Solvency Levels and Risk Loadings Appropriate for Fully Guaranteed Property-Liability Insurance Contracts: A Financial View

In the past, the determination of appropriate solvency levels for U.S. companies writing major property-liability insurance lines took a decidedly non-analytic approach. Verbal persuasion, reinforced by continual empirical observation, allowed for the dominance of the so-called Kenney Rules for the determination of an appropriate level of financial assets, relative to premiums written, as the required solvency level. Increasingly complex techniques were developed, mostly in Europe, under the rubic of "Ruin Theory", which sometimes seemed to show that surprisingly low levels of surplus were needed to keep the probability that liabilities would exceed assets ("ruin") at low levels. In most of the analytic endeavors, risk loadings were assumed to be simple proportions of liabilities determined either exogenously (1921 Profit Formula) or as some function of the variation of liabilities. Financial risk loadings, derived from asset pricing models such as CAPM or APT, have been introduced by Fairley [13], Hill [15], Hill and Modigliani [16] and Kraus and Ross [20] since the late 70‘s. These developments all ignored, or assumed away, any dependence of the appropriate risk loading on required solvency levels except possibly for the important effect of taxation of income on supporting surplus. Section II reviews the argument that a constant per-period risk adjustment requires that supporting surplus be allocated approximately in proportion to outstanding liabilities (reserves). Section III sets forth a proposed criterion for determining required solvency margins in terms of options pricing concepts. The proposal replaces the usual probability level criterion for solvency by a financial value criterion: the value of the premium to reinsure the liability portfolio given the current level of assets. Section IV discusses Cummins‘ newly developed guaranty fund premium model in order to provide for some examples of the required solvency margins as defined in Section III. Section V applies the notions of Sections III and IV to obtain the appropriate solvency margins for a fully guaranteed insurance contract using Massachusetts data. Section VI proposes to interpret the Cummins‘ risk premium to reinsure a policy cohort having an asset/liability ratio of 1 as a (first approximation to) quantification of the proper risk loading in a fully guaranteed insurance contract.