Robert C. Witt

Underwriting Cycles in Property and Liability Insurance: An Empirical Analysis of Industry and By- Line Data

Using industry and by-line data, we examine the causes of insurance cycles in a vector autoregressive model. Some of the important findings are summarized below. First, the uncertainty variable explains significant portions of forecast errors of premiums. Second, the significant factors that determine premiums are different for different lines. Third, investment incomes in general are more important for long-tail lines than short-tail lines. Evidence on the response of premiums to shocks suggests that all one-time shocks to variables tend to be relatively permanent. The overall results seem to imply that no single hypothesis is able to explain the insurance cycle.

Great (and not so great) expectations: An endogenous economic explication of insurance cycles and liability crises

ABSTRACT The causes of insurance cycles and liability crises have been vigorously sought, claimed, and debated by academic investigators for years. The model provided here partially synthesizes several stands of this literature and provides an additional cause. In addition to causes such as the loss-shocks and interest-rate changes included as explanations in the literature, this model posits changing expectations about the parameters of corporate net income as causes of cycles and crises. Since both sides of the market form expectations about losses and interest rates, changes in both demand and supply in the market are incorporated in the explanation. Changing expectations during the crisis reduced supply and made it more inelastic. The same changing expectations increased demand and made it more inelastic and so amplified the effect due to a change in supply. The model predicts an increase in the equilibrium premium, when the mean and variance of losses increase. The model also predicts an increase in the equilibri um premium when the mean interest rate decreases and variance increases. The empirical results of cross-sectional regression and time-series analyses are consistent with the predictions. The analysis then provides some insight on how to dampen future cycles and reduce the effect of future liability crises. INTRODUCTION Insurance cycles [2] have been recognized for decades and have been the object of study by academic investigators for that long (see Cummins, 1987). The reason for this intense study is both basic (theoretical) and practical. At a basic level, questions arise about whether such cycles conflict with rational corporate decision making in an efficient financial market. From a practical perspective, such cycles can, at their extreme-most valleys, create crises in affordability and availability of insurance, affecting the very productivity of the country involved. The liability insurance crisis in the United States from late 1984 through 1986 is an example of such an extreme in the insurance cycle, being characterized by significant economic disruptions in commercial liability insurance markets. The disruptions created concerns about both the availability and affordability of certain covers. For example, professional and commercial liability insurance consumers were adversely affected by the crisis, as were others such as chemical and pharmaceutical companies, day-care centers, doctors, and municipalities. The cycle ultimately resulting in the crisis was characterized by a sudden increase in liability premiums in late 1984 after about six years of relatively stable prices. An additional response to changes in this cycle included the lowering of policy limits and a reduction in scope of coverage in commercial liability lines that were characterized by long-tails. In addition, insurers were unwilling to provide any coverage at all for some risks, e.g., those involving pollution liability exposures. [3] Academics, attorneys general, consumers, insurers, and regulators have not agreed on the causes of insurance cycles, and the causes of the commercial liability insurance crisis of the late 1980s are still debated. The cycles and crisis theories that do appear in the literature share at least two common characteristics. First, the theories focus on the supply of liability insurance and ignore the demand. Although it is implicit in some theories, the demand for liability insurance during the cycles and crisis is generally not addressed. Second, the theories emphasize a single factor as the cause of the crisis or cycle, although exactly what the single factor is has varied from explanation to explanation. This shared single-factor approach to insurance cycle and crisis explications creates problems. First, the single-factor theories do not explain enough aspects of the crisis, even though each offers some insight. For example, the U. S. Justice Department (Justice, 1986) has cited the expansion of business liability under tort law as the factor explaining higher premiums and reduced coverage limits. …

Insurance Pricing and Regulation Under Uncertainty: A Chance-Constrained Approach

A financial model of the non-life insurer under uncertainty is developed. The model recognizes the stochastic nature of both the insurers underwriting and investment income. The total risk faced by the insurer, which includes both underwriting and investment risk, is considered. The impact of regulatory constraints on the insurers profits also is analyzed. Moreover, the costs of regulation imposed on the insurer are assessed in a non-linear, chance-constrained, programming framework. In general, the model shows that economic tradeoffs must be considered when management or regulatory decisions are made because of the numerous interrelationships among variables in the model and in the real world. A simplified financial model of a non-life insurers behavior under uncertainty is developed in this paper. It is an extension of an earlier paper by the authors (24) that examined insurer behavior under the simplified conditions of partial certainty where the assumption was that the insurer could accurately forecast its underwriting and investment results. In this paper, the stochastic nature of the insurers underwriting and investment income is considered which greatly complicates the model, but makes it considerably more realistic.

Industry Segmentation and Predictor Motifs for Solvency Analysis of the Life/Health Insurance Industry

This paper contributes one principal idea to the methodology of solvency studies for the life insurance industry. The idea is grouping, which is applied in two different ways. First, companies are grouped into industry segments by insurer specialization or by size. Second, predictor variables are grouped into thematically related motifs. The primary benefits of grouping are improved solvency prediction and improved interpretation of predictors. Improved prediction results from industry segmentation; improved interpretation from predictor motifs. The models are developed by the technique of cascaded logistic regression, which forecasts solvency status on the basis of motifs, rather than of individual variables. A key finding is that the segments differ in their significant motifs in anticipated ways. For example, investment motifs are important for solvency in the Life and Annuities segments, but not in the Health segment. A similar pattern characterizes the difference between large and small insurers. The study covers the 1990 through 1992 time period, when there were a historically high number of troubled companies.

A financial-economic evaluation of insurance guaranty fund system: An agency cost perspective

Abstract Recent occurrences of financial distress to some insurers have raised questions about whether the current guaranty system is adequate to protect policyholders. Four new systems have been proposed. Using the state preference model, it was found the Stewarts national system faring the best, if it adopts uniform regulation. Based on agency theory, the pre-assessment approach and the policyholder surcharge (or premium increase) recoupment method were found to be better than the current post-assessment approach and premium tax offset method. Furthermore, uniform policy limits and regulations are recommended.

A Comparative Economic Analysis of Tort Liability and No-Fault Compensation Systems in Automobile Insurance

Based on an analysis of annual loss ratio data by state for automobile liability insurance during 1975-1980, the economic impact of no-fault automobile insurance on the relative benefits and costs to consumers and on the predictability of relative loss costs for insurers is assessed. Several hypotheses are tested by using some regression models. The results suggest that no-fault automobile insurance tends to increase relative benefits or decrease relative costs (prices) to consumers, but in the short run it does not improve the predictability of relative loss costs for insurers. From a public policy viewpoint, these results seem to suggest that a no-fault compensation system performs more efficiently than a tort-liability system for automobile insurance consumers. I. Overview and Purpose Criticisms of the efficiency and fairness of the tort liability compensation system in automobile insurance culminated with the adoption of no-fault compensation systems in 24 states in the 1970s. No-fault automobile insurance is a first-party coverage under which each driver accepts financial responsibility for some or all losses and injuries sustained by occupants of his or her own car, pedestrians hit by his or her car, and himself or herself in exchange for partial immunity from liability for losses to third parties or other drivers and their passengers. This means that recovery of losses from automobile accidents within certain limits is available to victims without regard to fault. In contrast, under the tort liability compensation system, fault or

Insurance Versus Self-insurance: A Risk Management Perspective

The scientific risk-retention or self-insurance decision from a utility theoretic point of view is examined under the assumption that the risk manager has only partial stochastic information about the loss severity distribution. When only the range and a few central moments are known about the loss severity distribution, it is shown how to obtain maximally tight bounds on the expected utility of self insurance. Significantly, the extremal probability distributions derived do not depend upon the particular decision makers utility function and, therefore, should be applicable to a wide variety of financial decisions. Moreover, financial and/or risk managers in a business can make decisions without assessing the preference structure of the firms owners.

An Economic Analysis of Retroactive Liability Insurance

Retroactive liability insurance may be written to provide coverage for a known loss that occurred during a past time period. Some simplified financial models are developed in this paper in order to provide some economic insights about the market for this coverage. The financial motives and conditions for the development of this market are analyzed. In particular, federal income taxes provide economic incentives for writing the coverage. Tax arbitrage enables the insured to share the income tax deductions for loss reserves available to an insurer when the coverage is written. Interest rates, insurer expenses. and the expected time to settlement influence the development of the market. Potential incentive conflicts may arise, however.

Statistical tests of stochastic process models used in the financial theory of insurance companies

This paper presents a statistical test allowing the analyst to determine if a given time series is statistically incompatible with being modeled as a linear or log-linear process. Since the commonly used models for financial time series of interest to insurance professionals are linear or log-linear, this paper allows the analyst to verify the linearity of the model under investigation, or else points to the necessity of non-linear modeling. We also show how to test for time series Gaussianity using the same type of statistical test statistic. These results are applied to several financial data sets relevant to the financial operations of insurance companies.

Author's Reply: Underwriting Risk and Return: Some Additional Comments

In a recent paper, the author suggested that one would expect to find an inverse relationship between mean loss ratios and standard deviations of the associated annual loss ratios by state for automobile insurance if this coverage were properly priced.1 In other words, one would expect lower underwriting profits to be associated with higher loss ratios, and therefore, a company would have to anticipate lower underwriting risk in order to have an economic incentive to sell automobile insurance in such states. Accordingly, one would expect that the average loss ratios and standard deviations for a given coverage in the various states would vary inversely with each other if underwriting risk were properly reflected in the insurance rates for the coverage, other things being equal. In order to test this economic hypothesis for various automobile insurance coverages, the correlation coefficient between the mean loss ratios and standard deviations for the various states was calculated to determine if an inverse or negative relationship existed. However, a positive rather than a negative relationship was found between these variables. The author found this empirical relationship to be somewhat surprising.