Why Reconcile Inputs Before Using Them?
An overall rate indication can only be meaningful if its inputs describe compatible quantities. A loss estimate for a prospective period, a premium amount still at an old rate level, an expense measured per six-month policy, and a profit provision stated as a percentage of a different premium base may each be reasonable on its own. Used together without reconciliation, however, they do not describe one consistent portfolio or time period.
The purpose of reconciliation is not to select a new loss trend, expense assumption, or profit target. It is to verify how each selected input is defined and whether the adjustments already made to it match the intended use. This check is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
A useful record for each input is a short “basis statement.” For example: “losses are projected to the average date of the prospective period, in dollars per earned car-year” or “variable expense is 2.5% of premium at the current rate level.” A label such as “selected losses” or “expense provision” alone does not reveal enough to audit the input.
Three Dimensions of Consistency
Time period identifies when the experience occurred and when the selected value is intended to apply. Historical losses may be developed and trended to a future period; historical earned premium may be adjusted to a selected rate level. Those operations have different purposes. A loss trend does not, by itself, update premium to a new rate level, and an on-level premium adjustment does not trend losses for changes in claim costs.
Unit identifies the denominator or measurement basis. Examples include dollars per earned exposure, dollars per policy term, dollars per claim, or a percentage of premium. A per-term value cannot be treated as a per-year value unless the term length and exposure definition support that conversion. Likewise, a percentage of premium is incomplete unless the relevant premium base and its rate level are known.
Rate level identifies the prices represented by a premium amount. Historical earned premium may be adjusted to a common rate level before comparison with losses or expenses. Record whether a premium amount is historical as written, on-level to current rates, or otherwise projected. If an adjustment factor has already been applied, do not apply it again.
| Input | Questions to record |
|---|---|
| Losses | Which experience period? Developed to what maturity? Trended to what average date? Which exposure unit? |
| Premium | Earned or written? Which experience period? Adjusted to which rate level? Which exposure basis? |
| Expenses | Fixed or variable? Per what unit or percentage of which premium? At what cost level? |
| Profit or contingency provision | Expressed as dollars, per exposure, or a percentage? If a percentage, what premium base and rate level? |
Worked Reconciliation Method
The following sequence is a practical audit. It can expose a mismatch before calculations that use the inputs make that mismatch harder to see.
Specify the period, exposure unit, and premium rate level that the selected inputs are intended to represent.
Record whether the amount is observed, adjusted, or selected, and list each adjustment already applied.
Show the exposure or premium denominator. Do not silently equate policy terms with annual exposures or historical premium with on-level premium.
Confirm that required period or rate-level adjustments are present once—not zero times and not twice.
Only then compare, divide, or combine the inputs for their intended purpose.
Worked Examples
Worked Example: Separating Loss Trend From Premium On-Leveling
A hypothetical auto portfolio has $1,500,000 of losses from an experience period. The experience-period midpoint is 18 months before the intended prospective average date. Assume a constant annual loss trend of 4%, compounded annually. Earned premium for the same experience is $2,400,000; the supplied factor to adjust that premium to the current rate level is 1.075. There are 12,000 earned car-years. Reconcile the losses and premium to their intended bases and calculate the resulting loss ratio as a check.
Method: identify the separate adjustments and their target bases. The losses need a trend adjustment for 1.5 years. The premium needs its stated rate-level adjustment. The 4% loss trend is not applied to premium, and the 1.075 premium factor is not applied to losses.
The loss trend factor is:
Thus the projected losses are:
The on-level premium is:
Both totals refer to the same 12,000 earned car-years, but they have different adjustments: losses are trended to the prospective average date, while premium is on-leveled to current rates. As a diagnostic, the ratio of the adjusted totals is:
As a further unit check, projected losses per earned car-year are $1,590,894 / 12,000 = $132.57, and on-level premium per earned car-year is $2,580,000 / 12,000 = $215.00, rounded to cents. Their ratio is approximately 61.66% as well. Common mistake avoided: applying the premium on-level factor to losses or applying the loss trend factor to premium would mix distinct adjustments. The final check confirms that both adjusted totals use the same exposure count; it does not imply that the adjustments are interchangeable.
Worked Example: Converting Six-Month Policy Expenses to Annual Exposure Units
A hypothetical insurer reports $504,000 of fixed acquisition and servicing expenses for 14,400 fully earned six-month policy terms. Each term has $140 of earned premium. Reconcile the fixed expense and a 2.5% premium-based tax expense to an annual policy-year exposure basis.
Method: convert the number of policy terms to policy-years before calculating annual per-exposure amounts. Each six-month term represents one-half of a policy-year, so:
The fixed expense per six-month term is $504,000 / 14,400 = $35.00. On an annual policy-year basis, it is:
The total earned premium is:
The tax expense at 2.5% of that premium is $2,016,000 × 0.025 = $50,400. Expressed per policy-year, this is $50,400 / 7,200 = $7.00. As a cross-check, the tax per six-month term is $140 × 0.025 = $3.50; doubling for a full policy-year gives $7.00.
The reconciled amounts are therefore $70.00 of fixed expense per policy-year and $7.00 of tax expense per policy-year at the stated premium basis. Common mistake avoided: dividing $504,000 by 14,400 gives $35.00 per six-month term, not $35.00 per policy-year. Treating that term amount as annual would understate fixed expense per policy-year by half. The tax percentage is tied to premium, so its denominator and premium basis must remain visible.
Worked Example: Matching a Profit Provision to Its Premium Level
A hypothetical commercial portfolio has $3,200,000 of historical earned premium. A factor of 1.125 adjusts it to the current rate level. For a stated comparison, the profit provision is 4% of premium at the current rate level, and a separate contingency provision is selected as $6 per earned exposure. The portfolio has 8,000 earned exposures. Reconcile the dollar values without combining the provisions into an overall indication.
Method: translate each provision using its own stated basis. First calculate premium at the stated current rate level:
The profit provision on that premium base is:
The contingency provision is based on exposures rather than premium:
The resulting reconciled values are $144,000 for the stated profit provision and $48,000 for the stated contingency provision. They remain separate because they have different bases. If 4% were incorrectly applied to historical premium, the result would be $128,000, which is $16,000 below the provision on current-level premium. Common mistake avoided: using a percentage provision with a premium denominator at the wrong rate level. The calculation also shows why a per-exposure provision should not be converted using premium alone: its defined basis is the 8,000 exposures.
Why Consistent Bases Matter
A short algebraic check explains why unit mismatches can distort even familiar ratios. Suppose projected losses are \(L\) dollars and the premium on the intended basis is \(P\) dollars. Their loss ratio is \(L/P\). If both are converted from dollars to thousands, the ratio is unchanged:
But if only one amount is divided by 1,000, the ratio is multiplied or divided by 1,000. Similarly, a ratio may be arithmetically computable while conceptually invalid if its numerator and denominator refer to different experience periods or the premium has not been adjusted to the intended rate level. Arithmetic cannot repair an incompatible basis.
The same principle applies to provisions. A percentage such as 4% becomes a dollar amount only after a premium base is specified. A fixed amount per exposure becomes a total only after the exposure count and exposure definition are specified. Before using the result, verify that the base reflects the period and rate level relevant to the intended calculation.
Common Reconciliation Traps
- Confusing adjustment purposes. Trending losses for claim-cost change and on-leveling premium for rate changes are distinct operations. Confirm which adjustment belongs to each input.
- Mixing earned and written measures. Earned premium and written premium describe different timing bases. Do not substitute one for the other without establishing that the method and period call for it.
- Leaving the exposure unit implicit. “Per policy” could mean per term, per year, or per policy in force at a particular date. State the exact basis.
- Applying an adjustment twice. Trace the source of every factor and note whether it is already included in the selected value.
- Using a provision without its denominator. A percentage of historical premium is not automatically the same dollar amount as that percentage of on-level premium.
Check Your Understanding
For each problem, identify the relevant basis and complete the requested reconciliation.
- A hypothetical property portfolio has $900,000 of losses at an experience midpoint one year before the prospective average date. Annual loss trend is 5%, compounded annually. What are the trended losses? (Answer: $945,000.)
- A hypothetical book has $1,800,000 of earned premium and an on-level factor of 1.06. It has 9,000 earned exposures. Find the on-level premium per exposure. (Answer: $212.00 per exposure.)
- A hypothetical insurer incurs $360,000 of fixed expenses on 12,000 fully earned three-month policy terms. How many policy-years are represented, and what is fixed expense per policy-year? (Answer: 3,000 policy-years; $120.00 per policy-year.)
- A selected profit provision is 3.5% of current-level premium. Historical earned premium is $2,500,000 and the factor to current level is 1.08. Calculate the dollar provision on the current-level premium base. (Answer: $94,500.)
- A selected contingency provision is $4.50 per earned exposure for 6,400 exposures. Separately, the profit provision is 2% of $1,250,000 of on-level premium. Calculate each provision and state why they should not share a denominator. (Answer: contingency provision $28,800; profit provision $25,000; the first is based on exposures and the second on premium.)