The Momentum Effect on Estimating the Cost of Equity Capital for Property-Liability Insurers

Transcription

1 The Momenum Effec on Esimaing he Cos of Equiy Capial for Propery-Liabiliy Insurers Joseph J. Tien Tamkang Universiy Jennifer L. Wang Naional Chengchi Universiy Absrac The purpose of his paper is o es wheher he momenum effec has he significan impacs on he esimaion of he cos of equiy capial for propery-liabiliy insurers. Our empirical resuls show ha he cos of equiy capial for propery-liabiliy insurers may be underesimaed by using radiional CAPM model. Firs, i is imporan o consider infrequen rading facor in esimaing cos of equiy capial and he propery-liabiliy insurers sock reurns are ofen sensiive o he financial disress. Second, momenum facors have significan impacs on bea esimaions. Especially, adding he momenum facor in he model will enhance he magniude of bea for financial disress. Finally, differen business lines of he propery-liabiliy have differen coss of equiy capials. If he insurance supervisors use he same crierions o regulae hese business lines, i could mislead he fuure developmen of propery-liabiliy marke. We find ha he coss of equiy capial for some business lines increase more significanly han he ohers afer using FF3F and momenum models. Therefore, he governmen may need o se up a more sric regulaion on paricular lines when he propery-liabiliy insurers are facing a dangerous financial disress. Keyword: Momenum, Cos of Equiy 1

2 1. Inroducion How o esimae he cos of equiy capial correcly is an imporan issue for he insurance companies. The use of an incorrec cos of capial can have very serious impacs on he value of he firms and heir profis. Many recen sudies of insurance pricing, reserving and asse-liabiliy managemen (ALM) have discussed he imporan issues and problems of esimaing he cos of capial over he pas wo decades. The financial models can be served as a useful ool o provide more reliable mehods o remedy he deficiencies of radiional acuarial pricing because hey no only consider he risk of firms bu also conemplae oher imporan facors such as marke risks. Thus, he financial model (such as Capial Asse Pricing Model (CAPM)) can help propery-liabiliy insurers o esimae he cos of equiy more accuraely. Based on he porfolio heory of Markowiz (1952), Sharpe (1964) and Linner (1965) develop Capial Asse Pricing Model (CAPM) 1. However, in he lae 1970 s, some empirical sudies argued ha here exis oher facors such as earnings-price (E/P) raios, marke capializaion, book-o-marke equiy (B/M) raio and deb-equiy raios can also explain sock reurns (Basu, 1977 and 1981; Rosenberg, Reid and Lansein 1985; Bhandari, 1988). Fama-French(1992) use a Fama-French Three Facor (FF3F) model o conduc he empirical es on he cross-secional daa. They find ha he sysemaic marke risk (bea), size and book-o-marke raio are relaed o he sock reurns. However, FF3F is hardly a panacea. I s hard o explain he momenum effec 2, which is a sraegy ha buy winners and sell losers in he pas generae 1 Black (1972) develops anoher version of CAPM bu ges similar resuls wih Sharpe (1964) and Linner (1965) by relaxing he assumpions. Black, Jensen and Scholes (1972) use yearly daa from 1926 o 1965 o es CAPM and find ha bea can explain sock reurns. Fama and Macbeh (1973) remedy he deficiency of BJS(1972) by ime-series regression. Their resuls also suppor he CAPM. 2 Jagadeesh and Timan (1993) sugges he sraegy o buy winners and sell losers in he pas generaes significan posiive reurns over 3 o 12 holding periods in he U.S. marke. Rouwenhors (1998) and Chui, Timan and Wei (2000) also finds he momenum profis in he European marke and in he Asian markes such as Japan and Korea. Therefore, he momenum effec can be suppored by he global sock marke. 2

3 significan posiive reurns over cerain holding periods. Many recen empirical sudies had proven ha he momenum facors definiely play a criical role in esimaing he cos of equiy capial (e.g., Barberis, Shleifer and Vishny(1998); Cornad and Kaul(1998); Hong and Sein(1999); Jegadeesh and Timan(2001)). Fama and French (1997) sugges ha here is a significan indusry facor in esimaing cos of capial for insurers and ha insurance is a diverse enerprise, encompassing numerous lines of business wih differen risk characers. Some specific characers and issues (such as accouning principal, regulaions, reserve and lines of business) of propery-liabiliy insurers are indeed differen from oher indusries. Over he pas four decades, a considerable number of research sudies have invesigaed he asse pricing issue, bu only few aemps o apply he cos of equiy capial o propery-liabiliy insurers. Cummins and Harringon (1985) use quarerly daa o esimae he cos of capial and show ha bea esimaions were somewha unsable and conformed o he CAPM in he 1980 s bu no in he 1970 s 3. Cummins and Lamm-Tennan (1994) develop heoreical and empirical models showing ha insurers coss of capial are relaed o boh insurance leverage and financial leverage. 4 Lee and Cummins (1998) use he CAPM, he arbirage pricing heory (APT) model, and a unified CAPM-APT model 5 o esimae he cos of equiy for propery-liabiliy insurers during They discover ha APT and he CAPM-APT model perform beer han he CAPM in forecasing he cos of equiy capial for insurers. Cummins and Phillips (2005) esimae he cos of equiy for propery-liabiliy insurers by CAPM model and Fama-French hree facors model during They find ha he cos of equiy capial for insurers by using he 3 The sudy has small sample size. There are only foureen propery-liabiliy insurers in he sample. 4 Insurance leverage is he raio of policy reserves o asse. Financial leverage is he raio of financial deb o asse. 5 The CAPM-APT model is developed by Wei (1998). 3

4 Fama-French model is significanly higher han hose are esimaed based on he CAPM. Their evidence also suggess ha i exis grea differences in he cos of equiy capial across lines, indicaing ha he use of a single company-wide cos of capial is no appropriae. Wen e al. (2008) use he Rubinsein-Leland (RL) model o adjus cos of equiy capial for propery-liabiliy insurers due o he insurance claim process is highly skewed and heavy-ail disribuion. They find cos of equiy capial esimaed by RL model is beer han by CAPM when he insurer is small or is reurns are no symmerical. These previous papers have provided ingenious empirical mehodologies and generaed imporan empirical findings. However, here sill exis some problems in he esimaion of he cos of equiy capial for he propery-liabiliy insurance firms. Firsly, he liquidiy problem arises in esimaing he cos of equiy because many insurance companies are no publicly rading. The liquidiy premium could be conemplaed in he model for esimaing he cos of equiy capial for insurers. However, i has no ye been a fair esimaor. Secondly, previous lieraure does no consider he momenum effec. If he momenum facor is an imporan facor for he insurers, he equiy cos will be underesimaed wihou considering his facor ino he model. The purpose of his paper is o es wheher he momenum effec has he significan impacs on he esimaion of he cos of equiy capial for propery-liabiliy insurers. The remainder of he paper is organized as follows: Secion 2 proposes he sample selecion and he empirical model o esimae he cos of equiy for propery-liabiliy insurers. The empirical resuls are given in secion 3. Secion 4 makes conclusions. 4

5 2. Sample and Mehodology 2.1 Sample Selecion We obained he sock reurn daa from he Universiy of Chicago s Cener for Research on Securiies Pricing (CRSP). Daa were colleced for he period from 1993 hrough We use monhly reurn daa from CRSP o calculae cos of equiy capial for he period We also obain oher facors such as excess reurn for marke sysemaic risk, size, and financial disress and relevan daa abou he momenum facor from Kenneh French s websie 6. In order o esimae he cos of equiy capial by CAPM, FF3F and momenum model, we furher sor daa, sock reurns and insurer revenues, by lines of business. As for he revenue informaion abou lines of business, we use he daa from Naional Associaion of Insurance Commissioner (NAIC) annual saemen. 2.2 Esimaing he Cos of Capial for Propery-liabiliy Insurers We use hree differen models o esimae he cos of equiy capial for propery-liabiliy insurers: CAPM, FF3F and momenum model. In addiion o esimae he aggregae cos of equiy capial for insurers, we also predic coss of equiy capial by differen lines of business. In order o esimae he cos of equiy capial for differen lines more accuraely, we add firms characerisics ino Full-Informaion Indusry Bea (FIB) approach. (Kaplan and Peerson, 1998) We use he wo-sage approach o esimae cos of equiy capial for propery-liabiliy insurers. In he firs sage, he socks reurns are regressed on facors such as he marke risk, size, book-o-marke and momenum facors. In he second sage, he esimaed bea coefficiens from he firs-sage are added ino regression 6 hp://mba.uck.darmouh.edu/pages/faculy/ken.french. 5

6 equaions 7 along wih expeced risk premium for facors o obained cos of equiy capial Capial Asse Pricing Model (CAPM) The CAPM examines he relaionship beween sock reurns and marke bea. The firs sage regression is described as follows: r i, rf, i mi( rm, rf, ) i, (1) where r i, = he reurn on sock i in period, r, = he risk-free rae in period (Yield on 30-day Treasury bill), f r m, = he reurn on he marke porfolio in period, mi =he bea-coefficien for marke sysemaic for firm i, i,=he random error erm for sock i, The marke excess facor ( r r m f ) is defined as he value-weighed NYSE/AMEX/Nasdaq reurn minus he risk-free rae. We esimae he parameers i and mi from equaion (1). The regression sample periods consis of previous 72-monhs of reurn ending on June 30 of each year before calculaing cos of equiy capial period from 1999 o The cos of equiy capial of CAPM is given by he following formula: i f mi E( r ) r E( r ) r (2) where E r ) = he cos of equiy capial of CAPM for firm i, ( i r f= he expeced reurn of he risk-free asse, E( r m ) he expeced reurn on he marke porfolio, m f 7 The second-sage equaions are described as following such as (2), (4) and (6). 6

7 mi = he esimaed bea coefficien in he firs regression for firm i, The esimaed bea coefficien from equaion (1) from he firs-sage is hen insered ino equaion (2) o ge he CAPM cos of equiy capial. E r ) is calculaed as he value-weigh excess reurn on NYSE/AMEX/Nasdaq socks from 1926 unil June of Moreover, r f is he average of one-monh Treasury bill ( m yield a he same period. 8 Then, we can ge he cos of equiy capial of CAPM Fama-French Three Facors (FF3F) Model The FF3F model includes he risk premium for sysemaic marke risk (marke risk premium bea), he risk premium of firm size and financial disress ino he model. Firm size is defined in erms of oal marke capializaion and financial disress is subsiued by he raio of he book value of equiy (BV) o he marke value of equiy (MV). The firs-sage regression of FF3F model is described as follows: r i, rf, i mi ( rm, rf, ) sismb hihml i, (3) si = he bea coefficien for he size facor for firm i, SMB = he risk premium for firm size a period, hi = he bea coefficien for he financial disress facor for firm i, HML = he risk premium for financial disress a period, The sock reurns, risk-free rae, marke porfolio reurn and error erm are same as in he CAPM regression. The excess reurns for firm size and financial disress are calculaed by he sandard procedure in Fama and French (1992). We can esimae he parameers i, mi, si and hi from equaion (3). The sample selecing procedure is he same as CAPM. The cos of equiy capial for FF3F is given by he following 8 The marke risk premium is E( r m ) rf. We can use same marke risk premium in esimaing he cos of capial of FF3F and Momenum model. 7

8 formula: E( r r SMB HML E( r ) r ) (4) i f mi m f si hi where SMB = he expeced excess premium for size facor, HML =he expeced excess premium for financial facor, The esimaed bea coefficiens from equaion (3) are hen insered ino equaion (4) o ge he FF3F cos of equiy capial. As in he case of he marke risk premium esimaion, we calculae he average risk premium SMB and HML for size and financial disress from Then, we can ge he cos of equiy capial of FF3F model Momenum Model Jagadeesh and Timan (1993) add he exra facor momenum ino FF3F model. The firs-sage regression of momenum model is described as follows: r i, r, f i mi rm, rf, ) ( SMB HML Mom si hi moni i, (5) where moni = he bea coefficien for he momenum facor for firm i, Mom= he risk premium for momenum a period, The excess reurns for momenum are calculaed by he sandard procedure in Jagadeesh and Timan (1993) 9. We can esimae he parameers i, mi, si, hi and from equaion (5). The sample selecing procedure is he same as CAPM and moni FF3F model. The cos of equiy capial of momenum model is given by he following 9 A he beginning of every monh from June 1993 o June 2001, we rank all socks raded on NYSE, AMEX and he Nasdaq on he basis of pas one-monh reurns. Based on hese rankings, en decile porfolios are formed ha equally weigh he socks conained in he op decile, he second, he hird decile and so on. Then, i can calculae he weighed reurn by marke value of each decile porfolio. The op decile porfolio is called he winners and he boom decile porfolio is called he losers. In each monh, he sraegy buys he winner porfolio and sells he loser porfolio. The risk premium for momenum facor of every monh is esimaed for he difference beween he reurns on winners and on losers. 8

9 formula: E( r ) r ) i f mi E( r r SMB HML Mom m f si hi moni (6) where Mom = he expeced excess premium for momenum facor, The esimaed bea coefficiens from equaion (5) are hen insered ino equaion (6) o ge he cos of equiy capial of momenum model. As in he case of he marke risk premium, size and financial disress esimaion, we calculae he average risk premium Mom for momenum facor from Then, we can ge he cos of equiy capial of momenum model. 2.3 Adjus for Infrequen Trading The average rading volumes for propery-liabiliy insurance indusry is lower han oher indusry. In order o conrol his biases cause by infrequen rading, we uilize he sum-bea approach provided by Schole and Williams (1977) o adjus he infrequen rading. The CAPM bea is adjused as he following: r i, rf, i mi 1( rm, rf, ) mi0( rm, 1 rf, 1) i, (7) The esimaed sum-bea coefficien can be goen by sum of he conemporaneous and lagged bea esimaions ( mi mi1 mi0 ) from he equaion (7). Moreover, FF3F and momenum model adjus for infrequen rading as he following, respecively (8) and (9): ( r i, rf, ) a m 1( rm, rf, ) m0( rm, 1 rf, 1) HML HML k1 k 0 1 SMB SMB i, S1 S 0 1 (8) ( r i, rf, ) a m 1( Rm, Rf, ) m0( Rm, 1 Rf, 1) HML HML k1 k 0 1 mon1 Mom SMB SMB mon0 S1 Mom 1 i, S 0 1 (9) The differen kind of esimaed sum-bea coefficien can be gained by sum of each 9

10 he conemporaneous erm and lagged-erm bea esimaions (for example: ji ji1 ji0, j m, s, k, mon ) from he above equaion. By using he sum-bea approach, we can conemplae he risk premium for he infrequen rading of propery-liabiliy insurers. 2.4 Esimaing he Cos of Equiy Capial for Differen Lines of Business Afer obaining he sum-bea esimaors from CAPM, FF3F and momenum model, we furher calculaed he beas for differen lines of business by full-informaion bea (FIB) mehod. More deail abou how o esimae he cos of equiy capial for business line of propery-liabiliy insurers is described as follows. The purpose of he full-informaion bea mehod is o esimae he cos of equiy capial ha reflecs he lines of business composiion of he firm. The FIB mehod can be widely used o esimae he cos of equiy capial for non-raded sock insurers, muual and divisions for he firm. The fundamenal of he FIB mehod is ha he company can be regarded as a porfolio of asse, where he asses represen differen lines of business, individual deparmen or divisions. In his concepualizaion, he firm s overall marke bea coefficiens are he weighed average of he bea coefficiens of he separae divisions of lines of business. There exis wo seps in obaining bea esimaes for any given firm using FIB approach. In he firs sep, we can obain an esimaion of he bea coefficien for each firm in he sample. For example, we can ge he sum-bea esimaion mi, si, hi and mon from equaion (9) of momenum model. 10 The second sep is o process he i cross-secional regressions wih each of he sum-bea esimaion as a dependen variable and he raio of ne premiums in business lines as explanaory variables. 10 Similarly, we can obain he sum bea esimaions from equaion (1) of CAPM mi and mi, and si hi from equaion (3) of FF3F model. 10

11 The FIB regression is described as following: J ji fjk wik ij j1 (10) where ji = overall bea esimaion of ype j for insurer i, (j = m, s, h and mon) fjk = full-informaion bea of ype j for i in line of business k, (j = m, s, h and mon) w ik = ne premium weigh for insurer i in line of business k, ij = he error erm for insurer i of equaion j, 3. Empirical Resuls We provide he empirical resuls in his secion. Firsly, he overall bea and sum-bea esimaion resuls are presened. Then, we es wheher cos of equiy calculaed by CAPM, FF3F and momenum model are significanly differen. Finally, we compare he cos of equiy capial for hree separae lines of business including long-ail versus shor-ail, personal versus commercial, and auomobile versus workers compensaion versus all oher lines. 3.1 Bea Esimaions The bea esimaions by capial asse pricing model (CAPM), FF3F and momenum model are presened in Table 1. The able provides he average bea and average sum-bea for each year of he esimaed period. [Inser Table 1] The sum-bea coefficien esimaions are consisenly larger han he original bea 11

12 coefficien esimaions. In column (1) and (2), he average sum-bea by CAPM is and he average bea by CAPM is We also find he similar resuls in FF3F and momenum model. Therefore, i is imporan o consider infrequen rading facor in esimaing bea and calculaing cos of equiy capial for propery-liabiliy indusry. Moreover, by furher all samples ino he quarile, empirical resuls do no reveal ha large insurers consanly have smaller beas han small insurers 11. I is ineresing o noe ha, for boh bea and sum-bea, he coefficiens decline sharply in I may reflec he inerne bubble in 2000 and induce his phenomenon. Column (3) and (4) summarizes he bea and sum-bea esimaions based on Fama-French Three Facor Model (FF3F). The bea coefficiens for sysemaic marke, size and financial disress (book-o-marke value) are presened in he sample period ( ). The average sum-bea esimaions for marke risk premium, size premium and financial disress premium are respecively , and Generally speaking, he sum-bea esimaions are larger han radiional bea esimaions due o he infrequenly rading. The marke sysemaic risk facor has a higher bea coefficien han he financial disress, and he coefficien for size facor is he lowes. Our empirical resuls are consisen wih Cummins and Phillips (2005) For conserve space, we do no repor he bea resuls of quarile group in our able. However, in Table 2, readers can find he cos of equiy capial by he quarile group. 12 The sum-bea esimaions calculaed by Cummins and Phillips (2005) are respecively 1.04 (marke bea), (size bea) and (book-o-marke bea). Comparing wih Cummins and Phillips (2005), our bea esimaions are somewha lower han heir esimaions. I could be due o our esimaed period covers he marke collapse periods in

13 We also find he bea coefficiens decline in 2001 due o marke flucuaion. Therefore, we sugges using he average bea esimaions o calculae he cos of equiy is more reasonable and reliable han using he bea esimaions of he specific year. The marke bea and size bea esimaions for propery-liabiliy insurers are no significan differen from he all-indusry averages for hese wo parameers in Fama-French (1997). Our financial average disress bea esimaion by FF3F is which is larger han ha for all-indusry. Our resuls provide evidence ha propery-liabiliy sock reurns are more sensiive o financial disress han sock reurn in oher indusries in general. Therefore, he financial disress plays a vial role in esimaing cos of equiy capial for propery-liabiliy insurers. The bea coefficiens based on momenum model are shown in Columns (5) and (6). The average sum-bea esimaions for sysemaic and financial disress are and respecively. The average sum-bea esimaion for momenum facor is he smalles ( ) in all bea esimaors. 13 By using he momenum model, we also find he sum-bea coefficiens are larger han he beas wihou adjusmen. As for esimaing he cos of equiy capial in he momenum model, we find ha bea esimaions for marke sysemaic, size and financial disress are larger han hese esimaions in Fama-French FF3F model and CAPM. Alhough he esimaion of bea 13 For conserve he space, we do no repor he quarile empirical resuls in Table 1. Similarly, by using he momenum model, empirical resuls do no reveal ha large insurers consanly have smaller beas han small insurers. 13

14 for momenum facor is he lowes in all groups, i indeed enhances he magniude of beas for oher facors. In FF3F model, he bea esimaions of financial disress are lower han hose of sysemaic marke. However, if we consider he momenum facor in he model, he financial disress beas are almos he same as he sysemaic marke beas. I may imply ha he financial disress is more imporan and sensiive when considering he momenum facor in he model. 3.2 Overall Cos of Equiy Capial In his secion, we compare he difference of he cos of equiy capial esimaions by CAPM, FF3F, and momenum models. For esimaing he cos of equiy capial, we use he 30-days Treasury-bill rae as he proxy for he risk-free rae. As for he risk premium for sysemaic risk, size, financial disress and momenum facor, we uilize he long-run average hisorical daa of NYSE/AMEX/Nasdaq socks from 1926 o 2001 on Fama-French websie 14. [Inser Table 2 and Table 3] In Table 2, we find ha he average cos of capial for CAPM wih infrequen adjusmen is However, he average cos of equiy capial for FF3F model significanly enhance o Moreover, he cos of equiy capial from FF3F 14 The long-run average hisorical for risk-free rae is The risk premium for sysemaic risk, size, financial disress facors are respecively , and The risk premium for he momenum facor is

15 mehod is consisen higher han he esimaions based on CAPM mehod. Therefore, i seems o imply ha size and financial disress boh play imporan roles in esimaing he cos of equiy capial for propery-liabiliy indusry. For failing o adjus hese wo facors may underesimae he cos of equiy capial and mislead he financial decision of he company. The cos of equiy capial from momenum model wih infrequen adjusmen is In oher word, he cos of equiy capial from momenum model is consisenly higher han esimaions based on CAPM and FF3F mehod. Comparing wih Cummins and Phillips (2005), our cos of equiy capial (22.56%) is higher han nearly four percens han heir esimaion based on FF3F model (18.5%). Jagadeesh and Timan (1993) sugges ha momenum sraegy may generae significan posiive reurns. Table 3 shows he resuls of F-es for he differences of cos of equiy capial beween CAPM, FF3F and momenum model. We find significan resuls of F-es ( , , and ) in 1999, 2000 and I means ha he cos of equiy capial esimaed by FF3F is significanly higher han hose esimaed by CAPM. If we fail o adjus size and financial facors, we could underesimae he cos of equiy capial. Alhough he value of F-es is smaller, he empirical resuls show he momenum facor sill plays an imporan role in esimaing cos of equiy. The empirical resuls suppor ha momenum effec has some impacs on bea 15

16 esimaions. Especially, adding he momenum facor in FF3F model will enhance he magniude of bea for financial disress. This resul provides he evidence ha propery-liabiliy insurers wih poor financial saemen could reduce he value of companies and he willingness o inves. Financial disress for propery-liabiliy insurers plays an imporan role in many aspecs such as insurance purchase, regulaion, and cos of capial ec. The imporan implicaion of hese phenomena will be paricularly imporan afer considering he momenum sraegy because he insiuional invesors inend no o inves he bad companies. Therefore, he momenum facor may reflec he influence of financial disress and increase he cos of equiy capial for propery-liabiliy insurers. I is imporan for he regulaors or insurers in he propery-liabiliy indusry o seriously consider he momenum effec in esimaing cos of equiy capial. 3.3 Coss of Equiy Capial by Business Line In his secion, we use he FIB mehod o compose he overall cos of equiy capial and ge he cos of equiy for differen business line. The sum-bea cos of equiy capial esimaions from differen models for shor-ail 15 and long-ail 16 lines 15 Shor-ail lines of insurance includes propery coverages (such as fire, allied lines, homeowner mulperil, auomobile physical damage), all acciden, healh coverages and all financial guarany business. (such as fideliy, surey, morgage guarany, ec) 16 Long-ail business includes all liabiliy insurance coverages (such as oher liabiliy, produc liabiliy, personal and commercial auomobile liabiliy) and reinsurance. 16

17 are presened in Table 4. [Inser Table 4] The resuls show ha he coss of equiy capial do no differ significanly beween shor-ail and long-ail lines in CAPM and FF3F model, excep in he momenum model. In CAPM model, consisen o Cummins and Lamm-Tennan (1994), we find ha he cos of equiy capial is lower for shor-ail line ( %) han for long-ail lines ( %), bu i is no significan. However, in FF3F and he momenum model, he resuls which are consisen o Cummins and Phillips (2005) indicae ha he cos of equiy capial is higher for shor-ail ( % and %) han for long-ail line ( % and %). Our resuls afer considering size, financial disress and momenum facors seem o be conrary o he convenional houghs ha he long-ail lines are riskier han he shor-lines. One possible explanaion is ha asse and liabiliy end o move in he same direcion in response o ineres rae changes, herefore he long-ail lines may have higher discoun effec agains he ineres rae risk. However, shor-line lines are more suscepible o hurricanes and earhquakes, providing anoher possible explanaion o hese phenomena. Moreover, he cos of equiy capial in FF3F model is higher han CAPM and is lower han momenum model. The resuls confirm ha adding he size, financial disress and momenum facor in esimaing he cos of equiy capial are 17

18 imporan for propery-liabiliy insurers. We coninuously discuss he cos of equiy capial for personal lines 17 and commercial lines in Table 4. In all CAPM, FF3F and momenum models, he resuls shows commercial lines have higher cos of equiy capial han personal lines 18. Bu here is no difference beween commercial lines and personal lines while calculaing by he equal value weigh. These resuls provide evidences o sugges ha he commercial lines have a higher cos of equiy capial han he personal lines for he marke as a whole bu no for insurers on average. This may imply ha larger propery-liabiliy companies such as naional or inernaional insurers have more risky for commercial business han smaller insurers focusing on local or regional risks. I may also indicae ha larger insurers have superior abiliy o cover commercial lines risk because of heir beer capializaion. Generally speaking, esimaing he cos of equiy capial for propery-liabiliy insurers in momenum model is higher han CAPM and FF3F model. Therefore, he resuls furher confirm ha considering he marke facors in esimaing he cos of equiy seems necessary for propery-liabiliy insurers. Finally, he empirical resuls abou auomobile insurance, workers compensaion, 17 Personal lines of insurance include earhquake, personal auomobile liabiliy, homeowners, farmowners and auomobile physical damage. All oher lines of insurance are considered commercial lines. 18 We also calculae he cos of equiy capial by equal value weigh. For conserve he space, we do no repor he equal weigh value resuls in Table 4. The empirical resuls show he difference of equal weigh esimaion beween personal line and commercial line is no significan. 18

19 and all oher lines are shown in Table 4. Based on CAPM model, we find ha for boh equal or marke value weighed, he differences of cos of equiy capial among auomobile, workers compensaion and all oher propery-liabiliy lines are insignifican. We find ha he marke value weighed cos of equiy capial for auomobile insurance ( %) is lower han all oher propery-liabiliy lines ( %) and for workers compensaion is he lowes ( %). Bu he difference beween auomobile insurance and workers compensaion is no significan. However, based on he momenum model, we find ha he all oher propery-liabiliy lines sill have he highes cos of equiy capial bu he auomobile insurance become o have he lowes cos of equiy capial. As he FF3F model, he difference beween auomobile insurance and workers compensaion is no significan. In momenum model, he cos of equiy capial for all oher propery-liabiliy lines is he significanly highes in his group. The overall resuls indicae ha esimaing he cos of equiy capial based on he momenum model is higher han CAPM and FF3F model. This resul furher confirm ha fail o adjus some facors in he marke will mislead he cos of equiy capial for differen lines for propery-liabiliy insurers. Moreover, we also sugges ha insurance supervisors should enac suiable capial crierions for differen business lines of propery-liabiliy insurers. 19

20 4. Conclusions How o esimae he cos of equiy capial accuraely plays he prominen role for he insurers. The misundersanding he calculaion for cos of equiy capial could have very serious negaive impacs on he value of he firms. However, using he radiional aspec o look a he cos of equiy may underesimae some imporan facors exising in he capial marke. We believe our sudy has provided new insighs o he insurance lieraure. Firsly, he empirical resuls show ha he cos of equiy capial for propery-liabiliy insurers may be underesimaed by using CAPM model. Our resuls provide evidence ha he propery-liabiliy insurers sock reurns are sensiive o he financial disress. Thus, failure o adjus size and financial disress facor could lead o underesimae he cos of equiy capial significanly. Secondly, we find ha he cos of equiy capial could be biased wihou adjusing he momenum facor. Our resuls confirm ha he momenum facor indeed have significan impacs on bea esimaions. Especially, adding he momenum facor in FF3F model will enhance he magniude of bea for financial disress. In he propery-liabiliy indusry, he financial disress plays an imporan role in many aspecs such as purchase of insurance policies, regulaion requiremens of capial, and he esimaion for cos of equiy capial ec. The impacs of hese phenomena will be 20

21 paricularly significan afer considering he momenum sraegy because he insiuional invesors inend no o inves he bad companies. Therefore, he momenum facors will enlarge he influence of financial disress facor and increase he cos of equiy capial for propery-liabiliy insurers. Then, we find i is imporan o consider infrequen rading facor in esimaing cos of equiy capial. The average rading volumes of propery-liabiliy insurers are smaller han he rading volumes of companies in oher indusries. We use he sum-bea approach o adjus he infrequen rading and find he cos of equiy capial based on sum-bea approach is significanly larger han he cos of equiy capial wihou adjusmen. Finally, differen business lines of he propery-liabiliy have differen coss of equiy capial. If he insurance supervisors use he same crierions o regulae hese business lines, i could mislead he fuure developmen of propery-liabiliy marke. Moreover, some business lines are more sensiive o he financial disress and momenum facors. We find ha he coss of equiy capial for some business lines increase more significanly han he ohers afer using FF3F and momenum models. Therefore, he governmen may need o se up a more sric regulaion on paricular lines while he propery-liabiliy insurers are facing he serious financial disress. 21

22 Reference Barberis, N., Shleifer, A. and Vishny, R. (1998) A model of invesor senimen, Journal of Financial Economics, 49(1): Banz, R. (1981) The relaionship beween reurn and marke value of common socks, Journal of Financial Economics, 9(1): Barber, B. M., and Lyon, J. D. (1997) Firm size, book-o-marke raio and securiy reurns: a holdou sample of financial firms, Journal of Finance, 52(2): Barholdy, J., and Riding, A. (1994) Thin rading and he esimaions of beas: he efficiency of alernaive echniques, Journal of Financial Research, 17(2): Basu, S. (1983) The relaionship beween earnings yield, marke value, and reurn for NYSE common socks: Furher evidence, Journal of Financial Economics, 12(1): Bhanddari, L.C. (1988) Deb/Equiy raio and expeced common sock reurns: empirical evidence, Journal of Finance, 43(2): Black, F., Jesen, M.C. and Scholes, M.S. (1972) The capial asse pricing model: some empirical ess, Sudies in he Theory of Capial Markes, Praeger Publishers Inc. Black, F. (1993) Bea and reurn, Journal of Porfolio Managemen, 20(1): Capaul, C., Rowley, I. and William F. S. (1993) Inernaional value and growh sock reurns, Financial Analyss Journal, 49(1): Chan, L.K., Jegadeesh, N., and Lakonishok, J. (1996) Momenum sraegies, Journal of Finance, 51(3): Conrad, J. and Kaul, G. (1993) Long-erm overreacion or biases in compued reurns?, Journal of Finance, 48(1): Conrad, J. and Kaul, G. (1998) An anaomy of rading sraegies, Review of Financial Sudies, 11(2): Cox, L. A., and Griepenrog,G. L. (1988) The pure-play cos of equiy for insurance divisions, Journal of Risk and Insurance, 55(3): Cummins, J. D. (1990) Muli-period discouned cash flow raemaking models in propery-liabiliy insurance, Journal of Risk and Insurance, 57(1): Cummins, J. D., and Harringon, S. E. (1985) Propery-liabiliy insurance rae regulaion: esimaion of underwriing beas using quarerly profi daa, Journal of Risk and Insurance, 52(1): Cummins, J. D., and Harringon, S. E. (1987) Fair Rae of Reurn in Propery-Liabiliy Insurance (Hingham, MA: Kluwer Academic Publishers). Cummins, J. D., and Lamm-Tennan, J. (1994) Capial srucure and he cos of equiy capial in propery-liabiliy insurance, Insurance: Mahemaics and Economics, 15(2): Cummins, J. D., and Phillips R. D. (2000) Financial pricing of propery-liabiliy insurance, Handbook of Insurance Economics (Boson, MA: Kluwer Academic Publishers). Cummins, J. D., and Phillips R. D. (2005) Esimaing he cos of equiy capial for propery-liabiliy 22

23 insurers, Journal of Finance, 72(3): DeBond, F.M., and Thaler, R.H. (1985) Does he sock marke overreac, Journal of Finance 40(2): DeBond, F.M., and Thaler, R.H. (1987) Furher evidence on invesor overreacion and sock marke seasonaliy, Journal of Finance, 42(4): D Arcy, S. P. (1988) Use of he CAPM o discoun propery-liabiliy Loss Reserves, Journal of Risk and Insurance, 55(4): Fama, E. F., and French K. R. (1992) The cross-secion of expeced sock reurns, Journal of Finance, 47(2): Fama, E. F., and French K. R. (1993) Common risk facors in he reurns on socks and bonds, Journal of Financial Economics, 39(1): Fama, E. F., and French K. R. (1995) Size and book-o-marke facors in earnings and reurns, Journal of Finance, 50(1): Fama, E. F., and French K. R. (1996) Mulifacor explanaions of asse pricing anomalies, Journal of Finance, 51(1): Fama, E. F., and French K. R. (1997) Indusry coss of equiy, Journal of Financial Economics, 43(1): Harringon, S. (1983) The relaionship beween risk and reurn: evidence for life insurance socks, Journal of Risk and Insurance, 50(4): Hong, H., and Sein, J.C. (1999) A unified heory of underreacion, momenum rading and overreacion in asse markes, Journal of Finance, 54(4): Jegadeesh, N. and Timan S. (1993) Reurns o buying winners and selling losers: implicaions for sock marke efficiency, Journal of Finance, 48(1): Kaplan, P. D., and Peerson J. D. (1998) Full-Informaion indusry beas, Financial Managemen, 27(1): Kohari, S.P., Shanken, J. and Richard G.S. (1995) Anoher look a he cross-secion of expeced sock reurns, Journal of Finance, 50(1): Lakonishok, J., Shleifer A. and Vishny, R.W. (1994) Conarian invesmen, exrapolaion, and risk, Journal of Finance, 49(4): (4): Lee, A. C., and Cummins J. D. (1998) Alernaive models for esimaing he cos of equiy capial for propery/casualy insurers, Review of Quaniaive Finance and Accouning, 10(2): Lee, C. F., and Forbes, S. W. (1980) Dividend policy, equiy value, and cos of capial esimaes for he propery and liabiliy insurance indusry, Journal of Risk and Insurance, 47(2): Linner, J. (1965) The valuaion of risk asses and he selecion of risky invesmens in sock porfolios and capial budges, Review of Economics and Saisics, 47(1): MacKinlay, A. C. (1995) Mulifacor models do no explain deviaions from he CAPM, Journal of Financial Economics, 38(1):3-28. Meron, R.C. (1973) An ineremporal capial asse pricing model, Economerica, 41(3)

24 Markowiz, H.(1959) Porfolio Selecion: Efficien Diversificaion of Invesmens (Wiley, New York). Myers, S. C., and J. Read, Jr. A. (2001) Capial allocaion for insurance companies, Journal of Risk and Insurance, 68(4): Phillips, R. D., Cummins J. D., and Allen, F. (1998) Financial pricing of insurance in he muliple line insurance company, Journal of Risk and Insurance, 65(4): Quirin, G. D., and Waers W. R. (1975) Marke efficiency and he cos of capial he srange case of he fire and casualy insurance companies, Journal of Finance, 30(2): Rosenberg, B., Kenneh R., and Lansein, R. (1985) Persuasive evidence of marke inefficiency, Journal of Porfolio Managemen, 11(1), 9-17 Sharpe, W. F. (1964) Capial asse prices: A heory of marke equilibrium under condiions of risk, Journal of Finance, 19(2): Scholes, M., and Williams, J. (1977) Esimaing bea from nonsynchronous daa, Journal of Financial Economics, 5(3): Sommer, D. (1996) The impac of firm risk on propery-liabiliy insurance prices, Journal of Risk and Insurance, 63(4):

25 Table 1 Bea Esimaions by CAPM, FF3F and Momenum Model for Propery-Liabiliy Insurers (1) Bea by CAPM (2) Sum-Bea by CAPM (3) Bea by FF3F Model (4) Sum-Bea by FF3F Model (5) Bea by Momenum Model (6) Sum-Bea by Momenum Model m (1999) (1999) S (1999) h (1999) mon (2000) m (2000) S (2000) h (2000) mon (2001) m (2001) S (2001) h (2001) mon (Average) m (Average) S (Average) h (Average) mon 25

26 Table 2 Coss of Equiy Capial for Propery-Liabiliy Insurers YEAR Marke No. P&L Cos of equiy Cos of equiy Cos of equiy Value insurers esimaed by esimaed by esimaed by Quarile CAPM Model FF3F Model Momenum Model (Small) (Large) Toal (Small) (Large) Toal (Small) (Large) Toal All Toal Table 3 F-Tes on Cos of Equiy Capial for CAPM, FF3F and Momenum model Average CAPM FF3F F-Tes *** *** ** *** Average FF3F Momenum F-Tes *** ** ** *** *** ** *,, are significan a he 1, 5 or 10 percen level, respecively. 26

27 Table 4 Cos of Equiy Capial for Differen Business Lines Cos of equiy esimaed by CAPM Model Cos of equiy esimaed by FF3F Model Cos of Equiy Capial for Shor-ail Line and Long-ail Line (Marke Value Weigh) Cos of equiy esimaed by Momenum Model Shor-ail Line Long-ail Line F es : Cos shor Cos long ** Cos of Equiy Capial for Personal Line and Commercial Line (Marke Value Weigh) Personal Line Commercial Line F es : Cos personal Cos commercial ** *** Cos of Equiy Capial for Auomobile, Workers compensaion and oher P&L (Marke Value Weigh) Auomobile insurance Workers compensaion All oher P&L lines of insurance F F F es : Cosauo Cosworker es es : Cos : Cos worker auo Cos Cos Alloher Alloher *** *** *** *** *** 27