Risk-Based Capital Line of Business Diversification: Current RBC Approach vs. Correlation Matrix Approach

The NAIC RBC Formula treatment of line of business (LOB) diversification (referred to in this paper as the CoMaxLine% Approach) is very different from the Solvency II Standard Formula treatment. In this paper we show that, notwithstanding the differences, the NAIC RBC Formula, the correlation matrix approach used in Solvency II1 and the Herfindahl-Hirschman Index (HHI), widely used in economics, all produce similar risk-based capital underwriting risk values, for most companies. To the extent that there are differences between the CoMaxLine% and correlation matrix approaches, the differences are due, in part, to the fact that CoMaxLine% calculates diversification based on premium or reserve volume while the correlation matrix approach calculates diversification based on premium risk or reserve risk. To examine this feature of the RBC Formula, we also apply the CoMaxLine% idea to risk by LOB rather than volume by LOB. We refer to that as CoMaxLine%-Risk. The differences between CoMaxLine%-Risk and the correlation matrix approach are smaller than the differences to the RBC CoMaxLine% Approach. This is one of several papers being issued by the Risk-Based Capital (RBC) Dependencies and Calibration Working Party.

Keywords: Risk-Based Capital, Capital Requirements, Analyzing/Quantifying Risks, Assessing/Prioritizing Risks, Integrating Risks, dependency, correlation.