Does Reinsurance Need Reinsurers?

Transcription

1 Does Reinsurance Need Reinsurers? Guillaume Plantin 1 2 February Teer School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA Phone: glantin@andrew.cmu.edu 2 I thank articiants at the 27th EGRIE seminar, at seminars at the University of Chicago and the MIT Sloan School of Management, and in articular, Jean- Luc Besson, Bruno Biais, Pierre-Andre Chiaori, Georges Dionne, Rick Green, Pierre-Francois Koehl, Pierre Picard, Jean-Charles Rochet, Jean Tirole, and an anonymous referee for very helful comments. Errors are mine.

2 Abstract The reinsurance market is the secondary market for insurance risks. It has a very seci c organization. Direct insurers rarely trade risks with each other. Rather, they cede art of their rimary risks to secialized rofessional reinsurers who have no rimary business. This aer o ers a model of equilibrium in reinsurance and caital markets in which rofessional reinsurers arise endogenously. Their role is to monitor rimary insurers credibly, so that insurers can raise caital more easily. In equilibrium, the nancial structure of rimary insurers consists of a mix of reinsurance and outside caital. The comarative statics yield emirical redictions which are broadly in line with a number of stylized facts from the reinsurance market.

3 Introduction The reinsurance market is the secondary market for insurance risks. Reinsurance is an imortant feature of the non-life insurance industry. According to the latest global study on external reinsurance released by Swiss Re (1998), direct non-life insurers have ceded business worth USD 103 billion in This corresonds to an average cession rate, or ceded remiums in terms of direct insurance remiums, of 14%. 1 The reinsurance market has a very seci c, "yramidal" organization. The generic reinsurance deal involves two tyes of ure layers, a rimary, or direct, insurer and rofessional reinsurers. The rimary insurer cedes art of the risks she underwrites on the rimary market to the rofessional reinsurers. Professional reinsurers accet such secondary risks, but do not carry out any rimary business. This is not to deny that some risk transfer between direct insurers who are not art of the same grou also takes lace. But the bulk of external reinsurance transactions comly with this attern. According to estimates from Swiss Re (1998), the reinsurance business is dominated by secialized reinsurance comanies. Professional reinsurers rovide more than 80% of the global reinsurance caacity, with the to four roviding around 30% of this caacity. Economists have rovided two theoretical frameworks to analyze reinsur- 1 In this aer, we focus on external reinsurance, as oosed to internal reinsurance, where the former consists of reinsurance transactions comleted via the marketlace, while the latter oints at reinsurance arrangements within insurance grous. It is di cult in general to disentangle external from internal reinsurance in the data, because insurance accounting norms do not require searate accounting in many countries. The study of Swiss Re (1998) does deal with market transactions only. 1

4 ance. The rst one, ioneered by Borch (1962), consists in viewing reinsurance through the lens of otimal risk sharing among risk-averse agents. Several ieces of evidence suggest, however, that otimal risk sharing is not the only motive for reinsurance in ractice. For instance, studying the reinsurance demand of a samle of U.S. insurance comanies which are not art of a grou, Mayers and Smith (1990) nd that less diversi ed rms, either geograhically or across business lines, urchase less reinsurance, which seems inconsistent with the view of reinsurance as a diversi cation device. More generally, otimal risk sharing redicts that insurance comanies should end u with a net ortfolio equal to a deterministic function of the gross insurance market ortfolio. Professional reinsurers do indeed hold very diversi ed ortfolios, both geograhically and across insurance lines, and thus their behavior seems in line with the mutualization rincile. In contrast, however, rimary insurers use reinsurance mainly to cede risks, so that their net ortfolios are roughly a deterministic function of their own gross ortfolios only, aart from the introduction of reinsurers default risk. 2 The second framework to analyze reinsurance borrows from cororate hedging theory. The starting oint is to note, as in Mayers and Smith (1990), that the decision of an insurer to urchase reinsurance resembles the decision of any non- nancial rm to urchase insurance. Thus, the motivations that exlain why rms hedge and why insurers demand reinsurance may well be similar. This aroach has emhasized that reinsurers, because of their exertise in risk management, rovide real services to rimary insurers and are able to mitigate agency roblems within insurance comanies. The ev- 2 This risk has been historically small: There is no examle, to our knowledge, of contagion via reinsurance in the modern nancial era. 2

5 idence from Mayers and Smith (1990) that less diversi ed insurers demand less reinsurance is consistent with this view: highly focused insurers are more likely to develo the required exertise in-house. Both aroaches leave imortant oints unexlained. They do not o er clear-cut rationales for the yramidal organization of the market. They also miss the dual nature of reinsurance. As emhasized by Garven and Lamm- Tennant (2003), reinsurance is both a risk management and a nancing decision. A su ciently high credit standing is a necessary inut for insurance business (see, e.g., Doherty and Tinic, 1981), and caital and reinsurance are two (imerfect) substitutes which can be used to meet this requirement. This is documented by Garven and Lamm Tennant (2003); who nd that reinsurance demand increases with nancial leverage. That in most rudential regulations (e.g., the U.S. Risk Based Caital or the Euroean Solvency Margin), the minimum caital requirement is exlicitly reduced by reinsurance urchase is also consistent with this dual nature of reinsurance. Thus, it seems aroriate to model reinsurance as only one of the levers available to insurance comanies in search of an otimal nancial structure, and to take into account the interlay of reinsurance and other nancing decisions. This aer o ers a arsimonious theory of reinsurance which redicts the emergence of secialized reinsurers, and which addresses the coordination of reinsurance and nancing olicies. In the model, rimary insurance comanies make simultaneous reinsurance and nancial decisions. In equilibrium, they otimally mix cessions to rofessional reinsurers and issuance of outside equity. The key ingredient of our model is a di erence in the relative exertise of risk managers and outside nanciers. This creates a 3

6 moral-hazard roblem which may revent insurance comanies from meeting caital requirements with uninformed outside nance. A natural way to overcome this agency roblem is to have insurance comanies nanced artially with informed caital. This can be achieved by having insurers suly reinsurance caacity to each other. If reinsurers have a su cient stake in a rimary ortfolio, they are credible monitors in the eyes of outside nanciers, who then are willing to suly caital. However, if the imortant resource of this economy, informed caital, is too scarce, this comes at the cost of some insurers giving u their rimary business to devote their resources entirely to reinsurance: insurers become rofessional reinsurers. Moral hazard is a lausible friction in non-life insurance because of the inversion of the roduction cycle and the imortance of loss mitigation. The roduction costs of an insurance comany (claims) are revealed only a long time after business has been underwritten and remiums aid in. Moreover, the eventual losses deend heavily uon an insurer s ability and e orts to mitigate losses during the run-o eriod. These e orts are unlikely to be veri able by non-exert outsiders, such as shareholders without a seat on the board. Indeed, it is not di cult for a claims manager to underreserve, namely, underestimate the nal value of claims, for several years. Illiquidity does not recede insolvency as in industries with a normal cycle. The following statement from Warren Bu et in the Berkshire Hathaway 2002 Shareholders Letter eitomizes that this moral hazard roblem is an imortant concern in non-life insurance: "I can romise you that our to riority going forward is to avoid inadequate reserving. But I can t guarantee success. The 4

7 natural tendency of most casualty-insurance managers is to underreserve, and they must have a articular mindset which, it may surrise you, has nothing to do with actuarial exertise if they are to overcome this devastating bias." As is well acknowledged by ractitioners, reinsurers have the ability to mitigate this roblem because: (i) they have more information about claims and more risk-management skills than outside nanciers; and, (ii) they are in general involved in a long-run, reeated relationshi with ceding comanies who then behave so as to build a reutation. Doherty and Smetters (2002) nd evidence that reinsurers lay a role in loss mitigation, either by monitoring ceding comanies or by designing e cient dynamic contracts (exerience rating). The aer is organized as follows. Section 1 outlines the model and solves for the equilibrium. Section 2 draws emirical imlications from the comarative statics. Section 3 concludes. 1 Model The setu is an extension of the model of nancial intermediation develoed by Holmstrom and Tirole (1997). Roughly, while Holmstrom and Tirole consider an economy in which entrereneurs cannot monitor each other, 3 this assumtion is relaxed here: insurers can monitor each other. First, we introduce the main building block of the model, caital constraints in the 3 "We assume that rms cannot monitor other rms, erhas because they have insuf- cient caital to be credible monitors [:::] or because they do not have the informational exertise." 5

8 rimary insurance business. Then, we resent the general model, allowing insurers to reinsure each other, and solve for the equilibria in the reinsurance and caital markets. 1.1 Caital Constrained Insurers We consider an economy with a continuum of insurers with unit mass. Each insurer i 2 [0; 1] contemlates underwriting a rimary insurance ortfolio P i. Throughout the aer, what is referred to as an "insurer" is a close-knit team made of the to management and inside shareholders (e.g., members of the board) of an insurance comany. This grou has control over the risk management and loss mitigation strategy. Insurance comanies, like most nancial institutions, are more likely to have such skilled to managers and inside shareholders than industrial rms. In fact, this is required to obtain a license in most countries. The model is symmetric for notational simlicity. Each ortolio P i has the following characteristics. The gross outcome from underwriting it (initial caital lus remiums lus nancial ro ts minus claims and administrative costs) is either nonnegative, with value R, or a large loss. The ositive outcome occurs with robability if the insurer enters into active loss mitigation, or if she "shirks." However, loss mitigation is not observable and comes at the loss of a rivate bene t B: Thus, as is commonlace in models of moral hazard, e ort comes at a cost but enhances the outcome in the sense of rst-order stochastic dominance. This very simle stochastic structure enables us to abstract from any security design considerations and to focus on organizational issues. The 6

9 results are robust to more realistic claims models rovided this rst-order stochastic dominance roerty holds. As in Holmstrom and Tirole (1997), we also make the extreme assumtion that ortfolios are erfectly ositively correlated. This is intended to emhasize that reinsurance does not hinge on a diversi cation motive in this model. We assume that each insurer needs to commit an amount of caital I in order to be allowed to underwrite her ortfolio. The situation we have in mind is that otential olicyholders are disersed and/or not nancially sohisticated, but that they are reresented imerfectly by an institution that acts as their agent, a broker or a regulator. This is in line with the reresentation hyothesis for rudential regulation outlined by Dewatriont and Tirole (1994). By setting a caital requirement, this institution ensures that the exected default of each insurer is below some threshold. Such a view of caital as a simle bu er underlies the actuarial aroaches of insurance regulation, based on ruin theory, as well as the Value-at-Risk aroaches in banking. The reresentative of olicyholders may be either a broker who does not o er any business to insurers whose credit rating is too low, or a rudential authority who does not let insurers oerate if they fail to meet a statutory caital requirement. Each insurer has an initial net wealth K < I: She can ta cometitive outside investors who have unlimited nancing caacities. In this case, for simlicity, she makes the investors take-it-or-leave-it o ers. All agents are risk neutral and rotected by limited liability. An outside 7

10 investment oortunity is available to all the agents, which yields an exected return of > 0: Following Holmstrom and Tirole (1997); we assume that R > (1 + ) I > ( ) R + B: Thus, insurance is valuable only if insurers mitigate losses actively. The model is identical to Holmstrom and Tirole (1997) so far. If an insurer nds the funding and underwrites her ortolio, she has incentives to carry out e cient loss mitigation only if her stake in the ositive outcome, R I, is su cient. More recisely, the incentive comatibility constraint is R I B : However, outside nanciers must be willing to articiate, i.e., (R R I ) (1 + ) (I K) : As a result, insurance is feasible i K K 1 I R 1 + B : "One lends only to the rich." Because active loss mitigation is not veri- able, insurers need to commit a su cient amount of inside caital so as to credibly underwrite insurance business. Otherwise, the incentive comatible contracts do not leave an adequate surlus to outside nanciers. In other words, the caital requirement I induces an inside caital requirement K 1 which increases with I, as well as with the extent of the moral hazard roblem B and the cost of outside caital : Note that with a more general distribution of claims, the otimal form of outside nance under our rst-order stochastic dominance assumtion would 8

11 be subordinated debt (see Innes, 1990). However, insurers would still have to commit a su cient initial amount of caital in order for deals to take lace. 1.2 Reinsurance For the balance of the aer, we restrict the analysis to the interesting case in which B is large, so that 0 < K < K 1 I R 1 + B : Insurance remains ossible under such circumstances. Indeed, dearting from Holmstrom and Tirole (1997), we assume that insurers can monitor the loss mitigation carried out by their fellow insurers, because they are endowed with the required skills in risk management. Insurers are not as good, however, at monitoring the loss mitigation by the other insurers as they are in managing their own risks. One natural reason why rimary insurers are only imerfectly monitored by other insurers is that art of the information relevant to manage claims is by nature "soft." The rimary insurer has access to this soft information because, for instance, she owns the retail network, while the other insurers only have access to the "hard" information, essentially, that art of the information that is in the books and les of the rimary insurer, but miss the soft art. An examle of soft information is the rimary insurer s guess about the sychology of the claimholders and thus whether they are willing to reach a quick comromise or bargain aggressively. Such a guess is built during an ongoing close interaction with the claimholders, but is di cult to quantify or describe recisely in an administrative le. 4 4 see Berger, Miller, Petersen, Rajan, and Stein (2001) for a related discussion of the soft and hard information relevant for loans decisions in retail banking. 9

12 Formally, if the management of claims deriving from a rimary ortfolio i 2 [0; 1] is monitored by other insurers, then: 1. The best they can achieve by monitoring is reducing the rimary insurer i s rivate bene t from B to b I < B: 2. Monitoring entails a rivate cost, c R, shared fairly among the monitoring insurers. Reinsurance reduces only artially the moral-hazard roblem in loss mitigation (B reduces to b I ), and there is of course no reason outside investors, who cannot verify rimary insurers e orts, would have any ability to verify the monitoring e ort. We assume that R c R > (1 + ) I: In words, desite the monitoring cost, insurance with active loss mitigation remains more valuable than the alternative investment oortunity. Also, we restrict the arameters to R c R K < I: R c R This restriction is not necessary, but will enable us to focus on the most interesting case in which rimary insurers ta both reinsurance and outside caital in equilibrium. Because the monitoring of loss mitigation by other insurers comes at a rivate cost, there is an additional moral-hazard roblem. In order to be credible monitors in the eyes of the outside nanciers, the insurers who monitor a given insurer must have an incentive comatible stake in the outcome. 10

13 Thus, they need to commit some of their caital to this monitoring activity to nance their share in the surlus. Otherwise stated, they rovide reinsurance caacity to the insurer that they monitor in order to alleviate its nancing constraints. Since insurance creates excess value, it is otimal, if feasible, to have each insurer allocate art of her caital to her rimary oerations and art to suly reinsurance caacity to others, so that all the ortfolios are underwritten. However, the following Proosition shows that this rst-best situation cannot be attained if nancing constraints are too imortant: Proosition 1 If 0 < K < K 2 I R 1+ b I+c R, then, even with reinsurance arrangements, all the rimary risks cannot be underwritten. Thus, some insurers have to give u their rimary business and become rofessional reinsurers. Proof. See the Aendix. The intuition is straightforward. When a ortfolio is reinsured, the R resent value of the income which is ledgeable to outside investors is because b I and c R are the minimal incentive comatible stakes of the rimary insurer and of her reinsurers, resectively. 1+ If this resent value is b I+c R, smaller than the need for outside caital, because inside caital and reinsurance caacity are too small, then the caital requirements cannot be met for all the ortfolios. For the remainder of the aer, we study the case in which all the rimary ortfolios cannot be underwritten: we assume from now on that K < K 2 : 11

14 1.3 Reinsurers From Proosition 1, if K < K 2, all the rimary ortfolios cannot be underwritten. Thus, under such circumstances, it is must be the case that secialized reinsurers, who do not have rimary business and who devote their whole caital to the suly of reinsurance caacity, emerge. We now study the equilibria in this case. Let denote the roortion of insurers that act as ure reinsurers in equilibrium. Thus, the remaining 1 insurers underwrite the rimary ortfolio available to them. Let = 1 be the ratio of reinsurers for one rimary insurer. This ratio, which will turn out to fully characterize the equilibrium, may be interreted as the "cession rate" in the reinsurance market. Note that while K < K 2 ensures that there must be secialized reinsurers, it does not rule out the ossibility that rimary insurers also suly some reinsurance caacity with a fraction of their caital. We restrict the analysis to the equilibria in which the rimary insurers do not suly reinsurance caacity at all, and rather invest their whole caital in their rimary business. We make this restriction because these equilibria are the most tractable, and also for a more imortant reason that we outline below, after the derivation of the equilibria. There are now two moral hazard roblems for a given rimary ortfolio. The rimary insurer and her reinsurers must both behave. Thus, both the rimary insurer and her reinsurers must have a su cient stake in the ositive outcome. Let R I and R R denote their resective stakes. The residual surlus can be distributed to outside investors. This determines the quantity of out- 12

15 side nance that can be raised. Any shortfall has to be lled by the rimary insurer s caital and K R, the reinsurance caacity, namely, the caital committed by reinsurers. In equilibrium, rimary insurers choose the reinsurance cover which maximizes their exected ro t, and reinsurance and rimary insurance yield the same exected return on informed caital K. Then, each agent has no incentive to change her secialization. Thus, insurers maximize R I subject to: R I b I R R c R (II) (RI) (R R I R R ) (1 + ) (I K K R ) (OP ) R I = 1 (R R c R ) (1 + ) K (IP ) K R = K: (ER) (II) states that the contract has to be incentive comatible for the rimary insurer of a given ortfolio. Her stake must be su ciently high that she is better o managing claims e ciently given she is monitored by reinsurers. (RI) states that the contract has to be incentive comatible for the reinsurers of any given ortfolio. Their stake must be su ciently high so that they e ectively monitor her. (OP ) is the outside investors articiation constraint. (IP ) is the articiation constraints of rimary insurers and reinsurers. The unitary returns from investing in a rimary ortfolio or sulying reinsurance caacity must be equal, so that they are indi erent in equilibrium, and it must be higher than the return of the outside oortunity. 13

16 (ER) states that the market for reinsurance caacity clears. Note rst that (RI) must be binding in equilibrium: R R = c R. Reinsurance is more costly than caital because of the monitoring cost c R, so that insurers otimally minimize their cessions. Thus, substituting into (IP ) ; one nds that R I = 1 c R : Note also that (OP ) must be binding if outside caital is necessary, i.e., if K + K R < I. In this case, substituting R I, R R ; and K R into (OP ), we get that the equilibrium cession rate is the ositive root of 2 + I R = 0; where 8< : I = 1 + (R R = c R ) (1+)I (1+)K : c R (1+)K Note that I and R relate to the resective returns earned by rimary insurers and reinsurers on a given ortfolio, hence the notation. It remains to verify that for such an : R 1. (II) is satis ed: R I is incentive comatible for the rimary insurer. 2. The inequality in (IP ) is satis ed: Insurers and reinsurers do not refer the outside oortunity. 3. Outside caital is required: K + K R < I. Straightforward algebra shows that the inequality in (IP ) is satis ed since c R > (1 + ) I, and that outside caital is required because we assumed c R ) K < (R R c R I: 14

17 It is also easy to check that (II) amounts to K K 3 I The following Proosition summarizes the result: R 1+ b I +c R : bi 1+(1 ) c R Proosition 8 2 < I = 1 + (R Let : R = If K K 3 I c R ) (1+)I (1+)K : c R (1+)K R b I +c R 1+ 1+(1 ) c R bi, there is an equilibrium with secialized reinsurers in which rimary insurers use both reinsurance caacity and outside nance. The equilibrium cession rate is the ositive root of (X) = X 2 + I X R : Namely, = 1 2 q 2I + 4 R I : Proof. See above. Thus, assuming ex ante identical insurers with similar skills and oortunity sets, we have exhibited an equilibrium in which secialized reinsurers emerge and rimary insurers mix reinsurance and outside caital. Note that if monitoring by reinsurers is very e cient, namely if b I! 0, then K 3! 0: In words, it is always ossible to fund some insurance caacity in this economy, even when there is only a very small amount of informed caital available. As already mentioned, interestingly, there are also equilibria in which rimary insurers rovide some reinsurance caacity. Of course, secialized reinsurers still arise in these equilibria, as a consequence of K < K 2. Note that the existence of such equilibria only means that we do not redict secialized reinsurers AND secialized rimary insurers. This is not actually a 15

18 weakness of the model, but rather a strength: we mention in the introduction that while secialized reinsurers are dominant suliers in the external reinsurance market, rimary insurers also rovide some caacity. The equilibrium we have focused on is actually dominant in the sense that it is the only one which survives as the informed caital K gets close to K 3. The intuition is simle. If rimary insurers suly reinsurance caacity, they reduce the amount they invest in their rimary ortfolio. Thus, the share of the surlus they can claim shrinks because they must earn the same return as reinsurers in equilibrium. If their share in the surlus shrinks too much, it is no longer comatible with their incentive comatibility constraint, which is binding for K = K 3 : At this stage, the reader may wonder why we have ruled out the ossibility of reinsurers raising outside funds. This is because it is actually immaterial. All that matters in order to ease the nancial constraint is a su cient amount of informed nancing (caital of rimary insurers and reinsurers) being committed to a rimary ortfolio. Once this amount is rovided, whether outside nance transits in reinsurers balance sheets or not before ending in rimary ortfolios is irrelevant. 5 This irrelevancy roerty, which simli es the analysis, deends crucially uon erfect correlation. Relaxing this assumtion would add another bene t from reinsurance to the one emhasized here. Indeed, diversi cation within reinsurance comanies would mitigate their moral hazard roblem, because reinsurance treaties could cross-ledge each other (see Tirole, 1996, for an exosition of this broad idea, closely related to the rationale for intermediation ioneered in Diamond, 1984). In this 5 This oint is similar to the "certi cation versus intermediation" oint made in Holmstrom and Tirole (1997). 16

19 case, it would be otimal to have reinsurers intermediating outside nance. The next section studies the comarative statics of this equilibrium. 2 Emirical Imlications In this section, we determine the variations of the equilibrium cession rate with resect to the arameters of the model in Proosition 3, then we derive emirical imlications. Proosition 3 The cession rate increases with resect to I; c R, and ; and decreases with resect to K: Proof. See the Aendix. In order to gain some intuition and interret these results, it is worth describing the e ect of an increase in in more detail. If the cession rate increases, rimary insurers are more heavily reinsured in the sense that the reinsurance caacity K R rovided to each ortfolio increases. Thus, an increase in the cession rate reduces reinsurance ro tability. Because rimary insurance and reinsurance ro tabilities cannot di er in equilibrium, the stake of rimary insurers in the ositive outcome is reduced. This makes more cash ows ledgeable to outside nanciers, who at the same time have less caital to commit because K R has increased. As a result, an increase in the cession rate reduces the ro tability of insurance and reinsurance while making outside nance more ro table. Eventually, an increase in the cession rate transfers value from insiders to outsiders to ease nancial constraints. 17

20 A rst testable imlication of these comarative static roerties is therefore that reinsurance caacity and reinsurance ro tability, both endogenous in our model, should be inversely related. Weiss and Chung (2004) nd evidence in suort of this oint in the U.S. roerty and casualty reinsurance markets over The variation of with resect to the exogenous arameters described in Proosition 3 may now be interreted as follows. Reinsurance and rudential regulation. The reason increases with resect to I is clear. If the exogenous caital requirement increases, it means that more outside nance is required. This increases the stake of outsiders in the cash ows, or reduces the stake of rimary insurers and reinsurers. Because the stake of reinsurers must remain incentive-comatible, rimary insurers have to reduce their stake. This makes reinsurance more ro table than rimary insurance, hence more insurers give u their rimary ortfolio to exert reinsurance. As a result, this model delivers the well-known tradeo between solvency and caacity of the rimary insurance market faced by the regulator. Toughening caital requirements makes rms more solvent but reduces the number of rimary ortfolios underwritten (1 = 1 1+ ) and leads to more reinsurance. This relationshi between reinsurance and regulation is well acknowledged by ractitioners. Reinsurance and moral hazard. If c R increases, the share of reinsurers in the cash ows has to increase, and in turn they have to suly more caacity; hence, increases. The interretation is that when the monitoring of rimary insurers by reinsurers is more di cult, rimary insurers cede more. We oint out in the introduction that the reason risk managers are di cult to monitor 18

21 in non-life business is because a long time elases between claims occurence and settlement. The monitoring cost c R should thus be all the larger because the rimary business is a long-tailed one. Indeed, the true roduction costs of insurance are more noisily observed in this case. As a result, the rediction of the model is that rimary insurers with long-tailed business should cede more, consistent with the ndings of Garven and Lamm-Tennant (2003). Another reason the true costs of an insurance comany are more di cult to assess is that they are volatile. Consistent with this, Hassan et al. (1990) nd that rms with more volatile gross loss ratios demand more reinsurance. Reinsurance and informed caital. The cession rate decreases with K because as K increases, less outside nance is required and rimary insurers, who rovide a higher roortion of the funds, must have an increasing stake in the cash ows. In ractice, rms with low inside caital are tyically mutual rms, owned by their customers only by de nition. We redict that, all else equal, these rms should be more reinsured than stock rms. Conversely, we redict that rms with a higher level of institutional ownershi should be less reinsured, because institutional investors rovide better informed caital on average. This is consistent with recent ndings from Shortridge and Avila (2004). Reinsurance and cost of caital. The cession rate increases with resect to because if outside investors require a higher return, then value must be transferred from insiders to outsiders. We have stressed that an increase in the cession rate is a mechanism to achieve this transfer in this model. This is broadly consistent with the soft reinsurance market observed during the late 1990s, during which time outside nance was chea, and cession rates 19

22 were low (see, e.g., The Worldwide Reinsurance Review, 1999). This is also consistent with the cross-sectional ndings in Mayers and Smith (1990) that more widely held insurers demand less reinsurance: Stakes in such comanies should be more liquid, which reduces the oortunity cost of outside caital. 3 Concluding Remarks This aer o ers a model of equilibrium in reinsurance and caital markets in which reinsurers arise endogenously. The yramidal structure of the reinsurance market and the interaction between reinsurance and nancing decisions are both addressed. The model, admittedly very stylized, is only a rst ste towards a theory of reinsurance, but the consistency of some of its redictions with emirical evidence is encouraging. The main limitation of the aer is that it does not exlain why monitors which, unlike reinsurers, do not commit caital auditing rms and rating agencies co-exist with reinsurers in the insurance industry. An interesting route for future research is to study the interlay of reinsurers with rating agencies and auditors, who do not intervene directly in rms oerations but issue ublic signals about rms quality. Aghion et al. (2004) develo a model in which the issuance of a ublic signal by a "seculative" monitor increases the incentives of an "active" monitor involved in the management of a roject. Their general aroach suggests therefore that reinsurers and rating agencies rovide comlement rather than substitute monitoring services. Another limitation of the aer is the minimalist (though in line with the view of ractitioners) modelling of the interaction between the insurance comany and the olicyholders or their reresentatives, who can only imose 20

23 a caital requirement. A richer modelling of this interaction is an interesting route for future research. However, this limitation has also an uside; indeed, it means that the oint made here is fairly general and that "insurers" could be reinterreted as "bankers," who contemlate lending money but are subject to a moral hazard roblem. But then, why is it that the "rebankers" arising in the model seem absent from the real world? Note rst that they are not totally absent. Some institutions such as MBIA for municial bonds or Freddie Mac and Fannie Mae for housing loans strongly resemble reinsurers in the credit market, as they secialize in bearing the tails of credit risks, and this credit enhancement is a device to commit to monitor the originator. Note also that, interestingly, reinsurers are fairly active in credit markets, either by assuming a lot of credit reinsurance, 6 or more recently by being big layers in the credit derivatives market. However, such atterns are not as imortant in credit markets as they are in insurance markets, robably because they resond to a henomenon moral hazard due to the slow revelation of roduction costs which is a rst-order issue in roerty/casualty insurance but not in banking. Because they transform durations, distressed retail banks tyically face liquidity roblems much earlier than non-life insurance comanies. Note that if moral hazard is not too imortant (K K 2 ), our model redicts that the agents should carry out both rimary and secondary business, very much like banks who originate loans and intervene in the interbank market simultaneously. 6 Credit insurance is indeed very reinsured. 21

24 Aendix Proof of Proosition 1 Assume that each insurer i 2 [0; 1] is able to underwrite her insurance ortfolio. Let x i denote the fraction of her caital K she uses to suly reinsurance caacity to the other insurers. She and her reinsurers must have incentive comatible stakes R i I and Ri R in case of a nonnegative outcome, R i I b I ; Ri R c R ; and the outside nanciers must at least break even, (R R i I R i R) (1 + ) I (1 x i ) K K i R ; where K i R is the caacity rovided by i0 s reinsurers. Thus, necessarily (R b I R c R ) (1 + ) I (1 x i) K KR i and the market for reinsurance caacity clears, so that Z 1 x i di K = Z K i Rdi: Thus, integrating the above inequality between 0 and 1, one nds that a necessary condition for each insurer underwriting her rimary ortfolio is (R b I c R ) (1 + ) (I K) : 22

25 Proof of Proosition 3 4 R Recall the de nitions of ; I ; and R : = 1 q 2 2I + I R (1 + ) I I = 1 + R R = It follows that c R (1 + ) K ( ) c R (1 + ) K : 2 + I < I > 0: 1. increases w.r.t. I because I decreases w.r.t. I: increases w.r.t. c R because I and R decrease and increase, resectively, w.r.t. c R @ @ R = I K (1 + ) K I 1 = R 1 + = 1 (2 + I ) (1 + ) I + IK 1 R : 23

26 Now remember that, by de nition, I R = 2 = I (2 + I ) (1 + ) K 1 > 0 because the term between arentheses is nonnegative since < I K 1 means that K R + K < I, which is the case in equilibrium. and Thus, @ @ = 1 I = R = 1 (2 + I ) K ( ( I 1) R ) = 2 (2 + I ) K < 0 24

27 References [1] Aghion P., Bolton P., and Tirole J. (2004) Exit Otions in Cororate Finance: Liquidity versus Incentives, Review of Finance, 8 (3), [2] Berger A., Miller N., Petersen M., Rajan R., and Stein J. (2001) "Does Function Follow Organizational Form? Evidence From the Lending Practices of Large and Small Banks", mimeo University of Chicago. [3] Borch K. (1962) Equilibrium in a Reinsurance Market, Econometrica, 30, [4] Dewatriont M. and Tirole J. (1994) The Prudential Regulation of Banks, MIT Press. [5] Diamond D. (1984) "Financial Intermediation and Delegated Monitoring", The Review of Economic Studies, 51 (3), [6] Doherty N. A. and Smetters K. (2002) "Moral Hazard in Reinsurance Markets", working aer [7] Doherty N. A. and Tinic S.M. (1981) Reinsurance under Conditions of Caital Market Equilibrium: A Note, The Journal of Finance, 36 (4), [8] Garven J. R. and Lamm-Tennant J. (2003) "The Demand for Reinsurance: Theory and Emirical Tests", Insurance and Risk Management, 71 (2),

28 [9] Hassan M., Hoerger T. J., and Sloan F. (1990), "Loss Volatility, Bankrutcy, and the Demand for Reinsurance", Journal of Risk and Uncertainty, 3 (3), [10] Holmström B. and Tirole J. (1997) Financial Intermediation, Loanable Funds and The Real Sector, Quarterly Journal of Economics, 112, [11] Innes R. D. (1990) Limited liability and incentive contracting with exante action choices, Journal of Economic Theory, 52 (1), [12] Mayers D. and Smith Jr C. W. (1990) On the Cororate Demand for Insurance: Evidence from the Reinsurance Market, Journal of Business, 63 (1); [13] Swiss Re (1998) The global reinsurance market in the midst of consolidation, Sigma n 9/1998. [14] The Worldwide Reinsurance Review. November [15] Tirole J. (1996) "Lecture Notes on Cororate Finance", mimeo University of Toulouse. [16] Shortridge R. T. and Avila S. M. (2004) "The Imact of Institutional Ownershi on the Reinsurance Decision", Risk Management & Insurance Review, 7 (2), [17] Weiss M. A. and Chung J. (2004), "U.S. Reinsurance Prices, Financial Quality, and Global Caacity", Journal of Risk & Insurance, 71 (3),