Experience Rating

Study guides: Exam 5, Exam 8, Exam GH-101

Experience Rating modifies an individual insured's manual premium prospectively, using its own past loss experience, weighted by credibility. The output is an experience modification factor (mod): above $1.0$ for worse-than-expected experience, below for better.

$M = Z \times \frac{A}{E} + (1 - Z)$

$\text{Modified Premium} = \text{Manual Premium} \times M$

$A$ is the insured's actual losses over the experience period and $E$ the losses expected for a risk of its size and class. A mod is therefore a relative measure: it says how this risk compares with the average risk already reflected in the manual rate.
Credibility rises with size. A small risk's mod stays near $1.0$ however good or bad its recent record, because a few claims say little; a large risk approaches $Z = 1$ and effectively self-rates.
Losses are capped at a per-claim limit before entering $A$ . A single catastrophic claim should not dominate a mod, and the split between primary (capped) and excess losses is the mechanism the NCCI workers compensation formula uses to weight frequency more heavily than severity — the theory being that frequency is more predictive of future experience than severity.
Experience rating is prospective: it uses a completed experience period (typically three years, excluding the most recent, incomplete one) to modify the coming policy's premium. Retrospective rating instead adjusts the current policy's premium after the fact.
It creates a real incentive for loss control, and an equally real incentive for claim suppression — paying small claims outside the policy to keep them out of the mod. Both are consequences of the same mechanism.
Order of application: schedule and experience modifications apply to the manual premium to give standard premium, which is then the base for a retro plan or a large-deductible programme.

Computing an Experience Modification An insured has expected losses $E = \$200{,}000$ , actual capped losses $A = \$280{,}000$ , and credibility $Z = 0.60$ . The manual premium is $\$100{,}000$ .

Compute the mod and the modified premium.
Answer
 $\begin{align*} M &= 0.60 \times \frac{\$280{,}000}{\$200{,}000} + 0.40 \\ &= 0.60 \times 1.40 + 0.40 \\ &= 0.84 + 0.40 \\ &= 1.24 \end{align*}$ 
$\text{Modified premium} = \$100{,}000 \times 1.24 = \$124{,}000$

The insured's raw loss ratio was $40\%$ worse than expected; credibility passes $60\%$ of that through, giving a $24\%$ surcharge. Had $Z$ been $0.25$ — a much smaller risk with the same relative experience — the mod would be $1.10$ and the surcharge only $10\%$ .

Why Losses Are Capped Two insureds in the same class each have $\$200{,}000$ of expected losses and $Z = 0.50$ . Over the experience period:

Insured A: $40$ claims totalling $\$300{,}000$ , largest claim $\$25{,}000$ .

Insured B: $4$ claims totalling $\$300{,}000$ , of which one is $\$250{,}000$ .

Compute the mods with and without a $\$50{,}000$ per-claim cap, and comment.
Answer Uncapped — both have $A = \$300{,}000$ :

$M = 0.50 \times 1.50 + 0.50 = 1.25 \text{ for both}$

Capped at $\$50{,}000$ — A is unaffected; B's large claim is cut to $\$50{,}000$ , so $A_B = \$100{,}000$ . Expected losses must be capped on the same basis; suppose the capped expectation is $\$150{,}000$ :
 $\begin{align*} M_A &= 0.50 \times \frac{300}{150} + 0.50 = 1.50 \\[4pt] M_B &= 0.50 \times \frac{100}{150} + 0.50 = 0.83 \end{align*}$ 
The uncapped calculation treats these two risks as identical. They are not: A has a frequency problem — forty claims where the class expects far fewer — which is persistent, controllable and highly predictive of next year. B had one bad accident, which is largely luck and says little about its future.

Capping is what lets the mod respond to the signal (frequency) rather than the noise (one severity outcome). It is the same reasoning that caps large losses in a class rate indication, applied at the level of the individual risk.