Motor own-damage rate filing with a shifting distribution mix
You are the pricing actuary at a mid-sized Indian general insurer. The private-car own-damage (OD) portfolio wrote ₹4.2bn of premium in FY2024-25 and reported a loss ratio of 71%. The CFO notes three complications: a 14% rate increase was applied mid-year; 38% of policies now come through a digital aggregator whose loss ratio is 22 percentage points higher than the agency channel; and claims changed the total-loss settlement policy in October 2024, raising average severity by an estimated 9%. Exposure grew 15% while policy counts grew only 6%. You have 36 months of data by channel, vehicle-age band and sum-insured band. The CEO wants a 12% increase filed within three weeks because a competitor has raised rates. The product is file-and-use, so the filing needs an actuarial justification. The CFO also wants to preserve the aggregator relationship. Reserving has just flagged adverse development on the 2023 accident year.
1. Calculate an indicative rate change for the OD portfolio. Set out each adjustment you would make to the reported 71% loss ratio, the assumption behind it, and the resulting range.
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Start by converting the reported calendar-year loss ratio to a current-rate-level, forward-looking accident-year basis.
- On-level the premium. A 14% increase applied mid-year means the average earned rate level is roughly 7% below the current level. On-level earned premium = reported premium × 1.07, so the on-level loss ratio is 71% / 1.07 = 66.4%. If the increase was not uniform across channels, do this by channel.
- Project severity. The October total-loss change adds about 9% to severity, but it only affects part of the year. If it is fully in the current rate level, project losses by 1.09: 66.4% × 1.09 = 72.4%.
- Allow for claims inflation. If claims inflation is 7% and premium trend is 3%, add about 4% for the policy period: 75.3%.
- Allow for mix shift. If the aggregator share rose from 30% to 38% and the differential is 22 points, the mix effect is 0.08 × 22 = 1.8 points, giving 77.1%.
- Check large claims and IBNR. If the 71% includes a one-off large loss, remove it and load for a normal large-loss expectation. The 2023 adverse development suggests the earned loss ratio may be understated.
Now compare with a target loss ratio. With a 28% expense ratio and a 98% target combined ratio, the target loss ratio is 70%; for a 15% return on capital it may be nearer 65%. At a 66% target, indicated change = 77.1/66 − 1 = 16.8%. At a 70% target it is 10.1%. A defensible range is therefore 10–17%, with a point estimate around 14%. The CEO's 12% is inside the range but relies on a generous target and assumes no further aggregator mix shift. State the target loss ratio explicitly in the filing.
2. Explain how you would use credibility and segmentation to set differential rates for the aggregator channel, and what governance safeguards you would put in place.
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The aggregator differential should be priced from evidence, not from the raw 22-point gap. Build a frequency-severity GLM with channel, vehicle age, sum insured, vehicle type, geography and policy tenure. Channel may be correlated with sum insured, driver profile and policy tenure, so the marginal channel coefficient after other factors is the relevant one. Test interactions, for example channel × vehicle age, because aggregator customers may buy older vehicles.
Apply credibility weighting to cells with thin data. For a cell with expected claims count n and between-cell variance, use a Bühlmann-type weight; a simple practical rule is to require a minimum number of claims and to shrink the channel factor towards the portfolio factor when credibility is low. Do not create dozens of micro-segments that fit noise. Use out-of-sample validation and monitor stability over accident quarters.
Consider whether the differential is a risk factor or a cost factor. If the aggregator charges higher commission, recover it through a channel load in expenses rather than through the risk premium. If the behaviour is genuinely adverse, reflect it in underwriting rules and excesses as well as rate.
Governance: document the data, the model, the selected factors and the judgement. Have the model reviewed independently. Check that the filed rates are actuarially justified and not unfairly discriminatory. Monitor loss ratio by channel monthly and set a trigger for re-rating. Preserve the aggregator relationship by explaining that differential pricing protects the relationship from cross-subsidy, not by suppressing the evidence.
3. The CEO wants the 12% filed in three weeks. What are the principal risks of doing so and what would you recommend?
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The main risk is under-pricing. A 12% filing is at the low end of the 10–17% range, and it assumes the target loss ratio is 70% and that aggregator mix stabilises. If severity is 9% and claims inflation is 7%, the loss ratio could be 80% or more within 12 months. Adverse development on 2023 means the starting point may already be understated. A second risk is regulatory challenge: file-and-use does not remove the need for a credible actuarial basis, and a filing that ignores known severity changes is vulnerable.
A third risk is competitive: a competitor's increase does not prove the market rate is adequate. A fourth is distribution: a flat 12% may over-price the agency channel and under-price the aggregator, worsening selection.
Recommendation: file a base increase of 14–16%, with a channel differential that charges the aggregator for its excess experience and an underwriting rule for older vehicles. If the CEO insists on 12%, document the target loss ratio and the scenarios in which it fails, and propose a monitoring trigger for a further filing. Do not sign a justification that you do not believe. Put the uncertainty in the board paper and the filing. Separately, ask reserving for the 2023 accident-year range before the filing and reflect any strengthening in the rate indication.