Is the Risk Based Mechanism Always Better? The Risk Shifting Behavior of Insurers under Different Guarantee Schemes 1

Transcription

1 Is the Risk Based Mechanism Always Better? The Risk Shifting Behavior of Insurers under Different Guarantee Schemes 1 Ming (Ivy) Dong, Helmut Gruendl, and Sebastian Schluetter 2 Abstract: Insurance guarantee schemes (IGSs) aim to protect policyholders from the costs of urer olvencies. However, IGSs can also reduce the incentives of urers to conduct appropriate risk management. We investigate the risk taking behavior of a stock urer under urance guarantee schemes with two different financing alternatives: a flat rate premium assessment versus a risk based premium assessment. Previous studies indicate that the flat rate premium assessment can induce urers to take more risks, a problem that can be resolved under the risk based premium assessment. Our results show that the risk taking incentive of the urer can also occur under the risk based IGS. The risk based mechanism is superior to the flat rate one only if an appropriate premium loading is included. Furthermore, we identify which IGS leads to higher policyholders welfare, measured by their expected utility. We find that the risk based IGS can be more advantageous in improving the policyholders welfare due to the limited risk of the urer, compared to the flat rate IGS. [Key words: urance guarantee schemes, risk shifting, consumer protection.] JEL classification: G22, G28, G31. 1 Previous title: The Risk Shifting Behavior of Insurers under Different Insurance Guarantee Schemes. 2 Ming (Ivy) Dong and Helmut Gruendl are with the Chair of Insurance and Regulation, Goethe University, Frankfurt. Sebastian Schluetter is with Allianz Global Corporate and Specialty AG. We are grateful to Mike B. Adams, Mark J. Browne, Gregory Nini, Hato Schmeiser, and participants at the European Conference on Banking and the Economy (ECOBATE 2014), the American Risk and Insurance Association (ARIA) 2013 Annual Meeting, the 39th Seminar of the European Group of Risk and Insurance Economists (EGRIE) 2012, and the Annual Congress of the German Insurance Science Association 2012 for useful comments and discussions. 72 Journal of Insurance Issues, 2015, 38 (1): Copyright 2015 by the Western Risk and Insurance Association. All rights reserved.

2 THE RISK SHIFTING BEHAVIOR OF INSURERS 73 I INTRODUCTION nsurance guarantee schemes (IGSs) have been adopted in many countries as important implements for consumer protection, despite the existence of other solvency regulatory tools. 3 The main reason for establishing IGSs is that policyholders face high costs for diversifying the default risks of urers. 4 By pooling the default risks of several urance companies in the market, IGSs lower the costs of the olvency risk that policyholders are exposed to. Apart from the effect of diversifying risks, IGSs can depending on their premium principle significantly influence the risktaking behavior of urance companies. Several previous empirical studies examine the impact of the flat rate IGS on the U.S. property liability urers risks. For example, Lee et al. (1997) find that the risk of stock urers asset portfolios increases following the enactment of the flat rate ex post IGS. 5 Downs and Sommer (1999) provide evidence that the flat rate ex post IGS induces stock urers to take more risks, particularly for lesscapitalized urers. Lee and Smith (1999) show that urers under the flat rate IGS tend to lower their reserves and substitute IGS coverage for capital. A recent theoretical study by Schmeiser and Wagner (2013) demonstrates that in a competitive market setting, introducing a flat rate exante IGS entails a shift of the urer s equity capital towards minimized solvency requirements, which leads to a higher olvency probability. Cumm (1988) points out that the flat rate IGS, charging a fixed percentage of the urers premium income as the guarantee fund premium, does not reflect the risks of urers. The risk based IGS is, therefore, superior to the flat rate scheme in terms of considering the risks of urers when charging the guarantee fund premium. However, the superiority of the risk based IGS over the flat rate scheme in the sense of its influence on the risk incentive of urers, to our best knowledge, has not yet been studied in a theoretical format. Therefore, this article fills the gap by investigating the risk taking behavior of a stock urer under urance guarantee schemes with two different financing alternatives: an ex ante flat rate premium assessment versus an ex ante risk based premium assessment. The focus of this article 3 This is due to the fact that no matter how solvency regulation and supervision try to reduce the default risk of urance undertakings, it is not possible to eliminate altogether the possibility of failure. See Oxera (2007, p. 16). 4 See Merton and Perold (1997, p. 2). 5 An ex post IGS collects the guarantee fund premium from the surviving urance companies, provided that an urer has defaulted, whereas the ex ante IGS charges its guarantee fund premium in advance from all urers covered by the IGS.

3 74 DONG, GRUENDL, AND SCHLUETTER is to analyze under what conditions the risk based IGS is superior to the flat rate IGS in terms of its influence on the urer s risk taking incentive. Furthermore, we also aim to identify the impact of different IGSs on policyholders welfare, measured by their expected utility. In corporate finance theory, the risk shifting problem is known as the phenomenon that firms transfer welfare from bondholders to shareholders by increasing the firm risk after bonds have been issued. 6 As long as the shareholders cannot commit to a low risk strategy, this may lead to a situation that is disadvantageous for bondholders. This agency theoretical setting also maps the shareholder policyholder relationship for a stock urance company. 7 Specifically, after a stock urer receives urance premiums from policyholders, the urer can change its asset allocation towards a riskier investment portfolio, 8 choose a riskier reurance strategy, 9 or reduce its equity capital endowment. 10 Without loss of generality, this article focuses on investigating the risk shifting behavior in the sense of an altered investment strategy of an urer. In the urance field, Filipovic et al. (2014) have recently studied the risk shifting behavior through a change of the investment strategy in a theoretical format. In a one period economy with two agents (policyholders and an urer s shareholders), they determine the optimal investment and premium policies of an urer. Based on the model of Filipovic et al. (2014), we incorporate the urance guarantee fund 11 as the third counterparty and investigate how different IGS premium principles affect the optimal investment policy of an urer. Furthermore, our model considers shareholders of both the urance company and the IGS level. 12 The primary urance premium and the guarantee fund premium thus need 6 See, for example, Jensen and Meckling (1976), Green (1984), and MacMinn (1992). 7 See Mayers and Smith (1981, pp ). 8 See, for example, Lee et al. (1997), Downs and Sommer (1999). 9 See Cumm (1988, p. 824). 10 See Schmeiser and Wagner (2013). 11 We use the urance guarantee fund to represent the organization or agent that adapts the urance guarantee scheme (IGS), charges guarantee fund premiums, and compensates policyholders when a failure of urance undertakings occurs. 12 In order to incorporate the costs of holding capital at the IGS level, we explicitly consider the shareholders of the guarantee fund. This model setup maps the situation in Germany, where the life urance IGS is run as a stock company. In the U.S., IGSs are nonprofit statebased systems without explicit equity capital (see However, they encounter the possibility that the state would additionally compensate policyholders (using tax income) if the guarantee funds were ufficient. This would be the analogy to losing the equity capital in a stock company. We thus expect that taxpayers in the long run require a risk adequate return from an IGS, reflecting such reserve liability.

4 THE RISK SHIFTING BEHAVIOR OF INSURERS 75 to ensure that shareholders of both the urance company and the guarantee fund receive at least a risk adequate return on their equity capital provision. Our results indicate that the risk shifting incentive of the urer can also occur under the risk based IGS, meaning that the risk based IGS does not necessarily induce a safe strategy of an urance company. The urer might still find it optimal to take excessive risk after collecting the urance premium. In this case, the flat rate IGS and the risk based IGS do not differ in their influence on the risk taking behavior of an urer. The main reason behind this result is that the risk based IGS premium only ensures that the urer cannot exploit the shareholders of the IGS. Risk shifting still allows the urer to transfer wealth from policyholders to its shareholders. We also show that the risk based mechanism is superior to the flat rate one only if an appropriate premium loading is included in the guarantee fund premium. By including appropriate premium loadings, the risk of the urer is limited under the risk based IGS. Furthermore, the investment policies chosen by the urer lead to specific welfare levels of shareholders and policyholders, and we thus deduce the welfare effects of different IGS premium principles. Specifically, we find that the risk based IGS can be more advantageous to policyholders in improving their welfare, compared to the flat rate IGS. This positive effect on the policyholders welfare is driven by the limited risk of the urer under the risk based IGS. The paper is organized as follows: Section 2 presents the model framework. It first formulates the payoffs to the three stakeholder parties and then expla the two IGS premium principles as well as welfare measures. Finally, it describes the timeline and the interplay of actions between the three stakeholder parties. In Section 3, we conduct a numerical analysis to detect the impact of the two IGSs on the urer s risk shifting behavior and stakeholders welfare. Section 4 concludes and provides relevant policy implications. THE MODEL FRAMEWORK We consider a one period model that consists of three stakeholder parties: a stock urer, a policyholder collective, and an urance guarantee fund. We assume that the urer and the urance guarantee fund are risk neutral, whereas policyholders are risk averse.

5 76 DONG, GRUENDL, AND SCHLUETTER Payoffs to the Three Stakeholder Parties E 0 At t 0, the shareholders endow the urer with equity capital, 13 policyholders pay the primary urance premium, and the guarantee fund premium assets of the urer are thus P 0 P 0 is charged to the urer. The total initial A 0 E 0 + P 0 P 0. (1) Correspondingly, the initial assets of the urance guarantee fund comprise its equity capital and the guarantee fund premium : E 0 P 0 A 0 A 0 E 0 + P 0. (2) A 0 The urer invests the portion of its entire assets into risky investments and the portion 1 into risk free securities, and the guarantee fund invests all of its assets only into risk free assets. 14 At t 1, the urer receives investment returns, and the final asset values of the urer are thus A 0 A 1 A 0 e r risky + 1 e r f, (3) where e r risky is the stochastic rate of return for the risky investments, and denotes the risk free rate of return. Correspondingly, the final asset values of the urance guarantee fund are given by e r f 13 In this article, the equity capital of the urer is fixed and exogenously given. The model of Filipovic et al. (2014) considers how solvency capital requirements, which restrict certain investment policies, limit the risk shifting problem of the urer. Fischer and Schluetter (2014) also analyze how the stock risk calibration of the standard formula under Solvency II influences the equity capital position and the investment policy of the urer. 14 For the effectiveness of the urance guarantee fund, it is not necessary to involve more than one urance company, since we model the guarantee fund as a stock urance company that manages its risks by providing sufficient equity capital.

6 THE RISK SHIFTING BEHAVIOR OF INSURERS 77 A 1 A 0 e r f. (4) Policyholders file their claims at t 1 with the stochastic nominal L 1 amount of losses. The indemnity payment of the urer depends on its solvency situation at t 1. Specifically, if the urer is solvent, policyholders are indemnified at the amount of their nominal claims ; otherwise, policyholders receive all assets of the urer from the urer to policyholders is thus A 1 L 1. The payoff I 1 minl 1, A1. (5) Furthermore, in the case of the urer s default, policyholders receive an additional indemnity payoff I 1 from the urance guarantee fund as additional compensation. This indemnity payoff depends on the nominal claim to the urance guarantee fund L 1 and is limited by the final assets of the guarantee fund. Specifically, the nominal claim to the urance guarantee fund is the amount of money that the guarantee fund promised to pay out policyholders in the case of the urer s olvency, i.e., the default put 15 expressed as: A 1 L 1 L 1 I 1 max L 1 A 1, 0. (6) Hence, the payoff from the urance guarantee fund to policyholders is given by I 1 minl 1, A1. (7) As to the shareholders of the urer, they receive the residual equity capital of the urance company olvency: E 1, or nothing in the case of the urer s 15 In reality, the urance guarantee fund frequently indemnifies policyholders only at the percentage of the defaulted claims. See Oxera (2007, pp ) for the IGSs in the EU and the NCIGF (2011) brochure for the U.S. IGSs.

7 78 DONG, GRUENDL, AND SCHLUETTER E 1 max A 1 L 1, 0. (8) Correspondingly, the shareholders of the urance guarantee fund receive the residual equity capital guarantee fund defaults: E 1, or nothing in the case that the E 1 max A 1 L 1, 0. (9) Insurance Guarantee Fund Premium Principles We now distinguish two ex ante urance guarantee fund premium principles: the flat rate vs. the risk based financing approach. The flat rate guarantee fund premium flat P 0 of the primary urance premium : equals a predetermined percentage P 0 flat P 0 P 0. (10) risk The risk based guarantee fund premium P 0, depends on both the asset allocation of the urer () and (possibly) a loading factor that is predetermined by the urance guarantee fund. An actuarially fair guarantee fund premium is equal to the present value of the guarantee, which is, under the assumed risk neutral fund s indemnity payment ity, given by: I 1 risk P 0 e r f EI 1. (11) The main difference between the flat rate IGS and the risk based IGS is that the risk based guarantee fund premium is affected by the riskiness of the urer (), since influences the final asset values of the urer A 1 and consequently the indemnity payoff of the guarantee fund to policyholders I 1 (see Eq. (6) and (7)). Note that the asset allocation of the urer cannot be prescribed by the guarantee fund; however, we assume that the guarantee fund can predict the shareholder value maximizing asset allocation of the urer (*) and can adjust the guarantee fund premium accordingly.

8 THE RISK SHIFTING BEHAVIOR OF INSURERS 79 In the subsequent analyses, we also investigate the influence of a proportional loading factor () incorporated into the risk based guarantee fund premium. After including this proportional loading on the actuarially fair guarantee fund premium, the risk based premium is defined as Welfare Measures risk P 0, 1 + e r f EI 1. (12) Based on Eq. (8), which specifies the final equity capital of the urance company, the net shareholder value of the urer is SHV 0 e r f E max A 1 L 1, 0 E0. (13) Correspondingly, the net shareholder value of the urance guarantee fund is given by SHV 0 e r f E max A 1 L 1, 0 E0. (14) As to policyholders, we assume that the policyholder collective has an initial wealth of w 0 (after consumption). Policyholders pay out the primary urance premium P 0 and invest their remaining funds risk free. At t 1, random losses L 1 occur, and policyholders receive the indemnity payment from the urer I 1 and possibly from the guarantee fund. Therefore, the final wealth of policyholders at t 1 is calculated as I 1 w 1 w 0 + P 0 e r f L 1 + I 1 + I 1. (15) We measure the expected utility of policyholders by an exponential utility function with a constant absolute risk aversion parameter a: 16 EU 0 w 1 E e a w 1. (16) 16 See, for example, Eisenfuehr et al. (2010, pp ).

9 80 DONG, GRUENDL, AND SCHLUETTER For the subsequent analyses, we also convert the expected utility into the certainty equivalent CE 1, and the policyholders welfare is thus measured by the discounted certainty equivalent CE 0 : CE 0 e r f 1 -- ln EUw. (17) a 1 Timeline and the Interplay between Three Stakeholder Parties The timeline of decision making at t 0 is as follows: (i) the guarantee fund decides on the premium principle (the flat rate premium or the risk based premium assessment) including the pricing parameters (such as the flat rate () or the loading factor ()); (ii) policyholders pay the primary urance premium P 0 ; (iii) the urer decides on the portion of investment in risky assets (); (iv) the guarantee fund charges the guarantee fund premium P 0 to the urer according to the asset allocation of the urer. Insurance Guarantee Fund In order to ensure that the urance guarantee fund can be established without external subsidies, the guarantee fund premium must follow the principle that the shareholders of the guarantee fund receive at least riskadequate returns, i.e., the guarantee fund premium must fulfill the following participation constraint of its shareholders: SHV 0 0. (18) Policyholders Filipovic et al. (2014) build a one period model that captures the interest conflicts between policyholders and shareholders of urance companies due to limited liability. Their model describes the situation that limited liability provides urers with incentives to increase their investment risks, and in turn, may reduce policyholders willingness to pay for urance coverage. Therefore, although policyholders pay urance premiums before urers decide on their risky investment strategies, policyholders can anticipate the risk shifting behavior of urers and adjust urance premiums accordingly. We follow the basis model of Filipovic et al. (2014) by assuming that policyholders only pay a fair primary urance

10 THE RISK SHIFTING BEHAVIOR OF INSURERS 81 fair premium that reflects the risk of the urer, denoted as P 0. This case can occur, for example, under the setting of a competitive urance market where the size of the urance premium guarantees that the shareholders of the urer receive exactly the risk adequate return on their invested equity capital. Under these circumstances, the net shareholder value of the urer is zero: SHV 0 fair P 0 0. (19) Insurer The objective of the urer is to maximize its net present shareholder value by choosing an optimal risky investment policy (*). When deciding on its asset allocation, the urer is aware of the predetermined guarantee fund premium principle and anticipates the consequences for the size of the guarantee fund premium. Therefore, by combining Eq. (1), (3), and (13), the optimization question of the urer can be described as max SHV e r f E max A 1 L 1, 0 E0 E max E 0 + P 0 P0 e r risky + 1 e r f L 1, 0 NUMERICAL ANALYSIS e r f E 0 (20) In the following section, we first introduce stochastic processes for mapping the risky asset and liability developments of the urer. Then, through a numerical analysis, we present situations in which the two IGSs have the same or different influence on the risk incentive of the urer. Based on these results, we also identify the IGS premium principle that leads to the highest policyholders welfare and in the meanwhile satisfies the participation constraint of the guarantee fund s shareholders (i.e., nonnegative net shareholder value of the guarantee fund according to Eq. (18)). The reason for applying a numerical analysis is the complex payoff structure for each stakeholder party. The complexities are caused by, firstly, the limited liability of both the urer and the urance guarantee fund as well as the influence of the limited liability on the primary urance and the guarantee fund premium. Secondly, the circularity issues between the (risk based) guarantee fund premium and the urer s decision on risk as well as between the primary urance premium and the urer s risk are a further reason why closed form solutions are not viable..

11 82 DONG, GRUENDL, AND SCHLUETTER Model Specification We assume that both the risky asset and the liability processes follow geometric Brownian motions with the drift A and L and with the volatility A and L respectively. In a one period model setting, the solutions to the stochastic processes of the risky asset and the liability are 17 2 A A A W A, 1 A 1 A 0 e 2 L L L W L, 1 L 1 L 0 e, (21) (22) where the W A,1 and the W L,1 follow Wiener processes and are correlated with the correlation coefficient A,L. Combining Eq. (3) and (21), the final asset values of the urer at t 1 can be expressed as A 1 2 A A A W A, 1 A 0 e 1 e r f +. (23) Table 1 shows the parameter values applied in the numerical analysis. Specifically, we assume that the initial equity capital endowment of the urer and of the urance guarantee fund is E 0 15 and E 0 40 respectively. We also assume that the initial value of the urer s liabilities is L 0 40, the initial wealth of the policyholder collective is w 0 70, and the risk aversion of the policyholder collective is a The riskfree rate of return (r f ) is calibrated according to the Quantitative Impact Study 5 (QIS5) by the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS) (2010). 19 We also calibrate the asset drift 17 See Bjoerk (2009, p. 69). 18 Holt and Laury (2002) provide the risk aversion classification based on lottery game choices. The risk averse risk preference classification relates to a risk aversion coefficient ranging from 0.41 to A calibration of the constant absolute risk aversion (CARA) with the coefficient 0.5 can also be found in Laux and Muermann (2010, p. 343).

12 THE RISK SHIFTING BEHAVIOR OF INSURERS 83 Table 1. Parameter List for the Numerical Analysis Parameter Notation Value Insurer s equity capital endowment E 0 15 Guarantee fund s equity capital endowment E 40 0 Insurer s initial liabilities L 0 40 Insurer s asset drift A 0.05 Insurer s asset volatility A Insurer s liability drift L 0.08 Insurer s liability volatility L 0.2 Risk-free rate of return r f Policyholders initial wealth 0 60 Policyholders risk aversion a 0.5 Correlation coefficient between the asset and the liability risk of the urer AL, 0 ( A ) and the asset volatility ( A ) by using the historical data of the Euro Stoxx 50 prices from 1997 to The liability volatility L 0.2 is consistent with the calibration in Yow and Sherris (2008). Furthermore, we set up an initial situation where the correlation coefficient between the asset and the liability risk of the urer A,L equals 0. The numerical results in the following sub sections are derived through a Monte Carlo simulation using 5,000,000 iterations. Numerical Results In this section, we first assume that policyholders do not anticipate the risk shifting behavior of the urer, and the urer can thus charge an urance premium with a fixed mark up to policyholders. Under this assumption, we can illustrate the gain of the urer in its net shareholder value through risk shifting. In the second step, we introduce a competitive urance market where the primary urance premium follows the 19 See CEIOPS (2010, p. 11). 20 We assume that the risky investment class of the urer is mainly stocks. Hence, we calibrate the risky asset drift and volatility of the urer by the average annual return and the standard deviation of the Euro Stoxx 50 for the last 15 years.

13 84 DONG, GRUENDL, AND SCHLUETTER principle described in Eq. (19). For this setting, we investigate the impacts of different IGSs on the urer s risk incentive, and consequently on the policyholders welfare. We finally compare the flat rate IGS with the riskbased IGS with respect to their influence on risk shifting and consumer protection in a competitive market. In addition, we also show cases when there is no urance guarantee fund and when policyholders do not purchase urance contracts. Insurance Premium with a Fixed Mark-Up We assume that the primary urance premium is fixed as 50. Figure 1 (a) shows that the urer s net shareholder value increases for larger portions of risky assets under the flat rate IGS. Investing the entire assets at the maximum risk ( 1) leads to the highest urer s net shareholder value regardless of the flat rates () of the guarantee fund premium. A rise in the flat rate of the IGS reduces the total amount of available assets that can be invested riskily; the risk shifting incentive of the urer is, nevertheless, not affected. Figure 1 (b) illustrates the impact of risk shifting on the guarantee fund s net shareholder value and the policyholders welfare when the flat rate. The guarantee fund s net shareholder value declines as the portion of risky investment increases. This is due to the fact that a more risky investment strategy leads to higher default risks of the urer, which is not reflected by higher guarantee fund premiums. Furthermore, the urer s risk shifting behavior reduces the policyholders welfare. On the one hand, a high risk investment policy results in more volatile asset returns for the urer, which thus lowers the safety level of the urance company. On the other hand, in some cases severe asset losses occur, and the olvency probability of the guarantee fund thus increases. This means that the unpaid claims of the urer cannot be (fully or largely) compensated through the protection of the guarantee fund. To sum up, the urer exploits both the guarantee fund and policyholders through risk shifting under the flat rate IGS in a noncompetitive urance market. Based on the same model set up, Figure 2 presents the risk shifting behavior of the urer and welfare effects under the risk based IGS. Specifically, Figure 2 (a) shows the optimal investment policies under different premium loadings () of the risk based guarantee fund premium. When the premium loading, the urer maximizes its net shareholder value by investing its entire assets at the maximum risk (), despite that the guarantee fund premium adjusts according to the urer s risk. When higher premium loadings are applied (and 2.6 as examples), the urer no longer benefits from taking the maximum risk. The punishment of higher guarantee fund premiums for the substantial risk taking P 0

14 THE RISK SHIFTING BEHAVIOR OF INSURERS 85 (a) Risk shifting when the flat rate 2% and 5% (b) Welfare effects when the flat rate 2% Fig. 1. Risk shifting and welfare effects under the flat rate IGS in a non competitive urance market.

15 86 DONG, GRUENDL, AND SCHLUETTER (a) Risk shifting when the risk based IGS premium loading is 0, 1, 1.5, and 2.6 (b) Welfare effects when the risk based IGS premium loading Fig. 2. Risk shifting and welfare effects under the risk based IGS in a non competitive urance market.

16 THE RISK SHIFTING BEHAVIOR OF INSURERS 87 outweighs its ga. As a result, the optimal risky investment portion () decreases. To sum up, the mere presence of a risk based guarantee fund premium is ufficient for preventing risk shifting, and an adequate guarantee fund premium loading is necessary. Furthermore, we find that the minimum premium loading that is required to induce a lower than themaximum risk investment policy (i.e., ) is. In addition, in the examples shown in Figure 2 (a), a significantly high loading, e.g., can lead to an optimal risky investment strategy at. Figure 2 (b) describes the welfare effects of the risk based IGS without premium loading () on the guarantee fund s shareholders and policyholders. The risk based IGS with secures actuarially fair guarantee fund premiums agat different risks of the urer, and the guarantee fund s net shareholder value is thus zero. Furthermore, Figure 2 (b) shows that the policyholders welfare reduces under the actuarially fair guarantee fund premium, since risk shifting still takes place. Therefore, the riskbased IGS without an appropriate premium loading generates the similar negative effect on the policyholders welfare, as in the case under the flatrate IGS. The only difference to the situation under the flat rate IGS is that the guarantee fund s net shareholder value is protected from exploitation. Competitive Insurance Market In the following analyses, we assume a competitive urance market. The primary urance premium thus adjusts according to the default risk of the urer. Consequently, the net shareholder value of the urer is always zero (see Eq. (19)). Therefore, in the following sections, we concentrate on the influence of different IGSs on the guarantee fund s net shareholder value and the policyholders welfare. Another implication for a competitive urance market set up is that the policyholders welfare can also be affected by the level of the primary urance premium P 0, whereas in a non competitive urance market policyholders pay a fixed urance premium, and their welfare depends only upon the amount of indemnity payments from the urer I 1 and (possibly) from the guarantee fund. Firstly, our results show that the maximal risk taking is always optimal for the urer under the flat rate IGS regardless of the flat rate size, despite the existence of a competitive urance market. Figure 3 demonstrates the primary urance premium, the guarantee fund premium, and welfare effects when applying different flat rates. Figure 3 (a) illustrates that both the guarantee fund premium and the primary urance premium increase for greater flat rates. The slope of the primary urance premium function I 1

17 88 DONG, GRUENDL, AND SCHLUETTER (a) Primary urance and guarantee fund premium under different flat rates (b) Welfare effects under different flat rates Fig. 3. Premiums and welfare effects under the flat rate IGS in a competitive urance market.

18 THE RISK SHIFTING BEHAVIOR OF INSURERS 89 is less steep than the one of the guarantee fund premium function, since the primary urer bears a part of the higher flat rate. This reduces its shareholder value. However, fewer assets invested riskily lead to a higher default put value of the urer, driving its shareholder value back to zero. Consequently, bearing parts of the higher guarantee fund premium doesn t reduce the shareholder value of the urer. Furthermore, since the urer s net shareholder value is zero under perfect competition, Figure 3 (b) demonstrates that the guarantee fund s net shareholder value increases for a growing, which generates higher guarantee fund premiums. At the same time, the policyholders welfare declines as rises. This negative impact on the policyholders welfare results from an increase in the primary urance premium. Unlike the case under the flat rate IGS, the urer s optimal investment policy alters regarding different premium loadings under the riskbased IGS. Table (a) in Figure 4 shows that the urer is inclined to invest less riskily than the maximum risk 1 when the premium loading equals and is greater than 0.6. Figure 4 (b) illustrates that the guarantee fund premium first increases for greater premium loadings when 0.6, and then declines when 0.6. The reduced guarantee fund premiums when 0. 6 are due to less risky investment strategies of the urer. Furthermore, the primary urance premium rises as the premium loading increases. Two reasons are behind this effect: firstly, a higher guarantee fund premium is reflected by a surcharge on the primary urance premium when 0.6 ; secondly, the safety level of the urer improves when 0.6, which requires higher primary urance premiums. Figure 4 (c) demonstrates the welfare effects of the risk based IGS under different premium loadings. When the premium loading 0, the actuarially fair guarantee fund premium leads to the zero guarantee funds net shareholder value. For 0 0.6, the increased guarantee fund premium is the main driver for a positive guarantee fund s net shareholder value. When 0.6 1, the guarantee fund s net shareholder value declines slightly due to the less risky profile of the urer, which brings less guarantee fund premium income. However, the guarantee fund s net shareholder value returns to increase for 1, since the payments to policyholders in the event of urer olvencies are less due to the higher safety levels of the urer. As to the policyholders, they face three welfare effects under a positive premium loading: firstly, the increase in the primary urance premium due to a higher guarantee fund premium loading reduces policyholders welfare; secondly, the thus improved solvency situation of the guarantee fund is beneficial for policyholders; thirdly, a decrease of the urer in risky investments generates higher policyholders welfare. Figure 4 (c)

19 90 DONG, GRUENDL, AND SCHLUETTER (a) Insurer s optimal investment policies (*) under different premium loadings () (b) Primary urance and guarantee fund premium under different premium loadings (c) Welfare effects under different premium loadings Fig. 4. Optimal investment policies, premiums, and welfare effects under the risk based igs in a competitive urance market.

20 THE RISK SHIFTING BEHAVIOR OF INSURERS 91 shows that the policyholders welfare slightly declines at first. This is due to the fact that the increased primary urance premium is invested at the maximum risk when 0.5, and the disadvantage of a higher primary urance premium outweighs the advantage of an improved safety of the guarantee fund. However, the effects of the primary urance premium and of the guarantee fund safety level reverse for greater premium loadings (when ). This leads to an increase in the policyholders welfare, despite the fact that the optimal risky investment policy of the urer rema unchanged 1. As the premium loading increases further (for ), the increase in the policyholders welfare is mainly driven by the limited investment risk of the urer. Although policyholders bear high primary urance premiums, the advantage of obtaining the mitigating effect on the urer s risk shifting behavior outweighs this disadvantage. However, the effect of the primary urance premium and of the mitigating effect reverses for substantial premium loadings 1.4, which ultimately causes a decrease in the policyholders welfare. Comparison of the Two IGSs in a Competitive Insurance Market This section compares welfare effects under the flat rate IGS and the risk based IGS in a competitive urance market. In order to ensure the comparability of the two IGSs, we adjust the flat rate under the flat rate IGS so that each flat rate is equivalent to a given premium loading () under the risk based IGS. This means that both IGSs charge the same amount of guarantee fund premiums to the urer. Table (a) in Figure 5 lists different premium loadings, which are used for welfare effect analyses in Figure 5 (b) and (c), and their equivalent flat rates. Note that when 0.6, the optimal risky investment policy of the urer alters according to the previous results (see Table (a) in Figure 4). Consequently, the guarantee fund requires less guarantee fund premiums from the urer under the risk based IGS, and the equivalent flat rates ( e ) for 0.6 reduce correspondingly. Figure 5 (b) shows that the risk based IGS is, in most cases, more advantageous to the guarantee fund s shareholders in generating higher net shareholder value, compared to the flat rate IGS. This is due to the fact that the risk based premium mechanism can prevent the urer from exploiting the guarantee fund s shareholders through risk shifting. In some extreme cases the flat rate guarantee fund applies ufficient flat rates (i.e., e < 4.57%), and the guarantee fund s net shareholder value turns to be negative. In addition, for 0.6 the guarantee fund s net shareholder value is the same under the two IGSs, since the guarantee fund premium and the urer s optimal risky investment strategies are identical.

21 92 DONG, GRUENDL, AND SCHLUETTER (a) Different premium loadings and their equivalent flat rates % 5.27% 5.92% 5.96% 4.76% 4.10% 3.80% 3.59% 3.52% 3.44% 3.36% (b) Guarantee fund s net shareholder value under the two IGSs (c) Policyholders welfare under the two IGSs Fig. 5. Comparison between the two igss in a competitive urance market.

22 THE RISK SHIFTING BEHAVIOR OF INSURERS 93 Figure 5 (c) illustrates that policyholders are, in most cases, better off under the risk based IGS than under the flat rate IGS. However, in the cases where small premium loadings 0.6 are applied, the risk based IGS and the flat rate IGS do not differ in their influence on the policyholders welfare, since the urer chooses to invest at the maximum risk. For higher premium loadings 0.6, the risk based IGS improves policyholders welfare due to the limited urer s risk, despite that the primary urance premium grows with an increasing. The main difference between the flat rate IGS and the risk based IGS is how they improve the stakeholders welfare (both the guarantee fund s net shareholder value and the policyholders welfare). Under the flat rate IGS, the improvement of the stakeholders welfare only depends on increasing the capacity of the guarantee fund, which is realized by charging more guarantee fund premiums to the urer. Differently, the risk based IGS improves the stakeholders welfare based on its negative influence on the urer s risk. Finally, we also determine policyholders welfare in the case without any IGS and the case without purchasing urance contracts in a competitive urance market setting. The results show that the policyholders welfare is CE without any IGS and is CE without purchasing urance contracts. Both cases are detrimental for policyholders in comparison to the situation with urance and the existence of the urance guarantee fund. When there is no guarantee fund, the urer s initial equity capital endowment is the maximum compensation that policyholders can obtain in the cases of severe losses. The presence of a guarantee fund brings its equity capital into play, which serves as a further loss absorption buffer. In addition, policyholders welfare is the lowest, compared to all other cases, when policyholders do not purchase urance contracts. CONCLUSION AND POLICY IMPLICATIONS We construct a simple framework consisting of a stock urer and its stakeholders and an urance guarantee fund that is run as a stock company. Under this model set up, we investigate the influence of different IGSs on the risk shifting behavior of the urer. The major finding provides an ight that the risk based guarantee fund premium mechanism is not always superior to the flat rate mechanism, since the problem of the urer s risk shifting cannot be prevented under a risk based IGS without an appropriate premium loading. The two IGSs thus do not differ in their influence on risk shifting or on the stakeholders welfare for those cases in which an appropriate premium loading is missing for the risk based IGS.

23 94 DONG, GRUENDL, AND SCHLUETTER Once the risk based IGS with appropriate premium loadings induces safer investment strategies of the urer, the stakeholders welfare is improved, despite the fact that this positive effect is at the cost of higher primary urance premiums. Compared to a competitive urance market, in a non competitive urance market higher premium loadings on the guarantee fund premium are necessary for inducing lower investment risks of the urer. This is due to the fact that the punishment for risk shifting solely relies on the risk based guarantee fund premium in a non competitive urance market, in which case policyholders do not react to the urer s default. In other words, market discipline can assist in deterring the urer s risk shifting. The envisaged European regulatory regime on urers Solvency II aims to improve market transparency regarding the olvency risk in the urance market. This can, in principle, lead to a competitive urance market where urance premiums correctly reflect the default situations of urers. Therefore, the required supervisory reporting and public disclosure would, in the light of our results, contribute to the negative influence of a risk based IGS on urers risk taking behavior. The urance guarantee fund, which at first glance conflicts with the principle of enhancing market discipline, could influence urers risks in the same direction as other regulatory tools. There are two possible extensions of this article: Firstly, it would be interesting to include additional urance companies into the framework. In this case, we would face cross subsidization effects between urers through the IGS, and a prisoners dilemma effect would interfere with urers risk incentives. Furthermore, wealth transfer among policyholder groups from different urers may also occur, in which case the IGS may only be beneficial for certain types of policyholders. Secondly, this article considers the situation that the urance guarantee fund is run as a stock company as is the case in Germany. The more general setting would be to consider a guarantee fund that is run by the government. In the case that the guarantee fund defaults, the government could use the tax income from taxpayers to compensate policyholders. In a model that consists of urers, policyholders, the urance guarantee fund, and the government/taxpayers with different incentives, the urance guarantee fund might achieve different effects on consumer protection and welfare transfer. REFERENCES Bjoerk, T. (2009) Arbitrage Theory in Continuous Time (3rd edition), Oxford University Press.

24 THE RISK SHIFTING BEHAVIOR OF INSURERS 95 CEIOPS (2010) Quantitative Impact Study (QIS5). Calibration paper. Retrieved from paper_en.pdf Cumm, D. J. (1988) Risk Based Premiums for Insurance Guaranty Funds, The Journal of Finance 43(4): Downs, D. H. and D. W. Sommer (1999) Monitoring, Ownership, and Risk Taking: The Impact of Guaranty Funds, Journal of Risk and Insurance 66(3): Eisenfuehr, F., T. Langer, and M. Weber (2010) Rational Decision Making, Springer. Filipovic, D., R. Kremslehner, and A. Muermann (2014) Optimal Investment and Premium Policies under Risk Shifting and Solvency Regulation, Journal of Risk and Insurance (forthcoming). Fischer, K. and S. Schluetter (2014) Optimal Investment Strategies for Insurance Companies in the Presence of Standardised Capital Requirements, The Geneva Risk and Insurance Review (forthcoming). Green, R. C. (1984) Investment Incentives, Debt, and Warrants, Journal of Financial Economics 13(1): Holt, C. A. and S. K. Laury (2002) Risk Aversion and Incentive Effects, American Economic Review 92(5): Jensen, M. C. and W. H. Meckling (1976) Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure, Journal of Financial Economics 3(4): Laux, C. and A. Muermann (2010) Financing Risk Transfer under Governance Problems: Mutual Versus Stock Insurers, Journal of Financial Intermediation 19(3): Lee, S. J. and M. L. Smith (1999) Property Casualty Insurance Guaranty Funds and Insurer Vulnerability to Misfortune, Journal of Banking and Finance 23(9): Lee, S. J., D. Mayers, and C. W. Smith Jr. (1997) Guaranty Funds and Risk Taking Evidence from the Insurance Industry, Journal of Financial Economics 44(1): MacMinn, R. D. (1993) On the Risk Shifting Problem and Convertible Bonds. Advances in Quantitative Analysis of Finance and Accounting 2, Mayers, D. and C. W. Smith Jr. (1981) Contractual Provisions, Organizational Structure, and Conflict Control in Insurance Markets, Journal of Business 54(3): Merton, R. C. and A. Perold (1997) A Model of Contract Guarantees for Credit Sensitive, Opaque Financial Intermediaries, European Finance Review 1: NCIGF (2011) The Property and Casualty Guaranty Funds. Build to Work. Retrieved from Oxera (2007) Insurance Guarantee Schemes in the EU: Comparative Analysis of Existing Schemes, Analysis of Problems and Evaluation of Options. Retrieved from ec.europa.eu/internal_market/urance/docs/guarantee_schemes_en.pdf Schmeiser, H. and J. Wagner (2013) The Impact of Introducing Insurance Guaranty Schemes on Pricing and Capital Structure, Journal of Risk and Insurance 80(2): Yow, S. and M. Sherris (2008) Enterprise Risk Management, Insurer Value Maximisation, and Market Frictions, Astin Bulletin 38(1): 293.