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

Abstract

ABSTRACT 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 cu rrently 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. INTRODUCTION In response to concerns about the minimum capital standards applicable to insurance companies, the National Association of Insurance Commissioners (NAIC) adopted a regulatory risk-based capital (RBC) formula for property-liability insurers in 1994. The NAIC regulatory RBC formula computes a minimum capital requirement based on each insurer's risk profile. Most insurers, though, actually have much more than the minimum capital required by the NAIC formula. Many considerations affect the actual level of capital, including franchise value, taxes, reinsurance arrangements, and the level of risk aversion within the company. Insurers use internal RBC models to help develop optimal capital levels, and those optimal levels are almost always higher than the minimum standards under the NAIC RBC formula. In addition, private rating agencies such as A.M. Best and Standard & Poor's use their own internally developed RBC formulas to evaluate each insurer's capitalization as part of the quality rating process. Therefore, th e process of selecting appropriate RBC parameters, whether as part of a regulatory formula, a rating agency formula, or an internal management formula, affects virtually every insurer. Two of the competing approaches to assigning appropriate RBC parameters to the various risk elements in these RBC formulas are the traditional probability of ruin approach and the more recent expected policyholder deficit (EPD) approach (Bustic, 1994). This study will compare and contrast these two approaches. In recent years, the EPD methodology has been adopted as the basis for risk parameters in the capital adequacy models both A.M. Best and Standard & Poor's use. The American Academy of Actuaries' Risk-Based Capital Task Force has also used the EPD approach as the basis for recommendations on risk parameters in the NAIC's regulatory RBC formula (NAIC, 1993). Additionally, internal RBC models used by individual insurance companies may employ either of these approaches or yet another alternative approach. A firm grasp of the underlying mathematics of these approaches is necessary to evaluate the suitability of each approach in developing appropriate capital standards. This article is organized into four sections. The first section gives general background and descriptions of both the probability of ruin and the EPD approaches to setting capital standards. The second section compares the computation of risk parameters using different assumptions about the underlying risk of a particular insurer. …