Part VII Issues Related to Financial Institutions
C. William Sealey, John M. Gandar and Sumon Mazumdar
Abstract Third-party liability guarantees, such as the guarantees provided by state guaranty funds in the U.S. to property insurance companies, or federal deposit insurance provided to commercial banks in many countries, potentially create risk-taking incentives. Empirical evidence supports the risk-taking hypothesis in property liability insurance and banking. While a large body of literature has focused on the optimal design of regulations to address such moral hazard issues in banking, the potential risk-taking incentives that may arise in the property liability insurance context and their regulatory implications are much less understood. We develop a model that examines an insurance company’s risk-taking incentives in the presence of a guaranty fund that protects policyholders from loss if the insurer fails, a scheme that is provided in many countries. We propose a set of workable regulatory mechanisms that may be considered to alleviate such potential moral hazard incentives.
1 Introduction
Given the central role thatfinancial institutions play in the economy, the govern- ment (or a state agency) often provides such institutions with an explicit or implicit liability guarantee, i.e., promises to pay any remaining liability claims against the institution if the latter fails and is unable to fully pay such claims itself. Deposit insurance, designed to prevent bank runs, is perhaps the best known example of such a regulatory mechanism. Such insurance, provided by governments in many
C.W. SealeyJ.M. Gandar
University of North Carolina at Charlotte, Charlotte, USA S.C. Mazumdar (&)
Haas School of Business, University of California at Berkeley, Berkeley, USA e-mail: sumon.mazumdar@navigant.com
S.C. Mazumdar
Navigant Economics, Oakland, USA
©Springer India 2016
M. Roy and S. Sinha Roy (eds.),International Trade and International Finance, DOI 10.1007/978-81-322-2797-7_26
527
countries, has become even more wide spread after the 2007–2009financial crisis.1 However, it is well-understood that such a mechanism can increase a bank’s incentive to “go for broke” (commonly referred to as moral hazard) unless the insurance mechanism is properly designed, for example through a risk-adjusted premium structure imposed on banks.2There is now a large body of literature that examines such moral hazard incentives in banking, and the design of banking regulation (e.g., risk-adjusted deposit insurance and capital requirements, or closure rules) to address such incentives.3
There is relatively less extant research about the moral hazard issues associated with the liability insurance that state guaranty funds provide insurance companies (i.e., the guarantee that the fund would protect policy holders if an insurance company in the state defaults on benefit payments or becomes insolvent) even though such insurance guarantee schemes which“provide last resort protection to policyholders and beneficiaries when insurers are unable to fulfil their contract commitments” are commonly offered across the world. According to an Oxera (2007) study, 13 of the 27 countries in the European Union had put in place insurance guarantee arrangements.4Such arrangements are in place in several other countries as well, such as the U.K., U.S., and Japan.5
Even though empirical evidence indicates that risk-taking by insurance com- panies is greater in the presence of such a insurance guarantee,6possible solutions to this risk-taking problem are much less understood. To date, policy proposals have been directed almost exclusively to the banking industry. However, the insurance business and its system of third-party guarantees are considerably dif- ferent from its banking counterpart.
A bank’s moral hazard incentive stems from its use of insured deposit debt to fund its assets. Such deposit insurance creates a possible moral hazard incentive if the deposit insurance agency (such as the United States’Federal Deposit Insurance
1See Demirgỹỗ-Kunt et al. (2014) which provides a global database of deposit insurance arrangements as of 2013. The study also discusses the safety net provided in different countries to thefinancial system, which may include government protection of nondeposit liabilities and bank assets which increased during the recent crisis.
2Excessive risk-taking by banks resulting from deposit insurance-related moral hazard is consid- ered among the primary factors that resulted in unprecedented deposit insurance losses during the 1980s and early 1990s [See Benston et al. (1986) for comprehensive discussion of this issue]
Concerns about deposit insurance-related moral hazard continue today [See Demirgỹỗ-Kunt et al.
(2014) who note that “coverage of deposit insurance remains above precrisis levels, raising concerns about implicit coverage and moral hazard going forward.”].
3See e.g., Chen et al. (2006), Giammarino et al. (1993), Yoon and Mazumdar (1996), Mazumdar and Yoon (1996) and Mazumdar (1997).
4“Insurance Guaranty Schemes In The EU: Comparative Analysis Of Existing Schemes, Analysis Of Problems And Evaluation of Options,”Final report prepared for European Commission DG Internal market and Services,Oxera Consulting Ltd., November 2007.
5See Kuras (2013).
6See, e.g., Lee et al. (1997) and Downs and Sommers (1999), and Ligon and Thistle (2008).
Corporation or FDIC) charges the bank an insurance premium that is too low given the bank’s asset portfolio risk and capital position. Such mispriced deposit insur- ance can be viewed as an implicit subsidy that the bank and its shareholders get from the government and ultimately, taxpayers. The bank’s shareholders then have a moral hazard incentive to increase this subsidy’s value by increasing the bank’s asset portfolio risk.7
In contrast, the source of an insurance company’s moral hazard incentive is not its use of debtfinancing. Instead, even a wholly equityfinanced insurer may face a moral hazard incentive given an insurance guarantee scheme, as we describe in greater detail later. Among other differences between deposit insurance and an insurance guarantee scheme, the insurance guaranty scheme may not charge the insurer a premium. Instead, all solvent insurers in the guaranty fund’s jurisdiction may be required to collectively cover shortfalls of all insolvent insurers in the jurisdiction, with each solvent insurer contributing in proportion to its size, mea- sured by its relative size of total premiums collected by insurers in the jurisdiction.
Therefore, mechanisms proposed in the banking context to alleviate bank moral hazard (such as capital requirements, monitoring rules and actuarially fair deposit insurance pricing) are not directly applicable to the insurance industry.
To focus on a representative property insurance company’s (or insurer’s) risk-taking incentives in the presence of a insurance guarantee scheme, we develop a model that examines two particular decisions the insurer must make, namely, (i) its choice of assets in which to invest the premiums it collects (i.e., its asset qualitychoice); and (ii) the losses it chooses to insure (i.e., itsunderwriting quality choice). Our model examines the insurer’s relationship to regulators, the guaranty fund, and policyholders in an asymmetric information setting and highlights the factors that affect the insurer’s risk-taking choices. We next discuss a set of workable mechanisms that could mitigate such moral hazard problems associated with property insurance.
Before discussing our model and its implications a comment is in order. In practice, the factors that affect a particular insurance company’s risk-taking activity may be more complex than those addressed in our theoretical model. Nevertheless, we hope that our research may offer insights that guide future research and policy proposals that address potential risk-shifting in the insurance industry. In that connection it is worth noting that although our discussion is motivated by the moral hazard issues that property insurers face, our analysis may also shed light on the
7The intuition behind this result is straightforward. A riskier bank asset portfolio means that the bank’s future asset values are potentially higher in certain (“favorable”) states and worse in other
“unfavorable” states, when the bank is forced to default on its deposit debt. However, given limited liability the bank’s shareholders losses are limited to zero. Therefore, bank risk-taking increases the shareholders’payoffs in favorable states without any incremental loss in unfavorable states. Instead the deposit insurer’s burden (to pay off the bank’s depositors after the bank defaults) increases. But if deposit insurance is not actuarially fair the insurer is not compensated by the bank for bearing this additional risk. Hence, holding other factors constant, the greater the bank risk the greater is the deposit insurance mispricing (or size of the deposit insurance subsidy) and gains to the bank’s shareholders.
design of insurance guarantee schemes related to other types of insurance compa- nies that share certain characteristics of the insurer and insurance guarantee scheme we have modeled.8
2 The Model
We develop a model that examines the insurance company’s interaction with policyholders and the guaranty fund under conditions of moral hazard. The model’s results can be classified into three general categories
1. As a benchmark, we develop a model of insurer-policyholder interaction from the point of view of full information, no regulation, and no third-party guar- antees. The insurer’s optimal risk level, where the insurer acts in the interest of equity holders, is determined in this unregulated environment, and then com- pared to the socially optimal level of risk.
2. Next, we introduce a guaranty fund and examine the risk levels the insurer chooses when its asset and underwriting quality are private information and cannot be freely observed. Insurers are free to take advantage of their private information. We demonstrate that the insurer has an incentive to increase its risks (i.e., lower its asset and underwriting qualities) in the presence of a guaranty fund.
3. Finally, we examine regulatory mechanisms involving state-contingent pay- ments that the insurer must make to the guaranty fund that may alleviate the moral hazard problem. We demonstrate that such mechanisms, if suitably cal- ibrated, could lead an insurer to choose asset and underwriting qualities that are superior from the social planner’s point of view, even in a world with infor- mational asymmetry.
2.1 The Setup for the Insurer
Consider a simple one period model of a property liability insurance company (or insurer). At the beginning of the period (which we refer to as date t= 0), the representative insurer obtains paid-in equity capital, E, and underwrites liability insurance from which it collects premiums. Equity is assumed to be restricted to a specified a percent of premiums collected. For simplicity, it is assumed that the insurer invests all available funds (equity plus premiums) in risky assets, A. The
8Such key characteristics include: solvent insurance companies collectively bearing the loss of other insolvent insurers and insurance companies not being required to pay a risk-adjusted pre- mium for participating in the insurance guarantee scheme. We thank the referee for pointing out the potentially broader applicability of our theoretical framework.
underwriting activities generate liabilities to the insurer which may, but need not, be constrained by capital requirements or other restrictions set by a regulator. The insurer’s managers are assumed to make decisions in the interest of shareholders.
All parties in the model are risk neutral, and, for simplicity, the risk-free rate of return is assumed to be zero, i.e., the discount factor is equal to one.
Att= 0, the insurer faces a continuum of asset and underwriting options that differ only in terms of quality. LetqA2 ð0;1ị denote the quality of the insurer’s asset portfolio and letqL2 ð0;1ịdenote the quality of its underwriting liabilities.
The insurer’s management choosesqAandqL;ex ante(att= 0). The (gross) return on the insurer’s asset portfolio (principal plus return) and any losses from under- writing activities are realized at the end of the period (i.e., at date tẳ1). Such ex post outcomes depend, in the first instance, on the insurer’s ex ante quality decisionsqA andqL.
Outcomes for both asset returns and underwriting losses are assumed to be binomial. The return on assets will be favorable (relatively high) with probability qA, or unfavorable (low) with probability ð1qAị. Thus, higher levels of qA
indicate higher asset quality. If the outcome is favorable, the insurer’s return per dollar of assets is denoted byRðqAị ỵ~eA, where~eA is unique, asset-specific noise andEð~eAị ẳ0. If the outcome is unfavorable, the return on the asset portfolio is a fixed percentage of assets,R2. The expected return on assets in the favorable state is, of course, greater than the return in the unfavorable state, i.e.,
ẵRðqAị ỵEð~eAị[R2 8qA 2 ð0;1ị. Henceforth, to simplify notation, the expecta- tion ofRðqAịover~eA will be denoted byRðqAị.
For underwriting losses, if the outcome is favorable, losses are relatively small.
The probability of the favorable state isqL. If the outcome for losses is unfavorable, losses are high, with probabilityð1qLị. Thus, higher levels ofqLindicate higher underwriting quality. If a favorable outcome occurs then the insurer incurs a loss rate (per dollar of assets)LðqLị ỵ~eL, where~eLis unique, underwriting specific noise andEð~eLị ẳ0.9L2denotes the (fixed) underwriting loss rate per dollar of assets in the unfavorable state. Underwriting losses in the favorable state are always expected to be less than losses in the unfavorable state, i.e., L2[LðqLị ỵ Eð~eLị 8qL2 ð0;1ị, whereLðqLị ỵEð~eLịis hereafter denoted asLðqLị. Moreover, expected losses conditional on the favorable state are assumed not to be sufficiently great to bankrupt the insurer, irrespective of asset returns, i.e., LðqLị R2; 8qL2 ð0;1ị. Finally, L2[R2, which means that if the insurer’s assets earn unfavorable (low) returns and the insurer simultaneously experiences an unfavor- able large underwriting loss, the insurer will become insolvent, i.e., in that state of the world the insurer’s loss will exceed the value of its assets at the end of the period (at datet= 1).
The asset return function,RðqAị;is such thatR0ðqAị\0. That is, a higher asset quality level (a higherqA) increases the likelihood of a favorable return on invest- ments in assets, but also reduces the magnitude of the return in the favorable state. In
9The random noise terms~eLand~eA are assumed to be uncorrelated.
addition, the expected return in the favorable state,qARðqAị, increases with better quality, but at a decreasing rate, (i.e.,qARðqAịis increasing and concave inqA).
The loss function,LðqLị;is assumed to be such thatL0ðqLị\0,10whileqLLðqLị is decreasing and convex inqL. That is, higher underwriting quality lowers expected losses in the favorable loss state, but at a decreasing rate.
The insurer’s choice of qA and qL are private information, and cannot be observed, even ex post. The presence of noise in asset returns and underwriting losses,~eA and~eL, ensures that neither qA nor qL can be inferred from the ex post realization of returns. This gives rise to the usual moral hazard problem in that the insurer might have an incentive to choose asset and underwriting quality levels that may be suboptimal from a social or regulatory point of view. That is, an equity value maximizing insurer may choose to invest in lower quality assets that offer greater upside return albeit with greater risk, and/or underwrite lower quality risks with a higher probability of experiencing a larger loss, if it results in higher expected returns to its shareholders who enjoy the benefit of limited liability. Such risk-taking incentives may be exacerbated when the insurer also receives assurance from the guaranty fund that if it fails, the fund would cover its policyholders’losses.
Nevertheless, it may be possible for the insurer’s quality decisions,qAandqL, to be controlled through regulatory design as we discuss in later sections of this chapter.
2.2 The Insurer’s State-Contingent Payoffs
Given the binomial outcomes of asset returns and underwriting losses, there are four possible, mutually exclusive, states that may be realized at tẳ1. The random return per dollar of assets for the insurer attẳ1, is one of the following:
State 1: The outcome of the asset investment and the underwriting loss are both favorable. The insurer’s net payoff (net of its underwriting losses) is
ẵRðqAị ỵ~eA ẵLðqLị ỵ~eL, which occurs with probability qAqL. In this state,RðqAị[LðqLị. The insurer is expected to be solvent.
State 2: The outcome of the asset investment is favorable but the underwriting loss is unfavorable. The insurer’s net payoff isẵRðqAị ỵ~eA L2, which occurs with probability qAð1qLị. In this state, RðqAị[L2. The insurer is expected to be solvent.
State 3: The outcome of the asset investment is unfavorable but the underwriting loss is favorable. The insurer’s net payoff is R2 ẵLðqLị ỵ~eL, which occurs with probabilityð1qAịqL. In this state,R2[LðqLị. The insurer is expected to be solvent.
10In addition, it seems reasonable to assume that L00ðqLị[0; i.e., as underwriting quality decreases, losses increase at a decreasing rate.
State 4: The outcomes of the asset investment as well as the underwriting loss are both unfavorable. The insurer’s net payoff isR2L2, which occurs with probabilityð1qAịð1qLị. In this state, asðR2L2ị\0, the insurer is insolvent. Its equity holders receive nothing. The insurer’s assets are divided among its various policyholder claimants according to prespeci- fied priority rules, which are assumed for the time being to be pro-rated, based on premiums paid by policyholders. A shortfall in the payments to policyholders may be paid by a guaranty fund or reinsurer where such alternatives exist.
3 Optimal Quality Decisions from the Social Planner’s and the Insurer’s Perspectives
In this section, we examine two benchmark cases where the quality decisions of the insurer are observable. Constraints on insurer behavior (such as regulatory con- straints) are assumed to be absent and, in any case, are unnecessary. First, we determine the socially optimal,first-best levels for the insurer’s asset quality and underwriting qualities, qA and qL, i.e., the asset quality and underwriting quality levels which maximize social surplus. Such a socially optimal allocation is useful for the purpose of comparing the benefits of the regulatory mechanism that is considered later. Second, we determine the optimal asset and underwriting quality decisions from the insurer’s perspective where the insurer is assumed to act to maximize the value of its equity.
3.1 Underwriting Premiums
Premiums are collected at t= 0. The insurer’s available funds for investments in assets are the sum of premiums collected and paid-in equity capital. Given the assumption of risk neutrality, the maximum aggregate premium that an insurer can charge is the present value of the expected recoverable losses by policyholders.11In turn, expected recoverable losses are the policyholders’total expected losses less that part of losses that are unrecoverable in the event that the insurer is insolvent at t= 1 which occurs in State 4, as we discussed earlier. PðqA;qLị denotes total premiums collected by the insurer, and is a function of bothqA and qL, because policyholders’recoverable losses depend on the insurer’s underwriting quality as well as the quality of its invested assets. The size of the insurer’s asset portfolio at
11Obviously, even if policy holders are risk averse, as long as insurers are risk neutral they assume all risk and premiums are competitively priced at the level of expected loss plus operating costs.
For simplicity, operating costs are assumed to be zero.
t= 0 equals its total premiums plus its paid-in capital which is assumed to beα times its total premiums. As total premiums are a function of the insurer’s asset and underwriting quality choices, it follows that the size of the insurer’s asset portfolio, AðqA;qLị, depends on its quality decisions, i.e.,AðqA;qLị P qð A;qLịð1ỵaị. For the assumed discount factor of one, and in the absence of a guaranty fund or reinsurer, total premiums can be expressed as follows:
PðqA;qLị ẳ ẵð1qLịL2ỵqLLðqLị ẵð1qLịð1qAịðL2R2ị; ð1ị where the first term in brackets on the RHS is the total expected losses of poli- cyholders, and the second term in brackets is the expected unrecoverable losses by policyholders as a result of insurer insolvency. Other things equal, the greater the expected unrecoverable losses, the smaller the premiums that policyholders are willing to pay. On the other hand, the greater policyholders’expected total losses, the greater is the premium they are willing to pay.
As Eq. (1) suggests, since asset quality impacts only expected unrecoverable losses to policyholders, it is clear that the premiums collected by the insurer are increasing in asset quality, since expected unrecoverable losses are declining at a linear rate, i.e.,@PðqA;qLị=@qA[0 and@2PðqA;qLị=@q2A ẳ0.
Thefirst derivative of (1) with respect to qL is
@PðqA;qLị
@qL ẳ @qLLðqLị
@qL
qAL2 ð1qAịR2\0:
The second derivative is @2Pð@qqA2;qLị
L ẳ @2q@LLq2ðqLị L
[0. Thus, underwriting premiums are decreasing and convex in qL. These properties are intuitively appealing as expected losses should decline as underwriting quality increases, but losses decrease at a decreasing rate.
3.2 The Social Planner’s Problem
The social planner seeks to maximize expected social surplus.12 Expected social surplus, denoted by,pSPðqA;qLị, is given by
12Here, we assume that the social planner considers social surplus to be composed only of the expected monetary returns to all insurer claimholders. In the case of insurance companies, one might argue that society in general benefits from high-quality decisions by insurers through the positive externalities offinancial system stability. Although difficult to quantify, if such exter- nalities were included, the social surplus generated by high quality would increase and the first-best quality chosen by the social planner over that implied by thefirst-order conditions in Eqs. (3) and (4).