Risk-Based Capital and Firm Risk Taking in #Property-Liability Insurance 12*JIANG CHENG, Mary A. Weiss 5 (1. School of Finance, Shanghai University of Finance and Economics, ShangHai 200433; 2. Fox School of Business, Temple University, Philadelphia 19025) Abstract: This research investigates the relationship between capital and risk in property-liability insurers from 1993 to 2007. Three-stage-least-squares estimation is used to investigate the relationship between capital and two types of risk: underwriting and asset risk. Overall the results 10 suggest that risk and capital are positively related, so that capital increases are associated with increases in investment and underwriting risk. This positive relationship was not consistently significant in 1993, prior to the implementation of RBC requirements. Both under-capitalized insurers and marginally adequately capitalized insurers adjusted their capital and risk towards firm targets at a higher speed than well-capitalized insurers in the post RBC period. But underwriting and asset risk 15 also increased for less well-capitalized insurers. Keywords: Insurance Economics; Risk-Based Capital; Regulatory Effect; Capital; Risk 0 Introduction Maintaining insurer solvency has always been a focal point of insurance regulation. . 20 regulators use various methods to promote insurers’ financial strength and protect policyholders from losses due to insolvency. One important tool is embodied in Risk Based Capital (RBC) requirements which went into effect in the . property-liability insurance industry in 1994. An important feature of the RBC system is that it mandates intervention by the regulator when risk-based capital levels are deemed deficient. The degree of intervention varies with the degree of 25 deficiency, and ranges from regulatory approval of an insurer action plan to correct the deficiency to mandatory take-over of the insurer. Because it contains mandatory requirements, the RBC system is at least partly designed to eliminate regulatory forbearance in the industry. [1]Research by Cummins and Nini suggests that the imposition of RBC requirements may have been partly responsible for increased capital levels in the property-liability insurance industry 30 in the 1990s, enhancing solvency. But considerable research criticizes the RBC system. For [2] example, Cummins, Harrington and Niehushypothesize that imperfections in the existing RBC system will likely distort insurer’s behavior in undesirable and unintended ways so as to avoid being incorrectly identified as needing regulatory attention. Most studies of RBC have focused on the effectiveness of RBC requirements in predicting property-liability insurer insolvencies. 35 Research suggests that RBC results are not good predictors of insolvency (., Cummins, Grace [3][4] [5] [6]and Phillips, 1999; Cummins, Harrington and Klein, 1995). Cheng and Weiss (2012) find that the accuracy of the RBC ratio in predicting insolvencies is inconsistent over time. They provide summary statistics for the RBC ratios historically and the RBC classifications. Another possibility that exists is that insurers (especially weak insurers) will exploit anomalies in the RBC 40 formula so as to make their financial position appear to be more favorable than it really is. To understand the true effect of RBC requirements on insurers’ behavior, the relationship between capital and risk in insurers must be determined. For example, capital and insurer risk may be positively related so that increasing capital requirements leads to offsetting increases in risk. In this case, increases in risk corresponding to the increased capital requirements associated with Foundations: Specialized Research Fund for the Doctoral Program of Higher Education (New Teachers Grant #Z1025420); Scientific Research Foundation for the Returned Overseas Chinese Scholars (Grant #2012940) Brief author introduction: JIANG CHENG, (1971-), Male, Assistant Professor,Main research areas include Corporate governance and Insurance. E-mail: @ - 1 -
中国科技论文在线 45 RBC may have offset RBC’s intended effect of improving solvency. On the other hand, capital and risk may be unrelated or negatively related so that increases in capital requirements are accompanied by no change in insurer risk or decreases in insurer risk. Then, RBC requirements may have led to a net improvement in capital levels and enhanced solvency in the industry. In spite of these possibilities associated with the use of RBC in practice, little research is 50 aimed at addressing how insurers may have changed their capital decisions and risk taking [7]behavior before and after adoption of RBC. Cummins and Sommer determine the empirical relationship between capital and risk in property-liability insurers using a sample period of 1979 to 1990. They find the relationship between capital and risk to be positive in property-liability insurers. This result suggests that any increases in capital that may be attributable to RBC 55 requirements would be offset by increases in risk. However the period preceded implementation of RBC, and insurer behavior might be different as a result. The purpose of this study is to determine the relation between insurers’ capital positions and risk-taking behavior in 1993 (prior to the implementation of RBC) and from 1994 to 2007 (after RBC was adopted). The period 1993 in addition to 1994 to 2007 is examined because insurers 60 may have been readjusting their capital and risk portfolio in anticipation of RBC. Further, this research estimates the impact of RBC requirements on marginally adequately capitalized insurers and under-capitalized insurers in particular. The sample of insurers studied consists of pooled, cross-sectional . property-liability insurers included in the NAIC’s data base for the period 1992 to 2007. Thus this research also [7]65 updates the analysis of Cummins and Sommer. Following a long line of literature, the model used allows for capital and risk positions to be determined simultaneously, so that three-stage least squares (3SLS) estimation is used to estimate the capital and risk equations. The 3SLS model incorporates the possibility that insurers may be unable to adjust to their target risk or capital levels over the course of a year. That is, the capital and risk equations estimated allow for partial 70 adjustment of capital and risk. The capital measures rely on surplus, while measures of insurer risk are based on asset and underwriting risk. To measure the effect of RBC implementation on under- and marginally adequately capitalized insurers, indicator variables that reflect relative capitalization of insurers (using the RBC system) are included in the models. And the inclusion of these variables represents an [7]75 innovation from Cummins and Sommer. The results with respect to these variables can be interpreted as the impact of regulatory pressure on these insurers from RBC implementation. Ceteris paribus, we posit that weaker insurers may have had a larger response to the imposition of RBC requirements in order to avoid regulatory sanctions. By way of preview, the results overall suggest that risk and capital are positively related, so 80 that capital increases are associated with increases in asset and underwriting risk. This positive relationship was not consistently significant in 1993, prior to the implementation of RBC requirements. Further, both under-capitalized insurers and marginally adequately capitalized insurers adjusted their capital and risk towards firm targets at a higher speed than well-capitalized insurers in the post RBC period . 85 The remainder of this research is organized as follows. In the next section the RBC requirements for insurers are briefly described. Following this, the hypotheses are presented. The next sections focus on the methodology and the data description. The results are contained in the subsequent section, and the last section concludes. - 2 -
中国科技论文在线 1 Hypotheses Development 90 Capital adequacy is assessed with the RBC ratio, defined as the ratio of total adjusted capital (TAC) to RBC. TAC is composed primarily of surplus (or equity) of an insurer. RBC itself is determined from a formula that attaches weights (or factors) to detailed, risk-related items in the insurer’s financial statements. The risks encompassed by RBC requirements are primarily underwriting and asset risk; and these risks account for 87 percent of total risk based capital. 95 Based on their RBC ratios, insurers are classified into one of five ranked categories depending on the degree of any capital deficiency. The RBC categories (and required regulatory/insurer action) are C1 (no action needed), C2 (insurer required to file a plan with commissioner detailing its financial condition and how it proposes to correct deficiency), C3 (regulator examines the insurer and institutes corrective action if necessary), C4 (regulator has 100 legal grounds to rehabilitate the company) and C5 (regulator required to seize the insurer). Table 1 specifies the thresholds corresponding to each of these categories. For example, Table 1 indicates that insurers with an RBC ratio greater than or equal to 2 are associated with no regulatory action. Table 1. “Risk” Categories Based on the NAIC RBC Ratios (TAC/ACL RBC)Insurer "RRBC RatioNAIC Regulatory Action LevelClassifications in this StudyC1RBC ratio >= 2No action need N/ <= RBC ratio < 2Company action levelModerately financially distressed/Under-capitalized insurersC31 <= RBC ratio < action levelModerately financially distressed/Under-capitalized <= RBC ratio < 1Authorized control level Moderately financially distressed/Under-capitalized insurersC5RBC ratio < control levelHighly financially distressed/Under-capitalized insurersNote: TAC is the Total Adjusted Capital, and ACL RBC is the Authorized Control Level RBC. Several reasons exist to suggest that capital and risk are positively related. That is, capital and 105 risk may be considered as substitutes by an insurer. In this case, constraints on capital levels, such as those imposed by RBC, may induce insurers to take on more risk. If insurers are concerned with bankruptcy costs, then increases in risk may lead to higher capital and a positive relationship between risk and capital. Finally, agency costs may lead to a positive relationship between risk and capital if managers, because of their substantial human investment in the insurer, offset 110 increases in insurer risk by holding higher capital amounts. Thus, Hypothesis 1 states, Hypothesis 1: Insurers’ risk and capital are positively related to each other. However, the positive relationship between risk and capital might be weakened, if not completely reversed to a negative relationship, for insurers close to financial distress. Moral hazard is posited to exist in the insurance industry because of guaranty funds. More specifically, 115 insurers are not charged a risk-based default premium to cover costs in the event of their insolvency. Instead, when an insurer becomes insolvent, solvent insurers are assessed a flat rate to cover insolvency costs. Thus, maximizing shareholders wealth for insurers close to financial distress could entail increasing risk relative to capital to take advantage of the moral hazard posed by the guaranty fund system. 120 However, guaranty fund coverage is much less complete than deposit insurance in the . banking industry, so that the excessive risk-taking incentive is weaker in property-liability insurance. For example, some lines of insurance are excluded from coverage such as commercial insurance, and maximum guaranty fund payment limits exist where coverage does apply. Thus policyholders have an incentive to monitor insurers for excessive risk-taking. - 3 -
中国科技论文在线 125 Even if incentives were not weaker for excessive risk-taking in property-liability insurance, however, insurers could not increase risk relative to capital in an unchecked fashion. Besides regulatory surveillance (other than RBC), rating agencies provide policyholders with information on the credit-worthiness of the insurer. Following the moral hazard argument, insurers with marginally sufficient capital might have 130 different risk-taking behavior compared to well-capitalized insurers and under-capitalized insurers. The response of insurers’ capital and risk levels after imposition of RBC may depend on whether insurers were holding an amount of capital above the RBC requirements prior to RBC implementation. Insurers with capital levels significantly above the required level may not have responded to the imposition of RBC at all or may even have increased risk (relatively). Insurers 135 with relatively low capital buffers may have tried to build an appropriate buffer by raising capital and/or lowering risk at a higher speed toward firm targets than well-capitalized insurers. That is, insurers’ results are exposed to exogenous shocks related to developments in the overall economy or the property-liability insurance industry, hence insurers may wish to insulate their capital from such shocks with a buffer. In addition, reducing risk or raising capital at a higher speed than 140 well-capitalized insurers for these insurers may have served as a signal that they were in regulatory compliance leading to a reduction in regulatory costs. Insurers with RBC deficiencies may have had a stronger response to RBC requirements as these insurers likely experienced regulatory pressure to improve capital positions (or decrease risk) within a relatively shorter time frame. Thus Hypothesis 2 states, 145 Hypothesis 2: Capital and risk were more responsive in weaker insurers with the implementation of RBC. Imposition of RBC requirements may have changed the cost-return tradeoff between risk and capital in the insurance industry. In this case, one would expect that capital levels for insurers in different RBC categories responded differently prior to the time RBC became effective than 150 afterwards. Hypothesis 3 states, Hypothesis 3: Changes in capital and risk for insurers in varying financial condition were different prior to the imposition of RBC requirements than afterwards. 2 Methodology [7][8]The models used in Cummins and Sommer and Shrieves and Dahl with the modification [9][10]155 of Aggarwal and Jacques and Jacques and Nigro is used in this research. Three-stage least squares is used because the joint dependency between insurer’s leverage, investment, and [11]underwriting decisions means that OLS estimation is inefficient (Intrilligator, 1978) . More specifically, change in relative capital is modeled in a single equation, and two equations are used to specify relative changes in risk. Insurers’ risk decisions are assumed to entail underwriting 160 risk and asset risk. Underwriting risk reflects the amount and types of business that the insurer underwrites each year, while asset risk reflects the asset quality of the insurer’s investments. Year dummies are included in the models for the sample with years 1994 to 2007. Dependent Variables Capital Equation. The specification for capital is the same as used in prior insurance and 165 banking research: the surplus to total assets ratio. This measure is unaffected by (any anomalies in) the RBC formula. Risk Equations. Asset risk is proxied by investment in equities and real estate divided by [12]total invested assets in some specifications (Petroni and Shackelford, 1995), while in others it - 4 -
中国科技论文在线 is proxied for by the RBC risk weighted assets divided by invested assets. The rationale for using 170 equities and real estate divided by invested assets is that these investments are considered to be relatively risky (as evidenced, for example, by their high RBC risk factor loading), and this ratio is easy to compute and cannot be manipulated. Risk-weighted assets have been used in prior banking research; and these are calculated by multiplying the invested asset risk factors from the RBC formula with the values for these assets for each insurer. Prior to the implementation of RBC, 175 insurers would not have had an incentive to exploit any anomalies in the RBC formula, hence the results between the two periods studied are interesting for comparison purposes. Underwriting risk is measured as RBC risk-weighted net premiums written (NPW) divided by total NPW. RBC risk-weighted NPW is calculated by multiplying the NPW risk factors for each line from the RBC formula with the values for premiums by line for each insurer. Use of 180 this measure poses the same challenges as for risk weighted assets and the same analysis applies to observed results. As a robustness test, underwriting risk is proxied by the proportion of premiums written in risky lines (analogous to the asset risk specification based on real estate and mortgages). Use of risk measures such as these assumes that the RBC formula can identify risky lines (or risky assets), even if the factor loadings associated with these lines (or assets) do not 185 completely accurately incorporate the relevant inherent risk. The control variables in the equations estimated are for organizational form, size, group status, herfindahl index of lines of business written, geographical herfindahl index of business written and reinsurance utilization. Data 190 The sample data consists of pooled, cross-sectional data of . property-liability insurance companies included in the NAIC’s database for the period 1992 to 2007. After 1994, data for the RBC ratio were obtained from the NAIC database; unpublished RBC data obtained directly from the NAIC for 1992 were used in some models. The samples used in estimation include all insurers with positive net admitted assets, surplus and net premiums written (NPW). Certain specialty 195 insurers and insurers that did not file a statement with the NAIC are excluded from the RBC database and from this study. Finally, data for two consecutive years were required for each insurer sample, hence observations that did not meet this criterion were eliminated from the sample. 3 Results 200 Table 2 contains summary statistics for the 1993 sample and the sample for 1994 to 2007 along with the results of t-tests for differences in means for these samples. The results indicate that many significant differences exist between the two samples. Notably, the proportion of the sample that was undercapitalized in 1993 is significantly larger than in the 1994 to 2007 period. Underwriting risk (proxied by the (RBC risk-weighted NPW/Premiums) in year t and t-1 is greater 205 in 1993 compared to the 1994 to 2007 period. Also, the geographic herfindahl, and the proportion of mutuals are significantly greater in the 1993 period compared to the 1994 to 2007 period. All other variables are significantly lower in the 1992 period, except for the adequate capitalization indicator, and (Risky Assets/Invested Assets) in years t and t-1, which are not significantly different between the two periods. - 5 -
中国科技论文在线 Table 2Summary Statistics t-tests for19931994 to 2007differencesVariableSampleSamplein means(Geographic Herfindahl)***t-1(Lines of Business Herfindahl)***t-1(Reinsurance Usage)***t-1(Group Indicator (=1 if group))***t-1(Mutual Indicator (=1 if mutual))***t-1(Adequate Capitalization (=1 capitalization))t(Under Capitalized (=1 if ***capitalized))tLog(Assets)***t-1(Surplus/Assets)***t-1(RBC risk weighted NPW/***Premiums)t-1(Risky Assets/Invested Assets)-1(RBC risk-weighted ***Assets/Invested Assets)t-1(Surplus/Assets)***t(RBC risk weighted NPW/***Premiums)t(Risky Assets/Invested Assets)(RBC risk-weighted ***Assets/Invested Assets)tN188726671Note: *, **, *** significant at 10, 5 and 1 percent levels, : RBC risk-weighted NPW is the sum of RBC NPW risk factor for premium line* premiums inline. RBC risk-weighted Invested Assets is sum of RBC asset risk factor by type * asset usage is ceded loss reserves/Total direct and assumed loss reserves. An insurer isconsidered to be adequately capitalized if 2≤RBC ratio<3 and under-capitalized if RBC ratio < Invested Assets are the sum of stock and real estate Tables 3 through 6 contain the three-stage least squares regression results. Table 3 uses (RBC risk-weighted Invested Assets/ Invested Assets) as the risk measure for asset risk, while Table 4 uses the alternative measure for asset risk, (Risky Invested Assets/ Invested Assets). 215 Tables 5 and 6 are analogous to Tables 3 and 4 except that the analyses are carried out for insurers that are well above the “no action” threshold for RBC; that is only insurers with RBC greater than 3 are used in the analysis for Tables 5 and 6. The coefficients for the year dummies for the 1994 to 2007 samples have been suppressed in the results for space reasons. - 6 -
中国科技论文在线 Table 3Three Stage Least Squares Results (RBC risk-weighted Invested Asset/Invested Assets) used as Dependent VariabletAll Insurers Results for Year(s)19931994-2007 with year dummies (RBC risk-(RBC risk-weighted (RBC risk-(RBC risk-weighted(Surplus/weightedInvested Asset/(Surplus/weightedInvested Asset/Dependent VariableAssets)t NPW/Premium)tInvested Assets)tAssets)t NPW/Premium)tInvested Assets)tIndependent *************()()()()()()(Geographic Herfindahl)*****t-1()()()()()()(Lines of Business Herfindahl)******-1()()()()()()(Reinsurance Usage)********t-1()()()()()()(Group Indicator (=1 if group))****-1()()()()()()(Mutual Indicator (=1 if mutual))********t-1()()()()()()Log(Assets)***********t-1()()()()()()(RBC risk-weighted NPW/Surplus)***()()()()(RBC risk-weighted ***** Assets)()()()()t(Surplus/Assets)******t-1()()(Surplus/Assets)t-1*(Adequate (=1 if adequate capitalization))()()t-1(Surplus/Assets)t-1*(Under ** (=1 if undercapitalized))()()t-1(Surplus/Assets)********t()()()()(RBC risk-weighted NPW/Premiums)******()()(RBC risk-weighted NPW/Premiums)t-1*(******Capitalization(=1 if adequate capitalization))()()t-1(RBC risk-weighted NPW/Premiums)t-1*(***Capitalized (=1 if undercapitalized))()()t-1(RBC risk weighted Invested ******Assets/ Invested Assets)()()t-1(RBC risk weighted Invested Assets/ Invested Assets)t-1*******(Adequate Capitalization (=1 if adequate capitalization))()()t-1(RBC risk weighted Invested Assets/ Invested Assets)t-1******(Under Capitalized (=1 if undercapitalized))()(). of : *, **, *** significant at 10, 5 and 1 percent levels, respectively. z-statistics in parentheses below : RBC risk-weighted NPW is sum of RBC NPW risk factor for premium line* premiums in line. RBC risk-weighted Invested Assets is sum of RBC asset risk factor bytype * asset type. Reinsurance usage is ceded loss reserves/Total direct and assumed loss reserves. An insurer is considered to be adequately capitalized if 2≤RBCratio<3 and under-capitalized if RBC ratio <2. - 7 -
中国科技论文在线 Table 4Three Stage Least Squares Results(Risky Invested Assets/Invested Assets) used as Dependent VariabletAll InsurersResults for Year(s)19931994-2007 with year dummies (RBC risk-(Risky Inv- (RBC risk-(Risky Inv-(Surplus/weightedested Assets/(Surplus/weightedested Assets/Dependent VariableAssets)t NPW/Premium)tInvested Assets)tAssets)t NPW/Premium)tInvested Assets)tIndependent Variables ************()()()()()()(Geographic Herfindahl)*****t-1()()()()()()(Lines of Business Herfindahl)******-1()()()()()()(Reinsurance Usage)********t-1()()()()()()(Group Indicator (=1 if group))******t-1()()()()()()(Mutual Indicator (=1 if mutual))********t-1()()()()()()Log(Assets)*********t-1()()()()()()(RBC risk-weighted NPW/Surplus)***()()()()(Risky Invested Assets/ Invested Assets)***()()()()(Surplus/Assets)******t-1()()(Surplus/Assets)t-1*(Adequate (=1 if adequate capitalization))()()t-1(Surplus/Assets)t-1*(Under ** (=1 if undercapitalized))()()t-1(Surplus/Assets)******t()()()()(RBC risk-weighted NPW/Premiums)******()()(RBC risk-weighted NPW/Premiums)t-1*(******Capitalization(=1 if adequate capitalization))()()t-1(RBC risk-weighted NPW/Premiums)t-1*(***Capitalized (=1 if undercapitalized))()()t-1(Risky Invested Assets/ Invested Assets)******()()(Risky Invested Assets/ Invested Assets)t-1*(******Capitalization (=1 if adequate capitalization))()()t-1(Risky Invested Assets/ Invested Assets)t-1******(Under Capitalized (=1 if undercapitalized))()(). of : *, **, *** significant at 10, 5 and 1 percent levels, -statistics in parentheses below : RBC risk-weighted NPW is sum of RBC NPW risk factor for premium line* premiums in line. Reinsurance usage is ceded loss reserves/Total direct and assumedloss reserves. An insurer is considered to be adequately capitalized if 2≤RBC ratio<3 and under-capitalized if RBC ratio <2. Risky Invested Assets are the sum of stockand real estate - 8 -
中国科技论文在线 Table 5Three Stage Least Squares Results(RBC risk-weighted Invested Asset/Invested Assets) used as Dependent VariabletInsurers with RBC Ratio greater than 3 Results for Year(s)19931994-2007 with year dummies (RBC risk-(RBC risk-weighted (RBC risk-(RBC risk-weighted(Surplus/weightedInvested Asset/(Surplus/weightedInvested Asset/Dependent VariableAssets)t NPW/Premium)tInvested Assets)tAssets)t NPW/Premium)tInvested Assets)tIndependent **************()()()()()()(Geographic Herfindahl)*****t-1()()()()()()(Lines of Business Herfindahl)******-1()()()()()()(Reinsurance Usage)*************t-1()()()()()()(Group Indicator (=1 if group))******t-1()()()()()()(Mutual Indicator (=1 if mutual))*******t-1()()()()()()Log(Assets)************t-1()()()()()()(RBC risk-weighted NPW/Surplus)*****()()()()(RBC risk-weighted ***** Assets)()()()()t(Surplus/Assets)******t-1()()(Surplus/Assets)**********t()()()()(RBC risk-weighted NPW/Premiums)******()()(RBC risk weighted Invested ******Assets/ Invested Assets)()(). of : *, **, *** significant at 10, 5 and 1 percent levels, respectively. z-statistics in parentheses below : RBC risk-weighted NPW is sum of RBC NPW risk factor for premium line* premiums in line. RBC risk-weighted Invested Assets is sum of RBC asset riskfactor by type * asset type. Reinsurance usage is ceded loss reserves/Total direct and assumed loss reserves. An insurer is considered to be adequately capitalized if2≤RBC ratio<3 and under-capitalized if RBC ratio <2. - 9 -
中国科技论文在线 Table 6Three Stage Least Squares Results(Risky Invested Assets/Invested Assets) used as Dependent VariabletInsurers with RBC Ratio greater than 3Results for Year(s)19931994-2007 with year dummies (RBC risk-(Risky Inv- (RBC risk-(Risky Inv-(Surplus/weightedested Assets/(Surplus/weightedested Assets/Dependent VariableAssets)t NPW/Premium)tInvested Assets)tAssets)t NPW/Premium)tInvested Assets)tIndependent ************()()()()()()(Geographic Herfindahl)*****t-1()()()()()()(Lines of Business Herfindahl)******-1()()()()()()(Reinsurance Usage)**********t-1()()()()()()(Group Indicator (=1 if group))********t-1()()()()()()(Mutual Indicator (=1 if mutual))********t-1()()()()()()Log(Assets)*********t-1()()()()()()(RBC risk-weighted ***** **** Assets)()()()()t(Surplus/Assets)******t-1()()(Surplus/Assets)********t()()()()(RBC risk-weighted ******NPW/Premiums)t-1()()(Risky ******Assets/Invested Assets)()(). of : *, **, *** significant at 10, 5 and 1 percent levels, respectively. z-statistics in parentheses below coefficientsNote: RBC risk-weighted NPW is sum of RBC NPW risk factor for premium line* premiums in line. Reinsurance usage is ceded loss reserves/Total direct andassumed loss reserves. An insurer is considered to be adequately capitalized if 2≤RBC ratio<3 and under-capitalized if RBC ratio <2. Risky Invested Assetsare the sum of stock and real estate Hypothesis 1 states that insurers’ risk and capital should be significantly related to each other. - 10 -
中国科技论文在线 The results for 1994 to 2007 clearly show that this is the case. In these regressions, (Surplus/Assets) and (RBC risk-weighted NPW/ Premiums) are positive and significantly related tt230 to each other in Tables 3 and 4. Further, Table 3 indicates that (Surplus/Assets) and (RBC trisk-weighted Invested Assets/ Invested Assets) are positively and significantly related, while tTable 4 indicates that (Surplus/ Assets) and (Risky Invested Assets/ Invested Assets) are ttpositively and significantly related also. It is interesting to note that both asset risk measures used in Tables 3 and 4 are associated with the same results, even though some of the RBC factor 235 loadings for assets have been criticized. For 1992, the relationships between asset risk and capital are positive in most cases in Tables 3 and 4, but the relationships do not appear to be consistently significant. In the (Surplus/Assets) tequation for 1992 in Table 3, the coefficient for (RBC risk-weighted Invested Assets/Invested Assets) is and significant; and the corresponding coefficient for (Surplus/Assets) is tt240 significant too in the (RBC risk-weighted Invested Assets/Invested Assets) equation for 1992. t(The coefficient is .) However, the coefficient for (RBC risk-weighted NPW/Premiums) tis insignificant in the (Surplus/Assets) equation; and the corresponding coefficient for t(Surplus/Assets) is insignificant either in the (RBC risk-weighted NPW/Premiums) equation for tt1992 in Table 4. The relationships between underwriting risk and capital is insignificant in either 245 Table 3 or 4. The lack of simultaneity may be due to the lower degrees of freedom in these models. In any case, the inconclusive results for 1992 are similar to results found in prior studies for years before the imposition of new banking capital requirements. As indicated earlier, a positive or insignificant relationship between capital and risk can arise from exploitation of the RBC formula. This exploitation would most likely occur, if it occurred 250 at all, for insurers close to the ‘no action’ threshold or in the action level categories. Therefore, the analyses are carried out also for insurers with RBC ratios well above the threshold, ., for insurers with RBC ratios greater than three. And these results are in tables 5 and 6. The results in Tables 5 and 6 are the same with respect to the relationship between (Surplus/Assets) and underwriting risk and investment risk for 1992 and the period 1994-2007. t255 That is, (Surplus/Assets) in the 1994 to 2007 results is significant and positively related to tunderwriting and asset risk in Tables 5 and 6. Also, most coefficients are significant for (Surplus/Assets) and asset and underwriting risk in the 1992 results. Thus the results in Tables 3 tand 4 do not appear to be attributable to exploitation of the RBC formula in some fashion to improve results. 260 Robustness tests were carried out in which the proportion of premiums written in risky lines is substituted for (RBC risk-weighted NPW/Premiums); and the results are in Appendix Tables 1 through 4. The results generally support the significant and positive relationships between capital and underwriting and asset risk for the 1994 to 2007 period in Tables 3 through 6. Similar to the results in Tables 3 through 6, a positive relationship between capital and 265 underwriting risk as well as asset risk is present in the 1992 results. These results taken as a whole suggest that increases in capital are accompanied by increases in risk in the period after RBC implementation. These results are similar to those found by 5Cummins and Sommer. Thus, it does not appear that the imposition of RBC standards affected the basic relationship between capital and risk in property-liability insurers – the relationship 270 remains positive. For regulatory purposes, these results suggest that to the extent that RBC requirements led insurers to increase capital, an offsetting increase in risk took place. The coefficients for (Surplus/Assets), (RBC risk-weighted NPW/Premiums), (RBC t-1t-1risk-weighted invested Assets/ Invested Assets), and (Risky Invested Assets/ Invested Assets) t-1t-1- 11 -
中国科技论文在线 can be interpreted as the speed of adjustment towards a target for capital, net premiums written, 275 and assets, respectively, according to the model specification. In Tables 3 and 6 all of the speeds of adjustment variables are significant, and they are all between zero and one. The speed of adjustment results for well-capitalized insurers in Tables 3 and 4 vary from approximately to in the asset risk equations to to in the underwriting and capital equations in the results in Tables 3 and 4. These speeds of adjustment are very low compared to nonfinancial firms [13] [14] [15]280 (Flannery and Rangan, 2006; Huang and Ritter, 2009; Ovtchinnikov, 2010). The interaction terms of RBCA and RBCU with capital, underwriting risk, and asset risk, are used to test Hypothesis 2 which states that risk and capital vary for insurers in different financial shape. Hypothesis 2 is generally supported in the results for 1994 to 2007 in Tables 3 with respect to capital, asset risk, and underwriting risk. That is, the coefficient for the interaction terms of 285 RBCU with capital is significant and negative () in the capital equations, suggesting a higher adjustment speed toward targets of capital for under-capitalized insurers (speed=+=) than well-capitalized insurers (speed== ). The coefficient for the interaction terms of RBCU with capital is insignificant, indicating no effect of RBC on capital adjustment of marginally adequately capitalized insurers. In 290 underwriting risk equations, the coefficients of interaction terms of RBCA and RBCU with underwriting risk proxy is significant but with opposite sign. Thus, the adjustment speed of underwriting risk to firm’s target is () for well capitalized insurers, (+) for marginally adequately capitalized insurers, () for under-capitalized insurers. In conjunction with this, both marginally adequately capitalized 295 insurers and under-capitalized insurers were adjusting their investment risk at a higher speed toward their targets than well capitalized insurers. This is evidenced by the negative and significant coefficient for the coefficients of interaction terms of RBCA and RBCU with investment risk proxy in the investment risk equations. Further, under-capitalized insurers adjust their investment risk toward targets at a speed of (+), much higher 300 than the speed of (+) for marginally adequately capitalized insurers. Hence financially weaker insurers generally did respond more aggressively than marginally adequately capitalized insurers to overcome RBC related deficiencies, evidenced by a higher capital and asset risk adjustment speed, as Hypothesis 2 posits. The results in Table 4 are generally consistent with those in Table 3. 305 The results in the (Surplus/Assets) equations in Tables 3 and 4 indicate that, in 1993, neither tmarginally adequately capitalized insurers or undercapitalized insurers adjusted their capital more aggressively toward firm’s targets than insurers that were adequately capitalized. This is evidenced by insignificant coefficients of the interaction terms of RBCA and RBCU with (Surplus/Assets). The coefficient for the interaction terms of RBCU with underwriting risk is t-1310 insignificant but significant and positive () with asset risk, not supporting Hypothesis 2. However, the investment risk equation results do support Hypothesis 2 in the 1993 period, as the coefficients for the interaction terms of RBCA with asset risk is negative and significant. Table 4 presents similar results as Table 3. Thus the results are mixed with respect to Hypothesis 2 for the 1993 period. 315 The results for undercapitalized insurers are different in the 1994 to 2007 period with in the 1993 period in Tables 3 and 4 with respect to capital. That is, the coefficient for the interaction term of under-capitalization and (Surplus/Assets) is negative and significant in the capital t-1equations for the 1994 to 2007 period but not significant in the 1993 period in Tables 3 and 4. The coefficient for the interaction term of under-capitalization and underwriting risk proxy is positive - 12 -
中国科技论文在线 320 in the underwriting risk equation for the 1994 to 2007 period but insignificant in Tables 3 and 4. Finally, the coefficient for the interaction term of under-capitalization and asset risk proxy is negative in the asset risk equation for the 1994 to 2007 period but positive in Tables 3 and 4. Thus it appears that under-capitalized insurers adjust their capital and asset risk toward their targets at a higher speed than well-capitalized insurers in the 1994 to 2007 period. At the same time, 325 under-capitalized insurers adjust their underwriting risk toward their targets at a lower speed than well-capitalized insurers in the 1994 to 2007 period. This contrasts with the 1993 period. Thus overall, there does appear to be a difference for under-capitalized insurers in the 1994 to 2007 period. Under-capitalized insurers seem to respond to the RBC standard and increase their adjustment speed of capital and asset portfolio. Instead, underwriting portfolio has a higher cost 330 to adjust for under-capitalized insurers, compared to well-capitalized insurers. These results, overall, support Hypothesis 3 for under-capitalized insurers. The results are also different for marginally adequately capitalized insurers between 1993 and the 1994 to 2007 period. The coefficient for the interaction term of marginally adequate capitalization and underwriting risk proxy is negative and significant in the underwriting risk 335 equation in Table 3 and 4 for the 1994 to 2007 period, while the corresponding coefficient is positive and significant in the 1992 period. This indicates that marginally adequate capitalized insurers adjust to their target underwriting risk at a higher (lower) speed than well-capitalized insurers in the 1994 to 2007 (1993) period. Thus Hypothesis 3 is supported for marginally adequately capitalized insurers as well. 340 Overall, we find that generally both marginally adequately capitalized insurers and under-capitalized insurers adjusted to their capital, underwriting risk and asset risk at a higher speed than well-capitalized insurers (with an exception for under-capitalized insurers in adjusting underwriting business). Thus, to the extent that imposing RBC requirements were designed to enhance solvency, the results for both marginally adequately capitalized insurers and 345 under-capitalized insurers are consistent with this goal. 4 Conclusion This research investigates the relationship between capital and risk in property-liability insurers for 1993 and for 1994 to 2007. The periods selected allow for comparisons in insurer behavior for the period prior to RBC implementation and after. This research is important 350 because the NAIC is currently undergoing a review of its solvency mechanisms, including risk based capital requirements. Therefore, it is important to know if increased capital requirements are accompanied by increased, offsetting increases in risk. In the latter case, RBC requirements may not meet their intended goal which is to enhance solvency. Overall the results suggest that risk and capital are positively related. That is, a positive 355 relationship was detected between capital and asset and underwriting risk, so that capital increases are associated with increases in investment and underwriting risk. This significant and positive relationship was not consistently significant in 1993, prior to the implementation of RBC requirements in 1994. Further, both marginally adequately capitalized insurers and under-capitalized insurers generally adjusted to their target capital and risk portfolio at a higher 360 speed than well-capitalized insurers in the post RBC period. Thus, to the extent that RBC requirements were designed to enhance solvency, the results of this study suggest that the impact of RBC requirements is consistent with this goal for marginally adequately capitalized insurers and under-capitalized insurers. - 13 -
中国科技论文在线 365 References [1] Cummins, ., and Nini, . Optimal capital utilization by financial firms: Evidence from the property-liability insurance industry[J]. Journal of Financial Services Research, 2002 21: 15-53. [2] Cummins, ., Harrington, . and Niehaus, G. Risk-Based capital requirements for property-liability insurers: A financial analysis[A] in: E. Altman and I. Vanderhoof (eds.), The financial dynamics of the insurance 370 industry[C]. Homewood, IL: Irwin Professional Publishers, 1995 [3] Cummins, ., Grace, . and Phillips, . Regulatory solvency prediction in property-liability insurance: Risk-Based capital, audit ratios, and cash flow simulation[J]. Journal of Risk and Insurance, 1999, 66: 417-458. [4] Cummins, ., Harrington, . and Klein, . Insolvency experience, Risk-Based capital, and prompt corrective action in property-liability insurance[J]. Journal of Banking & Finance, 1995,19: 511-527. 375 [5] Cheng, J. and Weiss, . The role of RBC, hurricane exposure, bond portfolio duration, and macroeconomic and industry-wide factors in property-liability insolvency prediction[J]. Journal of Risk and Insurance, 2012, 79, 723-750. [6] Cheng, J. and Weiss, . Capital Structure in the Property-Liability Insurance Industry: Tests of the Tradeoff and Pecking Order Theory[J]. Journal of Insurance Issues, 2012, 35(1):1-43. 380 [7] Cummins, ., and Sommer, . Capital and risk in property-liability insurance markets[J]. Journal of Banking and Finance, 1996, 20: 1069-1092. [8] Shrieves, . and Dahl, D. The relationship between risk and capital in commercial Banks[J]. Journal of Banking &Finance, 1992, 16: 439-457 [9] Aggarwal, R. and Jacques, . The impact of FDICIA and prompt corrective action on bank capital and risk: 385 Estimates using a simultaneous equations model [J]. Journal of Banking and Finance, 2001,25: 1139-1160. [10] Jacques, K. and Nigro, P. Risk-Based capital, portfolio risk, and bank capital: A simultaneous equations approach[J]. Journal of Economics and Business, 1997, 49: 533-547. [11] Intrilligator, . Econometric Models Techniques and Applications[M]. Englewood Cliffs, NJ: 390 [12] Petroni, . and Shackelford, . The effect of Risk-Based capital on life insurers' investment portfolios[Z]. Michigan State [13] Flannery, . and Rangan, . Partial adjustment toward target capital structures[J]. Journal of Financial Economics, 2006 79: 469-506. [14] Huang, R. and Ritter, J. Testing theories of capital structure and estimating the speed of adjustment[J]. Journal 395 of Financial and Quantitative Analysis, 2009, 44: 237-271. [15] Ovtchinnikov, . Capital structure decisions: Evidence from deregulated industries[J]. Journal of Financial Economics, 2010, 95: 249-274. 产险公司的风险资本和风险趋避行为 12400 程江，Mary A. Weiss （1. 上海财经大学金融学院，上海 200433； 2. 美国天普大学FOX商学院，Philadelphia 19025） 摘要：该研究对美国产险公司的资本和风险趋避进行深入探讨. 我们选取1992到2007为样本区间以便于我们可以比较风险资本监管要求实施前后的公司行为变化. 我们用三阶段最405 小二乘法研究产险公司的风险资本与承保风险和投资风险之间的关系. 我们发现风险资本与承保风险和投资风险之间是有正相关关系.但是该正相关关系在1993年风险资本监管要求以前并不存在. 资本充足率低的公司在风险资本监管要求实施后比资本充足率高的公司更快地调整他们的风险资本与承保风险和投资风险.我们的研究表明美国风险资本监管要求减少了公司倒闭风险, 但是对资本充足率低的公司监管机构要提高监管频率.该研究对中国的410 保险业监管有相当的启发意义. 关键词：保险经济学；风险资本；保险监管；资本；风险 中图分类号：F84 - 14 -
