Stock vs. Mutual Insurers: Who Does and Who Should Charge More? Alexander Braun Przemys� law Rymaszewski Hato Schmeiser Institute of Insurance Economics University of St.Gallen, Switzerland Madrid, June, 2011 A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 1
Table of contents 1 Motivation and Contribution Relevant literature 2 Empirical analysis 3 Normative theory 4 Summary and Conclusion 5 A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 2
Motivation and Contribution Different rights and obligations associated with the legal form should affect the marginal insurance premium Motivation: • Private insurance companies are organized either as stock or mutual firms • There is no secondary market for mutual equity stakes • Distressed mutual insurers can call in additional premiums (recovery option) • Due to these aspects, marginal premiums of stock and mutual firms should differ Contribution: • Empirical and theoretical analysis of the premiums charged by stocks and mutuals • Panel data analysis for the German motor liability insurance sector • Contingent claims model framework for the pricing of stock and mutual insurance • Comparison of stock and mutual insurers (premium size, safety level, and capital) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 3
Relevant literature The large body of existing literature does not cover legal-form dependent premium difference • Agency issues (see, e.g., Mayers and Smith, 1981, 1986, 1988, 2005) ◮ Owner-policyholder conflict (more intense in stock insurance firms) versus... ◮ Owner-manager conflict (more intense in mutual insurance firms) • Information asymmetries (see, e.g., Smith and Stutzer, 1990, 1995) ◮ Parallel existence of both legal forms ◮ Size of mutual companies (see Ligon and Thistle, 2005) • Further differences between stock and mutuals ◮ Reasons for (de)mutualization (see, e.g., McNamara and Rhee, 1992; Viswanathan and Cummins, 2003; Zanjani, 2007) ◮ Differences in efficiency (see, e.g., Spiller, 1972; Cummins et al., 1999; Jeng et al., 2007) ◮ Differences in capital structure (see, e.g., Harrington and Niehaus, 2002) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 4
Empirical analysis Mutuals do not seem to charge significantly higher premiums than stocks Hausman-Taylor FEVD Procedure Fixed Effects Model (Intercept) -213.4151*** -237.3012*** — (-2.6692) (-12.1466) AvLoss 0.3420*** 0.3469*** 0.3420*** (15.4295) (9.9042) (10.9533) AvCosts 0.6053*** 0.5994*** 0.6053*** (7.3825) (6.1891) (3.9955) EqR 20.0231 15.7489* 20.0231 (1.0095) (1.9075) (0.5184) LTP 19.2463*** 18.7959*** 19.2463*** (7.0319) (17.3699) (7.3742) Stock -3.9429 33.7803*** — (-0.0470) (14.7292) Coefficients and t-statistics (in parentheses) for Hausman-Taylor estimator, the FEVD proce- dure, and the standard FE model. The average annual premium ( AvPrem ) is regressed on the following set of explanatory variables: average annual losses ( AvLoss ), average annual costs ( AvCosts ), equity ratio ( EqR ), and logged total premium ( LTP ). Hausman-Taylor and FEVD additionally include the time-invariant variable legal form ( Stock ). ***, **, and * denote sta- tistical significance on the 1, 5, and 10 percent confidence level. Tha analysis is based on the accounting data (2000-2006, source: Hoppenstedt) for German insurance companies offering motor vehicle liability insurance. A panel data set contains 99 stock and 14 mutual insurers covering 532 and 87 firm years for stock and mutual insurance companies, respectively. Table: Estimation results A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 5
Normative theory Model framework The employed contingent claims model framework is based on the work of Doherty and Garven (1986) • Stock insurer claims structure 0 = e − r E Q 0 = e − r E Q EC S 0 ( A 1 − L 1 )+ DPO S P S 0 = π S 0 ( L 1 ) − DPO S 0 0 • Mutual insurer claims structure ◮ Full participation in equity payoff EC Mf = e − r E Q 0 ( A 1 − L 1 )+ RO 0 + DPO M P M = e − r E Q 0 ( L 1 ) − RO 0 − DPO M 0 0 0 0 ◮ Partial participation in equity payoff EC M = γ e − r E Q 0 ( A 1 − L 1 ) − ( p L − γ ) DPO S � RO 0 + DPO M � 0 + p L 0 0 EC Mn = (1 − γ ) e − r E Q 0 ( A 1 − L 1 ) + ( p L − γ ) DPO S � RO 0 + DPO M � 0 + (1 − p L ) 0 0 P M = e − r E Q 0 ( L 1 ) − RO 0 − DPO M 0 0 A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 6
Normative theory Stock insurance company EC S 1 EC S 1 0 A 1 Figure: Payoff to the equityholders EC S 1 and policyholders P S 1 of a stock insurance company in t = 1 A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 7
Normative theory Stock insurance company EC S 1 DPO S 1 DPO S 1 EC S 1 45 ◦ 0 L 1 A 1 A 1 − L 1 Figure: Payoff to the equityholders EC S 1 and policyholders P S 1 of a stock insurance company in t = 1 A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 8
Normative theory Stock insurance company EC S 1 P S 1 DPO S 1 P S 1 DPO S 1 EC S 1 45 ◦ 0 L 1 A 1 A 1 − L 1 Figure: Payoff to the equityholders EC S 1 and policyholders P S 1 of a stock insurance company in t = 1 A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 9
Normative theory Mutual insurance company DPO S 1 DPO S 1 45 ◦ 0 L 1 A 1 Figure: Mutual insurer default put option payoff in t = 1 ( DPO M 1 ) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 10
Normative theory Mutual insurance company DPO M 1 DPO S 1 DPO M 1 C max DPO S 1 45 ◦ 0 X L 1 A 1 C max Figure: Mutual insurer default put option payoff in t = 1 ( DPO M 1 ) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 11
Normative theory Mutual insurance company DPO M 1 PO X 1 BPO 1 DPO S 1 DPO M 1 BPO 1 C max DPO S 1 PO X 1 45 ◦ 0 X L 1 A 1 C max Figure: Mutual insurer default put option payoff in t = 1 ( DPO M 1 ) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 12
Normative theory Mutual insurance company RO 1 C max RO 1 45 ◦ 0 X L 1 A 1 C max Figure: Mutual insurer recovery option payoff in t = 1 ( RO 1 ) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 13
Normative theory Mutual insurance company RO 1 DPO S 1 PO X 1 BPO 1 DPO S 1 C max RO 1 45 ◦ 0 X L 1 A 1 C max − PO X 1 − BPO 1 − C max Figure: Mutual insurer recovery option payoff in t = 1 ( RO 1 ) A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 14
Normative theory Premium comparison EC S EC Mf 0 0 Π M 0 P S π S P M 0 0 0 case I equity full participation γ = 1 excess of loss no recovery λ = 1 option stock insurer mutual insurer Figure: Comparison of premia A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 15
Normative theory Premium comparison EC Mn 0 EC S EC Mf 0 0 EC M 0 Π M 0 π M 0 P S π S P M P M 0 0 0 0 case I II equity full partial participation γ = 1 γ < 1 excess of loss no no recovery λ = 1 λ = 1 option stock insurer mutual insurer Figure: Comparison of premia A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 16
Normative theory Premium comparison EC Mn 0 EC S EC Mf EC Mn 0 0 0 EC Mf EC M 0 0 RO 0 + DPO M EC M 0 0 − DPO S 0 Π M 0 π M 0 π M P S π S P M P M 0 0 0 0 0 P M P M 0 0 case I II III IV equity full partial full partial participation γ = 1 γ < 1 γ = 1 γ < 1 excess of loss no no yes yes recovery λ = 1 λ = 1 λ > 1 λ > 1 option stock insurer mutual insurer Figure: Comparison of premia A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 17
Normative theory Premium comparison The mutual insurer can offer the same or a lower premium as the stock insurer if it holds less capital 85 Curves: Π 0 M (m utual premiums in PV terms) L 0 (PV of claims costs) L 0 − DPO 0 M (safety levels of mutuals with RO) M = P 0 S = π 0 S (PV of policyholder stakes) P 0 80 Points: M = L 0 − DPO 0 M Π 0 M = L 0 Π 0 M M , Π 0 75 S , P 0 S = π 0 70 P 0 65 60 0 5 10 15 20 25 S , EC 0 Mf EC 0 Figure: Equity-premium combinations for full equity participation/recovery option A. Braun, P. Rymaszewski, and H. Schmeiser, Stock vs. Mutual Insurance Premiums, June 2011 18
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