvduals who lve for a maxmum of three perods t = 0,,. In the workng perod t = 0 ndvdual earns a fxed labour ncome w, spends an amount A on annutes and consumes an amount for perod 0: c o. Ths gves the budget equaton () c0 = w A. The ndvduals retre at the end of perod 0. Through the purchase of annutes they make provson for future consumpton n the two perods of retrement t =,. An annuty contract s characterzed by the payoffs (q,q ): An annuty A = pays q t unts of money to the ndvdual n the retrement perods t =,, f she survves. ence, for ndvdual the budget equatons for the two retrement perods are () c = qa, (3) c = qa. The budget equatons () (3) are bult on the assumpton that the ndvduals do not save and buy other assets, n addton to annutes. At ths stage of the analyss we exclude holdng other assets, n order to concentrate on the desgn of the annuty 7
9 contracts. owever, the possblty of buyng bonds n the workng perod and n the frst perod of retrement s explctly consdered n Secton 3.4, and t wll be shown that ths does not change the man results derved n the basc model. Further, for the sake of smplcty, the assumpton s made that no publc penson system exsts. 4 Survval to perod t = s uncertan and occurs wth probablty π, 0< π <. In the same way, gven that an ndvdual s alve n perod, survval to perod occurs wth probablty π, 0< π <. Each ndvdual decdes on her consumpton plan over the uncertan duraton of her retrement by maxmzng expected utlty from a tmeseparable utlty functon U, (4) U ( π ( ) ( ) u( c 0) π ( π ) u( c 0) αu( c ) π π u( c 0) αu( c ) α u( c ) ) = , subject to condtons (), () and (3). In (4) uc ( t ) descrbes utlty of consumpton per perod, where we assume that u ( c t ) > 0, u ( c t ) < 0 and lm u ( c ) = c 0. α denotes the oneperod dscount factor of utlty, wth 0< α. Notce that the specfcaton n (4) means that the ndvduals dscount future consumpton for two reasons, rsk averson and tme preference. (4) can be reduced to (4 ) U = u( c ) + παu( c ) + ππα u( c ). 0 4 In Secton 4 we dscuss the consequences for our results, f a publc penson system s ntroduced n the model. 8
10 Insertng (), () and (3) nto (4 ) and dfferentatng wth respect to A yelds the frst order condton of ths maxmzaton problem as (5) u'( c ) + παqu'( c ) + ππα q u'( c ) = 0. 0 From () and (3) we know that c >_ < annuty demand determned by (5), for gven (q,q ). c corresponds to q >_ < q. et A (q,q ) be the From now on we assume that the otherwse dentcal ndvduals are dvded nto two groups =,, characterzed by dfferent rsks of a long lfe,.e. by dfferent probabltes of survval π t > π for t =,. et γ and ( γ) denote the share of the t hghrsk and lowrsk ndvduals, resp., wth 0 < γ <. The probabltes π t and the share γ are publc nformaton, known by the annuty companes. But t s the prvate nformaton for each ndvdual to know her type,.e. her probablty of survval. As a consequence, there s an adverseselecton problem n the annuty market. Ths s llustrated by the followng lemma, whch shows that hghrsk ndvduals buy more annutes than lowrsk ndvduals, gven any contract (q,q ). emma : For any contract (q,q ) an ndvdual wth hgh survval probabltes wll demand a larger quantty of annutes than an ndvdual wth low survval probabltes,.e. A (q,q ) > A (q,q ). 5 5 The proofs of all emmas and Propostons are relegated to the Appendx A.. 9
11 Ths result mples that f there s only a sngle contract offered n the annuty market, wth some gven payoffs (q,q ) per perod, then the share of annuty purchases of hghrsk ndvduals n total annuty demand s larger than γ, whch s the share of hghrsk ndvduals n the economy.. Separatng and poolng contracts An annuty contract ( q ) s sad to be ndvdually far for an ndvdual of type =,, f expected payoffs equal the prce,.e. f t fulflls q q = 0, (6) π ππ gven the assumpton of a zero nterest rate, whch s chosen for the sake of smplcty; a postve nterest rate would not affect the qualtatve results. Obvously, (6) mples that the annuty companes make zero expected profts, gven that solely ndvduals of type buy ther ndvdually far contracts. owever, as there exst many contracts ( q ) whch fulfll (6), t s nterestng to nvestgate whch of the ndvdually far annuty contracts s the most preferred one by an ndvdual of type. The next emma provdes a characterzaton. emma : Among all ndvdually far contracts ( q ) for an ndvdual of type, the most preferred s characterzed by 0
12 (7) u'( c) = αu'( c), whch mples that q > q, f α < and q = q, f α =. That s, n case of a zero rate of tme preference (α = ), an equal dstrbuton of the payoffs ( q/ q = ) over the two perods of retrement s optmal, for both types =,, gven ther respectve ndvdually far contract. For α <, however, the optmum rato q / q ( > ), determned by (7), wll n general be dfferent for the two types, because n ths case the optmum rato depends on the respectve annuty demand A and A, whch wll be dfferent. (But one checks easly that the most preferred rato q / q s ndependent of A and thus dentcal for both types, n case of a perperod utlty functon u whch exhbts a constant relatve rsk averson, rrespectve of the rate of tme preference.) Note, moreover, that wth the most preferred ndvdually far contract the relaton (7), whch characterzes the optmum dvson of consumpton between the two perods of retrement, also apples for the allocaton decson between consumpton n the workng perod and the frst perod of retrement, namely (8) u'( c0) = α u'( c). Ths can be seen when elmnatng u'( c ) n (5) by use of (7), whch yelds u'( c ) = αu'( c )( π q + π π q ). Substtutng (6) nto ths condton, t reduces to (8). It 0
13 follows that an ndvdual, who does not dscount future consumpton due to tme preference (α = ), consumes the same amount n all three perods of lfe,.e. c0 = c = c. Otherwse (α < ), she chooses 0 > > c c c. The assumpton π t < π, t =,, mples that ndvdual farness (condton (6)) for t each group can be fulflled only wth two separate contracts. If each s bought by the respectve rsk group, both produce zero profts. On the other hand, a contract (q,q ) whch s bought by both groups, s called a poolng contract. In order that a poolng contract produces zero profts, t must fulfll the condton (for shortness we use A nstead of A (q,q )) (9) γ A qπ qπ π γa qπ qπ π ( ) ( ) + ( ) = 0. Zeroproft contracts (whether separate or poolng) are of specal nterest, because under the assumpton of perfect competton n the annuty market, only such contracts can persst. (9) can also be wrtten as (9') ρ q q q( π ρ q q π ) q( π π ρ q q π π ) + (, ) + (, ) + (, ) = 0, where ρ s defned by (, ) ( ρ q q γa ( q) ) (( γ) A ( q) ), that s the rato of annuty demand of both groups. Note that ρ depends on (q,q ), but for shortness, we usually do not ndcate ths dependency. Of course, our assumptons on the survval probabltes mply that for the lowrsk ndvduals expected returns from a zeroproft
14 poolng contract are lower than requred for ndvdual farness ( qπ q ππ > 0), whle for the hghrsk ndvduals they are hgher ( qπ q π π < 0)..3 Varyng the payoffrato of a poolng contract In the emmas 3 and 4 below, we consder a zeroproft poolng contract and nvestgate the effect of a margnal change n the payoffs on ndrect utlty and on annuty demand of an ndvdual of type =,. Clearly, f q (or q ) s ncreased alone, then both groups beneft and buy more annutes. owever, such an ncrease would produce a loss for the annuty companes. ence, the nterestng case s when q s ncreased at the expense of q (or vce versa), such that the zeroproft condton (9) remans fulflled. We characterze the frstround effect on ndrect utlty and on annuty demand of a margnal ncrease of q, when the assocated change of q, such that (9') remans fulflled, s calculated under the assumpton of a constant rato ρ of annuty demand of the two groups. Moreover we dscuss the condtons necessary for the secondround effects (.e. the nfluence of the payoffs on ρ) not to outwegh the frstround effects. In emma 3() we consder a contract wth a rato of the payoffs, whch s optmal for an ndvdual of type accordng to condton (7) for an ndvdually far contract. We show that ths rato s no longer optmal n case of a zeroproft poolng contract: The lowrsk ndvdual benefts, f q s ncreased. An analogous result s found for a hghrsk ndvdual (emma 3()): She benefts f q s reduced. 3
15 emma 3: Consder two poolng contracts ( q ), ( q ) where each, together wth annuty demand of the two groups, fulflls the zeroproft condton (9'). () If the payoff rato q q satsfes the condton (7) for an optmal ndvdually far contract for type, a margnal ncrease of q (and thus a margnal decrease of q ) where (9') for fxed ρ remans fulflled, makes an ndvdual of type better off. () If the payoff rato q q satsfes the condton (7) for an optmal ndvdually far contract for type, a margnal ncrease of q (and thus a margnal decrease of q ) where (9') for fxed ρ remans fulflled, makes an ndvdual of type worse off. Ths frstround effect descrbed n emma 3 s of partcular nterest, because t reveals the mechansm whch s responsble for the negatve result concernng the exstence of a poolng contract n equlbrum (see Secton 3.). For an llustraton, consder the case α =, whch means as we know from emma  that both ndvduals prefer an equal dstrbuton of the payoffs over the two perods of retrement, gven ther respectve ndvdually far contract. owever, n case of a zeroproft poolng contract, such an equal dstrbuton of the payoffs s no longer optmal: Indvduals wth low lfeexpectancy are better off, f q, the payoff n the frst perod of retrement, s ncreased at the expense of q, whle the opposte holds for ndvduals wth hgh lfeexpectancy. Thus, the annuty companes have an ncentve to desgn separate contracts for the two groups. The ntutve reason why a lowrsk ndvdual fnds a shft of consumpton from perod to perod attractve can easly be explaned for α = (and thus startng from q = q ) 4
16 as follows: If q s ncreased by one s decreased by dq / dq, whch s determned by the requrement that the zeroproft condton (9') be preserved. Snce wth a poolng contract the assocated decrease of q goes more to the expense of the hghrsk ndvduals, t turns out from (9') that dq / dq < / π (for constant ρ). As a result, for type ndvduals the expected loss n perod, π dq / dq, s lower than one and they beneft from a shft towards ncreasng q. (Note that due to q = q, margnal utlty s equal n both perods.) By the same reasonng and observng that, on the other hand, dq / dq > / π holds, type ndvduals, who expect to lve longer, are better off by a shft towards reducng q. Smlar consderatons apply for the case of α <. Obvously also the secondround effect, that s the effect ρ q of the change of the t payoffs on (the rato of) annuty demand of the two groups, matters, as can be seen from (A6) n the Appendx. The above consderaton certanly mantans, f both ρ q, t t =,, are suffcently small, otherwse an approprate relaton between them must hold. (For nstance, a suffcent, but not necessary condton s π ρ q ρ q π ρ q, whch ensures that the secondround effect goes nto the same drecton as the frstround effect.) Remark: Inspecton of the proof of the foregong emma shows that an ncrease of q at the expense of q mproves welfare of lowrsk ndvduals also f ntally the rato q / q s lower than that determned by the optmalty condton (7) for ndvdually far contracts. It follows that ther most preferred poolng contract exhbts a hgher rato (that s, n case of α = : q > q ). By smlar reasonng one fnds for the hghrsk 5
17 ndvduals that ther most preferred poolng contract exhbts a lower payoffrato than that determned by (7) (whch means q < q n case of α = ). A characterzaton of the effect of a margnal change of q (and q ) on annuty demand s gven n the followng emma, agan startng from a zeroproft poolng contract wth a payoffrato whch satsfes (7) for the respectve optmal ndvdually far contract. We restrct attenton to the case where the dscount factor α equals one or the perperod utlty functon exhbts a constant coeffcent of relatve rsk averson n the sense of ArrowPratt, defned as R cu ( c ) u ( c ). Then, as mentoned above, the optmal t t t payoffrato, gven an ndvdually far contract, s the same for both rsktypes (and equal to, f α = ). emma 4: Assume that α = or that R s constant. Consder a poolng contract ( q ) whch, together wth annuty demand of the two groups, fulflls the zeroproft condton (9') and whose payoff rato q q s determned by the condton (7) for an optmal ndvdually far contract for both types =,. Then the effect of a margnal ncrease of q on the annuty demand of each ndvdual =,, where (9') for fxed ρ remans fulflled, depends on the relatve rsk averson n the followng way: Iff R < > _, then da dq < _ da > 0 and dq <> _ 0. Ths result follows from the fact that, per defnton, the effect of an ncrease of q on q u'(q A ),.e. on the margnal utlty of A n perod, can be wrtten as ( R), and the 6
18 same apples to perod. ence, whether an ncrease of q at the expense of q ncreases or decreases expected margnal utlty of A (n both retrement perods together) depends on ( + π dq / dq) ( R), where, as argued above, π dq / dq descrbes the expected loss n perod, f q s ncreased and the zeroproft condton s preserved. (Note that, by assumpton, ether q = q whch means that R s equal n both perods, or R s constant at all.) We know from above that + π dq / dq s postve for = and negatve for =, gven a fxed rato ρ of annuty demand of both groups. Thus we fnd that, n case of R <, for type ndvduals the expected margnal utlty of A n the two perods of retrement ncreases, f q s ncreased at the expense of q. On the other hand, the decson on annuty demand s made by balancng the (negatve) margnal utlty of A n the workng perod aganst the expected (postve) margnal utlty n retrement. It s ntutvely clear that demand ncreases, f the latter ncreases (the former s unaffected by a change of q and q ). Moreover, n case of R >, the effect obvously goes towards a decrease of A, and smlar consderaton hold for type ndvduals. 3 Equlbra Introducng two nstead of one retrement perod n the model allows annuty companes to offer contracts whch dffer n the dvson of the payoffs over tme. In ths secton t s shown that ths mples the possblty of a separatng equlbrum, whch means that annuty companes separate ndvduals accordng to ther survval probabltes. To obtan ths result we make use of the wellknown concept of a NashCournot equlbrum, whch was studed by ROTSCID AND STIGITZ [976] n the context of nsurance markets. Our result s n contrast to studes consderng one perod of 7
19 retrement only, whch fnd that under prce competton there wll be a poolng equlbrum. In Subsecton 3.3 we extend the analyss by ntroducng the concept of the WISON [977] equlbrum, where t s assumed that frms antcpate reactons of the other frms to new contract offers, vz. that they wll wthdraw unproftable exstng contracts. Frst we derve all results concernng the exstence and characterzaton of equlbra n the model consdered n Secton, where ndvduals provde for retrement by buyng annutes only, then we ntroduce, n Secton 3.4, the possblty of savng n rskless bonds. 3. The nonexstence of a poolng equlbrum We call a contract (q,q ) a poolng equlbrum, f together wth A (q,q ), =,, the zeroproft condton (9) s fulflled and f no other contract exsts, whch s preferred to (q,q ) by at least one group {,} and whch allows a nonnegatve proft. Our man result s that n general no poolng equlbrum exsts. As a preparaton we show: emma 5: et (q,q ) be a poolng contract whch together wth A (q,q ), =,, fulflls the zeroproft condton (9). Any contract ( q + δ q + δ q ), whch s close enough to (q,q ) and whch s chosen only by group (.e. A = 0) allows a nonnegatve proft. Ths result follows from the observaton n Secton. that a zeroproft poolng contract offers less expected returns to lowrsk ndvduals than requred for ndvdual 8
20 farness. Ths n turn mples postve profts, f only the lowrsk ndvduals buy ths contract or one close to t. We now ntroduce a further assumpton on U, n addton to strct concavty of the nstantaneous utlty functon u. et ndrect utlty U (q,q ) for any contract (q,q ) be defned n the usual way as utlty attaned wth annuty demand A (q,q ). We assume that ndfference curves n the (q,q )space satsfy the snglecrossng condton U q U q (0) < U q U q for all (q,q ). Ths condton, whch s famlar from other models wth asymmetrc nformaton, requres that the slope of an ndfference curve of a lowrsk ndvdual s always steeper than that of a hghrsk ndvdual. ence, ndfference curves of the two groups can cross only once. Usng the Envelope Theorem, (0) reduces to u'(q A )/(απ u'(q A )) > u'(q A )/(απ u'(q A )), and one observes that, as π < π, the condton s certanly fulflled for any utlty functon whch exhbts a constant coeffcent of relatve rsk averson, hence, n partcular, for logarthmc utlty. Snglecrossng s needed for a concse formulaton of the followng Proposton only; n the remark afterwards t wll be argued that n general the Proposton holds wthout ths assumpton. Proposton : No poolng equlbrum exsts, gven the snglecrossng condton (0). 9
21 Ths result can be llustrated n a dagram where the payoffs q and q are drawn on the axs (see Fgure ). The dashed lne ZP denotes the zeroproft condton (9) for a poolng contract, wth slope dq dq, as determned by (A6) n the Appendx. Consder any contract (q,q ) fulfllng (9),.e. any pont on ZP. Due to the snglecrossng condton the slope of the ndfference curve U correspondng to the lowrsk group s steeper than that of U, the ndfference curve of the hghrsk group. Therefore one can fnd a contract (q + δ q, q + δ q), close to (q,q ), whch s preferred by the lowrsk ndvduals only  and s, therefore, proftable for the annuty companes, as emma 5 tells us. ence (q,q ) does not represent a poolng equlbrum. Fgure The nonexstence of a poolng equlbrum q ( q ) U U (q + q + q ) ZP q Remark: By means of Fgure the sgnfcance of the snglecrossng condton can be dscussed. One observes mmedately that the result of Proposton certanly holds as 0
22 long as the slopes of U and U dffer n (q,q )space, ndependently of whch one s steeper. Even f U and U have the same slope, the result holds, gven that the slope of ZP s dfferent. In ths case one can fnd another poolng contract ( q + δ q + δ q ) close to (q,q ) whch s preferred by both groups and produces nonnegatve profts. Only f there exsts a pont on ZP n whch the slopes of ZP, U and U are dentcal, ths represents a poolng equlbrum. Clearly, ths case can occur for very specfc parameter constellatons only, a small perturbaton of γ or of π t would destroy the equlbrum. From these consderatons we can conclude that n general Proposton holds wthout assumng the snglecrossng condton. 3. The possblty of a separatng equlbrum We call a set of two contracts ( q ), ( q ) a separatng equlbrum, f each fulflls the respectve zeroproft condton (6), f group does not prefer ( q ) to ( q, q ) and vce versa,.e. f U ( q ) U ( q ), () () U q q U q q (, ) (, ), and f no other contract exsts, whch s preferred to ( q ) by at least one group {,} and whch allows a nonnegatve proft.
Adverse selection in the annuity market with sequential and simultaneous insurance demand. Johann K. Brunner and Susanne Pech *) January 2005
Adverse selecton n the annuty market wth sequental and smultaneous nsurance demand Johann K. Brunner and Susanne Pech *) January 005 Revsed Verson of Workng Paper 004, Department of Economcs, Unversty
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More information17 Capital tax competition
17 Captal tax competton 17.1 Introducton Governments would lke to tax a varety of transactons that ncreasngly appear to be moble across jursdctonal boundares. Ths creates one obvous problem: tax base flght.
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120
Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, PerreAndre
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER Revsed May 2003 ABSTRACT In ths paper, we nvestgate
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationThe Stock Market Game and the KellyNash Equilibrium
The Stock Market Game and the KellyNash Equlbrum Carlos AlósFerrer, Ana B. Ana Department of Economcs, Unversty of Venna. Hohenstaufengasse 9, A1010 Venna, Austra. July 2003 Abstract We formulate the
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationTrafficlight extended with stress test for insurance and expense risks in life insurance
PROMEMORIA Datum 0 July 007 FI Dnr 07117130 Fnansnspetonen Författare Bengt von Bahr, Göran Ronge Traffclght extended wth stress test for nsurance and expense rss n lfe nsurance Summary Ths memorandum
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationQuasiHyperbolic Discounting and Social Security Systems
QuasHyperbolc Dscountng and Socal Securty Systems Mordecha E. Schwarz a and Eytan Sheshnsk b May 22, 26 Abstract Hyperbolc countng has become a common assumpton for modelng bounded ratonalty wth respect
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationOn Competitive Nonlinear Pricing
On Compettve Nonlnear Prcng Andrea Attar Thomas Marott Franços Salané February 27, 2013 Abstract A buyer of a dvsble good faces several dentcal sellers. The buyer s preferences are her prvate nformaton,
More informationCautiousness and Measuring An Investor s Tendency to Buy Options
Cautousness and Measurng An Investor s Tendency to Buy Optons James Huang October 18, 2005 Abstract As s well known, ArrowPratt measure of rsk averson explans a ratonal nvestor s behavor n stock markets
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1119
Kel Insttute for World Economcs Duesternbrooker Weg 120 24105 Kel (Germany) Kel Workng Paper No. 1119 Under What Condtons Do Venture Captal Markets Emerge? by Andrea Schertler July 2002 The responsblty
More informationImplied (risk neutral) probabilities, betting odds and prediction markets
Impled (rsk neutral) probabltes, bettng odds and predcton markets Fabrzo Caccafesta (Unversty of Rome "Tor Vergata") ABSTRACT  We show that the well known euvalence between the "fundamental theorem of
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationHealth Insurance and Household Savings
Health Insurance and Household Savngs Mnchung Hsu Job Market Paper Last Updated: November, 2006 Abstract Recent emprcal studes have documented a puzzlng pattern of household savngs n the U.S.: households
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationHow to Sell Innovative Ideas: Property right, Information. Revelation and Contract Design
Presenter Ye Zhang uke Economcs A yz137@duke.edu How to Sell Innovatve Ideas: Property rght, Informaton evelaton and Contract esgn ay 31 2011 Based on James Anton & ennes Yao s two papers 1. Expropraton
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationWhen Talk is Free : The Effect of Tariff Structure on Usage under Two and ThreePart Tariffs
0 When Talk s Free : The Effect of Tarff Structure on Usage under Two and ThreePart Tarffs Eva Ascarza Ana Lambrecht Naufel Vlcassm July 2012 (Forthcomng at Journal of Marketng Research) Eva Ascarza
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationRESEARCH DISCUSSION PAPER
Reserve Bank of Australa RESEARCH DISCUSSION PAPER Competton Between Payment Systems George Gardner and Andrew Stone RDP 200902 COMPETITION BETWEEN PAYMENT SYSTEMS George Gardner and Andrew Stone Research
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationSubstitution Effects in Supply Chains with Asymmetric Information Distribution and Upstream Competition
Substtuton Effects n Supply Chans wth Asymmetrc Informaton Dstrbuton and Upstream Competton Jochen Schlapp, Mortz Fleschmann Department of Busness, Unversty of Mannhem, 68163 Mannhem, Germany, jschlapp@bwl.unmannhem.de,
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationEvidence of Adverse Selection in Automobile Insurance Markets
Evdence of Adverse Selecton n Automoble Insurance Markets by Georges Donne, Chrstan Gouréroux and Charles Vanasse Workng Paper 9809 Aprl 1998 ISSN : 106330 Ths research was fnanced by CREST and FFSA,
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationInequity Aversion and Individual Behavior in Public Good Games: An Experimental Investigation
Dscusson Paper No. 07034 Inequty Averson and Indvdual Behavor n Publc Good Games: An Expermental Investgaton Astrd Dannenberg, Thomas Rechmann, Bodo Sturm, and Carsten Vogt Dscusson Paper No. 07034 Inequty
More informationThe literature on manyserver approximations provides significant simplifications toward the optimal capacity
Publshed onlne ahead of prnt November 13, 2009 Copyrght: INFORMS holds copyrght to ths Artcles n Advance verson, whch s made avalable to nsttutonal subscrbers. The fle may not be posted on any other webste,
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More informationThe CoxRossRubinstein Option Pricing Model
Fnance 400 A. Penat  G. Pennacc Te CoxRossRubnsten Opton Prcng Model Te prevous notes sowed tat te absence o arbtrage restrcts te prce o an opton n terms o ts underlyng asset. However, te noarbtrage
More informationNo 144. Bundling and Joint Marketing by Rival Firms. Thomas D. Jeitschko, Yeonjei Jung, Jaesoo Kim
No 144 Bundlng and Jont Marketng by Rval Frms Thomas D. Jetschko, Yeonje Jung, Jaesoo Km May 014 IMPRINT DICE DISCUSSION PAPER Publshed by düsseldorf unversty press (dup) on behalf of Henrch Hene Unverstät
More informationChapter 11 Practice Problems Answers
Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationPrice Impact Asymmetry of Block Trades: An Institutional Trading Explanation
Prce Impact Asymmetry of Block Trades: An Insttutonal Tradng Explanaton Gdeon Saar 1 Frst Draft: Aprl 1997 Current verson: October 1999 1 Stern School of Busness, New York Unversty, 44 West Fourth Street,
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationChapter 15: Debt and Taxes
Chapter 15: Debt and Taxes1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt
More informationCombinatorial Agency of Threshold Functions
Combnatoral Agency of Threshold Functons Shal Jan Computer Scence Department Yale Unversty New Haven, CT 06520 shal.jan@yale.edu Davd C. Parkes School of Engneerng and Appled Scences Harvard Unversty Cambrdge,
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationReturn decomposing of absoluteperformance multiasset class portfolios. Working Paper  Nummer: 16
Return decomposng of absoluteperformance multasset class portfolos Workng Paper  Nummer: 16 2007 by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume
More informationWhat should (public) health insurance cover?
Journal of Health Economcs 26 (27) 251 262 What should (publc) health nsurance cover? Mchael Hoel Department of Economcs, Unversty of Oslo, P.O. Box 195 Blndern, N317 Oslo, Norway Receved 29 Aprl 25;
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationChapter 15 Debt and Taxes
hapter 15 Debt and Taxes 151. Pelamed Pharmaceutcals has EBIT of $325 mllon n 2006. In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net
More informationAbteilung für Stadt und Regionalentwicklung Department of Urban and Regional Development
Abtelung für Stadt und Regonalentwcklung Department of Urban and Regonal Development Gunther Maer, Alexander Kaufmann The Development of Computer Networks Frst Results from a Mcroeconomc Model SREDscusson
More information! # %& ( ) +,../ 0 1 2 3 4 0 4 # 5##&.6 7% 8 # 0 4 2 #...
! # %& ( ) +,../ 0 1 2 3 4 0 4 # 5##&.6 7% 8 # 0 4 2 #... 9 Sheffeld Economc Research Paper Seres SERP Number: 2011010 ISSN 17498368 Sarah Brown, Aurora OrtzNúñez and Karl Taylor Educatonal loans and
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationA Probabilistic Theory of Coherence
A Probablstc Theory of Coherence BRANDEN FITELSON. The Coherence Measure C Let E be a set of n propostons E,..., E n. We seek a probablstc measure C(E) of the degree of coherence of E. Intutvely, we want
More informationOPTIMAL INVESTMENT POLICIES FOR THE HORSE RACE MODEL. Thomas S. Ferguson and C. Zachary Gilstein UCLA and Bell Communications May 1985, revised 2004
OPTIMAL INVESTMENT POLICIES FOR THE HORSE RACE MODEL Thomas S. Ferguson and C. Zachary Glsten UCLA and Bell Communcatons May 985, revsed 2004 Abstract. Optmal nvestment polces for maxmzng the expected
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976761000
More informationFeasibility of Using Discriminate Pricing Schemes for Energy Trading in Smart Grid
Feasblty of Usng Dscrmnate Prcng Schemes for Energy Tradng n Smart Grd Wayes Tushar, Chau Yuen, Bo Cha, Davd B. Smth, and H. Vncent Poor Sngapore Unversty of Technology and Desgn, Sngapore 138682. Emal:
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationFormula of Total Probability, Bayes Rule, and Applications
1 Formula of Total Probablty, Bayes Rule, and Applcatons Recall that for any event A, the par of events A and A has an ntersecton that s empty, whereas the unon A A represents the total populaton of nterest.
More informationOptimality in an Adverse Selection Insurance Economy. with Private Trading. November 2014
Optmalty n an Adverse Selecton Insurance Economy wth Prvate Tradng November 2014 Pamela Labade 1 Abstract Prvate tradng n an adverse selecton nsurance economy creates a pecunary externalty through the
More informationGeneral Auction Mechanism for Search Advertising
General Aucton Mechansm for Search Advertsng Gagan Aggarwal S. Muthukrshnan Dávd Pál Martn Pál Keywords game theory, onlne auctons, stable matchngs ABSTRACT Internet search advertsng s often sold by an
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationCovariatebased pricing of automobile insurance
Insurance Markets and Companes: Analyses and Actuaral Computatons, Volume 1, Issue 2, 2010 José Antono Ordaz (Span), María del Carmen Melgar (Span) Covaratebased prcng of automoble nsurance Abstract Ths
More informationBuyside Analysts, Sellside Analysts and Private Information Production Activities
Buysde Analysts, Sellsde Analysts and Prvate Informaton Producton Actvtes Glad Lvne London Busness School Regent s Park London NW1 4SA Unted Kngdom Telephone: +44 (0)0 76 5050 Fax: +44 (0)0 774 7875
More informationNBER WORKING PAPER SERIES CROWDING OUT AND CROWDING IN OF PRIVATE DONATIONS AND GOVERNMENT GRANTS. Garth Heutel
BER WORKIG PAPER SERIES CROWDIG OUT AD CROWDIG I OF PRIVATE DOATIOS AD GOVERMET GRATS Garth Heutel Workng Paper 15004 http://www.nber.org/papers/w15004 ATIOAL BUREAU OF ECOOMIC RESEARCH 1050 Massachusetts
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationOn the Role of Consumer Expectations in Markets with Network Effects
No 13 On the Role of Consumer Expectatons n Markets wth Network Effects Irna Suleymanova, Chrstan Wey November 2010 (frst verson: July 2010) IMPRINT DICE DISCUSSION PAPER Publshed by Henrch Hene Unverstät
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationUnderstanding the Impact of Marketing Actions in Traditional Channels on the Internet: Evidence from a Large Scale Field Experiment
A research and educaton ntatve at the MT Sloan School of Management Understandng the mpact of Marketng Actons n Tradtonal Channels on the nternet: Evdence from a Large Scale Feld Experment Paper 216 Erc
More informationA Model of Private Equity Fund Compensation
A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationA Lyapunov Optimization Approach to Repeated Stochastic Games
PROC. ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING, OCT. 2013 1 A Lyapunov Optmzaton Approach to Repeated Stochastc Games Mchael J. Neely Unversty of Southern Calforna http://wwwbcf.usc.edu/
More information