Loss Ratio

Study guide: Exam 5

Loss Ratio is losses (usually with LAE) divided by earned premium — the share of premium consumed by claims, and the central measure of rate adequacy.

$\text{Loss Ratio} = \frac{\text{Losses} + \text{LAE}}{\text{Earned Premium}}$

$\text{Loss Ratio} = \frac{\text{Pure Premium}}{\text{Average Premium}}$

The second identity is worth remembering: the loss ratio is the pure premium divided by the average premium, so the Loss Ratio Method and the Pure Premium Method are two views of the same quantity.
A loss ratio is only interpretable once its basis is stated. Accident Year or Calendar Year? Reported or ultimate? Premium at current rate level or as written? With or without LAE? Four binary choices give sixteen different numbers from one book, and comparisons across them are meaningless.
Rate adequacy is judged against the Permissible Loss Ratio, not against $100\%$ : a projected loss ratio above the PLR means rates are inadequate even when the book appears to be making money.
An immature accident-year loss ratio always understates the ultimate answer, and a calendar-year loss ratio contains prior-year reserve movements. Both are routinely quoted and both mislead if used for pricing.
As a reserving diagnostic, the loss ratio series across accident years at a fixed maturity should move smoothly. A break in the series is a signal — a rate change not accounted for, a mix shift, a change in case adequacy — and is the entry point to the analysis, not the conclusion.

Rate Adequacy Against the Permissible Loss Ratio An insurer projects ultimate losses and LAE of $\$715{,}000$ against trended on-level earned premium of $\$1{,}000{,}000$ . Variable expenses are $25\%$ of premium and the target underwriting profit provision is $5\%$ ; there are no fixed expenses.

Is the book adequately rated?
Answer
 $\begin{align*} \text{Loss ratio} &= \frac{\$715{,}000}{\$1{,}000{,}000} = 71.5\% \\[4pt] \text{PLR} &= 1 - 0.25 - 0.05 = 70.0\% \end{align*}$ 
$\text{Indicated change} = \frac{0.715}{0.700} - 1 = +2.1\%$

The book is running a $71.5\%$ loss ratio and needs $70.0\%$ — inadequate by $2.1\%$ , despite the loss ratio being comfortably below $100\%$ . Comparing a loss ratio to $100\%$ rather than to the PLR is one of the most common errors in reading insurance results.

The Same Book, Four Loss Ratios For accident year $2024$ an insurer reports: earned premium $\$10{,}000{,}000$ (rates rose $10\%$ on $1/1/2024$ , so the average rate level index is $1.05$ against a current level of $1.10$ ); reported losses $\$5{,}800{,}000$ at $12$ months; selected CDF $1.32$ ; LAE load $12\%$ of loss.

Compute the loss ratio on four bases and identify which one drives a rate decision.
Answer
 $\begin{align*} \text{(1) Reported, no LAE, as-written premium} &= \frac{\$5{,}800{,}000}{\$10{,}000{,}000} = 58.0\% \\[6pt] \text{(2) Ultimate, no LAE} &= \frac{\$5{,}800{,}000 \times 1.32}{\$10{,}000{,}000} = 76.6\% \\[6pt] \text{(3) Ultimate with LAE} &= \frac{\$7{,}656{,}000 \times 1.12}{\$10{,}000{,}000} = 85.7\% \\[6pt] \text{(4) Ultimate, LAE, on-level premium} &= \frac{\$8{,}574{,}700}{\$10{,}476{,}200} = 81.8\% \end{align*}$ 
(On-level premium is $\$10{,}000{,}000 \times 1.10/1.05 = \$10{,}476{,}200$ .)

The spread between $58.0\%$ and $85.7\%$ is nearly thirty points, and every figure is arithmetically correct. Only (4) — ultimate losses including LAE, over premium at current rate level — answers "are today's rates adequate", and it is the number that goes into the indication. Figure (1) is the one most often quoted in a management report.