Combined Ratio

Combined Ratio is the sum of the loss and LAE ratio and the underwriting expense ratio — the share of premium consumed by claims and the cost of doing business. A combined ratio below $100\%$ means the book is profitable before investment income; above $100\%$ means underwriting is losing money.

$\text{Combined Ratio} = \frac{L + \text{LAE}}{\text{Earned Premium}} + \frac{\text{UW Expenses}}{\text{Written Premium}}$

$\text{Operating Ratio} = \text{Combined Ratio} - \text{Investment Income Ratio}$

The two terms use different denominators. The loss and LAE ratio is on earned premium (losses are incurred as coverage is provided); the expense ratio is conventionally on written premium (commissions and taxes are incurred when the policy is written). This is the "trade basis" combined ratio used in U.S. statutory reporting. A financial basis combined ratio puts both on earned premium. The two diverge whenever the book is growing or shrinking, so the basis must be stated.
Because it excludes investment income, a combined ratio above $100\%$ is not automatically unprofitable. Long-tail lines hold premium for years before paying claims, so they can sustain combined ratios well above $100\%$ ; short-tail lines have little float and need combined ratios below $100\%$ .
The target combined ratio implied by a ratemaking analysis is $1 - Q_T$ , where $Q_T$ is the target underwriting profit provision. A $5\%$ profit provision implies a $95\%$ target combined ratio.
As a reserving diagnostic, a combined ratio that drifts down across successive Accident Years at the same maturity may reflect genuine improvement — or under-reserving that later development will reverse (see Reserve Adequacy).

Trade Basis vs. Financial Basis An insurer reports earned premium $\$40{,}000{,}000$ , written premium $\$46{,}000{,}000$ , incurred losses and LAE $\$29{,}200{,}000$ , and underwriting expenses $\$12{,}420{,}000$ .

Calculate the combined ratio on both bases.

Answer Trade basis — losses on earned, expenses on written:

$\frac{\$29{,}200{,}000}{\$40{,}000{,}000} + \frac{\$12{,}420{,}000}{\$46{,}000{,}000} = 0.730 + 0.270 = 100.0\%$

Financial basis — both on earned:

$\frac{\$29{,}200{,}000}{\$40{,}000{,}000} + \frac{\$12{,}420{,}000}{\$40{,}000{,}000} = 0.730 + 0.3105 = 104.1\%$

The book is growing ( $\$46$ M written vs. $\$40$ M earned), so the trade basis spreads acquisition costs over a larger denominator and flatters the result by $4.1$ points. Growing insurers look better on a trade basis; shrinking ones look worse.