Insurance Risk Margin

Study guide: Exam 6C

The Insurance Risk Margin is the MCT component covering risk arising from the insurance business itself: that claim liabilities prove insufficient, that premium liabilities prove insufficient for the unexpired coverage, and that catastrophes occur. It is normally the largest part of Capital Required for a Canadian P&C insurer.

$\text{Insurance risk} = \text{Claim liabilities} + \text{Premium liabilities} + \text{Catastrophe}$

Claim liabilities margin — factors applied by line of business to the discounted LIC net of reinsurance credit. Long-tail liability lines attract higher factors than short-tail property, reflecting the greater uncertainty in their ultimate cost.
Premium liabilities margin — factors applied to the unexpired portion of coverage, reflecting the risk that claims on business already written but not yet incurred exceed expectations.
Catastrophe risk — an explicit requirement based on modelled exposure, with the earthquake requirement having its own detailed treatment covering the PML, reinsurance, and any capital markets protection.
Reinsurance reduces it, but only where the reinsurer is registered or the cession collateralised — and buying reinsurance substitutes a credit risk charge against the reinsurer for part of the insurance risk relieved.
It is why growth costs capital. More business means more claim and premium liabilities, so the margin rises with volume even when the business is written profitably. See Capital Required.
It is the target of the Diversification Credit, which recognises that insurance risk and market risk do not peak together and reduces the sum of the two.

Where a Line Mix Shift Shows Up An insurer with $\$500$ million of net claim liabilities is shifting from personal property (claim liability factor $15\%$ ) toward commercial liability (factor $25\%$ ). Currently the split is $70/30$ ; the plan moves it to $40/60$ over three years, with total liabilities unchanged.

What is the capital effect?
Answer Current claim liabilities margin:
 $\begin{align*} &= 0.70(\$500\text{M})(0.15) + 0.30(\$500\text{M})(0.25) \\ &= \$52.5\text{M} + \$37.5\text{M} \\ &= \$90\text{M} \end{align*}$ 
After the shift:
 $\begin{align*} &= 0.40(\$500\text{M})(0.15) + 0.60(\$500\text{M})(0.25) \\ &= \$30\text{M} + \$75\text{M} \\ &= \$105\text{M} \end{align*}$ 
An increase of $\$15$ million in the margin, which flows through to a $\$22.5$ million increase in the Base Solvency Buffer ( $1.5 \times$ ). On capital available of, say, $\$400$ million and a buffer of $\$210$ million, the ratio falls from $190\%$ to $172\%$ — with no growth, no losses, and no change in the size of the balance sheet.

What the strategy therefore requires. Commercial liability must earn a higher return on capital than the personal property it replaces, or the shift destroys value even if both lines are profitable. The correct comparison is not loss ratio against loss ratio but return on the capital each line consumes — and this calculation is where that capital consumption becomes visible.

The second-order effects to raise with management: longer-tail liabilities increase duration and therefore interest rate sensitivity; reserve uncertainty rises, which argues for a higher risk adjustment and a higher internal target; and the insurer is entering a line whose development it may not yet know — the PACICC failure pattern.