Tutorials › CAS Exam 8 - Advanced Ratemaking › Defining the Prospective Premium Base

CAS Exam 8 · Experience Rating Plan Design · Tutorial 505 of 989

Defining the Prospective Premium Base

Determine the correct future period and premium base for an experience adjustment, including when the adjustment takes effect at renewal or midterm.

Intermediate 11 min read

What You'll Learn

  • Define the prospective premium base in relation to an experience adjustment
  • Distinguish future premium from historical premium and experience-period premium
  • Select the base for a renewal term with updated exposure and rates
  • Calculate a midterm base for the remaining policy period
  • Avoid confusing an annualized premium or installment with the premium for the applicable period
  • Align the adjustment with the policy period and effective date specified by the plan

Why the Prospective Premium Base Matters

An experience adjustment is applied to a premium amount for a specified future period. Selecting the correct amount is a distinct design decision: a historical premium may relate to the experience being evaluated, but it is not necessarily the premium to which the resulting adjustment applies. Likewise, the premium for a full annual term is not automatically the right base when the adjustment takes effect partway through a term.

The key is to identify the prospective period first, using the plan’s effective-date rule, and then determine the premium calculated for that same period before the experience adjustment. The calculation should reflect the exposure and rating basis applicable to that future period. A plan may apply at renewal, at a specified midterm date, or to a defined set of policies or rated risk units. The base follows that scope.

Definition: The prospective premium base is the premium amount, before the experience adjustment being calculated, that is attributable to the future policy period or portion of a policy period to which the adjustment applies. It is determined using the plan’s stated effective date, rated risk unit, and premium basis. It is not, merely by definition, the premium from the experience period or the annualized premium in force on the calculation date.

This definition does not decide which premium components are included in the base; that is a separate plan-design question. Here, assume each problem states the applicable premium amount or provides the information needed to calculate it. The task is to match that amount to the period affected by the adjustment.

A Consistent Selection Method

Use the following sequence before applying any experience adjustment. In particular, do not start with a convenient premium figure and infer the period afterward.

1
Identify the adjustment’s effective date.
Determine whether the plan applies at renewal, on a midterm date, or at another stated point.
2
Define the affected policy period.
State the start and end dates, and identify whether the adjustment applies to a full term or only the remaining portion.
3
Calculate the premium for that same period.
Use the applicable prospective exposure and rating basis. If a problem assumes a flat annualized premium and pro rata time allocation, apply the period fraction.
4
Apply the adjustment to the selected base.
Keep the base and adjusted amount distinct, and check that the adjustment has not been applied to a different time period.

Under a flat-rate, pro rata assumption, an annualized premium \(P_{\text{ann}}\) for \(t\) months of coverage corresponds to a period premium \(P_t\) of:

$$ P_t=P_{\text{ann}}\frac{t}{12}. $$

This is a time-allocation rule, not a universal rule for all contracts. It is appropriate only when the problem specifies or supports a flat annualized premium and pro rata allocation. If the premium is explicitly given for the affected term, use that amount; if the contract uses a different calculation basis, follow that basis instead.

Justification: With a constant annualized premium rate and coverage accruing uniformly over time, each month represents \(1/12\) of the annual premium. Thus \(t\) months represent \(t/12\) of that amount. An experience adjustment for those \(t\) months should therefore use \(P_{\text{ann}}t/12\), not the full annualized amount. Applying the adjustment to the full amount would include premium for months outside the stated prospective period.

Renewal Bases

When an adjustment takes effect at renewal, the relevant period is ordinarily the new policy term identified by the plan—not the expiring term whose losses were used in the experience calculation. The renewal base should reflect the premium calculated for the renewed risk under the prospective rating basis. A prior-term premium may be useful background, but it does not replace the new-term calculation.

Worked Example: Renewal With Updated Exposure and Rates

A hypothetical commercial policy renews for a one-year term on January 1. Its experience adjustment applies to the renewal term. Before adjustment, the renewal rating schedule charges $220 per unit for 130 units in one category and $180 per unit for 75 units in another. The expiring term’s premium was $39,200. The plan’s experience adjustment factor for the renewal is 1.06. Find the renewal base and adjusted premium.

Method. Calculate the unadjusted premium for the new one-year term, then apply the factor to that amount. The expiring premium is not the base simply because it is known.

The first category contributes \(130 \times \$220=\$28{,}600\). The second contributes \(75 \times \$180=\$13{,}500\). Therefore the new-term base is:

$$ B=\$28{,}600+\$13{,}500=\$42{,}100. $$

Applying the stated factor gives:

$$ P_{\text{adjusted}}=1.06(\$42{,}100)=\$44{,}626. $$

The base is $42,100, and the adjusted renewal premium is $44,626. The result is higher than the $39,200 expiring premium because both the prospective exposure and the renewal rates differ. The common mistake avoided here is applying the factor to the expiring premium instead of recalculating the premium for the future term.

A renewal date also defines a boundary. If a plan applies only to the term beginning on that date, premiums for separate policies with different renewal dates do not automatically belong in the same base. The plan’s stated rated risk unit and effective-date scope determine which policies or terms are included.

Midterm Bases

If an adjustment takes effect during a policy term, first determine whether it applies only to the remaining coverage period or to some other explicitly defined period. In a remaining-term design, the base is the premium attributable to coverage after the effective date. Premium already attributable to elapsed months is outside that prospective interval.

A midterm calculation may need to include changes that are effective during the remaining period. For example, if an exposure change is rated at the same time as the adjustment, calculate the unadjusted premium for the remaining term using the post-change exposure. Do not use an amount for the old exposure and then silently treat it as the new prospective base.

Worked Example: Applying an Adjustment to the Remaining Term

A hypothetical policy runs from January 1 through December 31. On July 1, an experience adjustment factor of 0.95 takes effect through December 31. For July through December, the annualized premium for the existing exposure is $62,400. An exposure added on July 1 has an annualized premium of $16,800 for the same six-month remaining period. Assume flat annualized premiums and pro rata allocation. Find the base and adjusted premium for July through December.

Method. Calculate each prospective premium for six months, add them to obtain the remaining-term base, and then apply the factor.

The six-month fraction is \(6/12=0.5\). The existing exposure contributes:

$$ \$62{,}400(0.5)=\$31{,}200. $$

The added exposure contributes:

$$ \$16{,}800(0.5)=\$8{,}400. $$

Thus the base for the affected period is:

$$ B=\$31{,}200+\$8{,}400=\$39{,}600. $$

The adjusted amount is:

$$ P_{\text{adjusted}}=0.95(\$39{,}600)=\$37{,}620. $$

The July–December base is $39,600, and the adjusted amount is $37,620. The common mistake is to apply the factor to the combined annualized premium of $79,200. That amount describes a full year at the stated annualized rates, whereas the adjustment in this problem applies to six months.

Worked Example: Separating an Elapsed Term Portion From a Midterm Base

A hypothetical policy runs from July 1 through the following June 30. The premium charged for July through December was $25,000. On January 1, an experience adjustment of 1.10 applies only to the remaining six months. The unadjusted annualized premium for the January–June exposure is $56,000. Assume flat annualized premium and pro rata allocation. Find the base and adjusted amount for the period affected by the adjustment.

Method. Use only the unadjusted premium for January through June. The $25,000 already charged relates to the elapsed part of the policy term.

The remaining period is six months, so its unadjusted premium is:

$$ B=\$56{,}000\frac{6}{12}=\$28{,}000. $$

The adjustment applies to that base:

$$ P_{\text{adjusted}}=1.10(\$28{,}000)=\$30{,}800. $$

The base is $28,000, and the adjusted amount is $30,800. Adding the elapsed-period premium before applying the factor would produce \(1.10(\$25{,}000+\$28{,}000)=\$58{,}300\), which incorrectly adjusts premium for coverage before January 1.

Keep Period, Scope, and Amount Together

The prospective period and the premium amount are a matched pair. A correct amount for the wrong period is still the wrong base. For an account with staggered renewal dates, for example, a January renewal adjustment may apply to the January term only, while a separate policy renewing later remains outside that adjustment until its applicable date—unless the plan explicitly defines a different scope.

The same discipline prevents confusion between a term premium and the timing of cash collection. If a policy’s premium is billed in installments, an installment is a payment due on a billing schedule; it is not automatically the premium base for an experience adjustment. Use the premium amount for the affected period as defined by the plan, rather than substituting the next invoice amount.

Worked Example: A Renewal Applying to One of Two Policy Terms

A hypothetical account has two separately dated policies. Policy A renews on January 1 with an unadjusted one-year renewal premium of $22,000. Policy B renews on June 1 with a one-year premium of $30,000. The plan states that a factor of 1.10 applies on each policy’s renewal date to that policy’s new term only. Find the January adjusted premium and the combined premium for the two new terms after both policies have renewed.

Method. Apply the January factor to Policy A’s January renewal base only. Apply it to Policy B only when Policy B reaches its June renewal.

On January 1, Policy A’s base is $22,000, so its adjusted premium is:

$$ \$22{,}000(1.10)=\$24{,}200. $$

On June 1, Policy B’s separate renewal base is $30,000, and its adjusted premium is:

$$ \$30{,}000(1.10)=\$33{,}000. $$

After both renewals, the combined adjusted premium for the two new terms is:

$$ \$24{,}200+\$33{,}000=\$57{,}200. $$

The January adjustment base is $22,000, not $52,000. The combined amount after both renewals is $57,200. The key is that the plan explicitly applies separately at each policy’s renewal; it does not turn the January base into the total premium for every policy on the account.

Common Exam Traps

  • Using historical premium as the prospective base. The experience period supplies information for the adjustment; it does not determine the future premium amount by itself.
  • Applying a midterm adjustment to a full annualized amount. Check whether the adjustment applies to a full year or only the remaining months.
  • Using the old renewal premium after prospective exposure changes. Recalculate the future-term premium when the problem gives updated exposure or rates.
  • Combining policies without checking scope. A common account does not by itself establish that every policy belongs in the same adjustment base.
  • Treating an installment as the base. Match the amount to the coverage period, not to the billing date or cash amount due.
Key takeaway: State the adjustment’s effective date and affected period before selecting a premium figure. Then calculate the unadjusted premium for exactly that period and scope, and apply the experience adjustment only to that base.

Check Your Understanding

For each problem, identify the prospective base before applying the stated factor. Assume pro rata allocation only where the problem specifies it.

  1. A policy renews for 9 months with an unadjusted annualized premium of $48,000. The renewal adjustment factor is 1.04, and the plan applies to the entire 9-month term. What are the base and adjusted premium? (Answer: Base $36,000; adjusted premium $37,440.)
  2. A policy runs from April 1 through March 31. On October 1, a factor of 0.92 applies to the remaining six months. The unadjusted annualized premium for that remaining exposure is $70,000, with flat pro rata allocation. What are the base and adjusted amount? (Answer: Base $35,000; adjusted amount $32,200.)
  3. At renewal, a one-year policy has 140 units rated at $260 each and 60 units rated at $190 each. The adjustment factor is 1.03. Calculate the renewal base and adjusted premium. (Answer: Base $47,800; adjusted premium $49,234.)
  4. An account has two policies. A January renewal has an unadjusted one-year premium of $22,000, and a June renewal has an unadjusted one-year premium of $30,000. A factor of 1.10 applies separately at each policy’s renewal. What is the total adjusted premium for the two new terms after both have renewed? (Answer: $57,200.)
  5. A midterm adjustment factor of 1.08 applies for July through December. The unadjusted premium attributable to the existing exposure for those six months is $27,600, and a midterm exposure change adds another $5,400 for the same period. The premium already charged for January through June is $24,000. Find the prospective base and adjusted amount. (Answer: Base $33,000; adjusted amount $35,640.)
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