Interactions Between Risk-Taking, Capital, and Reinsurance for Property- Liability Insurance Firms

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1 Business School W O R K I N G P A P E R S E R I E S Working Paper Ineracions Beween Risk-Taking, Capial, and Reinsurance for Propery- Liabiliy Insurance Firms Selim Mankaï Aymen Belgacem hp://www.ipag.fr/fr/accueil/la-recherche/publicaions-wp.hml IPAG Business School 184, Boulevard Sain-Germain Paris France IPAG working papers are circulaed for discussion and commens only. They have no been peer-reviewed and may no be reproduced wihou permission of he auhors.

2 Ineracions Beween Risk-Taking, Capial, and Reinsurance for Propery-Liabiliy Insurance Firms Selim Mankaï a, Aymen Belgacem ab March, 2013 a IPAG Business School, Paris b Universié d Orléans, LEO-UMR 7322 Absrac: Theory and empirical evidence recognize ineracions beween capial and risk. This paper analyzes he effec of reinsurance, as a new endogenous decision variable, on his policy mix using simulaneous equaions model. Empirical resuls obained from a sample of U.S. propery-liabiliy insurance firms reveal significan ineracions beween capial, risk, and reinsurance. The relaionship beween risk and capial is posiive, highlighing he effeciveness of regulaory mechanisms. Reinsurance is negaively associaed wih capial, for which i appears o ac as a subsiue. These resuls are srongly sensiive o he level of capial held in excess of he regulaory minimum requiremens. Weakly capialized firms adjus heir reinsurance and risk levels more exensively and ry o rebuild an appropriae capial buffer. Unlike oher decision variables, he capial raio converges oward a arge level. Keywords: Risk-aking, Capial Regulaion, Reinsurance, Simulaneous Equaions, Insrumenal Variables. JEL Classificaion: G22, G28, G32

3 1. Inroducion Insurance firms have always been subjec o various consrains wih respec o risk-aking and capial holding. Since is inroducion in 1994, he risk-based capial (RBC) sysem has seadily consolidaed he inerdependence beween hese wo decisions (Cheng and Weiss, 2012). Capial adjusmens are generally made hrough earning reenion or new shares issuance. Hoerger e al. (1990) and Garven e al. (2003) demonsrae ha reinsurance indirecly affecs hese adjusmens by reducing risk and acing as coningen capial. Wells e al. (1995) find ha muual insurers use reinsurance o reduce funding difficulies. Moreover, he broad adopion of he Enerprise Risk Managemen (ERM) framework furher srenghens he links beween risk-aking, capial, and reinsurance (Nocco and Sulz, 1996). Similarly, recen regulaory changes are more amenable o defining capial requiremens in erms of cerain qualiaive aspecs of reinsurance (Holzmüller and Eling, 2008 and Scordis and Seinorh, 2012). Undersanding he ineracions beween capial, risk and reinsurance is of grea relevance, paricularly for regulaors, who mus craf prudenial rules for regulaing insurers behavior 1. Shareholders are also concerned by he possible ransmission of shocks o capial, resuling from unanicipaed losses. Negaive shocks ofen enail forced liquidaions of asses, which adversely affec he firm value. Among he relaionships beween he hree decision variables considered here, hose beween capial and risk are by far he mos sudied in he lieraure. Several hypoheses relaed o moral hazard, agency coss and regulaory pressures have been advanced o explain he ineracions beween hem. A firs hypohesis, based on agency coss and buffer capial heory, predics a posiive relaionship beween capial and risk. An alernaive hypohesis, based on informaion asymmery regarding he acivaion of he guaranee fund in case of bankrupcy, predics a negaive relaionship. The conflicing predicions of hese hypoheses have led o acive empirical research. Shrieves and Dahl (1992) were he firs o examine his issue for U.S. banks. In a subsequen paper, Cummins and Sommer (1996) invesigae he issue for non-life insurance firms, providing empirical suppor for a posiive relaionship beween capial and risk. Baranoff and Sager (2002) empirically explore hese ineracions in he case of life insurance, finding a posiive (negaive) relaionship beween capial and asse (liabiliy) risk. Recen sudies, such as Shim (2010) and Cheng and Weiss (2012), also confirm a posiive relaionship beween hese variables. Alhough his relaionship beween capial and risk has been exensively sudied in he lieraure, few papers o dae have explored he relaionship beween risk and reinsurance and even less, he ineracions beween capial and risk wih reinsurance. There are several reasons o believe ha reinsurance is endogenously influenced by he choice of capial and risk and vice versa. MacMinn (1987) and Planin (2006) find ha reinsurance is deermined joinly wih capial srucure. Dionne and Triki (2004) documen a srong posiive relaionship beween leverage as a risk indicaor and reinsurance demand. Shiu (2011) focuses on he endogenous naure of reinsurance and finds ha he laer is posiively relaed o leverage, and vice versa. All of hese resuls suppor he hypohesis of inerdependence beween reinsurance, capial, and risk. This sudy analyzes capializaion policy and is relaionship o risk-aking and reinsurance. More specifically, we aim o deermine he naure of adjusmens beween hese decision variables and wheher hey converge oward arge levels. To his end, we use a simulaneous equaion sysem, which considers heir poenial endogeneiy. The conribuion of his paper o he exising lieraure is wofold: Firs, we ry o fill in he gap in he lieraure by examining he ineracions among hese hree decision variables insead of sudying hem in pairs. We believe ha much is o 1The heoreical lieraure ofen provides conflicing answers o hese quesions (Scannella, 2012). Sric regulaion may creae disorions in he operaions of solven firms. In conras, permissive regulaions may lead o high-risk exposure, hreaening he crediworhiness of insurers. This siuaion ofen implies a slowdown in innovaion, inefficien invesmen sraegies, or passive capial accumulaion. 1

4 be gained hrough a join analysis of he hree decision variables. The second moivaion of he paper is ha mos of previous sudies (e.g. Cole e al. 2011; Shim, 2010, Shiu, 2011) argue ha ineracions differ according o several ransversal variables such as he size, he organizaional form and he group affiliaion. This led us o perform a subsample analysis in he second par of he paper. Our empirical resuls confirm his hypohesis and show ha he capial, risk and reinsurance inerac in boh direcions. The subsample analysis shows ha weakly capialized insurers ry o build an adequae capial buffer by increasing capial and reducing risk. In conras, hose wih large capial buffers end o increase boh risk and reinsurance demand. We provide empirical evidence ha he capial raio converges slowly oward a arge level. This paper is organized as follows. Secion 2 skeches he heoreical underpinnings of he poenial ineracions beween risk-aking, capializaion, and reinsurance and develops a se of hypoheses. Secion 3 idenifies and discusses he main deerminans of each decision. Secion 4 presens our economeric model specificaion and esimaion echniques. Secion 5 describes our sample and provides summary saisics. Secion 6 analyzes our empirical resuls and provides some robusness checks. Secion 7 provides some concluding remarks. 2. Theoreical background and research hypohesis In his secion, we briefly ouline he heoreical lieraure ha highlighs he ineracions beween capial, reinsurance, and risk-aking and posi he hypoheses used in our empirical analysis Ineracions beween capial and risk Ineracions beween capial and risk have been he focus of acive research, paricularly in he banking secor. The inroducion of RBC appears o reinforce he inerdependence beween hese wo decisions which are inerconneced under he influence of several facors, such as agency coss, moral hazard, and regulaory pressure. The lieraure makes conradicory predicions regarding he naure of such ineracions. A firs hypohesis predics a negaive relaionship beween risk and capial, reflecing insurers incenives o exploi guaranee fund in case of failure, given ha insolvency coss will be borne by guarany fund members. When conribuion in he fund is no correlaed wih acual risk, i.e. fla raher han risk-based premiums, his opporuniy can creae adverse incenives in insurance markes and encourage insurers o increase risk and reduce capial and hus, ake advanage of he moral hazard posed by he guarany fund sysem (Cummins, 1988; Horiuchi and Shimizu, 2001, Cheng and Weiss, 2012). However, he relevance of his hypohesis is empered by he fac ha he coverage of he guaranee fund is less complee han in he banking secor and by he growing effeciveness of supervisory mechanisms and marke discipline (Cheng and Weiss, 2012). Therefore, he incenive o ake excessive risk for non-life insurers is resrained. Anoher explanaion for a negaive relaionship beween capial and risk for U.S insurers may be due o flaws in he RBC formula. Cheng and Weiss (2012) argue ha some ypes of risk are overweighing, while ohers are underweighing. This encourages insurers o rearrange heir porfolios by choosing asses or lines of business wih low weighs. Then insurer risk would have increased while capial requiremens would have decreased, resuling in a negaive relaionship. A second hypohesis suggess a posiive relaionship beween hese wo variables. According o capial buffer heory, insurers hold an excess capial above he regulaory minimum as a guaranee agains unanicipaed exreme losses and in order o avoid regulaory coss (Shim, 2010). This relaionship beween capial and risk is more pronounced in he shor run han in he long run (Jokipii and Milne, 2011) and i also depends on capial level. Specifically, insurers wih accepable levels of capial may no respond o he RBC requiremens and may even increase heir risk level. 2

5 However, hose wih relaively low capial levels ry o build a capial buffer by raising capial or reducing risk and respond srongly o regulaory pressure and marke discipline. Fonseca and Gonzalez (2010) argue ha marke discipline can furher affec he recapializaion decision. Thus, insurers exposed o srong marke discipline are incenivized o adjus heir capial more quickly. Therefore, our firs hypoheses are as follows: H 1A : Capial and risk adjusmens are posiively relaed. H 1B : Weakly-capialized insurers adjus heir capial and risk more quickly han highly-capialized insurers Ineracions beween capial and reinsurance Shiu (2011) argues ha here is a relaionship in boh direcions beween reinsurance and capial srucure and hus, hey migh be joinly deermined. Under he rening capial hypohesis, reinsurance is ypically viewed as a subsiue for capial (Armsrong and Dror, 2007). Sulz (1996) and Adiel (1996) demonsrae ha reinsurance affecs solvency and can funcion as off-balance shee capial. In addiion, reinsurance increases he insurer s surplus and srenghens is underwriing capaciy (Graham and Rogers, 2002 Aunon-Nerin and Ehling, 2008, Zou and Adams, 2008, Barram, Brown and Fehle, 2009). Transferring risk o a reinsurer relaxes capial resricions for an insurer and allows expanding is capaciy o issue new policies. Thus, his risk ransfer means reduces he required capial on he insurer s balance shee by enabling i o use capial rened from he reinsurer. Using radiional sources of capial, such as corporae deb, coningen capial, or new equiy, in response o a shock is ypically an expensive and difficul operaion. Thus, Insurers prefer using reinsurance han holding more capial as i allows hem o mainain an accepable level of solvency. On he oher side, according o he bankrupcy-cos argumen, highly leveraged insurers are more exposed han ohers o risk of insolvency. Thus, reinsurance proecs hem agains unexpeced losses and reduces he risk of insolvency (Shiu, 2011). Thus, our hird hypohesis is as follows: H 2 : There is a negaive relaionship beween capial and reinsurance in boh direcions. 2.3 Ineracions beween reinsurance and risk One way o reduce volailiy, insolvency and/or specific risk and hus capial requiremens is o use reinsurance, especially when risk level moves closer o solvency consrains (Adams, 1996). Agency heory suggess a posiive relaionship beween risk-aking and reinsurance. Excessive riskaking limis he abiliy of insurers o reain projecs wih posiive ne presen value. Reinsurance is hus a way of miigaing his problem by ransferring par of he risk o reinsurers. In addiion, reinsurance can play he same role as he guaranee fund and encourage insurers o ake on more risk or reduce capial. Because reinsurers have an incenive o monior he underwriing risk of he insurers wih whom hey do business (Cole e al. (2011), his relaionship beween risk and reinsurance is more pronounced for affiliaed raher han for nonaffiliaed reinsurers due o he coss of monioring which are more imporan for he laer. Thus, we formulae he following hypohesis: H 3 : Risk and reinsurance adjusmens are posiively relaed. 3

6 2.4 Impac of ransversal facors Size The neoclassical heory of he firm idenifies several facors ha may affec he main financial decisions of insurers. Wihin his conex, size plays an imporan role in influencing he insurer s risk appeie hrough is effec on invesmen opporuniies, he firm s demand for reinsurance, and he firm s access o capial. Large firms are generally subjec o low informaion asymmery beween managers and poenial invesors, which reduces he cos of capial (Smih, 1977). Moreover, hey are likely o have a beer qualiaive and geographical allocaion of risks and hold proporionally less capial han small firms. Due o economies of scale in risk managemen and he greaer abiliy of large firms o raise capial in he shor run, large firms are expeced o require less capial o operae and can ake on larger risk (Timan and Wessels, 1988; Aggarwal and Jacques, 2001). Numerous sudies indicae ha firm size negaively affecs he demand for reinsurance (Hoerger e al., 1990; Adams, 1996 and Powell and Sommer, 2007). Small insurers depend more on reinsurance use because hey do no have economies of scale and scope, and hey have higher financing coss when raising exernal funds for a leas wo main reasons (Adams, 1996). Firs, he direc coss of financial failure are no proporional o he size of a company (Warner, 1977). Second, raising capial in financial markes is an expensive underaking. Cole and McCullough (2006) view size as an inverse measure of bankrupcy coss and find a negaive relaionship beween his variable and he demand for reinsurance. Thus, large insurers will be less dependen on reinsurance for expansions of heir underwriing capaciy. We formulae he following hypohesis: H 4 : Large firms hold less capial and reinsurance han small firms. The inverse effec is observed wih risk Organizaional form There are wo main forms of organizaion in he insurance indusry: sock firms, which are owned by shareholders, and muual firms, which are owned by policyholders. The managerial discreion hypohesis suggess ha sock insurers end o underake relaively more complex and risky projecs (Mayers and Smih, 1990). However, shareholders have more conrol over managers in such firms han in oher organizaion forms. The implicaions of pecking order heory will vary, depending on organizaional form. Sock firms have greaer access o he financial markes. Muual firms have more difficulies in raising capial han sock insurers. In addiion, agency coss vary depending on a firm s organizaional form. Conflics beween shareholder and policyholders may impac he choice of capial level. Harringon and Niehaus (2002) find ha muual insurers end o hold more capial han sock insurers. Cummins e al. (2001) predic ha managers of muual firms are more risk averse because of heir specific organizaion and oher difficulies in diversifying heir wealh. Thus, such firms are more likely o manage risk hrough reinsurance. Indeed, Cole and McCullough (2006) noe ha muual firms, which have less access o capial markes in cases of caasrophic loss, use more reinsurance. Thus, we formulae he following hypohesis: H 5 : There is a negaive (posiive) relaionship beween sock firms and reinsurance or capial (risk-aking). Affiliaed vs nonaffiliaed insurers An exensive lieraure has focused on capial ransfer wihin financial groups (Sein, 1997; Campello, 2002). Affiliaed insurers generally hold less capial and have incenives o ake more risk, as hey have access o inernal resources provided by oher affiliaes. I is also easier for hem o obain capial injecions from paren firms when heir capial levels become insufficien. Powell e al. (2008) invesigae wheher or no inernal capial markes are acive wihin insurance groups. 4

7 They find evidence ha hey play a significan role in he invesmen behavior of affiliaed insurers, and ha capial is allocaed o subsidiaries wih he bes expeced performance. Like capial and risk, reinsurance ransacions can also be grouped ino reinsurance wih affiliaes and reinsurance wih nonaffiliaed. According o Mayers and Smih (1990) and Powell and Sommer (2007), his decision can be regarded as an inernal capial marke ransacion. Reinsurance can ransfer income wihin he group and reduce he overall ax burden (Mayers and Smih, 1990). In addiion, i allows affiliaed insurers o ake advanage of risk diversificaion hrough inra-group reinsurance (Cole and McCullough, 2006). This is confirmed by Powell and Sommer (2007), who argue ha ransacions ino group have lower asymmeric informaion coss han hose wih nonaffiliaes and hus i implies lower monioring coss. Accordingly, we posi he following hypohesis: 3. Conrol variables The empirical lieraure idenifies several facors ha may affec he endogenous variables. Here, we presen he mos imporan facors in he empirical model developed below. 3.1 Deerminans of Capial Performance Firms wih high profiabiliy generally have sufficien inernal funds ha may be ransformed ino capial. According o pecking order heory, firms prefer inernal o exernal financing (i.e., deb or new equiy) due o he coss of issuing new equiy or deb. Alernaively, in he presence of asymmeric informaion, he use of exernal funding may convey negaive informaion o he marke abou he firm s value. If he behavior of insurers is consisen wih pecking order heory, we expec performance o posiively affec capial levels. Following Timan and Wessels (1988) and Fama and French (2002), we use reurn on asses as an indicaor of profiabiliy. Cos of capial The cos of holding capial is an imporan deerminan of capial levels (Esrella, 2004). Various coss, such as agency and informaion asymmery coss, are relaed o he use of capial, and he level of capial is expeced o be inversely relaed o such coss. The cos of holding capial is difficul o measure in pracice. Similarly o (Ayuso e al., 2004 and Jokipii and Milne, 2008), we approximae his cos as he average of posiive reurns on equiy (ROE) over he las five years. Informaion asymmery Signal heory suggess ha informaion asymmery and he opaciy of he insurance indusry are imporan deerminans of capial levels (Poier and Sommer, 2006 and Morgan, 2002). Insurers wih volaile incomes are likely o use reained earnings raher han exernal capial o address fuure losses or cope wih shocks. Insurers can overcome informaion asymmery by building a capial sock in periods of high profiabiliy. We use he volailiy of ROE as a measure of informaion asymmery (Cummins and Nini, 2002 and Grubisic and Leadbeer, 2007). Exposure o exreme risk Exposure o exreme risks is also likely o influence he level of capial. Zanjani (2002) illusraes ha companies ha insure heavily agains naural disasers have higher capial levels han hose ha are less exposed o such evens. The level of exposure o exreme risk is measured in our model as a percenage of oal premiums wrien in he earhquake line of business (Cummins and Song, 2008). Liquidiy risk Insurers wih a large share of liquid asses are more likely han ohers o face regulaory consrains. The low risk associaed wih hese asses allows for easy adjusmens o capial levels. 5

8 Therefore, insurers wih more liquid asses are expeced o have less capial and ake greaer risk. De Ceuser (2003) finds ha he major source of illiquidiy is asse-liabiliy mismach, which may encourage insurance firms o hold more capial. In his sudy, liquidiy risk is measured by he raio of liabiliies o liquid asses. Cos inefficiency Hughes and Moon (1995) emphasize he imporance of analyzing he impac of inefficiency on capial, esablishing a negaive relaionship beween hese wo variables. For insance, Alunbas e al. (2007) noe ha he cos inefficiency of European banks is due o heir high capial levels and moderae risk-aking. This facor is generally esimaed using non-parameric mehods. However, some sudies argue ha financial raios are very simple esimaes of cos inefficiency. For simpliciy, his variable is measured in his sudy as he raio of operaing expenses o ne income. Defici Deficis reflec he need for exernal financing when inernal cash flows are exhaused. This variable is used o es for he exisence of a preference ordering among funding sources for insurers. According o pecking order heory, his facor, which is measured hereafer by he level of invesmen plus changes in working capial minus inernal cash flow, has a posiive impac on he level of capial (De Bie and De Haan, 2007). Growh opporuniies Insurers wih beer growh opporuniies are expeced o hold more capial. The lieraure uses he book-o-marke raio or changes in R&D expenses o measure his variable. 2 However, due o a lack of daa, we use an alernaive measure, as in Carayannopoulos and Kelly (2005), namely, he pas growh (over five years) in premiums. 3.2 Deerminans of risk-aking Exising heoreical and empirical work suggess ha risk-aking will be affeced by various facors, including he following. Leverage Empirical work in he insurance indusry (e.g., Borde e al., 1994) confirms he relevance of firm leverage and argues ha risk-aking can be influenced by his facor, which ends o amplify reurns and/or losses. A high deb raio worsens he underinvesmen problem, he risk of insolvency, and bankrupcy coss. Thus, we expec a negaive relaionship beween risk-aking and leverage. Therefore, we expec a negaive relaionship beween risk aking and leverage. In he empirical model below, his variable is approximaed by he raio of liabiliies o surplus. Cos inefficiency Cos inefficiency can also have an effec on risk-aking. For he banking secor, Berger and DeYoung (1997) and Williams (2004) inroduce he bad managemen hypohesis and demonsrae ha a decline in coss or revenue efficiency emporally precede increases in riskaking. Thus, we expec a posiive relaionship beween inefficiency and risk-aking. Business mix The business mix is he degree of cenering on a firm s core business. Previous research has found ha differences in risk across a firm s various lines of business posiively affec reinsurance levels. Thus, we expec a posiive relaionship beween he degree of cenering and risk-aking. 2Hovakimian e al. (2001) and Fama and French (2002) use he book o marke raio as a proxy for a firm s growh opporuniies (GROWTH). This proxy is defined as he raio of he book value of oal asses minus he book value of equiy and deb plus he raio of marke value of equiy and deb o he book value of oal asses (Barclay and Smih, 1995; Rajan and Zingales, 1995). 6

9 This variable is approximaed by he Herfindahl index of he four major branches of non-life insurance business, namely, shor- and long-erm personal insurance and shor-erm and long-erm commercial insurance. Geographic and line of business diversificaion An insurer may reduce is overall risk by holding a porfolio whose componens are no perfecly correlaed across regions and/or aciviies. Empirical sudies find ha in he banking secor, diversificaion is associaed wih moderae risk-aking (Hughes, Lang and Meser, 1996 and Deng e al., 2007), a hypohesis based on he benefis of cos reducion and income synergy (Saunders and Corne, 2007). Alernaively, diversificaion may be associaed wih higher riskaking because of he agency problem and compeiion. The degree of diversificaion is measured by he Herfindahl index percenages of direc premiums wrien by line of business and geographical area. 3.3 Deerminans of reinsurance Researchers have documened ha reinsurance can be affeced by several firm-specific facors. Performance Adams e al. (2008) predic ha he poores-performing insurance companies end o use more reinsurance han profiable companies, which have more resources o cope wih financial risk and hus lower probabiliies of bankrupcy. This performance is measured by he reurn-on-asses raio. Loss volailiy Reinsurance is generally used o sabilize underwriing profis. When he loss raio is highly volaile, he insurer has less cerainy of fuure value losses and hus greaer incenive o use reinsurance. According o Hoerger e al., (1990), an increased volailiy of claims gives rise o increased reinsurance demand. This facor is approximaed by he sandard deviaion of he loss raio over he las hree years. Liquidiy risk Lee and Urruia (1996) find ha he liquidiy raio is an imporan indicaor of solvabiliy. An insurer wih relaively liquid asses has more sable finances and is hus expeced o use less reinsurance. Conversely, insurance companies wih insufficien liquidiy are likely o use more reinsurance (Planin, 2006). Reinsurance price Cole and McCullough (2006) explore he impac of reinsurance prices on reinsurance demand, finding a negaive correlaion beween he coss of he use of reinsurance and demand for his risk managemen ool. This price is approximaed by he raio of premiums ceded minus losses o claims recovered from reinsurers. Inefficiency The impac of inefficiency on reinsurance adjusmen is similar o ha of performance in he sense ha less efficien insurers end o use more reinsurance han oher firms. The relaionship beween inefficiency and he level of reinsurance is expeced o be negaive. Business Mix Mayers and Smih (1990) examine he effecs of he composiion of a firm s porfolio of aciviies on he demand for reinsurance. They observe ha an increased concenraion of aciviies increases he volailiy of cash flows and he risk of bankrupcy. Reinsurance could be a soluion o he risk of insolvency arising from his source. Moreover, Shorridge e al. (2004) and Cole e al. (2006) demonsrae ha his facor reflecs he degree of cenering on he core business. In 7

10 conras, he economic benefis of specializaion can reduce he demand for reinsurance. We predic a negaive relaionship beween he degree of specializaion and he demand for reinsurance. Line-of-Business and geographic concenraion A high concenraion of premiums in cerain lines of business exposes insurers o significan risk. However, high concenraion may also reflec specializaion and beer risk pricing. Thus, he effec of concenraion on he demand for reinsurance is no clearly defined. In conras, geographical concenraion reflecs he degree of diversificaion of an insurer across saes. Cole and McCullough (2006) find a negaive relaionship beween geographic concenraion and reinsurance and beween lines-of-business concenraion and reinsurance. Garven and Lamm- Tenan (2003) and Mayers and Smih (1990) also find a negaive relaionship using a differen measure of diversificaion. These variables are measured by he Herfindahl index of he percenage of direc premiums wrien by lines of business and geographic area, respecively. 4. Mehodology 4.1 Model In his secion, we invesigae he shor-run relaionships beween capial, reinsurance, and risk using simulaneous equaions. Imporanly, he observed variaions of hese variables are boh discreionary and caused by facors exogenous o he insurer (Shrieves and Dahl, 1992; Jacques and Nigro 1997; Cummins and Sommer, 1996; Baranoff e al., 2007; Shim, 2010). To accoun for his behavior, we inroduce lagged variables as parial adjusmen componens (cf. appendix 1). The model has he following specificaion: Cap Cap Reins Risk Perf Cos_cap Caasrophe + Assy i, 0 Cap i, 1 1 i, 2 i, 3 i, 4 i, 5 i, 6 i, + Lq _ risk + Cos_ineff + Growh Defici Org + Group + Size Year e 7 i, 8 i, 9 i, 10 i, 11 i, 12 i, 13 i, i, Reins Reins Cap Risk Loss_vol + Perf + Lq_risk + Reins_price i, 0 Reins i, 1 1 i, 2 i, 3 i, 4 i, 5 i, 6 i, + Mix Hibl Higeo Cos ineff Org Group + Size year u 7 i, 8 i, 9 i, 10 _ i, 11 i, 12 i, 13 i, i, Risk Risk Reins Cap Lev Mix Hibl Higeo i, 0 Risk i, 1 1 i, 2 i, 3 i, 4 i, 5 i, 6 i, Cos _ ineff Org Group + Size year v 7 i, 8 i, 9 i, 10 i, i, (1) (2) (3) where e, i, v, and i, u are error erms. i, Cap, Reins, and Risk denoe he capial raio, reinsurance raio, and risk level, respecively. The definiions and descripions of various conrol variables are repored in Table 1. Time effecs are included in he model o consider sysemaic evens and high losses associaed wih man made and naural disasers. 4.2 Variables consrucion Capial (Cap): As mos of he insurers in our sample are no lised, i is no possible o deermine heir marke values. Similar o Aggarwal and Jacques (2001), Cummins and Sommer (1996), and Shim (2010), we proxy he capial raio by he book value of he surplus divided by he oal value of asses. Reinsurance (Reins): This variable is given, for each insurer, by he raio of oal reinsurance premiums ceded o oal business premiums (Garven and Lamm-Tennan, 2003; Cole and McCullough, 2006; and Powell and Sommer, 2007). Risk (Risk): 8

11 Based on porfolio heory, we measure oal risk by he volailiy of he asse-o-liabiliy raio. According o Cummins and Sommer (1996) and Shim (2010), an insurer s asse volailiy can be expressed as follows: A L A. L where A and are he volailiy measures of he insurer s asses and liabiliies, respecively, and L is he covariance of he logarihms of he asses and liabiliy values. Le us denoe he AL, proporion of asses of asse ype (i) in he invesmen porfolio by x i and he proporion of liabiliies from business line (j) by y j. The respecive volailiies of he asse and liabiliy porfolios and he covariance of he logarihms of he liabiliy and asse reurns are given as follows: (4) N N 2 A xx i j Ai Aj Ai Aj i1 j1 M M 2 L yy i j Li Lj Li Lj i1 j1 (5) (6) A i L j N M (7) xy i j i j AL i j A L A L i1 j1 and denoe he volailiies of he log of asse ype (i) and he log of liabiliies in business line (j), respecively. The parameer AL i j reflecs he correlaion beween he log of he i h asse and he log of he liabiliies in he j h business line, whereas N is he number of asse caegories and M is he number of lines of business. To measure risk using his measure of volailiy, one mus firs define differen lines of aciviies and asse caegories. Following Shim (2010), we aggregae each insurer s lines of business ino 12 caegories: homeowners/farm-owners, auo physical damage, auo liabiliy, commercial muliple peril, special propery, fideliy/surey, acciden, healh, and financial guarany, medical malpracice, workers compensaion, oher liabiliy, special liabiliy, and miscellaneous liabiliy. The ypes of asses are classified ino seven caegories: socks, governmen bonds, corporae bonds, real esae, morgages, cash and oher invesed asses, and non-invesed asses. A second risk measure used o assess he robusness of our resuls is he RBC raio, inroduced by he Naional Associaion of Insurance Commissioners (NAIC). This measure offers an alernaive way of accouning for he risk of insurers (Chang and Weiss, 2012 b ). More specifically, i reflecs he minimal capial level required of insurers. All else equal, an insurer s capial requiremen mus be higher as more risk is aken on. 4.1 Esimaion mehodology In capuring ineracions beween capial, risk, and reinsurance, simulaneous equaion models have shown beer performance han esimaing he equaions individually, as he laer approach ignores he problem of endogeneiy and may violae he condiion of no correlaion beween exogenous variables and error erms (Balagi, 2005). To address his problem in he relaionship beween he key variables and o avoid biased OLS esimaes, we employed he hree-sage leassquares (3SLS) echnique (Shim, 2010; Rime, 2001; Jacques and Nigro, 1997 and Aggarwal and Jacques, 1998). We used insrumenal variables, checking heir validiy using he Sargan Hansen es. In he firs sep, we esimae he model using he OLS and 3SLS mehods, comparing he resuls using he Durbin-Wu Hausman es. As we find significan differences in he esimaes, he endogeneiy problem is confirmed. Regarding he choice of insrumens, we use he risk and reinsurance variables (lagged wo periods), he economic growh rae, and he raio of unrealized gains (wih no lag and lagged one period). All of he oher predeermined variables are used as 9

12 insrumens in he srucural esimaion. Prior o esimaion, we aemp o verify wheher he ime series are saionary based on he Levin-Lin-Chu es. Table 1. Variable definiions Variable Endogenous variables Measure ΔCap Expeced sign ΔReins ΔRisk Cap Raio of surplus o oal admied asses. (+/) (+/) Reins Raio of reinsurance premiums ceded o direc business wrien plus reinsurance assumed (). (+) Risk1 Volailiy of he asse o liabiliy raio (+) (+). Risk2 Raio of RBC o oal admied asses (+) (+). Exogenous variables Reg 1 if firm s ne premium o surplus raio = or >300%, 0 Oherwise... Perf Reurn on asses raio (+) (). Cos_cap Average of posiive ROE over he las five years ().. Caasrophe Roe_vol Proporion of direc premiums wrien in earhquake line of business The sandard deviaion of he firm s ROE over he las five years (+).. (+).. Cos_ineff Raio of oal expenses o ne earnings (+) (+) (+) Reinsprice Mix Raio of reinsurance premiums minus ceded-reinsurance commission earned o claims recovered from reinsurers Herfindahl index of shor and long ails of personal and commercial lines. ().. () (+) Lq_risk Raio of liabiliies o liquid asses (+) (+). Loss_vol Sandard deviaion of he loss raio over he las hree years. (+). Lev Raio of direc business wrien o surplus () Hibl Higeo Herfindahl index of direc premium wrien across all lines of business Herfindahl index of direc premium wrien across geographic areas. (+) (+/). (+) (+/) Growh Percenage growh of wrien premiums (+/).. Defici Financial defici raio calculaed as cash dividends plus invesmens plus change in working capial minus inernal cash flow. (+/).. Sock 1 if he insurer is a sock firm, 0 if i is a muual firm ().. Group 1 if he insurer is a member of a group in year, 0 oherwise ().. Size The logarihm of oal admied asses ().. Year Annual emporal effec... This able describes he variables used in he empirical model. 10

13 5. Daa 5.1 Sample The daa used in his sudy are colleced from he Naional Associaion of Insurance Commissioners (NAIC) annual saemen daabase for U.S. propery-liabiliy insurers from 1999 o The sample is limied o solven insurers reporing posiive values of admied asses, gross and ne premiums wrien, equiy capial, and ceded reinsurance premiums. We reain only acive insurers wih no regulaory acions in process. Afer applying hese sample screens, our final sample consiss of 11,929 year-firm observaions. I accouns for 81% (84%) of he enire U.S. propery-liabiliy marke in erms of oal asses in he year 1999 (2008). We use an unbalanced daa panel o allow for a comprehensive evaluaion of he propery-liabiliy marke. The sample includes firms ha enered or lef he marke during he sudy period. In addiion o he NAIC daabase, we also colleced daa from DaaSream o esimae asse reurns Descripive saisics and correlaion analysis Table 2 presens descripive saisics of all variables used in his sudy. The mean and median of he capial raio are approximaely 38% and 42%, respecively. These saisics are (39%, 34%) and (0.026, 0.004), respecively, for he reinsurance raio and risk level. These values exceed hose repored in Garven and Lamm-Tennan (2003), suggesing a significan increase in reinsurance demand over he las decade. The disribuions of he wo risk measures are posiively skewed. Wih regard o he diversificaion profiles measured by he wo Herfindahl indices (Higeo and Hibl), we noe small variaions across insurers. Approximaely 73% of insurers are sock firms, and 70% are affiliaed. Before conducing he regression analysis, we firs considered he possibiliy of muli-collineariy among independen variables, which may lead o biased esimaes. Table 3 repors he Pearson correlaion beween he variables included in he regression model. Table 3 indicaes ha he correlaion beween capial and risk is posiive, confirming he hypohesis ha insurers adjus heir capial levels upward following increases in risk. The relaion beween risk and reinsurance is negaive, which is in line wih he view of reinsurance as a guaranee fund. Anoher ineresing resul repored in Table 3 is he low correlaion beween he wo risk measures. 4 The Spearman nonparameric correlaion beween hese wo risk measures (no repored here) is saisically significan a he 1% level and is equal o 0.1. Ineresingly, cos inefficiency correlaes significanly wih all key variables. Consisen wih sandard economeric pracice, for each equaion, we assess he degree of muli-collineariy among he independen variables using he variance inflaion facor (VIF). All VIF values repored in Table 4 range beween 1.01 and 2.2. Thus, no muli-collineariy was observed among he independen variables. 3We use he S&P 500 global index, Barclays capial, US 20 year Treasury bond, Dow Jones Corporae bond index, Merrill Lynch Morgage, U.S. real esae & renal & leasing and he hree-monh U.S. reasury bill as proxies for asse reurns. 4 Many criicisms have been addressed regarding RBC as an insolvency predicor (e.g., Cummins, Grace and Phillips, 1999; Cummins, Harringon and Klein, 1995). Cheng and Weiss (2012) find ha he accuracy of he RBC raio in predicing insolvencies is inconsisen over ime. 11

14 Table 2. Descripive saisics This able repors he mean, median, minimum, maximum, sandard deviaion, fifh percenile, and 95h percenile of all variables. The daa are colleced from he NAIC and Daasream daabases covering U.S. propery-liabiliy insurance firms from 1999 o

15 Table 3.Correlaion coefficien marix * represens saisical significance a 1% level. Table 4.Variance inflaion facors For definiions of hese variables, see Table 1. 13

16 6. Resuls This secion discusses he empirical resuls. The sysem of equaions is esimaed under wo specificaions, which alernaively exclude and include he regulaory pressure mechanisms. We esimae he model for he full sample and for various subgroups, reflecing he level of capial, size, and organizaional form of firms. Finally, we perform several robusness ess Full sample Equaion of capial The main hypohesis esed in his paper concerns he exisence of inerconnecions beween risk-aking, capial, and reinsurance. Table 5 repors he 3SLS esimaion of he simulaneous equaions using volailiy as a risk measure. The Hansen and Sargan es shows he validiy of he seleced insrumenal variables used in he firs sep of he esimaion process. A closer look a he individual equaions coefficiens indicaes ha mos key variable esimaions are in line wih expecaions. The firs column of Table 5 repors he resuls for he capial equaion. Overall, he coefficiens are significan, excep for ha on exposure o exreme risks. The risk variable is posiive and saisically significan, a resul ha is consisen wih he capial buffer hypohesis, suggesing ha an increase in porfolio risk leads o posiive adjusmens of capialinsurers as a guarany agains unanicipaed exreme losses (Jokipii and Milne, 2011). Second, he negaive sign of he Reins adjusmen variable suppors he original hypohesis regarding he subsiuabiliy beween hese wo variables. This resul is consisen wih he findings of Sulz (1996) and Armsrong and Dror (2006), who argue ha reinsurance can serve as offbalance shee capial ha reduces capial requiremens and allows he insurer o expand is capaciy o issue new policies. Concerning he main conrol variables, he able shows ha he parial adjusmen facor, a measure of convergence oward he desired long-run capial raio, which is capured by he lagged endogenous variable, is low (0.0519). This resul can be explained by he presence of various adjusmen coss. 5 Performance appears o have a significan and posiive effec on capial, confirming pecking order heory and suggesing ha profiable firms prefer inernal financing and rely heavily on reained earnings o raise capial because of he coss of exernal funds. The cos of capial variable is negaive and significan, which highlighs he imporan coss relaed o he use of capial. Moreover, an increase in informaion asymmery, measured by he volailiy of ROE, drives insurers o hold more capial. This variable reflecs he level of risk o some exen and hereby confirms he posiive relaionship beween hese wo variables. Economic inefficiency is posiively relaed o capial adjusmen. The coefficien on his variable is significanly and negaively associaed wih liquidiy. We also noe he presence of significan emporal effecs, which may be explained by he impac of various macroeconomic shocks or exreme losses of capial. The inroducion of regulaory pressure mechanisms in he second specificaion (firs column of he righ-hand side of he able) slighly alers he esimaion resuls. For he mos par, he coefficiens of he new variables are saisically significan. The esimaes of he capial equaion provide suppor for he hypohesis ha undercapialized insurers bearing more risk seek o avoid regulaory inervenion. Only he coefficien onreg 1Reins 1is posiive and saisically significan. These resuls indicae ha highly leveraged companies in he previous period end o increase heir levels of reinsurance o adjus heir capial levels o avoid regulaory coss. 5 We do no examine he possibiliy of asymmeric adjusmen coss. I may be simpler o reduce capial by increasing dividends or by buying back equiy han by raising capial. 14

17 Equaion of reinsurance Table 5 also presens he esimaion resuls for he equaion of he raio of reinsurance. The chisquare saisic is significan a he 1% level, illusraing he validiy of he esimaion. Posiive adjusmens of risk-aking or capial generae an increase in he raio of reinsurance. Unlike he inverse effec, we find ha capial is no a subsiue for reinsurance. This resul can be explained by he fac ha he marginal cos of reinsurance per uni of risk is less han ha for capial, creaing an asymmeric relaionship. Anoher explanaion may lie in he imperfec subsiuabiliy beween he wo mechanisms in he sense ha reinsurance can play he same role as capial, whereas he reverse is no he case. For example, capial does no reduce he volailiy of losses. Moreover, he resuls show ha he parial adjusmen facor is no significan and illusrae ha he reinsurance policy does no converge oward a long-run arge level.an increase in inefficiency posiively affecs he level of reinsurance. Consisen wih he findings of Cole and McCullough (2006), diversified firms use less reinsurance. Moreover, sock firms appear o use less reinsurance han muual firms. This resul suppors he idea ha sock firms have easier access o exernal funding and are less risk averse han muuals. The size variable, which can be associaed wih diversificaion, is significan and negaive. Accordingly, large firms end o have beer risk allocaion and use less reinsurance. The inroducion of regulaory pressures does no change he paern of resuls. Equaion of Risk The las par of Table 5 presens he esimaion resuls for he risk equaion. The chi-square saisic is significan a he level. A posiive capial adjusmen leads o lower risk. We also noe he asymmeric relaionship beween capial and risk adjusmen, which can be explained by he lagged effec of capial on risk. Moreover, we noe ha a posiive adjusmen of reinsurance increases his risk. This finding is consisen wih he view of Shiu (2011) and Aunon-Nerin and Ehling (2008), who repor ha he heavy use of reinsurance leads o high risk-aking. The parial adjusmen facor is no significan, indicaing ha risk-aking does no converge o a long-run arge. The Mix and Hibl variables, which reflec he degree of concenraion of he main underwriing branches and lines of business, are posiive and significan. As he aciviies of he company become more concenraed, he company s risk-aking increases in he shor erm. Insurers wih a low level of efficiency are more prone o high risk-aking han insurers wih greaer cos efficiency. As expeced, size encourages risk-aking, which is more prevalen among sock firms han among muual firms. 15

18 Table 5. Esimaion resuls of he simulaneous equaions using volailiy as a risk measure This able repors he resuls of he 3SLS esimaion for he full sample, wihou (specificaion I) and wih (specificaion II) ineracion erms. *, **, *** represen saisical significance a 10%, 5% and 1% levels, respecively. The Hansen-Sargan es evaluaes he validiy of he insrumens. 16

19 Table 6. Esimaion resuls following he capial level This able repors he resuls of he 3SLS esimaion following he buffer level. *, **, and *** represen saisical significance a 10%, 5%, and 1% levels, respecively. The Hansen-Sargan es evaluaes he validiy of he insrumens Sub-sample esimaion To reduce he effec of sample heerogeneiy and he aggregaion bias ha i implies, we divided he overall sample ino several sub-samples. The firs sub-sample is based on he level of capial held beyond he regulaory minimum. We firs esimae a new regression using a sample of he boom hird of firms in erms of he raio of capial o he regulaory minimum. The hreshold obained for he firs sub-sample was Thus, his sub-sample includes all insurers ha have almos 2.5 imes he minimum capial requiremen. The esimaion resuls, repored in Table 6, illusrae ha he relaionship beween capial adjusmen and risk remains posiive. The coefficien is significan wih a relaively high value, indicaing a high sensiiviy of he raio of capial o risk. Adjusmens o he level of reinsurance appear o have a greaer impac on capial. Reinsurance is a perfec subsiue for capial for hese companies. The capial raio is he only variable ha converges o a long-erm level, wih he speed of adjusmen in his sub-sample greaer han ha observed in he overall sample. The second par of he able shows he op hird of mos capialized insurers, wih a hreshold of We observe a posiive fi in he relaionship beween capial and risk, alhough i is less han ha observed for small-cap companies. Parial adjusmen facors of he endogenous variables are all significan. These resuls can be explained by he fac ha insurers have significan flexibiliy in heir funding sources, which allows hem o achieve heir goals hrough differen financial policies. The sample is divided ino wo sub-groups by he value of asses corresponding o he op and boom hirds. The resuls presened in Table 7 generally confirm hose obained wih he oal sample, excep for he relaionship beween capial and risk for major insurance companies, a relaionship ha is negaive in boh direcions. A final esimaion is performed by dividing he sample ino muual and sock companies. The resuls, presened in Table 8, confirm our hypoheses. The resuls for he oher explanaory variables are also affeced by he organizaional form. 17

20 Table 7. Esimaion resuls for sock and muual firms This able repors he resuls of he 3SLS esimaion for sock and muual firms. *, **, and *** represen saisical significance a 10%, 5%, and 1% levels, respecively. The Hansen-Sargan es evaluaes he validiy of he insrumens. 18

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