Individual Risk Rating

Study guides: Exam 8, Exam GI-301

Individual Risk Rating is the adjustment of one insured's premium away from the manual (class) rate, to reflect that risk's own characteristics or its own loss experience. It works either prospectively, through experience and schedule rating, or after the policy period, through retrospective rating and other loss-sensitive plans.

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

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

$A$ is the risk's actual (usually capped) losses — its own experience. $E$ is the losses expected for a risk of its class and size. $Z = E/(E + K)$ is the credibility, where $K$ is the Bühlmann ratio of expected process variance to variance of the hypothetical means, in units of expected loss. As the study note requires, $Z$ lies between 0 and 1 and never falls as $E$ grows, while $Z/E$ falls — so a loss of a given size moves a large risk's mod less than a small one's.
Why rate individually. No class is perfectly homogeneous: experience rating picks up the variance of the hypothetical means within a class. It improves equity, strengthens the incentive for loss control, and makes more risks acceptable to write. A mod is a prospective estimate of loss potential, not a charge-back for past losses. Bailey and Simon found that the more refined the class plan, the less credibility individual experience deserves.
The spectrum by size. Manual rating → schedule and experience modification → retrospective rating or large deductibles → loss rating and self-insurance. Each step moves more of the risk, and more of the premium's sensitivity to actual losses, onto the insured (Commercial Lines Rating).
Design features. A maximum single loss or a primary/excess split (the NCCI plan weights primary losses more heavily, since they signal frequency), minimum and maximum mods, the experience period, and rules against double-counting a feature through both a schedule credit and the mod.
Plan balance. If the mods actually written average below $1.00$ , manual rates must be loaded by an off-balance factor. Whether mods separate risks correctly is tested with the quintiles and efficiency tests — see Rating Plan.

Credibility Grows with Size A plan uses $Z = E/(E + K)$ with $K = \$50{,}000$ . Two risks in the same class both ran at $70\%$ of expected losses: a small risk with $E = \$10{,}000$ and $A = \$7{,}000$ , and a large risk with $E = \$500{,}000$ and $A = \$350{,}000$ . Compute both mods.
Answer
 $\begin{align*} M_{\text{small}} &= \frac{7{,}000 + 50{,}000}{10{,}000 + 50{,}000} \\ &= 0.950 \\[6pt] M_{\text{large}} &= \frac{350{,}000 + 50{,}000}{500{,}000 + 50{,}000} \\ &= 0.727 \end{align*}$ 
The credibilities are $Z = 10/60 = 0.167$ and $Z = 500/550 = 0.909$ . The same relative experience earns the small risk a $5\%$ credit and the large one a $27\%$ credit. The small risk's good year is mostly noise, whereas the large risk's volume makes its record a genuine signal about its hazard.

The Experience Rating Off-Balance Class rates are set so that total manual premium of $\$10$ M equals the required premium. On the business actually written, $\$4$ M of manual premium is below the eligibility threshold and unrated. $\$5$ M carries credit mods averaging $0.85$ , and $\$1$ M carries debit mods averaging $1.15$ . What happens to collected premium, and what is the fix?
Answer
 $\begin{align*} \bar{M} &= \frac{4.0(1.00) + 5.0(0.85) + 1.0(1.15)}{10.0} \\ &= \frac{9.40}{10.0} \\ &= 0.94 \\[6pt] \text{Off-balance factor} &= \frac{1}{0.94} \\ &= 1.064 \end{align*}$ 
The book collects $\$9.4$ M against a $\$10$ M need, which is a $6\%$ shortfall that no individual mod reveals. The manual rates must be loaded by $6.4\%$ so the plan collects the required premium. Mods can average below $1.00$ when debit-mod risks leave for competitors or the residual market, or because of plan features that discount some losses. The off-balance has to be measured and reflected in each rate review.