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Insurer Performance & Profit

Note Section 4.1 • Reading time: ~5 mins

Ultimate Loss Components

Ultimate losses represent the total cost to settle all claims for a given period. They are estimated as:

Ultimate Losses=Reported Losses+IBNR\text{Ultimate Losses} = \text{Reported Losses} + \text{IBNR}

Where:

  • Reported Losses (Case Incurred): The sum of cumulative paid losses and current case outstanding. Reported Losses=Paid Losses+Case Outstanding\text{Reported Losses} = \text{Paid Losses} + \text{Case Outstanding}
  • IBNR (Incurred But Not Reported): Split into two distinct components:
    1. IBNYR (Incurred But Not Yet Reported): Also called Pure IBNR. Claims that have occurred but have not yet been reported to the insurer (due to reporting lags).
    2. IBNeR (Incurred But Not Enough Reported): Also called Case Development. Adjustments to reserves on claims that have already been reported but are not yet finalized.

Development characteristics by Aggregation Method

  • Report Year (RY) Aggregation: Because the report year cohort is fixed as soon as the year ends, there are no late-reported claims. Therefore, RY development consists only of IBNeR (case reserve development).
  • Accident Year (AY) Aggregation: Because claims can be reported years after the accident occurred, AY development must account for both IBNYR and IBNeR.

Key Actuarial & Financial Ratios

These metrics measure operating efficiency and profitability:

1. Frequency

The average number of claims per unit of exposure.

Frequency=Claim CountExposures\text{Frequency} = \frac{\text{Claim Count}}{\text{Exposures}}

2. Severity

The average cost per claim.

Severity=LossesClaim Count\text{Severity} = \frac{\text{Losses}}{\text{Claim Count}}

3. Pure Premium (Loss Cost)

The average loss cost per unit of exposure.

Pure Premium=Frequency×Severity=LossesExposures\text{Pure Premium} = \text{Frequency} \times \text{Severity} = \frac{\text{Losses}}{\text{Exposures}}

[!IMPORTANT] Despite the name, Pure Premium is not a premium; it is the historical average loss cost.

4. Average Premium

The average rate charged per unit of exposure.

Average Premium=PremiumExposures\text{Average Premium} = \frac{\text{Premium}}{\text{Exposures}}

5. Loss Ratio (LR)

The proportion of premium used to pay losses.

Loss Ratio=LossesPremium=Pure PremiumAverage Premium\text{Loss Ratio} = \frac{\text{Losses}}{\text{Premium}} = \frac{\text{Pure Premium}}{\text{Average Premium}}

6. Underwriting Expense Ratio (UW Ratio)

The portion of premium used to pay underwriting and acquisition expenses.

UW Expense Ratio=Underwriting ExpensesPremium\text{UW Expense Ratio} = \frac{\text{Underwriting Expenses}}{\text{Premium}}

7. Operating Expense Ratio (OER)

The total operating expense loading, including Loss Adjustment Expenses (LAE).

OER=UW Expense Ratio+LAE Ratio\text{OER} = \text{UW Expense Ratio} + \text{LAE Ratio}

8. Combined Ratio

The primary measure of underwriting profitability. A combined ratio under 100% indicates an underwriting profit.

Combined Ratio=Loss Ratio+LAE Ratio+UW Expense Ratio=Loss Ratio+OER\text{Combined Ratio} = \text{Loss Ratio} + \text{LAE Ratio} + \text{UW Expense Ratio} = \text{Loss Ratio} + \text{OER}

9. Underwriting Profit Margin

The portion of premium retained as profit before investment income.

Underwriting Profit Margin=1.0−Combined Ratio\text{Underwriting Profit Margin} = 1.0 - \text{Combined Ratio}