Considerations for Implementing Rates

Study guide: Exam 5

Considerations for Implementing Rates are the decisions that turn an indication into rates in force — how much to file, how to distribute it, what mechanism to use, and what to do when the full indication cannot be taken.

$\text{Base Rate}_{\text{new}} = \text{Base Rate}_{\text{current}} \times \frac{1 + \text{overall change}}{1 + \text{change in average rate differential}}$

Non-pricing levers. Werner's central point is that rate adequacy is not only achieved through rate. Where a full increase is unavailable, the same gap can be closed by:

reducing expenses — fixed or variable;
tightening underwriting criteria or non-renewing policies whose premium is grossly inadequate;
changing coverage — raising deductibles, lowering sub-limits, adding exclusions or restricting a peril;
shifting marketing away from the unprofitable segments;
better loss control — for example, medical management and return-to-work programmes in workers compensation.

Pricing mechanics.

The overall change is implemented through the rating algorithm, normally as a base rate adjustment, and must be off-balanced against any simultaneous change in relativities so the two together deliver the intended effect.
A minimum premium and expense fees interact with the base rate; a percentage change to the base does not flow through evenly to policies sitting at the minimum.
Capping limits how much premium can move: a cap on the change for any level of a rating variable is made up by adjusting the base rate and the other relativities, and a premium transition rule caps any one renewal's change (at $15\%$ , an insured due $+20\%$ gets $+15\%$ now and $1.20/1.15 - 1 = 4.3\%$ at the next renewal). The base rate must reflect the transition — the actuary decides whether the target average premium is reached over the whole period or by its end — and long transitions risk overlapping the next rate change.

Practical constraints. Regulatory filing and approval, systems changes when the structure of the rating algorithm changes, and communication of the expected effect to management, regulators and the sales and customer-service functions all stand between the analysis and the proposed effective date — and the trend period runs forward to the policies written from that date.

Phasing a Large Increase The indication is $+20\%$ . The insurer judges that a single $+20\%$ would trigger regulatory scrutiny and heavy non-renewal, and decides to phase it over two annual filings.

What second-year change reaches the same level, and what does the delay cost?

Answer Taking $+10\%$ now, the residual required is

$\frac{1.20}{1.10} - 1 = +9.1\%$

so $+10\%$ followed by $+9.1\%$ reaches the same cumulative level.

The cost of phasing is a full year written at an inadequate rate. If the book earns $\$40{,}000{,}000$ at the $+10\%$ level, the indicated level needs $9.1\%$ more, so the deficiency is roughly

$\$40{,}000{,}000 \times 0.0909 \approx \$3{,}640{,}000$

That is a real, quantified cost of the decision, and the reason phasing should be paired with non-pricing action — tightening underwriting in the worst segments recovers part of the gap without a filing.

Off-Balancing a Class Revision An insurer's overall indication is $+6.0\%$ . It is also revising class relativities; applied to the current distribution of exposures, the new relativities alone would produce $+3.5\%$ of premium. The current base rate is $\$480$ .

Compute the new base rate.
Answer
 $\begin{align*} \text{Off-balance factor} &= \frac{1.060}{1.035} \\ &= 1.0242 \\[4pt] \text{New base rate} &= \$480 \times 1.0242 \\ &= \$491.62 \end{align*}$ 
Check: $1.0242 \times 1.035 = 1.060 \;\checkmark$ .

Applying $+6.0\%$ to the base rate and the new relativities would deliver $1.06 \times 1.035 = +9.7\%$ — three and a half points more than the analysis called for, and distributed unevenly across classes.

One further check belongs here: the off-balance is computed on the current in-force distribution, which assumes the rate change will not alter the portfolio. If the relativity change is large enough to shift the mix — insureds receiving large increases non-renew — the realized average premium change may differ from $+6.0\%$ , and if the risks that leave are not equally profitable, the shift affects the adequacy of the overall rates.