Risk-Based Capital – Calibration of LOB Diversification in Underwriting Risk Charges

In this paper we analyze the Line of Business (LOB) diversification elements of the RBC Formula.We compare the diversification credit produced by the NAIC Property/Casualty RBC Formula to the indicated diversification credit, i.e., the observed reduction in risk1 with increasing diversification. For the larger/more diversified companies, with the bulk of the premium/reserves and receiving the bulk of the diversification credit, we find that:

•The data supports the approach in the RBC Formula, i.e., the data supports a diversification credit that is linear with respect to 100% minus the percentage of reserves/premium in the largest line of business, by company.

•The indicated maximum diversification credit is at least at least 50%, for premium risk and reserves risk, rather than the 30% maximum credit in the 2010 RBC Formula. Three natural alternatives to the diversification approach in the RBC Formula are the correlation2 matrix approach, the Herfendahl-Hirschman Index (HHI)approach, and the RBC approach applied to risk amounts rather than reserves/premium volume. We apply some simple tests of the extent to which each of these approaches fits the data. With our tests, the correlation approach is better than the approach in the RBC Formula for reserves, but the reverse is the case for premium. More interestingly, the RBC approach applied to risk amounts rather than reserves/premium volume is better than the approach in the RBC Formula for both premium and reserves. This is one of several papers being issued by the CAS RBC Dependencies and Calibration Working Party (DCWP).

Keywords: Risk-Based Capital, Capital Requirements, Analyzing/Quantifying Risks, Assess/Prioritizing Risks, Integrating Risks, Diversification, Correlation