Determine Claim Rate for Breakeven in Insurance Portfolio

Quick Overview

Evaluates weather-insurance portfolio profitability from premiums, servicing, regulatory costs, and expected claims. Strong answers derive break-even claim rate, segment-selection rules, and incremental profit formulas.

Determine Claim Rate for Breakeven in Insurance Portfolio

Company: Capital One

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Onsite

##### Scenario Weather-insurance portfolio profitability. ##### Question Given: premium $30/month paid 12 months upfront, servicing cost $3/month, benefit cost $8 000/claim, regulatory cost $4/quarter plus $300 per claim. What claim rate yields breakeven? Four customer segments A–D have different cumulative claim risks. Which combination maximizes profit and why? After choosing segments, illustrate how adding B, C, and D changes profit compared with only A. ##### Hints Compute expected value per policy; select segments with positive expected profit.

Overview: Evaluates weather-insurance portfolio profitability from premiums, servicing, regulatory costs, and expected claims. Strong answers derive break-even claim rate, segment-selection rules, and incremental profit formulas.

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Jul 12, 2025
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Weather-Insurance Portfolio Profitability

You price a 12-month weather insurance policy. Customers pay premiums upfront for the year. Each policy can generate regulatory and servicing costs, and possibly a claim. Treat the claim rate as the expected number of claims per policy-year; if at most one claim occurs, this equals the annual claim probability.

Inputs:

  • Premium: $30 per month, paid for 12 months upfront
  • Servicing cost: $3 per month
  • Benefit per claim: $8,000
  • Regulatory cost: 4perquarterplus4 per quarter plus 300 per claim

Constraints & Assumptions

  • Costs are per policy unless stated otherwise.
  • Ignore time value of money.
  • Regulatory fixed cost is $16 per policy-year.
  • Claim rate can be interpreted as expected claims per policy-year.

Clarifying Questions to Ask Guidance

  • Are claim rates independent across customers and segments?
  • Are policy counts by segment available?
  • Are there capital, diversification, regulatory, or fairness constraints on segment selection?
  • Is the goal expected profit, risk-adjusted profit, or break-even pricing?

Part 1 - Breakeven Claim Rate

What claim rate yields break-even on a per-policy annual basis?

What This Part Should Cover Guidance

  • Compute annual premium revenue, annual servicing cost, fixed regulatory cost, and per-claim cost.
  • Write expected profit as a function of claim rate.
  • Solve for the claim rate where expected profit equals zero.
  • Interpret the claim rate as annual probability if at most one claim occurs.

Part 2 - Segment Selection

Four customer segments A-D have different annual claim rates. Which segment combination maximizes profit, and why?

What This Part Should Cover Guidance

  • Compute expected profit per policy for each segment using its claim rate.
  • Include segments with positive expected profit, subject to constraints.
  • Exclude segments whose claim rate exceeds the break-even threshold unless there are strategic or diversification reasons.
  • If policy counts are available, multiply per-policy profit by segment size.

Part 3 - Incremental Segment Impact

After choosing the optimal set, illustrate how adding B, C, and D changes profit compared with offering only to A.

What This Part Should Cover Guidance

  • Provide a general formula for per-policy and total profit by segment.
  • Show incremental profit from adding each segment.
  • Include a small numeric example to make the decision rule concrete.
  • Discuss risk and concentration, not only expected value.

Follow-up Questions Guidance

  • How would the break-even rate change if the premium increased?
  • How would you handle correlated weather claims across customers?
  • What risk metric would you monitor beyond expected profit?
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