J. David Cummins* Gregory P. Nini. June 29, 2001

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1 OPTIMAL CAPITAL UTILIZATION BY FINANCIAL FIRMS: EVIDENCE FROM THE PROPERTY-LIABILITY INSURANCE INDUSTRY By J. Davd Cummns* Gregory P. Nn June 29, 2001 J. Davd Cummns* Gregory P. Nn The Wharton School The Wharton School 3641 Locust Walk 3641 Locust Walk Phladelpha, PA Phladelpha, PA Phone: Phone: Fax: Fax: Emal: Emal: *Please address correspondence, page proofs, etc. to Davd Cummns.

2 OPTIMAL CAPITAL UTILIZATION BY FINANCIAL FIRMS: EVIDENCE FROM THE PROPERTY-LIABILITY INSURANCE INDUSTRY Abstract Captalzaton levels n the property-lablty nsurance ndustry have ncreased dramatcally n recent years the captal-to-assets rato rose from 25 percent n 1989 to 35 percent by Ths paper nvestgates the use of captal by nsurers to provde evdence on whether the captal ncrease represents a legtmate response to changng market condtons or a true neffcency that leads to performance penaltes for nsurers. We estmate best practce techncal, cost, and revenue fronters for a sample of nsurers over the perod , usng data envelopment analyss, a non-parametrc technque. The results ndcate that most nsurers sgnfcantly overutlzed equty captal durng the sample perod. Regresson analyss provdes evdence that captal over-utlzaton prmarly represents an neffcency for whch nsurers ncur sgnfcant revenue penaltes.

3 1. Introducton Insurers hold equty captal to provde assurance to polcyholders that clams wll be pad f losses are hgher than expected or f nvestment returns fall short of expectatons. The objectve s to attan an optmal level of nsolvency rsk that balances the margnal benefts and costs of holdng equty captal. There are margnal benefts from holdng captal because safer nsurers command hgher prces and because nsurers rsk losng customers f nsolvency rsk s perceved as excessve (Sommer 1996, Cummns and Danzon 1997). However, holdng equty captal n an nsurance company s costly due to regulatory costs, agency costs from unresolved owner-manager and ownerpolcyholder conflcts, the costs of adverse selecton and moral hazard n nsurance underwrtng and clams settlement, corporate ncome taxaton (Cummns and Grace 1994), and other market frctons. Hence, nsurers do not hold suffcent captal to elmnate nsolvency rsk; rather, nsurers mantan market-drven ''safe'' or ''adequate'' levels of captal (Cummns, Grace, and Phllps 1999). 1 A puzzle has developed n the property-lablty nsurance ndustry as captalzaton has rsen to unprecedented levels n recent years. The rato of premums wrtten to surplus, the ndustry's standard leverage ndex, tradtonally fluctuated around two. Begnnng n the md-1980s, however, the rato began a precptous declne and dpped below one at the end of Lkewse, the equty captal-to-assets rato, tradtonally around 25 percent, ncreased to 35 percent by These developments rase questons about whether the ndustry s over-captalzed or whether structural changes n the nsurance or captal markets have altered the optmal degree of captalzaton. The objectve of ths paper s to analyze captalzaton n the property-lablty ndustry to provde new evdence on whether nsurers are over-utlzng equty captal. We employ a fronter effcency approach to analyze captal utlzaton of property-lablty nsurers over the perod Usng data envelopment analyss (DEA), a non-parametrc technque, we estmate ''best 1 Regulaton, ncludng the Natonal Assocaton of Insurance Commssoners (NAIC) rsk-based captal system, specfes mnmum levels of captal for nsurers. However, the vast majorty of nsurers mantan sgnfcantly hgher captal than requred by rsk-based captal rules (see Cummns, Grace, and Phllps 1999). 1

4 practce'' techncal, cost, and revenue fronters and measure the effcency of each frm n the sample relatve to the fronters, producng estmates of techncal, allocatve, cost, and revenue effcency. A key concept that we use n analyzng nsurer captal utlzaton s that of cost effcency, whch measures the frm's success n mnmzng costs. Cost effcency s defned as the rato of the costs that would be ncurred by a fully effcent frm producng the frm's outputs to the costs actually ncurred by the frm. Thus, fully effcent frms have cost effcences of one, and neffcent frms have cost effcency between zero and one. Cost effcency can be decomposed nto techncal effcency and allocatve effcency. Techncal effcency measures the frm's success n usng stateof-the-art technology,.e., n operatng on the producton fronter. Allocatve effcency measures the frm's success n choosng the cost mnmzng combnaton of nputs, condtonal on output quanttes and nput prces. To be fully cost effcent, a frm must operate wth full techncal and allocatve effcency. We also estmate revenue effcency, whch measures the frm's success n maxmzng revenues. Revenue effcency s defned as the frm's actual revenues dvded by the revenues of a fully effcent frm that utlzes the same quantty of nputs. As wth cost effcency, techncal, allocatve, and revenue effcency equal one for fully effcent frms and are between zero and one for neffcent frms. Lower effcency scores ndcate more neffcent frms. The concept of allocatve effcency provdes a natural way to analyze whether nsurers are under- or over-utlzng captal. Allocatve effcency measures the extent to whch a frm chooses the correct quanttes of nputs n order to produce ther outputs. Further, the estmaton procedure generates estmates of the optmal nput quanttes for each frm n the sample. By comparng the actual captal for a gven frm wth ts optmal captal, we can determne whether the frm s under or over-utlzng captal relatve to the captal that would be used by a fully effcent frm wth the same quantty of outputs. There are two possble reasons why frms may be measured as under- or over-utlzng captal 2

5 n our DEA analyss. The frst possblty s that measured sub-optmal captal utlzaton represents a ratonal response to market factors or frm characterstcs that legtmately requre dfferental captal utlzaton. If ths explanaton s correct, a frm's performance should not be adversely affected by dfferences between ts actual captal and ts measured optmal captal. The second possble explanaton s that measured under- or over-utlzaton of captal represents a true neffcency that degrades frm performance. To provde nformaton on whch explanaton s correct, we utlze revenue effcency and book-value return on equty (ROE) to measure frm performance and estmate the mpact of captal utlzaton on these performance measures. We regress revenue effcency scores and book-value ROE aganst a set of explanatory varables, ncludng the rato of the frms' actual less optmal captal to assets. Ths rato, whch we call the sub-optmal captal-to-assets rato, represents the amount of captal under- or over-utlzaton relatve to assets. A larger value for ths rato ndcates excessve use of captal relatve to our measured level of optmal captal. If measured sub-optmal captal utlzaton represents neffcency, then we expect the sub-optmal captal to assets rato to have adverse effects on frm performance, as explaned n more detal below. 2 In addton to measurng the effects of sub-optmal captal on frm performance, we specfy and test several hypotheses regardng the characterstcs of frms that are lkely to be assocated wth captal utlzaton. We regress the rato of the frm s actual-to-optmal captal aganst a vector of explanatory varables representng the theoretcal hypotheses. These tests enable us to control for dfferences among frms that may help to explan observed patterns of captal utlzaton n the ndustry. By way of prevew, we fnd that the run-up n equty captal of the past decade s prmarly attrbutable to captal gans on nvestments. Further, we provde evdence that captal levels n the ndustry are ''stcky'' n the sense that nsurers are reluctant to pay out captal accumulatons as 2 We also perform smlar regressons to test f the effect s symmetrc for under and over-utlzaton of captal. By separatng the sub-optmal captal-to-assets rato nto postve and negatve components, we test whether any adverse effects of sub-optmal captal utlzaton dffer dependng upon whether the nsurer s under- or over-captalzed. 3

6 dvdends, preferrng to mantan nternal funds to cushon the loss or nvestment shocks. Fnally, we fnd that nsurers are substantally over-utlzng equty captal and that the over-utlzaton represents neffcency that leads to sgnfcant revenue and cost of captal penaltes for neffcent frms. The remander of the paper s organzed as follows: Secton 2 provdes an emprcal overvew of captalzaton trends n the property-lablty nsurance ndustry to provde background for the subsequent dscusson. In secton 3, we formulate hypotheses about nsurer captal structure and specfy the varables used to test the hypotheses. Secton 4 dscusses hypotheses and varables regardng revenue effcency and ROE. Secton 5 dscusses our estmaton methodology, and secton 6 descrbes our sample and specfes the nputs and outputs used n the DEA analyss. The results are presented n secton 7, and secton 8 concludes. 2. CAPITALIZATION TRENDS IN PROPERTY-LIABILITY INSURANCE Leverage ratos for the property-lablty nsurance ndustry for the perod are graphed n Fgure 1. Two leverage ratos are shown - the rato of net premums wrtten to equty captal (surplus) and the equty captal-to-assets rato. The former s the tradtonal leverage rato used n the ndustry, whle the latter s used more commonly n the fnancal nsttutons lterature. Both leverage ratos llustrate that equty captalzaton n the ndustry has ncreased dramatcally over the past ffteen years. The premums-to-surplus rato was near 2.0 n 1985 but then began an almost unnterrupted declne to less than 1.0 by The captal-to-assets rato, whch stood at 25 percent n 1985, ncreased to 37 percent by The trends n the leverage ratos are prmarly due to growth n nsurer equty captal. Durng the ten-year perod , equty captal growth averaged 10 percent per year (on a book bass), whle premum growth was only about 3 percent per year. The dvergent growth rates n captal and premums are shown n Fgure 2, whch graphs the sx-year movng averages n the growth rates for these two varables. Except for bref perods such as the md-1980s, the growth rate n captal has far 4

7 exceeded the growth rate n premums. Durng the 1990s, the captal growth n the ndustry tracks the bullsh stock market (see further dscusson below). What can explan the dramatc changes n captal structure n ths ndustry? There are several possbltes, most of whch are explored n more depth below: (1) The ntroducton of a rsk-based captal (RBC) system by the Natonal Assocaton of Insurance Commssoners (NAIC) n The ntroducton of the RBC system was wdely antcpated and may have led nsurers to accumulate more captal to reduce the probablty of ncurrng regulatory costs under the new system. (2) The rse n mportance of ratng agences. The nsurance product market s known to react to ratngs downgrades by frms such as the A.M. Best Company, Standard & Poor's, and Moody's. For example, n the commercal lnes market, t s necessary for nsurers to mantan at least an A ratng n order to avod losng customers to compettors. The ratng agences have played a more aggressve role wth respect to nsurers followng the run-up n nsurer nsolvences n the late 1980s and early 1990s. Thus, some nsurers may have accumulated addtonal captal to protect ther fnancal ratngs. (3) The growth n the market for alternatve rsk transfer products, whch provde a substtute for conventonal nsurance. These nclude self-nsurance programs, captve nsurance companes, and securtzed fnancal rsk transfer nstruments. These products have draned many of the more predctable rsks out of nsurance markets, ncreasng the overall volatlty of nsurer lablty portfolos. Addtonally, the rse of the alternatve market has caused premum growth to stagnate, partally accountng for the gap between premum and equty growth. (4) An ncreased awareness by nsurers of ther exposure to catastrophc property losses coupled wth nadequate supply of rensurance for such losses. Followng hurrcane Andrew n 1992 and the Northrdge earthquake n 1994, nsurers revsed upward ther estmates of potental losses due to catastrophes such as hurrcanes and earthquakes. Smultaneously, t became apparent that 5

8 rensurance for these large events was nadequate (Swss Re 1997, Froot 1999). Thus, nsurers wth sgnfcant catastrophe exposure may have added captal to cushon catastrophc loss shocks. (5) The 1990s bull market n corporate equtes, combned wth nsurer reluctance ncrease stockholder dvdends. There s both theoretcal and emprcal evdence that there s consderable stckness among nsurers n adjustng dvdends n response to ncreases n equty (Wnter 1994, Gron 1994, Cummns and Danzon 1997). The stckness s drven by nformatonal asymmetres that make t dffcult for nsurers to rase captal after a loss or nvestment shock, nducng them to hold onto captal wndfalls n antcpaton of the next underwrtng crss. (6) Agency costs and other aspects of nsurer organzatonal and market structure. These factors, ncludng the role played by mutual nsurers, are dscussed n more detal below. Tracng the source of the ndustry's growth n equty captal may provde some ntal answers to the captal structure puzzle. Table 1 breaks down the ndustry's growth n book equty nto ts sources and uses for the perod Secton A of the table shows that total captal grew by $215.7 bllon from , net of $78.8 bllon n stockholder dvdends and $29.4 bllon n mscellaneous outflows. These captal dsbursements are added back to the net change n captal to gve the gross change n captal, and secton B of the table shows the percentages of the gross change from each source of captal. Captal gans provded the most mportant source of new captal durng the ten-year perod and the four-year perod , accountng for 51.7 percent durng the former perod and 57.0 percent durng the latter. The second most mportant source of gross new captal s retaned earnngs (net underwrtng ncome plus nvestment ncome), and the thrd most mportant source s new captal pad-n, from new equty offerngs or contrbutons from parent frms. The uses of the gross changes n equty are shown n secton C of the table. Insurers pad out as dvdends about onefourth of the total gross change n captal whle retanng about two-thrds, wth the remander devoted to mscellaneous uses. 6

9 Table 1 provdes some support for the captal stckness hypothess,.e., that captal accumulates because nsurers are concerned about the feasblty of rasng new captal followng the next major underwrtng or nvestment shock. The last column n secton A of the table shows the dvdend payout rate over the perod,.e., the rato of stockholder dvdends pad to the total gross change n captal. The average payout rate s sgnfcantly lower n the second half of the sample perod than durng the frst half, even though the second half of the sample perod accounted for about 70 percent of the total change n gross captal. Ths s consstent wth the vew that nsurers are reluctant to reduce captal durng perods of captal growth by ncreasng the dvdend payout rate. 3. Hypotheses: Captal Structure and Leverage In ths secton, we dscuss economc factors that nfluence nsurer decsons about captalzaton and formulate hypotheses about nsurer captal structure based on fnancal theory. In addton to dscussng the ratonale for nsurers to hold captal, we also formulate hypotheses about frm characterstcs lkely to be assocated wth under- and over-captalzaton. 3.1 Fnancal Dstress The costs of fnancal dstress are a common frcton dentfed as nfluencng captal decsons. As nsurers ncrease ther captal relatve to premums or labltes, the probablty of nsolvency declnes, reducng the assocated expected costs of fnancal dstress. However, holdng captal n an nsurance company s costly because of varous frctons and market mperfectons, ncludng agency costs, costs arsng from adverse selecton and moral hazard, regulatory costs, and corporate ncome taxaton (Merton and Perold 1998). Agency costs for an nsurer nclude the costs of unresolved owner-manager and polcyholder-owner conflcts. For example, managers may take actons that are nconsstent wth the maxmzaton of frm value such as falure to nvest n postve net present value projects whose rsk may be a threat to manageral job securty. Insurance markets are characterzed by adverse selecton and moral hazard, whch lead to hgher costs of captal to the extent that they cannot be fully controlled through contract desgn, underwrtng, and the clams 7

10 settlement process. Fnally, nsurers ncur sgnfcant regulatory costs and costs from corporate ncome taxaton to the extent that these costs cannot be fully passed along to polcyholders n premum rates charged for nsurance (Cummns, Grace, and Phllps 1999, Cummns and Grace 1994). Because of these and other captal costs, nsurers do not hold suffcent captal to reduce the probablty of bankruptcy to neglgble levels. Fnancal dstress occurs when an nsurer has dffculty honorng commtments to polcyholders and other credtors. The assocated costs nclude the transactons costs of bankruptcy, the loss of talented employees, the loss of non-marketable and relatonshp-specfc assets, reputaton losses, and other losses to the nsurer's franchse value. Further, nsurance s prced as rsky debt, and the prces an nsurer's products command n the market are nversely related to the probablty of bankruptcy (Sommer 1996, Cummns and Danzon 1997). All else equal, as the expected costs of nsolvency ncrease, the margnal beneft from holdng equty captal ncreases, and the optmal leverage rato (e.g., premums-to-surplus or labltes-to-surplus) decreases. For an nsurance company, the probablty of nsolvency s related to an nsurer's ablty to dversfy rsk. As proxes for nsolvency rsk, we defne three measures of lablty rsk and one measure of asset rsk. The frst measure of lablty rsk s the nsurer's dversfcaton across geographcal areas. Other thngs beng equal, an nsurer that s more geographcally dversfed s expected to have lower nsolvency rsk than nsurers that are more concentrated geographcally. To measure geographcal dversfcaton, we use a Herfndahl ndex of nsurer premum wrtngs by state. The second measure of lablty rsk s the nsurer's Herfndahl ndex across lnes of nsurance based on premum volume. 3 Insurers that are more dversfed by lne are expected to have lower nsolvency rsk than nsurers concentratng on one or a few busness lnes. Lower Herfndahl ndces mply hgher dversfcaton 3 The Herfndahl ndces are, respectvely, the sum of squares of the percentages of premums wrtten by state and the sum of squares of the percentages of premums wrtten by lne. 8

11 and, consequently, the geographcal and lne of busness Herfndahl ndces are predcted to be postvely related to the use of captal. The thrd measure of lablty rsk focuses on the nsurer's use of rensurance. Because rensurance represents dversfcaton among nsurance companes, frms that purchase more rensurance are expected to have lower nsolvency rsk. Our measure of the ntensty of an nsurer's rensurance actvtes s the rato of ceded loss reserves to drect plus assumed loss reserves. 4 We predct an nverse relatonshp between the rensurance varable and the utlzaton of captal. The measure of asset rsk used n our analyss s the percentage of an nsurer's assets nvested n stocks and real estate, because these assets expose nsurers to more volatlty rsk than ther fxed ncome nvestments, whch tend to be hghly rated bonds and notes. We expect a postve relatonshp between the percentage of assets n stocks and real estate and the utlzaton of captal. These propostons are stated formally n the followng hypotheses. H1. The Herfndahl ndces of premums wrtten by state and by lne of busness wll be postvely related to captal utlzaton. H2. Frms wth hgher ratos of ceded loss reserves to drect plus assumed loss reserves wll use less captal. H3. Frms wth hgher percentages of assets nvested n stocks and real estate wll use more captal. Part of the ncrease n captalzaton levels n the nsurance ndustry may be attrbutable to changes n the characterstcs of nsured rsks. Buyers have substtuted a varety of ''alternatve rsk transfer'' mechansms for nsurance, removng the more predctable rsks and contnung to nsure the more volatle rsks such as commercal lablty clams. If nsurer lablty portfolos have become ncreasngly volatle, ths could provde an explanaton of recent captalzaton trends. 5 Rsk levels 4 Ceded reserves are the labltes that an nsurer transfers to rensurers. Drect reserves represent the nsurer's oblgatons n the prmary nsurance market, and assumed reserves reflect ts oblgatons to other nsurers as a rensurer. Larger ratos of ceded loss reserves to drect plus assumed reserves ndcate more use of rensurance. 5 Changes n asset portfolo rsk also could help to explan the changng captalzaton levels n the ndustry. However, except for an ncrease n the proporton of assets held n corporate equtes, prmarly due to unrealzed captal gans, n general nsurer asset portfolos have changed lttle over our sample perod. We control for the 9

12 also are expected to dffer cross-sectonally among frms n the ndustry as a functon of both underwrtng and nvestment portfolo choces. To control dfferences n ncome volatlty across nsurers, we use the standard devaton of each nsurer's book-value ROE computed over the three years precedng each analyss year. We expect ths varable to be postvely related to captalzaton. H4. Hgher rsk, as measured by the standard devaton of ROE, wll be assocated wth hgher captal utlzaton. It s well known from statstcal and actuaral theory that the average loss n a pool of rsks becomes more predctable as the number of rsks n the pool ncreases. Ths means that the losses of larger nsurers are more predctable than those of smaller frms so that large frms should requre relatvely lower captalzaton to acheve a gven level of nsolvency rsk. Although n prncple smaller frms should be able to acheve smlar results through rensurance, n practce rensurance s costly due to frctons such as moral hazard, adverse selecton, and the need to provde a proft to the rensurer. Followng the recent nsurance effcency lterature (Cummns and Wess 2000), we use the natural log of frm assets to represent frm sze and propose the followng hypothess: H5. Captalzaton wll be nversely related to frm sze. 3.2 Agency Costs There are two prmary sources of agency costs n the nsurance ndustry: owner-manager conflcts and owner-polcyholder conflcts. Conflcts between owners and managers arse because managers do not share fully n the resdual clam held by owners and have an ncentve to behave opportunstcally. Conflcts between owners and polcyholders arse because polcyholders' clams to assets have legal prorty over owners' clams. Owners have an ncentve to explot polcyholder nterests by changng the rsk structure of the frm or takng actons that ncrease the value of equty, perhaps by decreasng the value of the polcyholders' debt clam on the frm. The owner-manager conflct s a classc example of moral hazard, snce the non-contractble ncreased mportance of corporate equtes by ncludng the rato of stocks and real estate to total assets as an ndependent varable n our emprcal analyss. 10

13 effort of the manager drectly affects the value of the clam held by the owner. Wthout possessng a 100 percent ownershp stake, managers face a reduced margnal beneft from nvestng ther effort nto the frm, alterng the ncentves for the manager to exert the optmal effort. Ths creates a sgnfcant agency cost that can be reduced by ncreasng leverage. Holdng constant the managers' level of ownershp, reducng equty captal ncreases the managers' stake n the frm, helpng to algn the nterests of owners and managers. Reducng equty also decreases the amount of free cash avalable for managers to pursue prvate nterests, such as takng on projects that ncrease the sze of the frm but do not maxmze the value of equty. Fnally, addtonal leverage ncreases the probablty of bankruptcy (a partcularly costly event for managers), makng value-destroyng pursuts more costly for managers. Mtgatng the conflct between managers and owners thus consttutes a beneft from ncreased leverage. When owners and polcyholders are separate classes of nvestors, a conflct arses because owners have a clam to frm value only beyond the clams of polcyholders. Due to lmted lablty, equty ownershp s equvalent to a call opton on the value of the frm, makng rsky nvestments attractve to owners. Snce polcyholders bear much of the consequences of faled nvestments, polcyholders prefer less rsky nvestments. When the opportunstc behavor of owners s antcpated, the effect s ncorporated nto the prce of nsurance, and owners bear much of the cost of the ncentve conflct. Ths cost can be reduced by decreasng leverage, whch mtgates the prce effect by reducng nsolvency rsk. Further, ncreasng the amount of equty captal relatve to premums reduces the beneft to owners from substtutng rsker nvestments, makng asset substtuton less attractve. Mtgatng the conflct between polcyholders and owners thus consttutes a beneft from decreased leverage. Jensen and Mecklng (1976) argue that the optmal captal structure s determned by tradng off the benefts from ncreased leverage (mtgatng the owner-manager conflct) wth the benefts 11

14 from decreased leverage (mtgatng the owner-polcyholder conflct). When the owner-manager conflct s partcularly severe, frms may appear under-captalzed to the extent that agency costs are not fully reflected n the cost of captal used n our effcency analyss. When the owner-polcyholder conflct s severe, frms may appear over-captalzed. Because both stock and mutual nsurers are present n the nsurance ndustry, organzatonal form provdes an excellent proxy for the degree of agency costs nherent n an nsurance frm. Compared wth stock companes, mutuals control the owner-polcyholder conflct by mergng these two roles. However, the owner-manager conflct s more severe n the mutual ownershp form because the mechansms avalable for owners to control managers are much more lmted than n the stock ownershp form. In a ratonal market, one would expect the benefts from removng the ownerpolcyholder conflct to exceed the costs of unresolved owner-manager conflcts n mutual nsurance frms. Consequently, the elmnaton of the owner-polcyholder conflct s lkely to result n a reduced margnal beneft from holdng captal n mutuals, suggestng that mutuals may be less captalzed than stocks, other thngs equal. Mutuals also may have less need for captal than stocks because they tend to nvest n less complex or less rsky projects requrng lmted manageral dscreton n prcng and underwrtng (Lamm-Tennant and Starks 1993). On the other hand, mutuals may have a greater tendency than stocks to hoard captal durng proftable perods because of ther lmted ablty to access captal markets n the event of a shock to captal. In addton, to the extent that holdng addtonal captal provdes benefts to managers (e.g., from controllng larger nvestment portfolos), mutuals may hold captal n excess of optmal levels because of a msalgnment of polcyholder and manager nterests. Because we do not have an unambguous predcton about ownershp form, we state the followng hypothess n null form: H6. Mutuals wll not utlze captal more or less ntensvely than stocks. Due to the tme lag between payment of premums and payment of clams, nsurance frm managers are n control of polcyholder funds for a sgnfcant perod of tme. Ths tme lag offers 12

15 managers the opportunty for engagng n actvtes that provde prvate benefts, possbly to the detrment of the frm and polcyholders. As the polcy length and clams tal ncreases, the problem worsens; and there s a beneft to removng excess funds from the frm and ncreasng the bankruptcy probablty. Reducng captal and ncreasng leverage can accomplsh ths. An nsurer's loss reserve and unearned premum reserve are labltes for losses not yet pad and premums receved for whch servce has not yet been provded. The rato of the sum of loss and unearned premum reserves to ncurred losses s used as a proxy for tme lag between polcy ssuance and the payment of clams, wth hgher ratos ndcatng longer taled busness. As ths rato ncreases, the margnal cost of captal ncreases and frms are predcted to choose lower captal levels. Thus, we hypothesze that: H7. The rato of reserves to losses ncurred wll be nversely related to captal utlzaton. 3.3 Asymmetrc Informaton and Growth Opportuntes If corporate managers possess superor nformaton about the frm's assets n place and new nvestment opportuntes than do owners, Myers and Majluf (1984) argue that these nformaton asymmetres may cause managers to forego postve net present value projects. Ths results n a ''peckng order'' theory of fnancng where managers prefer fnancng through nternal funds and debt rather than ssung new equty. As the degree of asymmetry between managers and nvestors ncreases, ths under-nvestment problem worsens and rasng equty captal becomes more costly. The mplcatons of the Myers-Majluf theory for our analyss depend upon the degree of the nformatonal asymmetry problem n the nsurance ndustry and the response to the problem by the frms n the ndustry. Because property-lablty nsurers nvest prmarly n marketable securtes, there are mnmal nformatonal asymmetres from the asset sde of the balance sheet, except perhaps wth respect to the credt rsk of recevables from agents and rensurers. The prncpal nformatonal asymmetry for property-lablty nsurers arses from uncertanty about the true value of reserves for the payment of unpad losses, whch averages about 65 percent of total labltes, ndustry-wde. A substantal component of the loss reserve represents nsurer estmates of the clams to be pad n the 13

16 future on long-tal polces such as commercal lablty nsurance. Insurers have sgnfcant actuaral and accountng flexblty n determnng the stated loss reserve, and most of the nformaton needed to evaluate the accuracy of reserve estmates s not avalable outsde the nsurer. Hence, there are sgnfcant nformaton asymmetres between managers and nvestors wth regard to the labltes for long-taled nsurance polces, especally n the commercal lnes. Insurers may respond to the nformatonal asymmetry problem by buldng up slack captal durng proftable perods to provde nternal funds to nvest n attractve future projects. Alternatvely, nsurers wth relatvely hgh nformaton asymmetres may become more hghly leveraged, especally durng unproftable phases of the underwrtng cycles, because they are at a net dsadvantage n rasng new equty relatve to nsurers whose labltes are more transparent to nvestors. That s, f nsurers wth the greatest reservng uncertanty have equal ablty to generate retaned earnngs as nsurers wth more transparent labltes, the former group wll lkely become more hghly leveraged over tme because ts costs of rasng external captal are hgher. Moreover, frms wth hgher reserve uncertanty may actually be less successful n generatng retaned earnngs because long-tal lnes of nsurance tend to generate less ncome from underwrtng than shorter-tal lnes. Thus, such nsurers may be dsadvantaged n rasng both nternal and external captal, mplyng that nformaton asymmetres between managers and owners are more lkely to lead to hgher leverage rather than addtonal slack captal n the nsurance ndustry. Another mplcaton of the Myers-Majluf theory s that for any gven degree of nformatonal asymmetry, frms wth more growth opportuntes are expected to hold addtonal captal to avod the need for rasng costly captal n the future. Ths dscusson suggests the followng hypotheses: H8. Frms wth hgher nformaton asymmetres between managers and owners wll be more hghly leveraged than frms wth lower nformaton asymmetres. H9. Frms wth more growth opportuntes wll hold relatvely more equty captal. The standard devaton of ROE over tme s used as a proxy for the degree of nformaton asymmetres between managers and nvestors. Insurers wth low earnngs volatlty are assumed to 14

17 possess assets and labltes that change very lttle over tme, makng ther future proftablty easly conveyed from manager to nvestor. However, nsurers wth hgher volatlty have operatons that are less predctable, and therefore have more severe nformaton asymmetres than less rsky nsurers. Based on ths ratonale, the standard devaton of ROE s predcted to be nversely related to captalzaton. Recall, however, that H4 predcts a postve relatonshp between ROE rsk and captal, based on the fnancal dstress costs argument. Thus, the sgn of ths varable wll depend upon the extent to whch t measures frm opacty versus the probablty of fnancal dstress. The rato of reserves to losses ncurred, dscussed n connecton wth H7, also serves as a proxy for nformatonal asymmetres, to the extent that lengthenng the clams payment tal ncreases uncertanty about reserve accuracy. The reserves varable thus has a predcted negatve sgn under both H7 and H9. To proxy for growth opportuntes, we use the one-year percentage growth rate n premums. As the measure of growth ncreases, t s hypotheszed that nsurers wll be motvated to hold more captal to be able to take advantage of growth opportuntes usng nternal rather than external funds. Thus, the premum growth rate s predcted to be postvely related to captal utlzaton. 3.4 Product Market Interacton Because the purpose of nsurance s to dversfy rsk and ndemnfy polcyholders for losses due to contngent events, the nsurance market s senstve to nsurer nsolvency rsk, and safer nsurers command hgher prces. In addton, postve swtchng costs and prvate nformaton possessed by the ncumbent nsurer can create a sgnfcant advantage to remanng wth the same nsurer (Kunreuther and Pauly 1986, D'Arcy and Doherty 1990). Due to economes of scale and the exstence of nsurance brokers, corporate nsurance buyers face sgnfcantly lower swtchng costs than personal buyers, makng relatonshps wth corporate buyers more fragle than those wth personal buyers. The commercal lnes nsurance market s consdered a ''commodty market,'' where buyers choose nsurers on the bass of prce, from the set of nsurers wth adequate (often A or better) 15

18 fnancal ratngs (.e., the market s characterzed by a tendency for ''flght to qualty''). Moreover, commercal lnes buyers and ther brokers are more profcent than ndvdual buyers n assessng nsurer fnancal qualty, suggestng the followng hypothess: H10. Captalzaton wll be nversely related to the percentage of an nsurer's revenues comng from personal lnes of nsurance. To test H10, we nclude n the regressons the rato of the nsurer's personal lnes premums to total premums. Ths varable s expected to be nversely related to captalzaton. We predct a negatve coeffcent on the personal lnes varable based on the flght to qualty argument. 3.5 Regulaton In response to an ncrease n nsurer nsolvences n the 1980s and early 1990s, the Natonal Assocaton of Insurance Commssoners (NAIC) nsttuted rsk-based captal (RBC) requrements n Varous regulatory actons are stpulated f the rato of the nsurer's actual captal to rsk-based captal falls below a seres of thresholds begnnng at 200 percent (see Cummns, Grace, and Phllps 1999). The ntroducton of rsk-based captal created a regulatory opton that reduced the market value of nsurers. Because the opton value s nversely related to captalzaton, the ntroducton of RBC s predcted to have ncreased captalzaton levels n the ndustry. To control for dfferences n captalzaton by year, we nclude year dummy varables n our regresson equatons. If captal levels were adjusted followng the RBC ntroducton year (1994), the coeffcents of the year dummy varables may be larger n the later years of the sample perod. On the other hand, f nsurers antcpated the ntroducton of RBC, any captal adjustments may have occurred pror to our sample perod, and the year dummy varable coeffcents wll have no systematc pattern. 4. Hypotheses: Revenue Effcency and Return on Equty In addton to regressons to explan nsurer captal structure, we also conduct regressons desgned to detect relatonshps between captal structure and frm performance. We use two ndcators of performance - revenue effcency and book-value return on equty (ROE). In ths secton, we dscuss hypotheses and expected sgns for the frm performance regressons. 16

19 4.1 Revenue Effcency The prmary purpose of the revenue effcency analyss s to determne whether measured captal under- or over-utlzaton s a ratonal strategy that s rewarded by the market wth addtonal revenues or a true neffcency that leads to revenue penaltes. The mantaned hypothess about the relatonshp between captalzaton and revenue effcency s that nsurance buyers are senstve to nsolvency rsk but that nsurance market equlbrum occurs at a non-neglgble probablty of default. The prmary reason s that holdng equty captal n an nsurance company s costly because of the varous market, tax, and regulatory frctons dscussed above. Thus, at some pont, the margnal beneft of addng captal to reduce nsolvency rsk falls below the margnal cost of the added captal, producng an optmal captal-to-assets rato that maxmzes frm value. Our analyss of cost effcency enables us to estmate the optmal quantty of captal for each frm n the sample. Frms wll be rewarded or penalzed for measured sub-optmal captal utlzaton dependng upon whether holdng captal that devates from the measured optmum represents a legtmate response to market forces or a true neffcency. Sub-optmal captal-utlzaton does not represent a true neffcency f captal levels reflect legtmate dfferences n captal requrements across frms because of heterogenety n underwrtng or nvestment portfolos, corporate governance, or other factors. On the other hand, f devatons from optmal captal represent a true neffcency, nsurers holdng sub-optmal amounts of captal are lkely to be penalzed by the market n terms of lower revenues. Ths s ether because they hold too lttle captal and thus have hgher nsolvency rsk than buyers fnd desrable or because they hold too much captal and perhaps try to recover the costs of the excess captal by chargng prces that buyers vew as too hgh. To test the relatonshp between revenue effcency and captal utlzaton, we use as an explanatory varable the sub-optmal captal-to-assets rato, defned as the rato of actual mnus optmal captal-to-assets. If measured captal under- or over-utlzaton represents legtmate usage of captal, the sub-optmal captal-to-assets rato s expected to be postvely related to revenue 17

20 effcency. However, f measured under- or over-utlzaton reflects neffcency, the sub-optmal captal-to-assets rato s expected to be negatvely related to revenue effcency. In order to determne whether the market responds symmetrcally to captal under and over-utlzaton, we defne two addtonal varables based on the sub-optmal captal-to-assets rato the captal over-utlzaton rato, whch s equal to the sub-optmal captal-to-assets rato when that varable s postve and equal to zero otherwse, and the captal under-utlzaton rato, whch s equal to the sub-optmal captal-toassets rato when that varable s negatve and zero otherwse. Most of the explanatory varables dscussed n the precedng secton also are ncluded n the revenue effcency regressons, prmarly as control varables. In most cases, the expected sgns of the explanatory varables are ambguous a pror. For example, the lne of busness Herfndahl ndex s predcted to have a negatve sgn under the conglomeraton hypothess, whch holds that t s valuemaxmzng for frms to offer multple lnes of busness, ether because of dversfcaton benefts or because buyers are wllng to pay more for ''one-stop shoppng.'' On the other hand, the strategc focus hypothess, whch holds that frms can maxmze value through focusng on one or a few lnes of busness where the frm has a comparatve advantage, predcts that the lne of busness dversfcaton varable wll have a postve sgn, recallng that hgh Herfndahl ndces mply more concentraton. 6 Lkewse, the geographcal Herfndahl ndex could have a postve or negatve sgn dependng upon whether focusng on a narrower geographcal area allows the frm to become more knowledgeable about the market and hence to buld stronger relatonshps wth customers versus reducng rsk through dversfcaton. Gven that there are other varables n the equaton relatng more drectly to nsolvency rsk, a postve sgn on the geographcal Herfndahl may be more lkely than a negatve sgn. Interpretng asset rsk as ndcatve of hgher nsolvency probabltes, we expect the rato of stocks and real estate to assets to be nversely related to revenue effcency. Frm sze s expected to be postvely related to revenue effcency f larger frms have lower 6 The conglomeraton and strategc focus hypotheses are further dscussed further n Berger, et al. (2000). 18

21 nsolvency rsk and/or are able to earn hgher revenues because sze conveys market power. The mutual dummy varable s predcted to have a negatve coeffcent f mutuals are less effcent than stocks due to unresolved agency conflcts that allow managers to behave neffcently. The premum growth rate s expected to have a postve sgn f frms wth more growth opportuntes tend to generate hgher revenues, other thngs equal. Fnally, the proporton of personal lnes output to total nsurance output s predcted to have a negatve sgn f commercal lnes nsurers have lower nsolvency rsk or hgher value-added because of hgher servce ntensty n the commercal lnes. 4.2 Return on Equty The ROE regressons are desgned to provde addtonal nformaton on the relatonshp between frm performance and captalzaton. Agan, we seek to determne whether measured captal under- or over-utlzaton s a ratonal response to market forces or a true neffcency. Fnancal theory predcts that frms wth relatvely more equty (lower leverage) are less rsky and thus should have lower costs of equty captal. Consequently, to the extent that realzed returns on equty are correlated wth the ex-ante cost of captal, we expect the rato of optmal captal-toassets to have a negatve coeffcent n the ROE regressons. If holdng addtonal captal above or below the measured optmum s a ratonal strategy, the rato of sub-optmal captal-to-assets s also expected to have a negatve coeffcent of roughly the same magntude as the coeffcent of the optmal captal-to-assets varable. However, f holdng too much or too lttle captal represents neffcency, the leverage-reducng benefts of holdng addtonal captal wll be partally or fully offset by a market penalty for the neffcency. Hence, the sub-optmal captal-to-assets rato could be negatve wth a smaller (n absolute value) coeffcent than the optmal captal-to-assets rato or concevably could be nsgnfcant or postvely related to ROE. Also ncluded n an ROE regresson s the frm's revenue effcency score and an ndcator varable set equal to 1 f an nsurer has a Best's ratng of A or hgher and equal to zero otherwse. To 19

22 the extent that hghly rated frms can charge hgher premums because of buyer perceptons that they have lower nsolvency rsk, we predct a postve coeffcent for the Best's ratng ndcator varable. The revenue effcency score s also predcted to be postvely related to ROE because revenue effcent frms lose smaller proportons of ther revenues due to neffcency, gvng them hgher profts, other thngs equal. The Best's ratng varable and revenue effcency are jontly determned wth ROE. Consequently, they are treated as endogenous varables, usng an nstrumental varables approach dscussed below. The explanatory varables ncluded n the revenue effcency regressons also are ncluded n the ROE regressons. There are several unambguous predctons based on the fnancal theory relatonshp between rsk and return. If geographcal and lne of busness dversfcaton reduce frm rsk, the coeffcents on the geographcal and lne of busness Herfndahl ndces are predcted to be postve n the ROE regressons because hgher Herfndahl ndces mply less dversfcaton and a hgher cost of captal. The rato of stocks and real estate to total assets also has a predcted postve coeffcent due to the hypotheszed relatonshp between rsk and the cost of captal. Lkewse, f buyng more rensurance reduces frm rsk, our rensurance varable, the rato of ceded loss reserves to drect plus assumed loss reserves, s predcted to be nversely related to ROE. Frms wth more growth opportuntes are lkely to be vewed favorably by captal markets, predctng a negatve sgn on the premum growth varable. Based on our argument that commercal lnes nsurers wll be relatvely safe compared to personal lnes nsurers, we predct a postve coeffcent on the rato of personal lnes output to total nsurance output. The predcted sgn of the sze varable n the ROE regresson s ambguous. On the one hand, f larger frms are more dversfed than smaller frms, we would expect sze to be nversely related to ROE. On the other hand, f larger frms earn hgher revenues due to market power, sze could be postvely related to ROE. In ths regard, t would reflect the frm's earnng economc rents rather than a hgher ex ante cost of captal. The predcted sgn of the long tal lnes varable (loss reserves 20

23 dvded by losses ncurred) s also ambguous. If long-tal lnes are more rsky than short-tal lnes and/or frms wth more long-tal busness are more hghly levered, a postve coeffcent would be predcted. On the other hand, long-tal lnes are known to have lower underwrtng profts than shorttal lnes because long-tal premums have a hgher dscount for the tme value of money. If ths effect domnates, the long-tal lnes varable could have a negatve coeffcent n the ROE regressons. Fnally, f mutual frms are more hghly levered than stocks, the mutual dummy varable s predcted to have a postve coeffcent, but f mutual frms wrte lower rsk busness than stock frms (Lamm-Tennant and Starks 1993), the mutual varable could have a negatve coeffcent. 5. METHODOLOGY Ths secton dscusses the estmaton methodologes used n our analyss of frm captal structure and performance. We begn by dscussng the economc effcency concepts underlyng our analyss. Next, we dscuss the estmaton of effcency utlzng (DEA). The secton concludes wth a dscusson of the regresson methodology used to analyze captal structure and the sub-optmal captal utlzaton on frm performance. 5.1 Effcency To analyze producton fronters, we utlze nput-orented dstance functons (Farrell 1957, x = x, x,..., 2 x K ' R + Shephard 1970). Suppose producers use nput vector ( ) K M vector y = ( y, y,..., 1 2 )' R +. The dstance functon ( y x) y M 1 to produce output D, s nterpreted ntutvely as the dstance of a gven frm's output-nput vector ( y, x) from the best practce producton fronter. For a sngle-nput, sngle-output frm, the fronter can be envsoned as an upward slopng lne n ( x, y) space. The operatng ponts of fully effcent frms, D ( y, x) = 1, le on the fronter, ndcatng that they operate wth the mnmum amount of nputs needed to produce ther quantty of output. Ineffcent frms, D ( y, x) > 1, le to the rght of the fronter, ndcatng that they could reduce ther nput consumpton whle producng the same quantty of output f they operated on the fronter (.e., 21

24 were fully effcent). More formally, we can defne the dstance functon n terms of the producton technology that transforms the K nputs nto M outputs. The producton technology s represented by the nput correspondence ( y)= V { x ( y, x) frm as D( y, x) sup{ θ : x V ( y) }. ( y x) = θ : s feasble}. The nput-orented dstance functon for a specfc D, s equal to 1 for effcent frms because they are already on the fronter and hence cannot reduce ther nput usage. ( y, x) > 1 D for neffcent frms and equals the recprocal of the mnmum equ-proportonal contracton of the nput vector x that can stll produce y. A smlar nterpretaton can be gven to the dstance functons wth respect to the cost and revenue fronters dscussed below. 7 The Farrell measure of nput techncal effcency reflects the ablty of a frm to mnmze nputs utlzed to produce a gven quantty of output. It s defned as TE 1, = = nf{ θ : θx V ( y) }. D ( y x) ( y, x) The techncal effcency measure θ s equvalent to one mnus the equ-proportonal reducton n all nputs that stll allows producton of the same outputs. It follows that TE ( y, x) 1. The Farrell measure of techncal effcency can be estmated wth respect to a producton fronter characterzed by constant returns to scale (CRS) or varable returns to scale (VRS). From an economc perspectve, frms should operate wth CRS, so total techncal effcency s gven by Farrell effcency wth respect to a CRS fronter, ( y x) respect to a VRS fronter, PTE( y x) TEVRS ( y, x) TE CRS,. Pure techncal effcency s gven by Farrell effcency wth, =, and scale effcency s gven by the remanng total techncal neffcency not explaned by pure techncal effcency, SE( y x) where SE ( y, x) denotes scale effcency. Frms wth ( y, x) = 1 SE are operatng wth CRS. ( y, x) ( y, x) TECRS, =, TE VRS 7 For further dscusson of dstance functons and operatng fronters see Charnes, et al. (1994), Grosskopf (1993) and Lovell (1993). 22

25 By explctly modelng the economc objectve of cost mnmzaton, we can estmate the cost effcency of each frm. When the economc objectve s to mnmze the costs assocated wth producng a gven output, then economc cost effcency s measured by the rato of mnmum possble cost to actual observed cost. Supposng producers face nput prces K ( w1, w2,..., ), the mnmum cost fronter s defned as c( y, x) = mn{ w' x : D( y, x) 1} w = w K ' R + + The optmal nput vector x * mnmzes the costs of producng y gven the nput prces w. Cost effcency then s smply defned as: CE w' x *, =. w' x ( y x) Cost effcency captures pure techncal effcency, scale effcency, and allocatve effcency. Allocatve effcency measures a frm's ablty to mnmze costs usng nputs n the optmal proportons, gven ther relatve prces. Gven a measure of total techncal effcency and cost effcency, allocatve effcency s determned resdually as AE ( y x) ( y, x) ( y, x) CE, =. TE Therefore, we have the followng decomposton of cost effcency: ( y, x) AE( y, x) PTE( y, x) SE( y x) CE =,. Fnally, by specfyng the addtonal economc objectve of maxmzng revenues, we can estmate the revenue effcency of each frm. Assumng output prces ( ) M x p = p, p2,..., p M ' R + + 1, the objectve s revenue maxmzaton, subject to the constrants mposed by nput supples and the producton technology. The revenue maxmzaton problem s: r( y, x) = max{ p' y : D( y, x) 1} Gven the optmal outputs y *, revenue effcency s gven by the rato of actual revenue to p' y RE =. p' y * maxmum revenue: ( y, x) y.. 23

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