The Stochastic Characteristics of Property-Liability Insurance Company Underwriting Profits

Abstract

Research on property-liability insurance often depends on the assumptions that combined ratios are normally distributed and/or uncorrelated with yield rates on common stocks. This study examines 206 combined ratio time series for nine major lines of insurance in order to gauge the accuracy of these assumptions. The normality hypothesis is accepted for approximately one-half the series, many are highly correlated with the industry-wide combined ratio, and almost none are significantly correlated with equity yields. An important implication is that mean-variance models should not be used in insurance research without validating the normality assumption or determining the impact of departures from normality. Managerial and public policy research on property-liability insurance often depends on assumptions about the stochastic characteristics of the profit margins for various types of insurance. These assumptions are of two principal types: (1) assumptions about the distributional properties of the profit margins, and (2) assumptions about the systematic risk inherent in various types of insurance. The first type of assumption is common in portfolio optimization research. Kahane [ 13], for example, has developed a quadratic programming model for use in determining the optimal product mix of a multiple line propertyliability insurer. This model will be valid if profits in the various product lines are normally distributed or if quadratic utility functions are appropriate. As quadratic utility functions are considered undesirable by many researchers, the usefulness of the model may hinge on the validity of the normality assumption. Decision making models developed by Thompson, Matthews, and Li [2 1 ], by Hammond, Shapiro, and Shilling [ 10], and by other researchers also depend on this assumption.