Designaion and Deecion of he Bes Capal Buffer of Nonlife Insurance Counercyclical Regulaion in China Su Fang, sofiasu@mail.shufe.edu.cn Wu Jie oucmahwj@126.com (Finance School, Shanghai Universy of Finance and Economics, Shanghai, 200433) 1
Absrac Counercyclical regulaion was an imporan research field in insurance in hese years. The insurance regulaion deparmen of mos counries all ook researches abou he counercyclical regulaion consanly. In his aricle, he appropriae monor conrol index of nonlife insurance counercyclical regulaion was go by panel daa model on he foundaion of hisory daa of nonlife insurance in China. Using Markov regime swching model, he deailed regulaion sysem of nonlife insurance counercyclical regulaion was designed in deail and he bes capal buffer was go. The resuls showed ha premium increasing rae was he bes monor conrol index of nonlife insurance counercyclical regulaion, as kep a deep relaionship wh solvency margin. The smooh possibily in Markov regime swching model could show correcly he regime of differen ime. If he regulaion deparmen required appropriae posive or negaive capal buffer according wh he smooh possibily, he premium increasing could be urned over quickly. Then, he flucuaion of insurance marke would be smooher and smooher. Excep ha, he nonlife insurance counercyclical regulaion was mos effecively if we ook he capal buffer raio c as 2.5%. Those research resuls were useful for he Solvency II designaion in China. Key Words: Nonlife Insurance; Counercyclical Regulaion; Capal Buffers; Markov Regime Swching Model 2
Inroducion Afer he financial crisis of 2008, he financial regulaion deparmen realized he problem of financial regulaion sysem a ha ime. Mos of hose counries began o develop macro-prudenial regulaion. Basel III was published in G20 conference in 2010 soon, which suggesed developing Counercyclical Regulaion in he finance indusry. So, his became o be he revoluion direcion of financial regulaion in he world. In he insurance regulaion, Inernaional Associaion of Insurance Supervisors (IAIS) also suggesed ha insurance regulaion deparmen should pu macro-prudenial regulaion ino effec, develop and enhance Counercyclical Regulaion imporanly. IAIS were keeping research of he uniform regulaion framework of he world. In China, China Insurance Regulaory Commission (CIRC) almos kep he same speed wh IAIS. They have finished Regulaion Framework of Solvency II in China, and confirmed ha Counercyclical Regulaion would be implemened in he fuure, which would require insurance companies draw capal buffers of Counercyclical Regulaion according wh he macro-prudenial regulaion. In fac, here were so many aricles in China which esed he cycle of nonlife insurance in China (Sun Qixiang, 2011). Counercyclical Regulaion based on he cycle of insurance marke, which ook some adverse measure wh he marke cycle. For example, when he marke was very low, he regulaion would be a lle looser so ha he marke would recover soon. While when he marke was very ho, he regulaion would be very sricer o make he speed slower and avoid bubble. So ha, he sysem risk of marke would be counerac because of Counercyclical Regulaion, and he sabily of marke would be beer han before. Capal buffer was he core of Counercyclical Regulaion Sysem, which was some exra capal requiremen according wh he cycle of insurance marke. In deailed, when he insurance marke was very low, here should be a negaive capal buffer. So, he capal requiremen would be decreased a lle. The operaion expense and capal expense would be decreased, he developing speed of insurance company would increase and all marke could recover soon. While when he insurance marke was very ho, here should be a posive capal buffer. So, he capal requiremen would be increased a lle, which increased he operaion expense and capal expense, insurance company mus decrease he developing speed as hey didn have enough exra capal. So ha, he developing speed of premium would decrease and he marke could go back o raional marke soon. In China, CIRC has published he Exposure Draf of Solvency II on April 2014. They said he requiremen of counercyclical regulaion capal buffer would be published separaely. Bu unil now, he deailed counercyclical regulaion and capal buffer haven come on ye. So, how o design he counercyclical regulaion and capal buffer in China? Wha s he bes index o be monored? How much rae was suable? There were so many deailed quesions o be answered before designing he counercyclical regulaion sysem. Basel Commission made he raio of cred ousanding wh GDP as he monor conrol index of cycle in he 3
counercyclical regulaion of bank, hen, wha should be he monor conrol index in insurance? Which one is beer for premium, ne income or combined raio? When was he bes ime o draw capal buffer? How many capal buffers should be drawn in order o realize he effec of he counercyclical regulaion? The framework of counercyclical regulaion sysem would be clearer if we can answer hose quesions above. In his aricle, we ried o answer hose quesions by using panel daa model and Markov regime swching model. The monor conrol index of counercyclical regulaion for nonlife insurance was go wh panel daa. Then, he deailed counercyclical regulaion mehod was designed by using Markov regime swching model. The bes rae of capal buffer was go a las afer comparing he regulaion effec of differen capal buffer. This aricle ried bes o make some innovaion below: (1) Geing he suable monor conrol index of nonlife insurance counercyclical regulaion in China according wh he pro-cyclicaly of solvency margin. (2) Designing he deailed counercyclical regulaion schedule. (3) Comparing he regulaion effec of differen capal buffer and deciding he bes capal buffer. The resuls of his aricle could provide some suggesion o he insurance regulaion deparmen in China. The conens of his aricle included below. The second par was leraure review. The hird par was heory and model. The fourh par was demonsraion. The fifh par was esing and final par was resuls and suggesions. Leraure Review In hese years, he financial regulaion deparmen of many counries ook more and more aenions on macro-prudenial regulaion and reinforced counercyclical regulaion. Those scholars also ook more and more researches abou counercyclical regulaion. Bu mos of hem concenraed hemselves on he counercyclical regulaion of bank. The deailed counercyclical regulaion sysem of bank was almos clear and would be born soon. Bu in insurance, more researches sill focused on he es of premium cycle or claim cycle, and calculae he lengh of cycle. Only lle aricles ook research abou he deailed mehods and schedule of counercyclical regulaion in insurance. So, we could do some deep research in insurance and ake he research resuls of counercyclical regulaion in bank as a reference. Basel Commission published Guiding Principle of Counercyclical Capal Regulaion for Bank in 2010. They ook he monor conrol index of counercyclical regulaion of bank as he deviaion of General Cred/GDP wh s secular rend. The regulaion deparmen would decide he capal buffer wh he secular rend of he deviaion in General Cred/GDP. They ook he capal buffer as 2.5%. This decision based on he research of Bank for Inernaional Selemens (Drehmann e al. 2010). They analyzed he daa from 30 counries in 40 years. They found General Cred/GDP could reveal he accumulaion of sysem risk in bank. So, hey suggesed making as he monor conrol index of counercyclical regulaion in bank. Bu some oher academics analyzed he same daa of differen counries and go differen resuls. Repullo & Saurina (2011) hough GDP increasing rae wasn posive correlaed wh 4
he secular rend of deviaion in General Cred/GDP. I s useless o sop he fas cred increasing rae if he counercyclical regulaion based on General Cred/GDP. Li Wenhong & Luo Meng (2011), Gao Guohua (2013) also hough General Cred/GDP can monor he accumulaion of sysem risk in China. Some aricles also made researches abou he drawing of counercyclical regulaion. Edge & Meisenzahl (2011) hough he counercyclical regulaion mehod of Basel Commission would change bigly wh he differen sample, differen calculaion of secular rend and differen parameer. These would affec he effeciveness of regulaion. Peng Jiangang e al. (2010) agreed wh ha he counercyclical regulaion of Basel Commission was insufficienly a lle. The deailed counercyclical regulaion of insurance hasn been decided, neher in he framework of inernaional insurance regulaion from Inernaional Associaion of Insurance Supervisors (IAIS, 2006), nor in he solvency II of European. Academics all were making some exploraion in he insurance counercyclical regulaion and aking ha of bank as references. Cerchiara & Lamania (2009) designed he counercyclical regulaion model of simple insurance company on he foundaion of claim cycle of insurance, which was from he poin of inernal model of Solvency II in European. They chose solvency margin and premium change as he monor conrol index. Bu he defec of he model was very obvious as jus can be used o simple insurance company which ook inernal model, can be popularized o all insurance indusry. Boyle & Kim (2012) designed a heory model o measure he sysem risk wh he CoCTE model, and designed he capal buffer model wh Markov regimes swching model. Bu hey jus provided a possible idea for he counercyclical regulaion, insead of designing a really operable model. They even didn es wheher he model could realize he regulaion objec really. In China, mos academics were sill focused on he verificaion of insurance cycle in he nonlife insurance marke, he procyclical effec wh macroeconomics, and some heory suggesions for he counercyclical regulaion. Wang Bo & Shi Anna (2006) found ha he cycle of main insurance producs were 6 years, bu he cycle of nonlife insurance indusry wasn very obvious on he foundaion he claims raio for 22 years. Zhang Lin & Zhu Yuanli (2007) also go he similar resuls. Ji Yuna & Zhen Haao (2009) found here were some cycles of all insurance producs, which were same wh Li Xinyu & Li Jie (2010) and Zhang Lin & Tang Linjuan (2012). Gen Yunjie (2011) hough here were some pro-cyclical effecs beween premium and GDP. She analyzed he cycle reason from accouning sysem and solvency regulaion sysem. Huang Xi & Zhou Hui (2012) found insurance indusry was pro-cyclical wh economics. Mos of hem esed he operaion cycle of nonlife insurance. They didn ake deep accoun wh he objec, mehod and index of counercyclical regulaion. Some provided lle suggesions abou ha. Liu Chao & Liu Zhiwei (2010) and Zhao Guangyi & Wang Rui (2010) suggesed ha counercyclical regulaion could be realized from underwring regulaion, reserves rules, fair value and solvency regulaion a he same ime. Bu acually, if he regulaion deparmen would inervene he operaion of insurance companies by reserve drawing and fair value calculaion, 5
s a good chance for insurance company o manipulae he prof. Wu Jie & Su Fang (2014) disinguished he concep of premium cycle and claim cycle. They hough hose wo cycles boh exised and hey relaed wh each oher. Every nonlife insurance producs had heir own premium cycle and claim cycle. Differen facors affeced hose wo differen cycles. The counercyclical regulaion should focus on he claim cycle which showed he real change of sysem risk in marke. Bu s a lle difficul o cach he claim cycle correcly. We could decide he bes chance of counercyclical regulaion hough observing he premium cycle as he significan relaionship beween premium cycle and claim cycle. In he Exposure Draf of Solvency II in China CIRC, counercyclical regulaion was focused on solvency margin. On he foundaion of above researches, he counercyclical of nonlife insurance in China was designed aking ha of bank ino reference. As he deailed schedules were all designed, his aricle was a good suggesion o Solvency II of insurance regulaion. Theory and Model There were wo imporan poins in he counercyclical regulaion sysem. Firs, wha is he monor conrol index o judge he cycle? Tha was o say, when should we require he capal buffer of counercyclical regulaion? How o judge he righ ime? Second, how much capal buffer should ake? Should be posive or negaive? The difficuly of counercyclical regulaion was solved if we found he answers for hose wo quesions. So ha, he logic of his aricle was as below: Firs, he monor conrol index should be found. We can judge wheher o ake capal buffer according wh he change of monor conrol index. Second, he rae of capal buffer should be defined. We should ake differen rae of capal buffer according wh he differen developing of insurance company. Third, he effec of capal buffer for counercyclical regulaion should be esed. We could know wheher he sysem we designed realize he objec of counercyclical regulaion. Monor Conrol Index There were some aricles abou he monor conrol index of counercyclical regulaion in nonlife insurance. Bu hey had differen suggesions abou ha. Cerchiara & Lamania(2009)calculaed he premium cycle of insurance company by premium income. They also hough premium income should be he monor conrol index of counercyclical regulaion. Boyle & Kim(2012)made he monor conrol index as he difference beween deb and asse in he balance shee (which was he oppose number of ne asse). Sun Qixiang (2011) and Wu Hong (2011) hough he insurance marke in China should be differen wh oher counries as s a developing counry. We should disinguish he difference beween insurance qualy cycle and insurance quany cycle. Premium income should be aken as he monor conrol index for insurance quany cycle, while reained prof (or loss raio) should be aken 6
as he monor index for insurance qualy cycle. Bu hey didn decide which cycle should be regulaed by counercyclical regulaion, insurance qualy cycle or insurance quany cycle. According wh he Regulaion Framework of Solvency II in China, he counercyclical regulaion was aim a keeping away he excess or insufficien of solvency and keeping he sabily of solvency. Bu he solvency margin was a lle hysereic wh he developmen of insurance marke 1. There wasn any dynamic solvency regulaion in real-ime in China. I wasn feasibily o make he solvency margin as he monor conrol index of counercyclical regulaion of nonlife insurance. We d beer hink from he original inenion of counercyclical regulaion. Those indexes should be he bes monor conrol index which has an apparen relaionship wh solvency margin, measureable and easy o be go. Oherwise, if he monor conrol index wasn correlaed wh solvency margin, he regulaion can changeover he developmen of insurance marke and he solvency margin hough capal buffer was required according wh he change of monor conrol index. On he oher hand, would ake a long ime o calculae and saisic he monor conrol index if was oo complex. The delaying of index would affec he qualy of regulaion and make he regulaion decision incorrec. In his aricle, panel daa model was used firs in order o find a measureable index correlaed wh solvency margin. 1. Dependen variable Minimum Capal was he basis of counercyclical regulaion in he Framework of Solvency II in China. The solvency margin would be changed because of he changing of Minimum Capal. So, solvency Margin could be chosen as he independen variable (Solvency). 2. Independen variable Possible Monor Conrol Index: According wh he regulaion sysem in China, Solvency Margin equals o Minimum Capal divided by Real Capal. Minimum Capal is relaed wh premium income or claims amoun. Real Capal equals o he difference beween admed asses and admed liabily. As a resul, hose indexes which correlaed wh admed asse, admed liabily, premium income and claims amoun should relaed wh solvency margin (Boyle & Kim, 2012; Sun Qixiang e al., 2011; Wu Hong, 2011; Wu Jie & Su Fang, 2014). The possible monor conrol indexes would be premium 2 (premium) or increasing rae of premium, reained prof (NeP), equy (NeA), combined raio (CosR) and invesmen (invesmen). Premium affeced Minimum Capal. Solvency margin would decrease if he premium increased. While, reained prof, equy, combined raio and invesmen affeced Real Capal by affecing o he admed capal and admed liabily. Solvency Margin would increase if reained prof, equy and invesmen increased and combined raio 1 Solvency Margin is a daa a some imes in he Regulaion sysem of China. There isn dynamic solvency regulaion unil now. CIRC will show he solvency margin of all insurance companies a each April, so he solvency margin is a lle hysereic. 2 I s gross premium income in his aricle. 7
decreased. All of hose possible indexes would be aken as depended variable in order o find he bes one. Bu here were mulicollineary among reained prof, equy, combined raio and invesmen. Three differen models were designed o avoid mulicollineary in order o find he differen affecs o solvency margin from reained prof, equy, combined raio and invesmen. The index which had he mos sensively correlaed wh solvency margin could be chosen as he monor conrol index afer comparing he resuls of hose hree models. Conrol Variables: The conrol variables were decided from oher relaed research aricles. (1) Capal rae (CapalR). Shim (2010) hough ha higher capal rae, higher he solvency margin is. Wang Lizhen e al. (2012), Zhao Guiqin and Wu Hong (2013) also esed he relaions beween capal rae and solvency margin in China nonlife insurance marke and go he same resuls. (2) Size (Size). Size was defined as he logarhm of asse. Cummins & Sommer (1996) hough big insurance company was sronger o disperse risk. I would make he solvency margin of big insurance company lower. Bu hey were more capable o inves and ge money so ha hey would have higher operaion conrol capabily han ha of small insurance companies. I would make he solvency margin higher. So, he relaionship beween size and solvency margin can be confirmed. (3) Reinsurance Rae (Rein). Reinsurance was a popular mehod o disribue risk of nonlife insurance companies. Minimum Capal was lower if he reinsurance rae was higher and he ne premium was lower. Yuan Cheng and Yang Bo (2014) confirmed ha reinsurance rae was posive correlaed wh solvency margin in China nonlife insurance marke. (4) Ownership (D). According wh he corporae governance, he relaionships among solvency margin and premium, reained profs were differen in he differen ownership companies (Zhao Guiqin & Wu Hong, 2013). Dummy variable was designed o show he ownership of companies. 1 was for Chinese insurance companies and 0 for foreign insurance companies 1. Three panel daa models were below 2 : Solvency 0 1 Premium 2NeP 3CapialR 4Size 5 Rein 6 D i (1) Solvency 0 1 Premium 2NeA 3Size 4Rein 6 Solvency 0 1 Premium 2CosR 3Invesmen 4CapialR 5Size 6Re in 7Di (3) The differences for all daa were calculaed before regulaion as no all daa were sable, which can also avoid of spurious regression. All variable were in Table 1. Table 1 Variables Definion and Calculaion 1 We divided all companies ino Chinese company and Foreign company according wh he sandard of CIRC. 2 There wasn CapalR in he Model (2) because of he mulicollineary of NeA and CapalR. 8 D (2) i
Name Definion Relaionship Dependen Variable ΔSolvency Firs differences of solvency margin Independen Variables ΔPremium Firs differences of he logarhmic for gross premium - ΔNeP Firs differences of reained prof + ΔNeA Firs differences of logarhmic for equy + ΔCosR Firs differences of combined raio - ΔInvesmen Firs differences of logarhmic for invesmen + ΔCapialR Firs differences of asse rae + ΔSize Firs differences of logarhmic for asse +/- ΔRein Firs differences of reinsurance rae - D 1 for Chinese companies, 0 for foreign companies +/- Designaion of Counercyclical Regulaion The monor conrol index should be he mos sensive variable o solvency margin, afer he analyzing of panel daa model. The regulaion decision could be made according wh he periodical change of he monor conrol index. Usually, he periodical change of variable could be mached by AR(p) model (auoregression model of p orders). Bu AR(p) model couldn idenify he srucural jumping in he differen period. I jus can describe he linear relaionship beween variables. For example, he increasing speed of premium may change o inermediae increasing from low increasing suddenly. AR(p) model couldn idenify such phenomenon. Hamilon (1989) raised Markov Regime Swching Model o idenify such jumping phenomenon and judge he regime of differen period, which saisfied he requiremen of capal buffer in he counercyclical regulaion. 1. Idenificaion of cycle by Markov Regime Swching Model The monor conrol index was unsable maybe. The secular rend should be removed before maching o cycle in order o show he cyclical flucuaion beer. The cyclical flucuaion was kep a las. According wh Hamilon (1989), HP smoohing was chosen o remove he secular rend and keep seasonal medium-high frequency flucuaions and random noise flucuaions. The model was: Y S p i1 Y S i i S, (4) S 1S1 2S2 3 S 3 S S, i i 1S1 i2s2 i3s3, 1S1 2S2 3 S 3 Y was he monor conrol index of counercyclical regulaion. S ( 1,2, 3) was he differen regime in he flucuaion. In his aricle, hree regimes model were aken, which were low regime, mediae regime and high regime. High regime showed he ho and hard insurance marke. Mediae regime showed he normal insurance marke and low regime was he sof and cold insurance marke. For example, if he monor 9
conrol indexy was somehing like premium which showed he increasing speed, hree regimes were low speed increasing regime, mediae speed increasing regime and high speed increasing regime. If he monor conrol index Y was somehing like combine raio which showed he operaion level of insurance marke, hree regimes were low cos regime, mediae cos regime and high cos regime. If Si = i, S =1 and S =0, j i. S was a consan in he condion of j ( 1,2,3 ). S was he regulaion coefficien of lagged variable in he condion of S, i S S was he sandard deviaion in he condion of S, possibily among regimes of firs order Markov as below: p P p p 11 21 31 p p p 12 22 32 p p p 13 23 33 ~ N(0,1). The ransion (5) P[ S j S 1 i] p, i, j 1,2, 3 and 1. The duraion of each regime ij 3 p ij j1 could be go according wh he ransion possibily and he duraion of one cycle would be go. The formula was D 1 1 p ii, i 1,2, 3. (6) In addion o his, he smooh possibily of all sample periods would be go according wh he parameer esimaion of model and informaion updaing of Markov. The smooh possibily showed he possibily in he suaion of which wo regimes coninuously were boh low, or mediae or high regime. Suppose ˆ [ P( S 0 I ), P( S 1 I ), P( S 2 I )]' showed he smooh possibily of ime, could be go by he mehod in Kim (1994). 2. Designaion of Capal Buffer Smooh possibily described he possibily of differen regimes in differen ime reasonably. We can judge he regime by he bigges smooh possibily of ha period. The insurance company mus whdraw differen capal buffer when hey were in differen regim. Of course, would be beer if he capal buffer were differen as he differen smooh possibily hough hey were in he same regime. The suggesions for capal buffer were below: (1) Low Regime:Low regime showed he sof and cold insurance marke. The requiremen of capal should be decreased. When he smooh possibily of low regime was in [ a, b], he capal buffer for counercyclical regulaion should be - c ; When he smooh possibily of low regime was more han b, he capal buffer should be -2 c ; while when he smooh possibily of low regime was below a, no any capal 10
buffer was required. (2) High Regime:High regime showed he hard and ho insurance marke. The requiremen of capal should be increased. When he smooh possibily of high regime was in [ a, b], he capal buffer for counercyclical regulaion should be c ; When he smooh possibily of high regime was more han b, he capal buffer should be 2 c ; while when he smooh possibily of high regime was below a, no any capal buffer was required. (3) Mediae Regime: Mediae Regime was a normal regime. No any capal buffer was required. Demonsraion Monor Conrol Index 1. Daa sources and descripions In China, Solvency Margin was announced from 2009. This aricle can only use he daa from 2009 o 2013 o analysis he monor conrol index. On he oher side, he analysis should consider he normal suaion of he insurance indusry. Only hose companies for more han 10 years could be considered. Those maure companies have passed he urbulen period of he seing up and operaed sable very well. A las, we colleced 33 insurance companies from 2009 o 2013. Some singular poins were deleed, 163 samples were go finally. And 130 difference daa were go afer differenial reamen. All daa were go from he webse of he Associaion of Insurance Indusry in China. The descripions of all variable were shown in Table 2. Variables Observaion Mean Table 2 Descripions of All Variables 11 Sandard Variaion ΔSolvency 130 0.2021 7.4130-16.62 74.53 ΔPremium 130 0.1795 0.3056-1.4630 1.7050 ΔNeP 130 115.7148 667.361-1497.75 3428.26 ΔNeA 130 0.1907 0.4859-1.1507 2.5052 ΔCosR 130-0.0108 0.1865-0.9475 0.9637 ΔInvesmen 130 0.1683 0.7335-3.2883 2.3342 ΔCapialR 130 0.0087 0.1673-0.8671 0.7794 ΔSize 130 0.0687 0.1575-0.6940 1.2374 ΔRein 130-0.0059 0.1519-0.8585 0.9192 D 130 0.6933 0.4626 0 1 2. Analysis Resuls Which model should we ake according wh hose shor samples, fixed effec model or random effec model? We esed and chose models by Hausman es (Table Min Max
3). P value of Hausman in hose hree regression models all were above 0.05. We can rejec he null hypohesis. So, random effec model should be aken in his aricle. Table 3 also showed he regression resuls of random effec model. Independen Variables Table 3 Regression wh Random Effecs Model Dependen Variables(ΔSolvency) Model 1 Model 2 Model 3 ΔPremium -4.3605** (-2.10) -5.6035*** (-2.68) -3.3350*** (-3.60) ΔNeP -0.0002 (-0.23) ΔNeA 7.3236 (1.43) ΔCosR 5.0345 (1.30) ΔInvesmen -1.4908** (-2.04) ΔCapialR 25.8501*** (6.07) 27.2350*** (6.48) ΔSize 28.8778*** (4.79) 20.0784*** (2.90) 29.0480*** (4.74) ΔRein -4.5285 (-1.16) -4.9114 (-1.23) -3.1351 (-0.79) D 1.0116 (0.86) 1.2245 (1.03) 0.8264 (0.72) Consan -1.9029* (-1.73) -2.4095** (-2.18) -1.6898 (-1.57) Samples 130 130 130 R 2 0.4614 0.4231 0.4882 P value of Hausman 0.1318 0.3106 0.1739 Noe: Daa in he bracke are Z values. *** ** and * showed he significance level of 1%, 5% and 10% respecively. his aricle. 12 All were same in In able 3, ΔSolvency was negaive correlaed wh ΔPremium in Model 1. The significance level was 5%. Bu he correlaion beween ΔSolvency and ΔNeP wasn significan. In Model 2, ΔSolvency was negaive correlaed wh ΔPremium a 1% significance level, bu wasn correlaed wh ΔNeA. In Model 3, ΔSolvency was also negaive correlaed wh ΔPremium a 1% significance level, and negaive correlaed wh ΔInvesmen a 5% significance level. Bu ΔSolvency wasn correlaed wh ΔCosR. In all hree models, ΔSolvency was all negaive correlaed wh ΔPremium significanly. They were all same wh our expecaion. Bu, ΔSolvency almos wasn correlaed wh ΔNeP,ΔNeA and ΔCosR significanly. Though ΔSolvency was significan correlaed wh ΔInvesmen negaively, bu he significance was lower han ha wh ΔPremium. So, solvency margin was more sensively wh he change of premium, bu wasn sensively wh Reained Prof, Equy and Combined Rae. Tha was also o say, solvency margin was sensively wh he Minimum Capal which was denominaor, bu no sensively wh Real Capal which was numeraor. This also showed ha he solvency margin requiremen was a lle sricer in China. A oher side, s rue ha he relaionship beween ΔSolvency and ΔPremium was negaive. When he premium of insurance companies was increasing rapidly, solvency margin would decrease because of he explosion of operaion scale. We suggesed o ake premium increasing as he monor conrol index of counercyclical regulaion in China jus below. Firs, he correlaion beween solvency margin and premium increasing was he highes one. Second, s very easy o ge
gross premium, and he daa was very imeless. Third, s beer o ake a simple index as he monor conrol index. The index of premium increasing was saisfied wh all requiremens above. So, we should ake Premium Increasing as he monor conrol index of counercyclical regulaion. When premium was increasing very rapidly, insurance companies should whdraw exra capal buffer according wh he requiremen of counercyclical regulaion. So, he increasing speed of premium should be lower and lower as hey didn have enough capal o suppor he requiremen of solvency margin. The objec of counercyclical came rue. On he conrary, when he premium was very low, he requiremen of Minimum Capal would decrease. So, insurance company had exra capal o develop business. Premium would urn o increase soon. In he bank, Basel Commission suggesed o make he monor conrol index as he raio of cred ousanding wh GDP. This index also showed he scale of business in bank, neher he quany of business. Similarly, we suggesed o make he monor conrol index as he increasing of premium. I also showed he scale of business in insurance, neher he quany of business. Wha we suggesed for insurance kep he same logic and means wh ha of bank. Designaion of Counercyclical Regulaion 1. Daa Resource The resuls would be more correc if we had more daa o analyze he cycle. The insurance companies in China began o develop from 1980, which was a lle lae han ha of oher counries. So, here were so less year daa of premium. There were only 33 years from 1980 o 2013. In his aricle, season daa was aken in order o ge more samples. We go 63 daa from he firs season of 1999 o he hird season of 2014. All daa came from he webse of CIRC. 2. Designaion of Counercyclical Regulaion Now, we decided he monor conrol index as premium increasing. The secular rend was removed by HP smoohing and only kep seasonal medium-high frequency flucuaions and random noise flucuaions. 13
0.5 0.4 Premium 保 费 收 入 increasing 增 长 率 趋 Trend 势 成 分 波 Flucuaion 动 成 分 0.3 0.2 0.1 0-0.1-0.2 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Figure 1 Premium Increasing afer HP Smoohing In Figure 1, hisogram showed he flucuaion of cycle. There were obviously cycles in he flucuaion of ΔPremium. In 2005 and 2008, he premium kep lower increasing really. And kep high increasing in 2004, 2007 and 2010. Bu, we can decide wheher here were some srucure changes in he flucuaion of premium increasing. According wh Markov regime swching model, he hree regimes based on premium increasing. They were low speed increasing regime (Regime 1), mediae speed increasing regime (Regime 2) and high speed increasing regime (Regime 3). Using Malab o design he model, we designaed ha he lag order was 2 in he auoregression model according wh AIC and SIC of differen lag order models. In order o compare wh he resuls of Markov and choose he bes model, he parameer of AR(2) also go hough can show he designabily jumping. All resuls were in Table 4. Table 4 Parameer Parameer Esimaion of AR(2)and Markov Regime Swching Model AR(2) Markov Regime Swching Model Regime 1 Regime 2 Regime 3 S 0.0004-0.1188*** -0.0266*** 0.0912*** S 1 S 2 S 0.2103* -0.1105 0.0879* -0.2185 0.3242** -0.1544** 0.0720** 0.467** 0.0849*** 0.0390*** 0.0295*** 0.0632*** In able 4, he parameer of mean value S wasn significan in AR(2), bu was significan a 1% level in he hree regimes of Markov model. I showed ha he mean value S of hree regimes were differen ousanding. There were some designabily jumping in ΔPremium. Markov model could mach he changing of premium increasing beer. The swching possibilies were shown in able 5. 14
平 滑 概 率 Smooh Possibily Table 5 Possibily of Regime Swching Swching Possibily p Regime 1 Regime 2 Regime 3 Regime 1 Regime 2 Regime 3 0.72 0.09 0 0 0.86 0.20 0.28 0.05 0.80 Log-likelihood Funcion Value 79.7565 Smooh possibilies were go according wh he definion before. Figure 2 showed he smooh possibily in differen regimes, which showed he regimes of differen ime. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 低 Low 速 Speed 增 长 Regime 区 制 Mediae 中 速 增 Speed 长 区 Regime 制 High 高 速 Speed 增 长 Regime 区 制 Figure 2 Smooh Possibily of Regime Each Season Figure 2 was almos he same wh Table1. Overall, he premium of China nonlife insurance kep mediae and high speed increasing in las 15 years. There were 3 high speed regimes in 2004, 2007 and 2010 obviously. Bu he low speed regimes were very shor relaively, which were in 2005 and 2008. In Figure 2 of he financial crisis in 2008, he premium of China nonlife insurance jus had a very shor low speed regime. Then, urned o high speed increasing regime quickly afer he Chinese governmen invesed four rillion o promoe economics in 2008. From 2011, he premium increasing changed o mediae speed increasing regime mainly from high speed regime. All hese change were correlaed wh he economy policy. Figure 2 almos showed he real marke in nonlife insurance marke of China. The lengh of period could be go afer we go he lengh of differen regimes by formula (6). The lengh of low speed increasing regime was 3.52 monhs, while ha for mediae regime was 7.13 monhs and was 5.06 for high speed increasing regime. I also showed ha was high speed increasing regime mainly. Of course, one cycle includes wo mediae speed increasing regime, one high speed increasing regime and one low speed increasing regime. The lengh of one cycle of nonlife insurance marke of China should be 5.5 years (22 seasons). This resul was almos he same wh Li Xinyu & Li Jie (2010) and Sun Qixiang (2011). When should he insurance company whdraw capal buffer? How much hey 15
计 提 逆 周 期 附 加 资 本 比 率 Capal Buffer of Counercyclical Regulaion should whdraw? We should answer such wo quesions o finish he designaion of counercyclical regulaion. The deailed capal buffer wasn decided In he Regulaion Framework of Solvency II in China. I jus said ha would be decided laer. Gao Guohua (2013) suggesed ha he bank should whdraw capal buffer for 5% in he bank. Basel Commission sipulaed he capal buffer as 2.5% in he Guiding Principle of Counercyclical Capal Regulaion for Bank of 2010. Taking he regulaion of bank for reference, we supposed a=0.5, b=0.9 and c=2.5%. So ha, differen capal buffers were required according wh differen smooh possibily and differen regimes. No capal buffer should be whdrawn in he mediae speed increasing regime. I s -2.5% or -5% o be whdrawn in he low speed increasing regime. And s 2.5% or 5% o be whdrawn in he high speed increasing regime. The capal buffers were shown in Figure 3 according wh he flucuaion of nonlife insurance marke. 6% 4% 2% 0-2% -4% -6% 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Figure3 Capal Buffer of Counercyclical Regulaion According wh he Counercyclical Regulaion we designed in his aricle, here were 17 sample periods in which we need increase capal buffer, while here were only 10 sample periods in which we need decrease capal buffer and 32 sample periods in which no capal buffer was needed 1. Tha showed ha no capal buffers were needed in mos periods. We only need increase or decrease capal buffer occasionally. The resuls coincided wh he objec of counercyclical regulaion, which showed ha don inervene he marke excessively and coninually. Excep ha, he number of periods in which we need o increase capal buffer (17 periods) were a lle more han he number of periods (10periods) in which we need o decrease capal buffer. This also agreed wh he overheaing premium increasing in he sample years. Before he financial crisis of 2008, he insurance marke was a lle oo ho and need increase capal buffer. As he inflecion of financial crisis, he insurance marke was caugh in faigued and weak marke quickly. We need decrease capal buffer from he second season of 2008. Afer 2011, he increasing rae of premium was very smooh, so ha no any capal buffer was needed. The resuls of capal 1 Noe: Premium increasing was he monor conrol index, which was a differenial daa. So, he daa of 1999 was a base, which was disappear afer we go he differenial daa. The samples reduced 4 daa a all. The firs daa began form he firs season of 2000. 16
buffer whdrawing were almos he same wh he real insurance marke. Tesing How abou he effec of capal buffer in he counercyclical regulaion? Was he change of premium smooher? Was he solvency margin more sable? Has he objec of counercyclical regulaion been realized? Was he monor conrol index of 2.5% suggesed before he bes? We need o es he resuls o know wheher s useful o keep counercyclical regulaion. Designaion of Tes Model Le analyze he logic of his aricle firs. The premium increasing was chosen o be he monor conrol index as correlaed wh solvency margin closely. If premium increasing was smooher, esed he effec of counercyclical regulaion. The mehod o es was as below. Firs, he change of solvency margin was go afer increasing or decreasing he capal buffer. Second, he change of premium income was go according wh he relaionship beween premium and solvency margin. Finally, we compared he real premium change wh ha afer capal buffer. I mean he counercyclical regulaion was useful if he premium income became smooher. So, we should calculae he elasic coefficien beween solvency margin and premium increasing. Double logarhmic model was aken as below. ln Solvency 1 ln Pre _ raio 0 (7) ln Solvency was he logarhm of solvency margin for insurance company i in year. ln Pre _ raio was he logarhm of premium increasing for insurance company i in year. 1 was he elasic coefficien beween solvency margin and premium increasing. And 1 ( dsolvency / Solvency ) ( d Pre _ raio / Pre _ raio ). When he increasing of nonlife insurance was very fas, insurance companies should increase minimum capal by whdraw capal buffer. Suppose he real capal kep same as before, so he solvency margin would decrease. Insurance companies would ry heir bes o keep he solvency margin in order o saisfy he requiremen of regulaion deparmen. There were wo ways o be chosen. Firs, hey could keep solvency margin by decreasing premium and decreasing minimum capal. Second, hey could keep solvency margin by geing more capal and increasing real capal. Bu here were so many difficulies o ge more money from capal marke. I would ake a long ime o apply and operae. Regulaion deparmen may no agree wh heir financial plan. So, s easy and effecive o decrease premium income. And s in he insurance company s conrol. On he oher hand, minimum capal would decrease if 17
he capal buffer was negaive. Solvency margin would increase. There were exra capals o develop new business and new marke for hose insurance companies. Premium income would be increased very soon. Suppose he capal buffer was c (c was posive) required by regulaor, solvency margin would decrease c/(1+c). The elasic parameer was beween solvency margin and premium increasing. Premium increasing should be decreased for c/ (1+c) if he insurance company mus keep he solvency margin 1. I would be he same on he conrary. For example, if 1=-0.1, regulaors would require more 2.5% capal buffer if he premium increasing was in high increasing speed regime. The solvency margin would decrease 2.439%, and premium increasing would decrease 24.39%. So, according wh he elasic relaionship beween solvency margin and premium increasing, he premium increasing would be go afer we know he change of solvency margin came from capal buffer. We would know he difference of premium increasing before and afer capal buffer. Tes and Choose Bes Raio The daa for double logarhmic was also from 2009 o 2013 as he solvency margin were public from 2009. Also, we should decide he bes model, random effec model or fixed effec model (leave ou he deailed calculaion). The P value for Hausman was 0.1344, which was more han 0.05. The null hypohesis couldn be rejeced. So, random effec model was beer. The resuls of double logarhmic were showed in Table 6. Independen Variable Table 6 Elasic Analysis Regression Resuls Regression Parameer Sandard Error Z Value P Value ln Pre _ raio -0.1062** 0.0537-1.98 0.048 Consan 1.3240*** 0.1421 9.32 0.000 1 1 The elasic parameer 1 beween solvency margin and premium increasing was -0.1062 from Table 6. I was ousanding a 5% level. was negaive, which mean ha he relaionship beween solvency margin and premium increasing was negaive. When he capal was kep no change, premium increasing was higher, solvency margin was lower. So, when he solvency margin decreased 1% according wh he requiremen of regulaor, he premium increasing would decrease 9.42% a 1 1 1 was posive or negaive. I was showed by increasing or decreasing in he aricle. So, jus show he change using absolue value. 18
mos in heory 1. Wha was he bes rae of capal buffer? The differen solvency margins were go when capal buffer c were 1.25%, 2.5%, 5% and 10%. The premium increasing were also go according wh he elasic analysis. We compared he cyclical flucuaion of differen premium increasing afer HP smoohing wh he real premium increasing 2 (Figure 4). 0,5 0,4 Premium Increasing c=1.25% c=2.5% c=5% c=10% -0,1-0,2-0,3-0,4 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014-0,5 Figure 4 Premium Increasing for Differen Capal Buffer There were five curves in Figure 4, which shown he flucuaion of original premium increasing, capal buffer o be 1.25%, 2.5%, 5% and 10% respecively. When he capal buffer c was 1.25%, he flucuaion of premium increasing was a lle sable han ha of original. Bu he regulaion effec was very lim. The premium increasing waved sill obviously. When he capal buffer c was 2.5%, he regulaion effec was he bes. The flucuaion of premium increasing was very sable han whaever. Bu wh he increasing of capal buffer c, he premium increasing urned over o decreasing quickly when c was equal o 5% or 10%. In such suaion, counercyclical regulaion inervened he marke excessively. The sandard value and range of he flucuaion in he premium increasing also old he same sory (Table 7). Table 7 Sandard Value and Range of Premium Increasing Raw Premium Increasing c =1.25% c =2.5% c =5% c =10% Sd. Value 0.0864 0.0583 0.0440 0.0828 0.2192 Range 0.3998 0.2874 0.2436 0.3182 0.8803 From Table 7, he sandard value and range of he flucuaion for raw premium increasing was a lle big. Bu hey all decreased when he capal buffer of c =1.25% was whdrawn. I kep decreasing coninually when he capal buffer of c =2.5%, 1 0,3 0,2 0,1 0 When he solvency margin decreased for 1%, he premium increasing wouldn decrease 9.42% really in order o keep he solvency margin no change, as here were so oher facors and resric. For example, insurance company could ge more money from financial marke and improve solvency margin. They needn o decrease he premium increasing rae. Bu should be 9.42% in heory a mos. Especially when he insurance marke developed very fas, capal wasn enough and regulaion was very sric. The whdrawing of Capal buffer could decrease he increasing of premium very soon. 2 The value of a and b shown he bound of smooh possibily. Bu s very lim o affec he effec of capal buffer. In Figure 2, he smooh possibilies of all regimes were beween 0.5 and 0.9 rarely. I s useless o change he value a and b. he core in his aricle was he monor conrol index. The value of a and b weren discussed in his aricle. 19
and was he leas one a all, which shown he premium increasing was very sable a ha ime. Bu he sandard value and range of flucuaion for premium increasing became larger and larger when he capal buffer of c =5% and 10%, which shown he premium increasing became more flucuae. All his shown ha he counercyclical regulaion effec was bes when he capal buffer was c =2.5%. In conclusion, he capal buffer c shouldn be very low, neher very high. The regulaion effec wouldn be very obviously when he capal buffer was very low. The premium increasing flucuaed sill very big. Bu he regulaor inervened he marke excessively if he capal buffer was oo big. The premium would develop o he adverse direcion. Relaively, s he bes one when capal buffer c equaled o 2.5%. When he marke was in low or mediae increasing speed regime, he capal buffer should be 2.5% if he smooh possibily was in [ a, b]. The capal buffer should be 5% if he smooh possibily was more han b. Resuls and Suggesions In his aricle, he monor conrol index of counercyclical regulaion was go as he sensive index wh solvency margin using panel daa model. The sysem of capal buffer in he counercyclical regulaion was designed basing on Markov Regime swching model. The bes monor conrol index was found and he effec of counercyclical regulaion was esed. Those resuls below were go. (1) The change of solvency margin was very sensive wh he premium increasing, bu wasn correlaed wh he change of reained prof, ne asse and combined raio. The monor conrol index of counercyclical regulaion in insurance should be premium increasing, which were he similar wh ha in bank. (2) The smooh possibily of differen regime would be go by Markov regimes swching model. Differen capal buffer should be whdrawn according wh differen regimes. This sysem could decrease he flucuaion of premium increasing really and made he developmen of insurance marke more sable. (3) The value of capal buffer would affec he regulaion effec, which should be 2.5% bes. Beyond is as wrong as falling shor. We can describe he capal buffer of counercyclical regulaion clearly below. Firs, he monor conrol index should be premium increasing; Second, he smooh possibily would be go by Markov regime swching model and he regime of he differen period was go. The capal buffer should be posive if s in high speed increasing regime, and s negaive in he low speed increasing regime. Third, differen capal buffer was required according wh he smooh possibily of differen regimes. I s 0 when smooh possibily was less han 0.5. I s +2.5% or -2.5% when he smooh possibily was beween 0.5 and 0.9. I s +5% or -5% when he smooh possibily was more han 0.9. Excep he designaion of deailed regulaion sysem, regulaor should hink abou hose quesions below. (1) There was cycle flucuaion in he nonlife insurance marke of China. Counercyclical regulaion could urn over he developing of insurance 20
marke. Insurance regulaion changed from imposing uniformy in all cases o adoping differen arrangemen according wh he operaion cycle. I s a righ way really. We should work hard on his way. Though he relaively research was abou he discussion abou he idea of counercyclical regulaion, he resuls in his aricle shown he srong effec of counercyclical regulaion. I s possibly o make he regulaion ino realy. So, insurance regulaor should ake counercyclical regulaion as he imporan mehod in he fuure. (2) The monor conrol index of counercyclical regulaion should be simple and saisical. Premium increasing was he bes index for hese characers. I s correlaed wh solvency margin very obviously. So, premium increasing should be he bes and only index for counercyclical regulaion. On he oher hand, premium increasing only shown he developing cycle of insurance, didn show he qualy cycle. Bu he qualy cycle (Claim cycle) was a lag of he developing cycle of insurance (Premium cycle). The counercyclical regulaion basing on premium cycle affeced claim cycle really. (3) Regulaors could monor he change of smooh possibily in differen regime by Markov Model and decided wheher o whdraw capal buffer. The change of smooh possibily in differen regime could show he change of premium increasing well and shown he real suaion of insurance marke. Regulaor could judge he insurance marke was ho or cold and ook differen capal buffer according wh he requiremen of counercyclical regulaion. (4) I s very imporan o design he suable capal buffer for regulaors. The effec of counercyclical regulaion could be realized when he capal buffer were appropriae. The regulaion was useless if he capal buffer was very small, while bended over backwards if he capal buffer was very big. Relaively, he capal buffer should be 2.5% bes. Of course, all resuls of his aricle based on he sample, which limed our research. When CIRC was going o design he Solvency II in he fuure, hey should collec more daa, and ge more accurae resuls by big daa. They also should design a sandard schedule o simplify he complex model. The capal buffer should adap wh he developmen of insurance marke. Regulaor should adjus now and hen. References -----Based on Insurance Cycle and Underwring Cycle Theory [J]. Journal of Insurance, 2014, 9: 29-41. [1] Boyle, P., & Kim, J. H. T. Designing a Counercyclical Insurance Program for Sysemic Risk [J]. The Journal of Risk and Insurance, 2012, 4(79): 963-993. [2] Cerchiara, R., & Lamania, F. Solvency 2: an Analysis of he Underwring Cycle wh Piecewise Linear Dynamical Sysems [EB/OL]. 2009. [3] Cummins, J. D., & Sommer, D. W. Capal and Risk in Propery-Liabily Insurance Markes 21
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