Risk-Based Capital

Study guides: Exam 6U, Exam GH-201U, Exam GI-302

Risk-Based Capital (RBC) is the NAIC's standardised formula for the minimum capital a U.S. insurer needs given its asset, credit, underwriting and catastrophe risks, together with the model act that ties regulatory action to the ratio of the insurer's Total Adjusted Capital (TAC) to its Authorized Control Level (ACL) RBC.

\text{RBC}_{\text{cov}} = R_0 + \sqrt{R_1^2 + R_2^2 + R_3^2 + R_4^2 + R_5^2 + R_{\text{cat}}^2}

\text{ACL RBC} = \tfrac{1}{2}\big(\text{RBC}_{\text{cov}} + \text{Operational risk charge}\big)

\text{RBC ratio} = \frac{\text{TAC}}{\text{ACL RBC}}

• The P&C components:
  • R_0 — affiliated insurance companies, plus off-balance-sheet and miscellaneous items (guarantees, contingent liabilities); added in full, outside the square root.
  • R_1 — fixed-income assets: bonds by NAIC designation, mortgage loans, cash and short-term investments, plus an asset-concentration charge.
  • R_2 — equity assets: unaffiliated common and preferred stock, real estate, other long-term assets.
  • R_3 — credit risk: reinsurance recoverables and other receivables.
  • R_4 — reserve risk: line-of-business factors on unpaid loss and LAE, adjusted for the company's own development and for investment income, plus a charge for excessive premium growth.
  • R_5 — written premium risk: line factors on net written premium, from the excess of an investment-income-adjusted combined ratio over 100\% and blended with company experience, plus a growth charge.
  • R_{\text{cat}} — catastrophe risk: modelled hurricane and earthquake losses; other perils, such as wildfire, have been reported for information while the NAIC evaluates them. Older texts show the formula without R_{\text{cat}}.
• Covariance. Adding the charges would assume every risk goes wrong at once; the square root treats R_1–R_5 and R_{\text{cat}} as independent. An operational risk add-on of 3\% of \text{RBC}_{\text{cov}} follows, and ACL is half the total.
• The reinsurance split. If the loss-reserve charge exceeds the other credit charges plus half the reinsurance-recoverable charge, half of the reinsurance charge moves from R_3 into R_4 (Example 2).
• TAC is statutory surplus, adjusted — chiefly by removing any non-tabular reserve discount and by affiliate adjustments; credit for capital and surplus notes is capped.
• Action levels (RBC ratio):
  • \geq 200\% — none, except that a ratio of 200–300\% with a combined ratio above 120\% fails the trend test and is treated as Company Action Level.
  • 150–200\%, Company Action Level — the insurer files an RBC plan within 45 days.
  • 100–150\%, Regulatory Action Level — RBC plan, examination or analysis, and a corrective order.
  • 70–100\%, Authorized Control Level — the commissioner may take control.
  • < 70\%, Mandatory Control Level — the commissioner must, with narrow exceptions, place the insurer under regulatory control (rehabilitation or liquidation).
• What it is not. The NAIC says RBC is not meant to rank insurers: it is a floor that triggers legal authority, one tool of Solvency Monitoring alongside the IRIS Ratios. The great majority of insurers trigger no action level.

RBC Ratio and Action Level A P&C insurer (no life affiliates) reports, in $$$$$ millions: R_0 = 6, R_1 = 4, R_2 = 18, R_3 = 10, R_4 = 55, R_5 = 38, R_{\text{cat}} = 12. TAC is 105 and the trend-test combined ratio is 123\%. Find the RBC ratio and the action level.

Answer

\begin{align*}
\sum R_i^2 &= 16 + 324 + 100 + 3{,}025 + 1{,}444 + 144 \\
&= 5{,}053 \\
\text{RBC}_{\text{cov}} &= 6 + \sqrt{5{,}053} \\
&= 6 + 71.08 \\
&= 77.08 \\
\text{Operational risk} &= 0.03 \times 77.08 \\
&= 2.31 \\
\text{ACL RBC} &= \tfrac{1}{2}(77.08 + 2.31) \\
&= 39.70 \\
\text{RBC ratio} &= \frac{105}{39.70} \\
&= 264.5\%
\end{align*}

The undiversified sum of the charges is 143; covariance cuts it to 77.08. Most of the saving comes from the four smaller charges, which total 44 but add only about 4 once squared alongside R_4 and R_5.

On capital alone, 264.5\% \geq 200\% means no action. But the ratio lies between 200\% and 300\% and the combined ratio exceeds 120\%, so the trend test is failed: the insurer is at Company Action Level and must file an RBC plan.

Why Half the Reinsurance Charge Moves to R4 Credit RBC on non-reinsurance receivables is 3, the reinsurance-recoverable charge is 8, and the loss-reserve charge is 50. Allocate R_3 and R_4, and compare R_3^2 + R_4^2 with keeping the whole reinsurance charge in R_3.

Answer The test: 50 > 3 + \tfrac{1}{2}(8) = 7, so the charge is split.

\begin{align*}
R_3 &= 3 + 4 = 7 \\
R_4 &= 50 + 4 = 54 \\
R_3^2 + R_4^2 &= 49 + 2{,}916 \\
&= 2{,}965
\end{align*}

With the whole charge in R_3: 11^2 + 50^2 = 121 + 2{,}500 = 2{,}621.

The split adds 344 inside the square root. Adding to the largest component earns almost no diversification credit — the formula is treating half of reinsurance credit risk as moving with reserve risk, because reinsurers are hardest to collect from exactly when reserves develop adversely and recoverables balloon.