A property-casualty (P-C) insurance firm has estimated the following risk-based capital charge for its individual risk classes: $\begin{array}{|c|c|c|}
\hline \text { Risk } & \text { Description } & \text { RBC Charge } \
\hline \text { R0 } & \text { Affiliated P-C } & \$ 6.0 \text { million } \
\hline \text { R1 } & \text { Fixed-income assets } & \$ 2.0 \text { million } \
\hline \text { R2 } & \text { Common Stock } & \$ 1.0 \text { million } \
\hline \text { R3 } & \text { Reinsurance } & \$ 3.0 \text { million } \
\hline \text { R4 } & \text { Loss Adjustment Expense } & \$ 1.0 \text { million } \
\hline \text { R5 } & \text { Written Premiums } & \$ 2.0 \text { million } \
\hline \text { R6 } & \text { Hurricane } & \$ 1.0 \text { million } \
\hline \text { R7 } & \text { Earthquake } & \$ 0.5 \text { million } \
\hline \text { Total } & & \$ 16.50 \text { million } \
\hline
\end{array}$ Using the model recommended by the National Association of Insurance Commissioners (NAIC), what is the total risk-based capital charge for the P-C firm?

Question

Quizplus · Accepted Answer

The NAIC model calculates the total RBC charge by taking the square root of the sum of the squares of the individual risk charges, excluding R0. Thus, $\sqrt{(2^2 + 1^2 + 3^2 + 1^2 + 2^2 + 1^2 + 0.5^2)} = \sqrt{(4 + 1 + 9 + 1 + 4 + 1 + 0.25)} = \sqrt{20.25} = 4.5$. Adding R0, the total RBC charge is $6 + 4.5 = 10.5$ million.

A Property-Casualty (P-C) Insurance Firm Has Estimated the Following Risk-Based