Risk-Based Capital and Credit Insurance Portfolios

This paper analyzes the risk-management practices of a vulnerable credit insurer by studying the effects of time-varying correlations, asset risks and loan maturities on the risk-based capital that backs credit insurance portfolios. Since asset correlations may change over a business cycle, we have analyzed these effects by means of a one-factor Gaussian stochastic model as part of an extended contingent claims analysis. Our results show the need to account for cyclical changes to correlations in the pricing of credit insurance. When compared with the reserve of risk-based capital recommended by the Basel II Internal Ratings-Based (IRB) approach, our model provides a better capital buffer against extreme credit losses, especially in times of recession and/or in a risky business environment. Using a risk-adjusted performance metric (RAPM), we find insurers perform better when insuring relatively short-term loans. We also make several policy recommendations on creating a reserve of risk-based capital to protect against possible loan losses.     

Deposit Insurance, Capital Adequacy Requirements and Interest Rate Dynamics

This paper examines the long run interaction among deposit insurance, bank deposit rates and capital adequacy requirements. Using analysis similar to the price discrimination model of Lott and Roberts (1991) we find that a competitive environment among banks would link the spread between insured and uninsured deposit rates to the size of the insurance premium. We also find that banks that choose to operate at the regulatory minimum capital level, would increase asset risk with increased capital requirements if (1) the implicit interest paid to insured and uninsured depositors is equally sensitive to changes in risk and capital adequacy and (2) the insurance premium is independent of the level of risk and capital adequacy. Under the present risk-based premium structure, asset risk has the potential to decline when the regulatory agency raises capital requirements. Finally, we examine the time series behavior of insured and uninsured interest rates to see if it is consistent with our theoretical model. We find that insured and uninsured rates, along with deposit insurance premiums, are cointegrated series as suggested by our model.     

The Effectiveness of Public and Private Sector Summary Risk Measures in Predicting Insurer Insolvencies

This article investigates the abilities of four key summary risk measures to predict property-liability insurer insolvencies. The four summary risk measures studied are the NAIC's risk-based capital ratios, the NAIC's financial analysis solvency tools (FAST) scores, A.M. Best's Capital Adequacy Relativity ratios, and A.M. Best's ratings. The empirical tests find that the risk measures produced by the private sector are superior in predictive ability to the measures produced by regulators, perhaps because of the qualitative adjustments made by private sector analysts. The results also demonstrate that overall measures of risk are substantially better than risk-based capital measures in predicting insolvencies. Another finding is that the predictive ability of the NAIC's RBC ratios can be improved substantially if ranks are used rather than the ratios themselves.     

Risk-based capital standards, deposit insurance, and procyclicality

This article shows that risk-based deposit insurance premiums generate smaller procyclical effects than do risk-based capital requirements. Thus, Basel II's procyclical impact can be reduced by integrating risk-based deposit insurance. If deposit insurance is structured as a moving average of contracts, its procyclical effects can be decreased further. Empirical illustrations of this are presented for 42 banks over the period 1987 to 1996. The results confirm that lengthening the contracts' maturities intertemporally smooths premiums but raises the average premium level needed to compensate the insurer for greater systematic risk. The distribution of risk-based premiums across banks is skewed.     

Grenzen der Auskunfts- und Belegpflicht in der D&O Versicherung

A large number of claims brought under German D&O insurance regard Insured vs. Insured cases, i.e. claims brought by the company against its own directors and officers (Executive Directors, Supervisory Board Members etc.). After notification of and examination by the insurer of such an insured event, the insurer will in most cases opt to grant the insured defence cover in order to fight off the claim. The insurer hereby expresses that it regards the claim of the company (= its own policyholder) against the board member (= the insured) to be without merit. This situation—where the policyholder is at the same time the damaged party—though typical under (German) D&O-policies is uncommon for liability insurance cover in general. It, thus, raises the issue as to the limits of the policyholder’s duty to disclose information. The scope of said obligation is not unlimited. It rather has to be ascertained pursuant to Sect. 31 VVG (German Insurance Contract Act), by taking into account the policyholder’s interests in commercial and industrial confidentiality and the burden of poof as provided by Sect. 93 para. 2 AktG (German Stock Companies Act). In case legal proceedings ensue between the company and the insured, and, as a consequence, the insurer exercises its obligation to conduct the case for the insured or the insurer joins the lawsuit on the side of the insured (by declaring a Third Party Notice [Streiverkündung]), the insurer clearly becomes an adversary to the company. Under such circumstances, the company is irrevocably released from its duty to disclose information.     

Capital and risk in property-liability insurance markets

This paper investigates the capital and portfolio risk decisions of property-liability insurance firms. A theoretical model based on option pricing theory is developed which predicts a positive relationship between insurer capital and risk, as firms balance these two factors to achieve their desired overall insolvency risk. The implications of the model are then tested empirically using a simultaneous equations methodology. The results support the predictions of the model. They also provide evidence that managerial incentives play a role in determining capital and risk in insurance markets. The findings have significant implications for insurance solvency regulation.     

Risk-Based Premiums for Insurance Guaranty Funds

Insurance guaranty funds have been adopted in all states to compensate policyholders for losses resulting from insurance company insolvencies. The guaranty funds charge flat premium rates, usually a percentage of premiums. Flat premiums can induce insurers to adopt high-risk strategies, a problem that can be avoided through the use of risk-based premiums. This article develops risk-based premium formulas for three cases: a) an ongoing insurer with stochastic assets and liabilities, b) an ongoing insurer also subject to jumps in liabilities (catastrophes), and c) a policy cohort, where claims eventually run off to zero. Premium estimates are provided and compared with actual guaranty fund assessment rates.     

Dynamic Prevention in Short-Term Insurance Contracts

This article looks at the dynamic properties of insurance contracts when insurers have a better technology at preventing catastrophic losses than the insured. When the prevention technology is irreversible and its benefits last for all future periods although its cost is borne in the period in which it is made, a hold‐up problem occurs because the insured can change insurer after his initial insurer has invested in prevention. Investment in prevention is then delayed compared to the first best outcome. When the audit cost must be incurred by the insured when he wants to change insurer, the incumbent insurer has an informational advantage so that he can keep his client over the entire investment horizon, even though long‐term contracts are not possible. This does not avoid the delay in investment, however.     

Issuing bonds during the Covid-19 pandemic: Was there an ESG premium?

We rely on the ESG ratings assigned by four distinct agencies (MSCI, Refinitiv, Robeco, and Sustainalytics) to study the link between ESG scores and firms’ cost of debt financing during the Covid-19 pandemic. We document the existence of a statistically and economically significant ESG premium, i.e. better rated companies access debt at a lower cost. Despite some differences across rating agencies, this result is robust to additional controls for the issuer’s credit standing as well as several bond and issuer’s characteristics. We find that this effect is mainly driven by firms domiciled in advanced economies, whereas creditworthiness considerations prevail for firms in emerging markets. Lastly, we show that the lower cost of capital for highly rated ESG firms is explained both by investors’ preference for more sustainable assets and by risk-based considerations unrelated to firms’ creditworthiness, such as exposure to climate change risks.     

A note on increased probability of loss and the demand for insurance

It is shown that the effect of increased probability of loss on the demand for insurance depends on whether both insured and insurer are aware of the change. When both insurer and insured share the same beliefs about the probability of loss (symmetric information), an increase in the loss probability may lead risk-averse agents to demandless insurance.     

Insurance Market Effects of Risk Management Metrics

We extend the classical analysis on optimal insurance design to the case when the insurer implements regulatory requirements (Value-at-Risk). Presumably, regulators impose some risk management requirement such as VaR to reduce the insurers’ insolvency risk, as well as to improve the insurance market stability. We show that VaR requirements may better protect the insured and improve economic efficiency, but have stringent negative effects on the insurance market. Our analysis reveals that the insured are better protected in the event of greater loss irrespective of the optimal design from either the insured or the insurer perspective. However, in the presence of the VaR requirement on the insurer, the insurer's insolvency risk might be increased and there are moral hazard issues in the insurance market because the optimal contract is discontinuous.     

The benefit of life insurance contracts with capped index participation when stock prices are subject to jump risk

We analyze the benefit to the insured of newly traded, innovative life insurance contracts. On a sequence of yearly reference days, the insured can choose between a guaranteed return (linked to the insurer’s asset result) and a capped index participation. The cap is adjusted at the beginning of each year such that both alternatives have the same value and the option to select is costless (product structuring condition). We point out that this condition cannot always be met. If the guaranteed return exceeds the upper bound of the capped index participation, the insurer can make a side profit. We show that a rather low insurance result also implies a rather low stock exposure, even if the insured opts for the index participation. Concerning the impact of the index dynamics, we emphasize that it is important to distinguish between jump and diffusion risk because the pricing of jump risk has an impact on cap rates that can be offered to an insured. Finally, we show that the optimal decision strategy of a CRRA investor implies an index selection even if it is unfairly priced such that the insurer indeed makes a side profit.     

The Pricing of Insurer Demutualization Initial Public Offerings

This article examines the pricing of the initial public offerings (IPOs) that follow insurance company demutualizations. Insurers that convert from mutual to stock form typically cite the need for capital as a key motivation. Given that capital adequacy is a primary regulatory objective for insurers, one would expect that for a given number of shares to be sold, these firms would price their offerings to maximize proceeds. However, the vast literature on IPO pricing suggests various theories as to why it may be in the issuing firm's best interest to underprice its offering. By examining the initial and long‐run stock returns for these conversion IPOs, the existence and degree of underpricing, as characterized by large initial returns, can be determined. It is observed that on average demutualization insurer IPOs post significantly higher first‐day returns than nondemutualization insurer IPOs. These gains would accrue to the initial investors and to those policyholders who receive compensation in the form of shares in the newly created stock insurer. Attractive returns are sustained for both groups of insurers during the first few years after IPO.     

A Continuous-Time Optimal Insurance Design with Costly Monitoring

We provide a theoretical and numerical framework to study optimal insurance design under asymmetric information. We consider a continuous-time model where neither the efforts nor the outcome of an insured firm are observable to an insurer. The insured may then cause two interconnected information problems: moral hazard and fraudulent claims. We show that, when costly monitoring is available, an optimal insurance contract distinguishes the one problem from the other. Furthermore, if the insured’s downward-risk aversion is weak and if the participation constraint is not too tight, then a higher level of the monitoring technology can mitigate both problems.     

论投保人缴纳保费或保险公司签发保单附条件条款的法律效力

我国保险实践中普遍将投保人缴纳保费或者保险公司签发保单作为保险合同的成立、生效或者保险责任开始的条件。但该条件不是新《保险法》规定的附条件保险合同所指的条件。同时该附条件条款赋予了保险公司对要约进行承诺时或者履行合同义务时不受时间限制的权利,该附条件条款因不具有合理性应为无效合同条款。     

Optimal insurance and reinsurance policies chosen jointly in the individual risk model

The paper studies the so-called individual risk model where both a policy of per-claim insurance and a policy of reinsurance are chosen jointly by the insurer in order to maximize his/her expected utility. The insurance and reinsurance premiums are defined by the expected value principle. The problem is solved under additional constraints on the reinsurer’s risk and the residual risk of the insured. It is shown that the solution to the problem is the following: The optimal reinsurance is a modification of stop-loss reinsurance policy, so-called stop-loss reinsurance with an upper limit; the optimal insurer’s indemnity is a combination of stop-loss- and deductible policies. The results are illustrated by a numerical example for the case of exponential utility function. The effects of changing model parameters on optimal insurance and reinsurance policies are considered.     

从博弈论看保险市场信息不对称的本质及规范举措

博弈论是研究信息不对称问题的一种有效方法。保险业作为信息不对称最为集中的行业，保险人与被保险人之间存在着严重的信息不对称，特别是被保险人的逆向选择、道德风险和保险人的违规操作等现象普遍存在，长期困扰着保险界。     

A Dynamic Model of the Firm: Structural Explanations of Key Empirical Findings

We derive a dynamic model of the firm in the spirit of the trade‐off theory of capital structure that explains firm behavior in terms of firm characteristics. We show our model is consistent with many important findings about the cross‐section of firms, including the negative relations between profitability and leverage, and between dividends and investment‐cash flow sensitivities. The model also explains the existence of zero‐debt firms and their observed characteristics. These results have been used to challenge the trade‐off theory and the assumption of perfect capital markets. We revisit these critiques and provide structural explanations for the regularities we replicate.     

Who Obtains Greater Discounts on Automobile Insurance Premiums?

Insurance purchasers obtain varied discounts for insurance. This paper examines what drives these differences, specifically whether the loss probability and the wealth of the insured affect the size of the premium discount in automobile insurance. To describe a bargain between a client and an insurer over premiums and coverage, we first develop a sequential insurance bargaining game where the client has an outside option to bargain with another insurer. We find that the equilibrium involves full coverage and, based on the results of comparative statics, we propose hypotheses regarding the effects of the loss probability and the wealth of the insured on the size of the premium discount. We then use a unique data set of 85,806 observations of Taiwanese automobile liability insurance for property damage to empirically test the predictions. After controlling for underwriting and macroeconomic variables, we find that both (1) the insured with a lower claim probability (as a proxy for the insured with a lower loss probability) and (2) the insured with a higher salvage value car (as a proxy for the wealthier insured) receive a greater premium discount. These results support our theoretical results.     

Risk in Banking and Capital Regulation

This paper investigates the role of bank capital regulation in risk control. It is known that banks choose portfolios of higher risk because of inefficiently priced deposit insurance. Bank capital regulation is a way to redress this bias toward risk. Utilizing the mean-variance model, the following results are shown: (a) the use of simple capital ratios in regulation is an ineffective means to bound the insolvency risk of banks; (b) as a solution to problems of the capital ratio regulation, the “theoretically correct” risk weights under the risk-based capital plan are explicitly derived; and (c) the “theoretically correct” risk weights are restrictions on asset composition, which alters the optimal portfolio choice of banking firms.