Capital asset pricing models with default risk: Theory and application in insurance

The Capital Asset Pricing Model has been used frequently to derive a fair price of insurance. But the use of this model overestimates insurance premiums because it does not account for the insolvency risk of insurers. This paper examines how the insurance price should be fairly adjusted when insurers' default risk is considered. It develops a model which shows that fair insurance premiums are lower when insurance firms have a positive probability of being insolvent. Using data of property liability insurers during the period from 1943–99, the paper further estimates the effects of the insolvency risk on insurers' underwriting profit rate. It shows that the incorporation of the default risk of insurers in the model, by significantly reducing the required price for insurance, would lead to lower profit potentials. Some writers argue that including the insolvency risk when calculating insurance premiums is not so necessary because of the existence of states' guaranty insurance funds which protect consumers. However, as shown in the paper, these funds have provided inadequate protection to consumers. Therefore, because of the increase in the number of insolvencies in recent years, and because of the limited coverage provided by states' guaranty funds, it seems that considering the insolvency risk in insurance pricing has become very necessary.     

保险资金持股与股价崩盘风险——市场“稳定器”还是崩盘“加速器”?

现阶段,有关保险资金持股与资本市场稳定相互关系的讨论多止于推测,少有学者以大样本数据进行实证考察。在理论上,保险资金持股上市公司,一方面可以抑制经理人负面信息隐藏,作为市场“稳定器”降低股价暴跌风险;另一方面,也能引发投资者跟风炒作,导致市场情绪高涨和股价高估,成为股价崩盘风险的“加速器”。本文基于2007—2016年中国沪深两市A股上市公司的数据,实证分析保险资金持股上市公司是否加剧市场暴跌及其作用机制。结果显示:保险资金持股加剧了股价崩盘风险,是公司股价崩盘的“加速器”。这一结论在经过DID模型、工具变量回归、PSM+OLS等内生性分析,以及稳健性检验之后依然成立。进一步研究表明,相比于民营、小型和财产保险公司,在股市投资规模更大的国有、大型和人寿保险公司更能引发市场跟风炒作,加剧股价崩盘风险;不过,当保险资金作为前十大股东参与公司治理时则能够降低股价崩盘风险。本文不仅为保险资金持股与资本市场稳定相互关系的讨论提供了经验证据,也为规范保险资金股权投资,维护资本市场稳定提供有益借鉴。     

Ambiguous protection

Import regulations are globally the most prevalent form of intervention in international trade. The regulations should, under rules of the WTO, protect consumers and the environment but can be used to protect producers. We investigate the ambiguity of intent of the regulations. We set out a model that when applied empirically suggests, as a benchmark estimate, equal divide between social benefit and producer protection. Inefficiency and distributional effects of the regulations are consistent with producer-protecting trade policy. Country diversity in use of regulations supplements our estimates in suggesting presence of producer-protecting intent. We look at how WTO procedures have allowed producer protection in the guise of social benefit.     

我国保险监管问题研究

在保险经营全球化和国际化的背景下,国际保险监管的组织形式和监管模式越来越朝着趋同的方向发展,主要表现为：关注保险公司未来的风险状况,强化风险资本监管,并实施动态的偿付能力监管。为了加强对保险公司偿付能力的监管,不断完善监管体系,自2008年9月,保监会开始实施新的监管规定——《保险公司偿付能力监管规定》,该规定将保险公司的偿付能力状况作为衡量和防范风险的核心监管依据,在保险监管制度的建设与完善过程中具有里程碑的意义。然而,我国目前的保险监管与以偿付能力为核心的监管体系还存在一定的差距,偿付能力监管制度也只初步完成了框架性的工作,还需要不断的完善和丰富。本文在分析国际保险监管制度特点及发展趋势的基础上,针对我国保险监管中实际存在的问题,提出完善我国保险监管制度的若干建议,以助于保险监管机构提高监管效率,促进我国保险业的健康和可持续发展。     

Insurance,self-control,and contract flexibility

We study a competitive insurance market in which some consumers have too optimistic expectations regarding their future use of preventive measures. When contracts are long-term and inflexible, such naive consumers would increase the costs of insurance for low-risk consumers. The competitive insurance market therefore offers flexible contracts that allow for switching between different tariffs. Sophisticated consumers choose a partial insurance tariff and remain low-risks. Naive consumers choose the same tariff, but later switch to full insurance, and become high-risks. If there are sufficiently many naive consumers, they pay a transfer to sophisticated consumers (so that high-risks subsidize low-risks). In contrast, there are no such transfers when contracts are short-term. The model generates novel implications for the time frame of insurance contracts and insurance requirements.     

Insurance market games: Scale effects and public policy

We propose a game-theoretic model to study various effects of scale in an insurance market. After reviewing a simple static model of insurer solvency (in which all customers have inelastic demand), we present a one-period game in which both the buyers and sellers of insurance make strategic bids to determine market price and quantity. For the case in which both buyers and sellers are characterized by constant absolute risk aversion, we show that a unique market equilibrium exists under certain conditions. For the special case of risk-neutral insurers, we then consider how both the price and quantity of insurance, as well as other quantities of interest to public-policy decision makers, are affected by the number of insurance firms, the number of customers, and the total amount of capital provided by investors.     

How does issuing contingent convertible bonds improve bank's solvency? A Value-at-Risk and Expected Shortfall approach

This paper examines how issuing an innovative financial instrument called contingent convertible bond (CoCo) may enhance bank's solvency in comparison to issuing a conventional bond. CoCos convert automatically into common equity or have a principal write-down when bank's regulatory capital fails to meet a predetermined level. They have been invented and put into legislation with an objective to absorb losses thus preventing institutions from bankruptcy. From the standpoint of an issuer CoCos bring about two counter effects regarding his solvency: on one hand they recapitalize a bank approaching insolvency on the other hand CoCos pay much higher coupon comparing to conventional bonds. In our model a bank has two funding alternatives: either to issue CoCos or conventional bonds. We measure issuer's default risk using the concept of Value-at-Risk (VaR) and Expected Shortfall (ES). We conclude that CoCos have the potential to strengthen the resilience of the issuer on the condition that the probability of conversion triggering is higher than the VaR's significance level. Our findings can be helpful to the policymakers and banks to better understand the impact of CoCos on issuer's solvency.     

Birth,death and taxes

"This paper analyzes the effects of lump-sum tax policy in an overlapping generations model in which consumers have uncertain longevity. It extends previous analyses by considering the case in which private insurance arrangements are actuarially unfair. In addition, it considers the polar case of actuarially fair insurance and the polar case of no insurance. A general condition for debt neutrality is derived. This condition depends explicitly on the degree of actuarial unfairness in insurance and on the extent to which parents care about the utility of their children."     

International Capital Mobility in the Presence of Unemployment Insurance

The paper develops a general–equilibrium model with layoff unemployment to examine the effect of different unemployment insurance policies on international capital mobility. Conditions are derived under which capital will flow to the high–benefit country. Incentives for international capital movements are unaffected by how the burden of financing unemployment benefits is distributed between workers and firms. It is shown that capital outflows might have positive welfare effects for workers. This contrasts with results from standard models of international factor movements.     

State mandated benefits and the small firm's decision to offer insurance

In the last decade, the number of Americans without health insurance has grown, partly due to an erosion in employer-based coverage among workers. This paper examines the extent to which state-mandated benefit requirements and other state insurance regulations discourage small firms in the private sector from providing health benefits. Using data on 1320 firms observed in 1985 and 492 firms observed in 1988, we estimate two models of small firms' decisions to offer health insurance (one for each data set), and then use them to assess the effects that mandates had on purchasing decisions in both years. We estimate that 19 percent of noncoverage among sample businesses in 1985 and 43 percent of noncoverage in the 1988 sample was attributable to state-mandated benefits. State continuation-of-coverage requirements were particularly burdensome for firms. With continued growth in the number of state mandated benefit requirements, we should expect a steady rise in the small firm's propensity to forgo insurance coverage.     

Why are credit card rates sticky?

Summary This paper investigates credit card rate stickiness using a screening model of consumer credit markets. In recent years, while the cost of funds has fallen, credit card rates have remained stubbornly high, spurring legislators to consider imposing interest rate ceilings on credit card rates. The model incorporates asymmetric information between consumers and banks, regarding consumers' future incomes. The unique equilibrium is one of two types: separating (in which low-risk consumers select a collateralized loan and high-risk consumers select a credit card loan), or pooling (in which both types of consumers choose credit card loans). I show that a change in the banks' cost of funds can have an ambiguous effect on the credit card rate, so that the credit card rate need not fall when the cost of funds does. Usury ceilings on credit card rates are detrimental to consumer welfare, so would be counter to their legislative intent.I thank George Mailath, Paul Calem, Gerhard Clemenz, Sally Davies, George Kanatas, Leonard Nakamura, Tony Santomero, Tony Saunders, participants in the 1990 Financial Management Association Meetings, and co-editor Michael Woodford for helpful comments.The views expressed here are those of the author and do not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.     

保险公司偿付能力监管:国际趋势及其对我国的启示

偿付能力监管是保险业监管的核心内容.目前,国际上有代表性的偿付能力监管模式包括以欧盟偿付能力I为代表的基于业务量的模式和以美国风险资本为代表的基于风险的模式.在保险业发展过程中,基于风险的模式将成为保险公司偿付能力监管的趋势.在我国完善保险公司偿付能力监管体系的过程中,应充分借鉴国外已经取得的成果和经验.     

ENTREPRENEURSHIP AND JOB LOCK: THE INTERACTION BETWEEN TAX SUBSIDIES AND HEALTH INSURANCE REGULATIONS

This paper demonstrates that health insurance tax subsidies increase self‐employment, but that the effect differs substantially based on nongroup market regulations and health status. Using the Panel Study of Income Dynamics, I show that households that cannot purchase health insurance because of a preexisting condition do not respond to tax subsidies in states in which they would be denied insurance, but they respond strongly in states in which they face risk‐rated premiums. Households respond similarly to tax subsidies in states with nongroup market regulations similar to those established by the Affordable Care Act, regardless of preexisting conditions. (JEL H20, I13, J30)     

How Changes in Financial Incentives Affect the Duration of Unemployment

This paper studies how changes in the two key parameters of unemployment insurance—the benefit replacement rate (RR) and the potential benefit duration (PBD)—affect the duration of unemployment. To identify such an effect we exploit a policy change introduced in 1989 by the Austrian government, which affected various unemployed workers differently: a first group experienced an increase in RR; a second group experienced an extension of PBD; a third group experienced both a higher RR and a longer PBD; and a fourth group experienced no change in the policy parameters. We find that unemployed workers react to the disincentives by an increase in unemployment duration, and our empirical results are consistent with the predictions of job search theory. We use our parameter estimates to split up the total costs to unemployment insurance funds into costs due to changes in the unemployment insurance system with unchanged behaviour and costs due to behavioural responses of unemployed workers. Our results indicate that costs due to behavioural responses are substantial.     

Consumption adaptation,anticipation‐bias,and optimal income taxation

Adaptation is omnipresent but people systematically fail to correctly anticipate the degree to which they adapt, leading them to make irrational intertemporal decisions. This paper concerns optimal income taxation to correct for such anticipation‐biases in a framework where consumers adapt to earlier consumption levels. The analysis is based on a general equilibrium OLG model with endogenous labor supply and savings where each consumer lives for three periods. The results show how a paternalistic government may correct for the effects of anticipation‐bias through a combination of time‐variant marginal labor income taxes and savings subsidies/taxes. The optimal policy mix remains the same, irrespective of whether consumers commit to their original life time plan for work hours and consumption or reoptimize later on when realizing that they have already adapted more than expected.     

Regulation and efficiency in European insurance markets

With a series of directives completed in 1994 the European Commission tried to open and harmonize national European insurance markets. This has led to considerable deregulation in several countries. This paper surveys pre-1994 regulation in Germany and the UK and the Commission's policy. It argues that it is unlikely that the policy will have a significant impact on direct international competition between European insurance markets, until there is standardization of insurance law. However, the tightly regulated markets will become more like the loosely regulated UK market. The paper evaluates this outcome and concludes that the European Commission's policy may thereby have improved the welfare of insurance buyers in the previously highly regulated countries such as Germany. The paper also uses efficiency-frontier estimation to compare the dispersion of firm efficiencies in the German and British life insurance market. The results support the hypothesis that tighter solvency regulation allows the survival of a larger proportion of higher-cost firms.     

中国国情下的保险费率监管模式选择及影响分析--来自车险市场的经验证据

我国保险监管朝着“放开前端、管住后端”的模式发展,保险费率市场化改革的呼声始终较高。文章以财险市场中市场份额最大的车险为研究对象,基于2001－2014年样本分析了费率市场化与费率水平合理性之间的关系。研究发现,我国车险市场的实际费率水平明显低于理论费率;费率监管的严格程度的确会影响费率水平的合理性,其中适度监管模式下的费率水平最为合理。文章进一步深入探究了费率水平合理性对偿付能力的影响机制,发现费率差异的波动性会通过净利润而间接影响偿付能力。费率差异的波动性越小,净利润越高,偿付能力越强,因此应慎重选择费率监管制度。文章建议我国保险市场应采用适度监管的费率制度,完全放开的费率市场化略显激进,不适合当前国情。这样不仅能使费率水平更加合理,还不会威胁保险公司的偿付能力,从而使保险市场更加健康稳步的发展。     

Understanding the welfare effects of unemployment insurance policy in general equilibrium

This paper analyzes the welfare effects of unemployment insurance reforms in a general equilibrium incomplete market model. In particular, it decomposes the total welfare effect for each individual into different factors. I consider a model where the consumers face an uninsurable unemployment risk, can save in an interest-bearing asset, and are subject to a borrowing constraint. The labor market is modeled using a Diamond–Mortensen–Pissarides style search and matching model. The decomposition exercises reveal how each factor contributes to the heterogeneity of welfare effects among different consumers.     

Endogenous Categorization in Insurance

This paper analyzes the welfare properties of equilibrium when insurers use observable actions to classify consumers into different risk categories, and consumers' choice is influenced by the insurance market consequences of their actions. Specifically, we analyze this problem at the example of a car insurance market, in which individual preferences over car types are correlated with risk type and used by insurance firms for ratemaking. Equilibrium premiums for each car are determined by the losses that it generates. Consumers take insurance premiums into account when deciding which car to buy. This creates an incentive to buy the car that is preferred by more low risk individuals. From a utilitarian point of view, this incentive is excessive. Depending on parameters, it may even be possible to construct a tax‐subsidy scheme with balanced budget that Pareto improves on the market equilibrium.     

The effect of unemployment insurance on the riskiness of occupational choice

This paper examines the effect of unemployment insurance on the riskiness of occupational choice by postulating a model of job search in which job offers have two characteristics; their wage and their security of tenure. Two versions are considered: a general case in which the unemployment benefit is earnings-related, and a special case in which the benefit is of a flat-rate form. Of particular interest in the paper is the individual's desired trade-off between wage and security of tenure, and how this trade-off is affected by the type of insurance scheme in operation. Perhaps surprisingly, we find that an earnings-related scheme encourages risk-taking behaviour by the poor, and risk-avoiding behaviour by the rich; in contrast, a flat-rate scheme neither encourages nor discourages risk-taking.