Surplus Allocations for Insurance Companies

This paper clarifies how option pricing methods can be used to determine how much surplus an insurance company should carry and how that surplus requirement should be allocated across the company‘s lines of insurance business. Surplus is important because more surplus means more collateral for outstanding policies. Surplus is costly for at least two reasons. First, agency and information costs may attach to risk capital in any financial intermediary. These costs are described by Merton and Perold (1993). Second, the U.S. tax system subjects investment income to double taxation, first at the corporate level and again when it is realized by the corporation‘s shareholders. When an insurance company raises additional surplus and invests it in securities to collateralize policies, the company‘s equity investors are essentially holding these securities in a taxable mutual fund. The shareholders‘ investment is subject to a layer of taxes not encountered in direct investment in securities or in ordinary mutual funds. To survive the insurance company has to recover these tax costs. Because surplus is costly, competitive premiums - and fair regulated premiums - depend on total surplus requirements and on their allocation to lines of insurance. The line-by-line allocations are important. If surplus allocations are wrong, cost allocations will be wrong too. In a competitive setting, allocation errors may lead firms to write unprofitable business and lose profitable business to competitors. In a regulated setting, some lines will cross-subsidize others, and companies will be tempted to "push" lines with too-low surplus allocations. Our main conclusions are as follows: - Option pricing methods can be used to estimate surplus requirements for insurance companies and to allocate surplus line by line. Given the line-by-line composition of the insurance company‘s business, that allocation is unique and not arbitrary. - A line‘s surplus allocation depends not just on the uncertainty about the line‘s losses, but also on correlations with other lines‘ losses and with the returns on the company‘s assets. - Given a company‘s assets and the present value of losses by line of business, option pricing methods can be used to calculate a default value, that is, the premium the company would have to pay in a competitive market for a policy guaranteeing payment of losses if the company defaults. The default value can be allocated uniquely line by line. - To calculate the cost of writing policies in different lines of insurance, surplus requirements should be allocated so that the marginal default value is the same in all lines. - This does not imply that regulated premiums should differ by company for the same line of insurance. In a competitive insurance industry, the premium for a given line will reflect an efficient composition of business - that is, an efficient tradeoff between the marginal benefits of diversification and the marginal costs of operating and administering a less focused and specialized operation.