Capital Required

Study guide: Exam 6C

Capital Required is the MCT's measure of how much capital an insurer's risk profile demands. It is built by computing a margin for each category of risk and subtracting a credit for the fact that they do not all crystallise together.

\text{CR} = \text{Insurance} + \text{Market} + \text{Credit} + \text{Operational} - \text{Diversification}

• The four risk margins:
  • Insurance risk — factors applied to claim liabilities and premium liabilities by line, plus catastrophe and earthquake requirements. Usually the largest component for a P&C insurer.
  • Market risk — interest rate, equity, real estate, currency and other market exposures on the asset side.
  • Credit risk — counterparty default on invested assets, receivables and reinsurance recoverables.
  • Operational risk — a formula-based charge on premium, liabilities and growth.
• The Diversification Credit recognises that insurance risk and market risk are not perfectly correlated, and reduces the total accordingly.
• The Base Solvency Buffer is 1.5 \times capital required, and it is the denominator of the MCT ratio — so the effective requirement is that capital available exceed 1.5 times capital required.
• Growth raises it. Writing more business increases claim and premium liabilities and therefore the insurance risk margin, so an insurer growing fast needs capital simply to stand still — a mechanism that turns rapid growth into a capital problem before it turns into a loss problem.
• Reinsurance reduces it, but only where the reinsurer is registered or the cession is collateralised, and buying reinsurance itself creates credit risk against the reinsurer. The net capital benefit is the reduction in insurance risk less the credit charge.
• The formula is standardised, which makes insurers comparable but means it cannot capture every insurer's actual risk — which is exactly why ORSA requires the insurer to form its own view of required capital alongside it.

The Capital Cost of Growth An insurer's capital required is \$140 million, of which \$88 million is insurance risk. Capital available is \$330 million. It plans to grow premium 20\%, which will raise the insurance risk margin proportionally, with other margins unchanged and the diversification credit of \$18 million rising to \$21 million.

What happens to the MCT ratio, assuming the growth is written at break-even?

Answer Before:

\begin{align*}
\text{BSB} &= 1.5 \times \$140\text{M} = \$210\text{M} \\[4pt]
\text{MCT} &= \frac{\$330\text{M}}{\$210\text{M}} = 157\%
\end{align*}

After. Insurance risk rises 20\% to \$105.6M, an increase of \$17.6M; the diversification credit rises \$3M:

\begin{align*}
\text{CR} &= \$140\text{M} + \$17.6\text{M} - \$3\text{M} \\
&= \$154.6\text{M} \\[4pt]
\text{BSB} &= 1.5 \times \$154.6\text{M} = \$231.9\text{M} \\[4pt]
\text{MCT} &= \frac{\$330\text{M}}{\$231.9\text{M}} = 142\%
\end{align*}

The ratio falls 15 points and breaches the 150\% supervisory target — from growth alone, with no losses. Break-even business adds nothing to capital available while adding materially to the buffer.

What this means in practice. Growth must be funded. To hold 157\% the insurer needs capital available of 1.57 \times \$231.9 = \$364 million, or \$34 million more than it has. The sources are retained earnings (so the growth must be profitable, not break-even), a capital injection, or reinsurance to hold the insurance risk margin down.

And this is the benign case. PACICC's failure research describes insurers that grew fast at inadequate rates — where capital available falls at the same time the buffer rises, and both sides of the ratio move against them at once.