Actuarial Notes

Regulatory Capital

Study guides: Exam CFE-101, Exam CP-321, Exam CP-351, Exam GH-201U, Exam ILA-101, Exam ILA-201I, Exam ILA-201U

Regulatory capital is the capital a supervisor requires an insurer to hold, measured by a prescribed formula, together with the capital the supervisor will count against that requirement. The two are compared as a ratio, and falling below set levels of the ratio triggers supervisory action. The main frameworks are the NAIC's risk-based capital in the U.S., Canada's LICAT for life insurers and MCT for P&C insurers, the EU's Solvency II, and the IAIS's Insurance Capital Standard (ICS) for international groups.

\text{Capital ratio} = \frac{\text{Available capital}}{\text{Required capital}}

\text{RBC}_{\text{life}} = C_0 + C_{4a} + \sqrt{Q}

Q = (C_{1o} + C_{3a})^2 + (C_{1cs} + C_{3c})^2 + C_2^2 + C_{3b}^2 + C_{4b}^2

  • Symbols: Available capital is what the framework counts as able to absorb losses, and required capital is the formula's amount. In the U.S. life formula, C_0 is affiliate risk and C_1 is asset risk, split into C_{1o} for bonds and other assets and C_{1cs} for unaffiliated common stock. C_2 is insurance risk, C_3 is interest rate (C_{3a}), health credit (C_{3b}) and market (C_{3c}) risk, and C_4 is business risk, with C_{4b} for health administrative expenses.
  • The two halves: Available capital starts from the balance sheet and removes what would not absorb a loss, such as goodwill. The U.S. calls it total adjusted capital (TAC), the MCT capital available and Solvency II own funds. Required capital is built from charges for each risk, usually factors applied to assets, liabilities and premiums, or the result of a stress at a stated confidence level.
  • Aggregation: Most formulas add some charges in full and combine the rest by a square root, which assumes the main risks are independent or correlated by a set matrix. The square root is a diversification credit: reducing one large charge lowers the total by less, because the others still dominate. See Risk Diversification.
  • U.S. RBC: The NAIC has separate formulas for life, P&C and health insurers. The ratio is TAC divided by the authorized control level (ACL), which is half the formula's result. Action levels fall at ratios of 200% (company action), 150% (regulatory action), 100% (authorized control) and 70% (mandatory control), with a trend test just above 200%.
  • Canada: OSFI's LICAT compares available capital, plus a surplus allowance and eligible deposits, with a base solvency buffer of risk charges, credits and a 1.05 scalar. It sets supervisory target ratios for total and core capital. The P&C test is the MCT, whose base solvency buffer is 1.5 times capital required against a supervisory target of 150%.
  • Solvency II and the ICS: Solvency II's solvency capital requirement is calibrated to a one-year 99.5% value at risk on a market-consistent balance sheet, and an approved internal model may replace the standard formula. The ICS applies the same kind of calibration to internationally active insurance groups, on a market-adjusted valuation.
  • Regulatory against economic capital: The formula is the supervisor's floor, set for every insurer alike. Economic capital is the insurer's own estimate, and through the ORSA the insurer sets an internal target above the regulatory one. CFE-101 compares these with accounting measures, embedded value and EVA as measures for decisions.
  • Managing the ratio: An insurer raises the ratio by adding capital, retaining earnings or cutting dividends, or lowers the requirement through reinsurance, a safer asset mix or a change of business mix. Each lever has a cost, such as ceded margin, lower investment return or forgone growth, so capital management weighs the ratio against return.

A Life Insurer's RBC Ratio and a Quota Share A U.S. life insurer's RBC components, in $ millions and illustrative, are C_0 = 10, C_{1o} = 120, C_{1cs} = 40, C_2 = 90, C_{3a} = 60, C_{3b} = 5, C_{4a} = 25, with C_{3c} = C_{4b} = 0. Its TAC is $230 million.

(a) Find the RBC ratio and the action level.

(b) A quota share cedes half the mortality risk, which halves C_2. Ignoring its effect on TAC and on other charges, find the new ratio.

Answer (a) The interest rate charge combines with the asset charge before squaring.

\begin{align*}
Q &= 180^2 + 40^2 + 90^2 + 5^2 \\
&= 42{,}125 \\
\text{RBC} &= 10 + 25 + \sqrt{42{,}125} \\
&= 35 + 205.24 \\
&= 240.24 \\
\text{ACL} &= 0.5 \times 240.24 \\
&= 120.12 \\
\text{Ratio} &= 230 / 120.12 \\
&= 191.5\%
\end{align*}

The ratio is between 150% and 200%, which is the company action level. The insurer must file a plan to restore its capital.

(b) With C_2 = 45:

\begin{align*}
Q &= 180^2 + 40^2 + 45^2 + 5^2 \\
&= 36{,}050 \\
\text{RBC} &= 35 + \sqrt{36{,}050} \\
&= 35 + 189.87 \\
&= 224.87 \\
\text{ACL} &= 0.5 \times 224.87 \\
&= 112.43 \\
\text{Ratio} &= 230 / 112.43 \\
&= 204.6\%
\end{align*}

Halving a $90 million charge cut the RBC by only $15.4 million, because the square root lets the larger asset and interest rate charges dominate. The reinsurance lifts the ratio above 200%, but the margin ceded and the reinsurer's credit risk are costs the insurer has to weigh against it.

How it appears on the exam

  • ILA-201I: Candidates explain and calculate regulatory capital under international frameworks, such as LICAT, Solvency II and the ICS, and compare their valuation bases, calibrations and ratios.
  • ILA-201U: Candidates explain and calculate required capital under the U.S. framework, which is the life RBC formula and its action levels, and apply the methods of financial capital management.
  • GH-201U: Candidates evaluate a health insurer's capital needs using RBC, and the use of reinsurance to reduce capital strain, as in the example.
  • CP-321: Required capital is one of the projections, alongside premiums, claims, expenses and liabilities, that the manual rate objective asks candidates to evaluate.
  • CFE-101: Candidates compare regulatory capital requirements with economic capital, embedded value, EVA and accounting measures as inputs to decisions.

Exam traps

  • ACL, not the formula total: The U.S. ratio divides TAC by the authorized control level, which is half the post-covariance RBC. Dividing by the full RBC halves the ratio and puts the insurer two action levels too low.
  • Combining before squaring: In the life formula, C_{1o} and C_{3a} are added before squaring, because asset and interest rate risk are treated as moving together. Squaring them separately understates the requirement.
  • Proportional thinking: Under a square-root aggregation, halving one charge doesn't halve its effect on the total. The saving depends on how large that charge is relative to the others.
  • Mixing frameworks' ratios: A 150% MCT ratio, a 200% RBC ratio and a 100% LICAT total ratio are each set against a different denominator. Comparing the percentages across frameworks says nothing about which insurer holds more capital.