A Comparison of Risk-based Capital Standards under the Expected Policyholder Deficit and the Probability of Ruin Approaches

Two competing approaches to setting risk-based capital (RBC) parameters are the traditional probability of ruin approach and the more recent expected policyholder deficit (EPD) ratio approach. The probability of ruin approach develops capital standards based on a fixed maximum probability of insolvency regardless of risk. The EPD ratio approach allows tradeoffs between the risk of insolvency and the average cost of insolvency so as to force the product of these two numbers, the EPD, to some fixed value. After an explanation of the underlying mathematics, the author develops risk-based capital parameters for private passenger auto liability reserve risk using both methods. The author shows that capital standards developed using the EPD approach increase the risk of insolvency for larger insurers that pose the greatest potential indirect costs to the insurance market through market disruptions in the wake of a major insolvency. These findings have important public policy implications because the EPD approach currently forms the basis for both the Standard & Poor’s capital adequacy model and the A.M. Best Company’s Best’s Capital Adequacy Ratio (BCAR), and it is also used by the American Academy of Actuaries’ Risk-Based Capital Task Force as a basis for recommendations to the National Association of Insurance Commissioners (NAIC) on parameters in the regulatory RBC model.