Solvency Measurement for Property-Liability Risk Based Capital Applications

In 1990 the NAIC began a project to establish risk-based capital formulas. This paper shows, how risk can be quantified for setting RBC for property-liability insurers. From an understanding of the general process, rules and methods are formed for practical use, either in regulation or to an insurer’s in-house capital management. The valuation of policyholders’ security forms the economic basis for the development. Capital and risk are defined, leading to the expected deficit to policyholders as the relevant solvency risk measure. A balance sheet model relates capital and expected deficit amounts, giving results for the normal and lognormal distributions. The paper shows how insurance risk is time-dependent, concluding that market valuation is needed to remove measurement bias and that a proper time horizon is the period between risk-based capital evaluations, even though the realization of assets and liabilities may extend beyond one period. The present value of the policyholder deficit is shown to be equivalent to a financial option implicitly given by the policyholders. Finally, covariance of risk elements is discussed, indicating that the degree of correlation is a critical factor in properly setting capital levels. A linear approximation gives a simple square root rule to treat covariance.