Deductible Change in a Prior-Approval Rate Filing
Prairie Mutual writes personal auto liability in a single state. Its last filing produced $12.0 million of earned premium; incurred losses were $7.8 million and fixed underwriting expenses $2.4 million. Variable expenses (commission and premium tax) run 12% of premium. Loss costs trend +6% per year, and the proposed rates will be in effect for policies written roughly two years after the average date of loss in the experience period. The company also intends to raise the mandatory deductible from $500 to $1,000; its consulting actuary estimates this will cut losses by 8%, while the corresponding deductible credit reduces premium by 10%. The experience contains 1,450 claims against a full-credibility standard of 1,082 claims. The state requires prior approval and imposes a 60% minimum loss ratio.
1. Compute the indicated overall rate-level change, being explicit about how the deductible change enters the calculation.
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Step 1 - trend losses to the new rate level. 7.8 x 1.06^2 = 7.8 x 1.1236 = $8.764M.
Step 2 - apply the deductible effect. 8.764 x 0.92 = $8.063M.
Step 3 - permissible loss ratio. 1 - 0.12 (variable) - 2.4/12.0 (fixed) = 1 - 0.12 - 0.20 = 0.68.
Step 4 - required premium. 8.063 / 0.68 = $11.857M.
Step 5 - premium available at current rates under the new deductible. 12.0 x 0.90 = $10.800M.
Indicated change = 11.857 / 10.800 - 1 = +9.8%.
The trap is to stop at Step 4 and divide by the old $12.0M premium, which gives 11.857/12.0 - 1 = -1.2%. That figure is the indication if the deductible were unchanged (it is 12.888/12.0 - 1 = +7.4% before the deductible factor). Once the 10% credit is given, premium falls 10% while losses fall only 8%, so the file must carry an additional factor of 0.92/0.90 = 1.0222 on top of the +7.4%: 1.074 x 1.0222 = 1.098. The credit is two points more generous than the loss saving it is supposed to reflect.
2. The CEO wants to file for +12%. Using your answer above, state what +12% would imply about the loss ratio, and identify the specific items in the calculation you would re-examine before supporting or opposing it.
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What +12% buys. A 12% change applied to the post-credit premium base gives 10.8 x 1.12 = $12.096M, hence a projected loss ratio of 8.063/12.096 = 66.7%, about 1.3 points below the 0.68 target, or roughly $0.24M of redundant premium. The filed ratio still clears the 60% regulatory floor, but a 12% increase on a -1.2%-style indication invites a disapproval and a lengthy hearing.
Items to re-examine, in order of leverage:
- Trend period. Two years assumes policies written exactly two years past the average loss date. If the rates take effect mid-year the period is closer to 2.5 years, adding about 3% to the indication - the single largest swing item.
- Fixed expense circularity. The 0.20 fixed ratio was measured on $12.0M. Re-solving on the target premium iterates to about $11.89M and adds only ~0.3%, so it does not justify 12%; watch that it is not double-counted.
- Deductible support. The 10% credit and 8% loss saving must come from the company's own deductible relativity study, not a rule of thumb.
- Credibility. 1,450 claims exceeds the 1,082 standard, so frequency is fully credible (1,082 = (1.645/0.05)^2, the 5%/90% standard). Severity is not separately tested and is where the risk sits.
- Trend source. Confirm the 6% is fitted to this book and reflects current severity, not a stale industry index.
3. Beyond the arithmetic, what insurance-principle and regulatory concerns does a deductible increase from $500 to $1,000 raise, and how should they influence the filing?
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Adverse selection. Raising the mandatory deductible forces every policyholder to self-insure the first $1,000. Low-frequency insureds gain most from the offsetting credit and stay; high-frequency insureds lose most and shop elsewhere, so the retained book becomes worse than the one used to set the credit. That is precisely why a credit larger than the loss saving (10% vs 8%) is dangerous: it under-prices retention for the risks that leave and over-prices it for the risks that stay.
Moral hazard and claim suppression. A higher deductible reduces small-claim frequency, which is a real loss saving, but it also shifts small losses into the policyholder's hands, encourages late reporting and inflates the average severity of what remains. The 8% estimate should be split into a frequency effect and a severity effect.
Regulatory review. In a prior-approval state the department will test the deductible relativity against filed support and against the effect on the minimum loss ratio. A credit that raises the loss ratio while the level indication falls will be read as rate inadequacy hidden inside an optional coverage change, and may be disapproved even though the overall level is defensible.
Practical response. File the deductible change with its own supporting exhibit, keep the credit no larger than the loss saving it reflects, and disclose the expected retention by deductible tier rather than assuming the existing distribution survives.