Rate Change

Study guide: Exam 5

Rate Change is the percentage by which rates are altered. Two numbers must be kept distinct: the indicated change that falls out of the ratemaking analysis, and the selected (implemented) change actually filed after judgment, competitive and regulatory considerations.

$\text{Indicated Change} = \frac{\text{Indicated Rate}}{\text{Current Rate}} - 1$

$\text{Indicated Change} = \frac{\text{Projected Loss \& LAE Ratio} + \text{Fixed Expense Ratio}}{1 - V - Q} - 1$

The second form is the Loss Ratio Method indication with fixed expenses in the numerator: $V$ is the variable expense ratio and $Q$ the target underwriting profit provision. The Pure Premium Method reaches the same answer through an indicated rate per exposure.
The selected change may differ for reasons that are legitimate and must be documented: credibility weighting against a complement, regulatory caps, rate capping to limit policyholder disruption, competitive position, and retention economics.
An overall rate change is implemented through the rating algorithm — usually a base rate adjustment — and any simultaneous change to classification relativities must be off-balanced so the two together produce the intended overall effect, not the sum of both.
Every rate change enters the rate level index used to compute on-level premium in future analyses, so the history of changes (dates, magnitudes, and whether they applied to new business, renewals or in-force policies) is part of the ratemaking data.
A rate change also changes the mix: price-sensitive risks shop, so a large increase can worsen the remaining experience through adverse selection — an effect the indication itself does not capture.

Indicated vs. Selected Change A personal auto indication produces $+14.2\%$ . The state's largest competitor filed $+4\%$ last quarter; the regulator has informally signalled that increases above $10\%$ will draw a hearing; the book's retention is $88\%$ and each point of rate historically costs $0.4$ points of retention.

What should the actuary recommend and document?

Answer The indication is $+14.2\%$ and that number does not change — it is the estimate of the rate needed to cover expected costs and target profit, and it belongs in the filing.

A selected $+9.9\%$ is defensible, with the reasoning stated explicitly:

Filing under the $10\%$ threshold avoids a hearing that would delay the whole change by months, during which the book earns at the current inadequate level.

At the competitor's $+4\%$ , a $14\%$ increase would cost roughly $5.7$ points of retention and the shoppers who leave are disproportionately the better risks.

The shortfall is not abandoned: it is carried into the next filing, and the actuary should say so, together with the expected underwriting result at $+9.9\%$ .

What is not acceptable is quietly re-deriving the indication to make it come out at $9.9\%$ — adjusting the trend selection or the profit provision until the answer matches the desired filing. The CAS principles and actuarial standards require the indication and the departure from it to be separately identified.

Off-Balancing a Simultaneous Relativity Change An insurer's overall indication is $+8.0\%$ . At the same time it revises territory relativities; applied to the current book, the new relativities alone would produce $+3.0\%$ of premium.

What base rate change is needed?
Answer The relativity revision already delivers part of the increase, so the base rate must supply only the remainder — multiplicatively, not by subtraction:
 $\begin{align*} \text{Off-balance factor} &= \frac{1.080}{1.030} \\ &= 1.0485 \end{align*}$ 
The base rate rises $+4.85\%$ . Combined with the relativity change:

$1.0485 \times 1.030 = 1.080 \;\checkmark$

Taking $+8.0\%$ on the base rate and implementing the new relativities would deliver $1.08 \times 1.03 = +11.2\%$ — three points more than intended, arriving unevenly across territories. See Considerations for Implementing Rates.