Coinsurance Rating

Study guide: Exam 5

Coinsurance Rating prices the two distinct provisions that go by the name coinsurance: the percentage participation under which the insured shares each covered loss, and the property coinsurance clause, which penalizes an insured who carries limits below a required percentage of value.

$\text{Loss Cost}_{\text{participation}} = c \times \text{Full-Coverage Loss Cost}$

$\text{Recovery}_{\text{clause}} = \min\!\left(\frac{\text{Insurance Carried}}{\text{Coinsurance \% } \times \text{Value}},\, 1\right) \times \text{Loss}$

Percentage participation (an $80/20$ plan, common in health and some property covers): the insurer pays share $c$ of every covered dollar above any deductible.

Because the insurer's share is a constant fraction of each loss, the loss cost scales directly by $c$ — unlike a deductible, which removes small losses entirely and so requires a loss elimination ratio rather than a simple proportion.
The saving is slightly less than $(1-c)$ in practice, because the insurer still investigates and adjusts the whole claim: claim-handling cost does not fall with the payment share, and fixed expenses do not fall at all.

Coinsurance clause (standard commercial property): the insured agrees to carry limits of at least, say, $80\%$ of the property's value. Fall short and every partial loss is settled at the ratio of insurance carried to insurance required.

Its purpose is insurance-to-value. Because most property losses are partial, an insured carrying $50\%$ of value would otherwise pay half the premium for nearly the same expected recovery, and the rate per $\$1{,}000$ would have to rise for everyone.
The clause applies only up to the policy limit, and full limits are still paid on total losses up to that limit.
The insurer's exposure to the clause is itself a rating consideration: books with poor insurance-to-value discipline show higher loss ratios per $\$1{,}000$ of stated value, which is mix, not cost.

Pricing a Participation Plan A full-coverage plan has a manual rate of $\$1{,}200$ a year, of which $\$780$ is loss cost, $\$120$ fixed expenses, with variable expenses of $20\%$ and profit $5\%$ . The insurer offers an $80/20$ plan.

Price the coinsurance option.
Answer The loss cost falls to $80\%$ ; expenses do not:
 $\begin{align*} \text{Loss cost} &= 0.80 \times \$780 = \$624 \\[4pt] \text{Rate} &= \frac{\$624 + \$120}{1 - 0.20 - 0.05} \\ &= \frac{\$744}{0.75} \\ &= \$992 \end{align*}$ 
The rate falls $17.3\%$ , not $20\%$ — the $\$120$ of fixed expense is unchanged, so a $20\%$ cut in losses buys less than a $20\%$ cut in premium.

Crediting the full $20\%$ ( $\$960$ ) would leave the fixed expenses under-funded on every coinsurance policy, and the shortfall grows as the participation share falls.

The Coinsurance Clause in Action A commercial building is worth $\$1{,}000{,}000$ . The policy carries a $\$600{,}000$ limit with an $80\%$ coinsurance clause. A fire causes $\$200{,}000$ of damage.

What does the insurer pay?

Answer Insurance required is $80\%$ of value:

$0.80 \times \$1{,}000{,}000 = \$800{,}000$

Insurance carried is $\$600{,}000$ , so the coinsurance ratio is

$\frac{\$600{,}000}{\$800{,}000} = 0.75$

$\text{Recovery} = 0.75 \times \$200{,}000 = \$150{,}000$

The insured absorbs $\$50{,}000$ — a penalty for under-insurance, not a deductible.

The pricing logic behind the clause: had the insured carried the required $\$800{,}000$ , it would have paid $33\%$ more premium for a recovery on this claim that is only $33\%$ larger. Without the clause, under-insuring would be free money on partial losses, and the rate per $\$1{,}000$ of stated value would have to be set as though every policy were under-insured.