Costly Risk Bearing and the Supply of Catastrophic Insurance

Abstract

INTRODUCTION Efficient contracts for sharing risk will allocate risk according to comparative advantage. For many insurance contracts, the comparative advantage is straightforward. The policyholder faces the prospect that she can lose a significant proportion of her wealth by single events such as car crashes, illnesses, and home accidents. In contrast, the insurer spreads its risk over tens of thousands of such exposures and, with such numbers, can rely on a predictable proportion of policies producing a predictable average loss. In short, the policyholder is undiversified whereas the insurer is diversified. This comparative advantage is established only in the event that the correlation of losses between insureds is low. Earthquakes do not fit this description. The high correlations between the claims on the insurer's policies will (in the limit) equalize the costs of risk bearing for the insurer and insured. But the insurer's comparative advantage is not necessarily entirely removed. Correlations are not perfect; while the same earthquake will affect a large proportion of policies in any seismic zone, structures will have very different levels of damage. This feature alone offers some degree of diversification. Further opportunities for diversification of this risk are present when the insurer writes policies in different locations (earthquake risk near the San Andreas system in California may have zero correlation with earthquake risk on the New Madrid fault in the midwest). Still further opportunities for diversification are available to the insurer that pools earthquake insurance with other lines of business such as fire, automobile, and liability insurance. Insurance markets for earthquake risk can, and do, exist. The players in this market, and the amount of business they write, may still be explained by comparative advantage. However, the respective abilities of insurers to write this risk depend not simply on their ability to write large numbers of policies, but on the characteristics of their entire portfolio as well as on financial features that influence the costs of risk bearing. Several recent contributions have shown why risk is costly to corporations such as insurers. The costs of risk arise from tax convexity, principal agent relationships within the firm, and the costs of financial distress. This article addresses how these types of features jointly determine the capacity of insurers to write insurance for catastrophic losses, using earthquake as a specific example. From this we estimate a cross-sectional model of earthquake insurance which emphasizes the differing capacity of insurers to write this line of business. THE COST OF RISK TO INSURERS One of the major effects of writing insurance for earthquake losses is the increase in the variance of insurers' cash flows due to correlated losses and uncertainty regarding the parameters of the loss distribution. The extent to which such an increase in risk matters has been debated. According to modern financial theory and, in particular, the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT) - diversifiable risk is not priced in the capital market. Stakeholders will receive a risk premium for bearing systematic risk but not unsystematic risk, because the latter is diversifiable and therefore not priced. These theories imply that decreasing risks at the corporate level that are diversifiable at the portfolio level will not benefit stockholders because such company-specific risks can be efficiently managed by diversifying their asset holdings. More recently, it has been argued that large, unmanaged, unsystematic risks can decrease the value of the firm by lowering the level of expected cash flows (Mayers and Smith, 1982; Smith and Stulz, 1985; Shapiro and Titman, 1985; and Cornell and Shapiro, 1987). Modigliani and Miller (1958) show that, If there are no taxes, no transactions costs, and if the firm's real investment activities are fixed, then the firm's financial decisions will not affect firm value. …