Equity Insurance Research Articles

Asset Pricing of Insurance Loss Liabilities: Some Examples

I construct examples of valuing insurance loss liabilities with asset pricing models, comparing the Rubinstein-Leland model with the better-known CAPM. The two models give different values only if the loss payment is asymmetric and correlated with the market portfolio, conditions which can result from the nature of the underlying loss or from the impact of insolvency on the insurer's payment. In examples where insolvency is not possible and there is no liquidity cost of raising new equity on short notice, the value of a loss liability is equal to the value of the underlying loss, i.e., of the promised coverage, and depends neither on (1) the size of the loss pool; nor on (2) the unsystematic risk of the insurer's liabilities; nor on (3) the composition of an insurer's investment portfolio; nor on (4) the amount of insurer equity. These factors do affect the value of a loss liability in examples where insolvency and liquidity costs are considered. Other things equal, if a factor increases the likelihood of insolvency, the fair value of a loss liability is lower because the insured is partially self-insuring; but the liquidity cost of maintaining solvency by raising new equity on short notice is higher, implying a higher fair value of the loss liability.

Loss Ratio on Insurance Equity Securities: A New Step in Insurance Securitization

The recent trend of integrated risk management has resulted in corporations reassessing their risk management practices. Insurance derivatives and insurance‐linked securities are emerging as alternatives or complements to traditional resisurance capacity. Despite its theoretical benefits, the market for insurance‐linked transactions has not matured, due to problems of information asymmetry and lack of transparency. This article proposes a solution to resolve the conflicting interests preventing insurers/reinsurers and investors from more widely trading insurance risk.

Workers’ Compensation Rate Regulation: How Price Controls Increase Costs

In the 1980s, regulation constrained workers’ compensation insurance premiums in the face of rapid growth in loss costs. We develop and test the hypothesis that rate suppression exacerbates loss growth, leading to higher losses and premiums. The empirical analysis using rating class data for eight states for the period 1985–91 confirms that rate suppression, measured by lagged residual‐market share of payroll, increased loss growth. The cost‐increasing effects are greater in the residual market than in the voluntary market, but premiums increased more rapidly in the voluntary market. The resulting pattern of cross subsidies between and within classes is consistent with a simple model of political influence, with subsidies to high risks and small firms at the expense of low risks and insurer equity.

Moral Hazard in Home Equity Conversion

Home equity conversion as presently constituted or proposed usually does not deal well with the problem of moral hazard. Once homeowners know that the risk of poor market performance of their homes is borne by investors, they have an incentive to neglect to take steps to maintain the homes values. They may thus create serious future losses for the investors. A calibrated model for assessing this moral‐hazard risk is presented that is suitable for a number of home equity conversion forms: (1) reverse mortgages, (2) home equity insurance, (3) shared‐appreciation mortgages, (4) housing partnerships, (5) shared‐equity mortgages and (6) sale of remainder interest. Modifications of these forms involving real estate price indexes are proposed that might deal better with the problem of moral hazard.

Financial Pricing of Insurance in the Multiple-Line Insurance Company

INTRODUCTION Since insurance contracts are financial instruments, it seems natural to apply financial models to insurance pricing. Financial pricing models have been developed based on the capital asset pricing model (Biger and Kahane 1978; Fairley 1979), arbitrage pricing theory (Kraus and Ross 1982), capital budgeting principles (Myers and Cohn 1987) and option pricing theory (Merton 1977; Smith 1979; Doherty and Garven 1986; Cummins 1988; and Shimko 1992). Financial models represent a significant advancement over traditional actuarial models because they recognize that insurance prices should be consistent with an asset pricing model or, minimally, avoid the creation of arbitrage opportunities. A limitation of the existing financial pricing models is the implicit or explicit assumption that insurers produce only one type of insurance, even though most insurers produce multiple types of coverage (e.g., automobile insurance, general liability insurance, workers' compensation insurance, etc.). The purpose of this paper is to remedy this deficiency in the existing literature by providing a theoretical and empirical analysis of insurance pricing in a multiple line firm. An option pricing approach is adopted to model the insurer's default risk. The standard Black-Scholes model is generalized to incorporate more than one class of liabilities, and pricing formulae are generated for each liability class. The theoretical predictions of the model are tested using data on an extensive sample of publicly traded U.S. property-liability insurers. Option models of insurance pricing have two primary advantages: First, they explicitly incorporate default risk. This is important given the increase in insurer insolvency rates since the early-1980s (see BarNiv 1990). Second, because of data limitations, the key parameters can be estimated more accurately for option pricing models than for competing models such as the Myers-Cohn (1987) or Kraus-Ross (1982) models.(1) The standard option pricing model of insurance views the liabilities created by issuing insurance policies as analogous to risky corporate debt. The insurer is assumed to issue an insurance policy in return for a premium payment, analogous to the proceeds of a bond issue. In return, it promises to make a payment to the policyholders at the maturity date of the contract. Using this bond analogy, the value of the insurer's promise to policyholders can be thought of as being like the value of a default risk-free loan in the amount of the promised payment less a put option on the value of the insurer. In reality, however, most insurers issue more than one type of insurance and in this case the analogy with a single debt issue is no longer exact. The problem of pricing multiple classes of debt has been considered by Black and Cox (1976). In their analysis senior debt has priority over junior debt in the event of bankruptcy. However, with multiple lines of insurance, each line has equal priority in the event of bankruptcy (see National Association of Insurance Commissioners 1993), and this is the case investigated in our paper. In a multiple line insurance company, equity capital is held in a common pool. If one or more lines incur deficits of losses over premiums, the lines in difficulty can draw upon the full amount of the firm's equity capital, including earnings from the solvent lines. Given this sharing of resources, it is not obvious how to allocate the cost of equity capital to each line. There have only been a few prior papers on insurance pricing in a multiple line firm, mostly in the actuarial literature. Nearly all have approached the problem by assuming that the insurer's equity capital is allocated among lines of business, usually in proportion to each line's share of the insurer's liabilities (see Knuer 1987; Derrig 1989; and D'Arcy and Garven 1990). Prices for a given line of insurance then incorporate an aggregate profit charge equal to the assumed cost of capital for the line multiplied by its assigned equity. …

Evidence on the Time Series Properties of Insurance Premiums and Causes of the Underwriting Cycle: New Support for the Capital Market Imperfection Hypothesis

Introduction Numerous studies document that underwriting profit rates and insurance prices in the property-liability insurance industry have been cyclical in the postwar period (for example, see Cummins and Outreville, 1987; Doherty and Kang, 1988; and Venezian, 1985). A hard where prices and profits are high and coverage is restricted tends to be followed by a soft where prices and profits are low and coverage is expanded. The cycle in property-liability underwriting profits has a period of about six years.(1) The of this underwriting cycle has been the subject of much debate. In a perfect market, a price cycle would occur only if insurers' expected costs--the present value of expected losses--were cyclical. Most explanations, however, attribute the cycle to imperfections on the supply side of the property-liability insurance market.(2) Cummins and Outreville (1987) present a model in which insurers set prices rationally, but in which almost all relevant information in forming expectations of future losses is contained in past loss reports. These assumptions, along with regulatory and accounting lags, induce a cycle in reported profits and prices, Venezian (1985) attributes the cycle to the extrapolative methods used in the rate setting process. Several recent articles show that capital market imperfections can generate a cycle. For example, Winter (1989) assumes that the quantity of insurance is constrained by an insurer's equity and that internal equity is a cheaper source of capital than external equity (Myers, 1984). Consequently, a reduction in capital (e.g., due to unexpected losses) causes industry supply to contract and insurance prices to increase.(3) These hypotheses have different implications for the determinants of premiums, which are tested using time series regressions similar to the causality tests proposed by Granger (1969) and Sims (1972). In a perfect market with rational expectations, insurers set premiums equal to the present value of expected future losses, where expectations are formed using all relevant information. Premiums are therefore the best predictors of future losses in the sense that premiums aggregate all information about future losses.(4) In the terminology of Sim's causality tests, premiums cause losses; that is, current premiums can be explained by future loss payments. After controlling for expected future loss payments, other information such as past losses and past surplus will not help explain premiums. In contrast, the capital market imperfection hypothesis (Winter, 1989; also see Gron, 1992, and Cummins and Danzon, 1992) implies that premiums are not the best predictors of actual losses because past surplus affects premiums. Venezian's (1985) model implies that premiums are not the best predictors of actual losses, because premiums are mechanically set based on the realizations of past losses. Accordingly, past loss experience affects premiums. Although data problems limit the strength of the conclusions, our results suggest that market imperfections play an important role in insurance pricing. Consistent with the capital market imperfection hypothesis, the evidence suggests that past values of surplus affect premiums. Weaker evidence is presented that past values of losses affect premiums, which is consistent with Venezian's hypothesis. The article proceeds as follows. In the next section, the hypotheses are described in more detail. In the third section, the methodology and data are presented along with potential econometric problems. The results are then summarized. The article concludes with a short summary and some caveats. Hypotheses Perfect Markets/Rational Expectations Hypothesis In a perfect market, the price of insurance would be determined by discounting expected cash flows by the appropriate discount rates. To be more specific, consider a competitive insurance market with no transaction costs and no information costs. …

Index- Based Futures And Options Markets In Real Estate

Most institutional and individual portfolios are very undiversified in real estate: many hold no real estate at all, many have holdings highly concentrated in certain regions or types of real estate. The risk of these concentrated holdings is not hedged. We propose here that cash-settled futures and options markets be opened on real estate to better allow diversification and hedging, and show that these markets solve problems that have hampered other real estate hedging media in the past. Related institutions, such as home equity insurance, might develop around the futures and options markets. The establishment of these markets is likely to increase the quantity of reproducible real estate, and lower rents on real estate. It may also reduce the amplitude of speculative real estate price movements and dampen the business cycle.

Tax Sheltering Behavior of Property-Liability Insurers: Some Additional Evidence

Tax Sheltering Behavior of Property-Liability Insurers: Some Additional Evidence

Efficiency and Equity in Insurance

The pooling of heterogeneous risks is shown to increase financial efficiency as viewed by the insurer or by an insured individual, though not necessarily from the point of view of society. When heterogeneous risks are pooled, issues of equity among groups of insurance purchasers arise. The use of the same premium loadings for all groups of policyholders can result in inequities so blatant that a group may pay more in a multiline company than it would in a monoline company. The data to test whether such violations occur are not available.