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Earned and Written Premium Bases for Expense Ratios

Calculate expense ratios on earned and written premium bases, and select and interpret each denominator consistently with the expense timing and period being measured.

Intermediate 11 min read

What You'll Learn

  • Distinguish written premium from the portion earned as coverage is provided
  • Calculate expense ratios using each premium basis
  • Match expense recognition and premium measurement periods
  • Explain how growth or decline in premium changes the ratio comparison
  • Identify denominator mismatches and interpret the resulting distortion

Why the Premium Denominator Matters

An expense ratio expresses expenses relative to a premium measure. The same expense amount can produce different ratios depending on whether the denominator is written premium or earned premium. The distinction matters because written premium is generally recorded when a policy is issued or renewed, while earned premium is recognized as insurance coverage is provided. A ratio is interpretable only when its premium basis, expense recognition, and measurement period are clear.

For example, an insurer may incur an acquisition expense when a policy is written, even though the policy provides coverage over the following year. Dividing that expense by written premium describes expense relative to business written. Dividing it by earned premium in a short calendar period describes expense relative to the premium recognized in that period. Those are different measurements, not competing calculations of one uniquely defined ratio.

Definition: Written premium is premium recorded on policies written during a stated period, subject to the applicable accounting treatment for endorsements, cancellations, and other adjustments. Earned premium is the portion of written premium recognized as revenue for the coverage provided during a stated period. An expense ratio is a stated expense amount divided by a stated premium base. Always identify the expense amount, its recognition period, and whether the denominator is written or earned premium.

Calculating the Two Ratios

Let \(C_t\) be expenses recognized in period \(t\), \(P^W_t\) be written premium recorded in that period, and \(P^E_t\) be earned premium recognized in that period. When \(C_t\) is the same numerator in both calculations, define the period expense ratios as follows:

$$ R^W_t=\frac{C_t}{P^W_t}, \qquad R^E_t=\frac{C_t}{P^E_t}. $$

The superscript \(W\) identifies a written-premium basis; \(E\) identifies an earned-premium basis. These formulas do not determine which ratio is appropriate. That depends on the purpose of the measurement and the expense recognition convention. For instance, an expense reported when incurred may be compared with the period's written premium for a written-basis view. An expense measure intended to represent the cost of coverage provided during a period may instead be compared with earned premium for that same period.

A ratio using paid expenses is also possible, but it measures cash paid in the period rather than necessarily measuring expenses incurred in that period. Do not silently switch between paid and incurred expenses, or between written and earned premium. The numerator and denominator need to be stated explicitly.

Worked Example: Comparing Calendar-Year Bases

A hypothetical insurer writes two annual policies during 2025. A policy issued January 1 has written premium of $120,000. A policy issued July 1 has written premium of $240,000. Assume each policy earns premium uniformly over its 12-month term, with no cancellation or endorsement. The insurer recognizes $54,000 of expenses in calendar year 2025. Calculate the written-premium and earned-premium expense ratios for 2025.

Method. First calculate each premium base for the calendar year, then divide the same 2025 expense amount by each base. The uniform earning assumption means an annual policy earns one-twelfth of its premium per month.

Written premium. Both policies were written in 2025, so:

$$ P^W_{2025}=\$120{,}000+\$240{,}000=\$360{,}000. $$

Earned premium. The January policy is in force for all 12 months of 2025 and earns its full premium: \(12/12\times \$120{,}000=\$120{,}000\). The July policy is in force for 6 months of 2025 and earns \(6/12\times \$240{,}000=\$120{,}000\). Therefore:

$$ P^E_{2025}=\$120{,}000+\$120{,}000=\$240{,}000. $$

Written-premium ratio.

$$ R^W_{2025}=\frac{\$54{,}000}{\$360{,}000}=0.15=15.00\%. $$

Earned-premium ratio.

$$ R^E_{2025}=\frac{\$54{,}000}{\$240{,}000}=0.225=22.50\%. $$

Check and interpretation. Earned premium is $120,000 less than written premium because part of the July policy's coverage falls in 2026. With the same positive expense numerator and the smaller earned-premium denominator, the earned-basis ratio is larger. The common mistake is to call \( \$54{,}000/\$360{,}000=15.00\% \) an earned-premium ratio; it is the written-premium ratio.

Why the Ratios Differ

When both premium bases are positive and the same expense amount is used, their relationship follows directly from the definitions. Substitute \(R^W_t=C_t/P^W_t\) into the right-hand side below:

$$ R^E_t =\frac{C_t}{P^E_t} =\frac{C_t}{P^W_t}\frac{P^W_t}{P^E_t} =R^W_t\frac{P^W_t}{P^E_t}. $$

Thus, if written premium exceeds earned premium, then \(R^E_t\) exceeds \(R^W_t\), provided \(C_t\) is positive and common to both ratios. If earned premium exceeds written premium, the direction reverses. Equal premium bases give equal ratios. This is an arithmetic relationship, not evidence that one basis is inherently more accurate.

For policies with level premium earned uniformly over a 12-month term, a useful special case arises when policies are written evenly throughout each of two successive calendar years. Half of the current year's written premium is earned in that year, on average; the other half is earned in the next year. Half of the prior year's written premium is earned during the current year. Therefore:

$$ P^E_t=\frac{1}{2}P^W_t+\frac{1}{2}P^W_{t-1}. $$

This identity requires the stated conditions: uniform writing within each year, annual policies, level premium, straight-line earning, and no material cancellations or adjustments that change the pattern. It is not a general rule for every portfolio. A seasonal book, a different policy term, or a nonuniform earning pattern requires a direct earned-premium calculation.

Worked Example: Premium Growth and the Earned Ratio

A hypothetical insurer writes annual, level-premium policies uniformly throughout each year. There are no cancellations or adjustments, and premium is earned straight-line over 12 months. Written premium is $800,000 in 2024 and $1,200,000 in 2025. Expenses of $150,000 are recognized in 2025. Calculate the 2025 expense ratios on written and earned bases.

Method. Use the two-year earning identity under the stated uniform-writing assumptions, then use the same 2025 expense numerator for both ratios.

2025 earned premium. One-half of 2025 written premium and one-half of 2024 written premium are earned in 2025:

$$ P^E_{2025} =\frac{1}{2}(\$1{,}200{,}000)+\frac{1}{2}(\$800{,}000) =\$600{,}000+\$400{,}000 =\$1{,}000{,}000. $$

Written-premium ratio.

$$ R^W_{2025} =\frac{\$150{,}000}{\$1{,}200{,}000} =0.125 =12.50\%. $$

Earned-premium ratio.

$$ R^E_{2025} =\frac{\$150{,}000}{\$1{,}000{,}000} =0.15 =15.00\%. $$

Check and interpretation. Written premium grew by $400,000, so current-year written premium exceeds current-year earned premium by $200,000 under these assumptions. The factor relating the ratios is \(P^W_{2025}/P^E_{2025}=\$1{,}200{,}000/\$1{,}000{,}000=1.2\), and \(12.50\%\times1.2=15.00\%\). The common mistake is to apply the half-current-year rule alone and omit the earned portion of prior-year writings.

Expense Timing and the Intended Measurement

The premium basis should reflect what the ratio is intended to describe. A written-basis ratio is useful when the measure is deliberately tied to policies recorded as written in a period. An earned-basis ratio relates expenses recognized in a period to premium recognized for coverage provided in that period. But when expenses are concentrated at policy inception, a calendar-period earned ratio can be elevated early in the policy term and lower later, even if the total cost over the full term is unchanged.

The next example separates that timing effect from the total cost of a policy cohort. It assumes that an acquisition expense is recognized at issue; it does not assume that all expense categories follow the same timing.

Worked Example: Acquisition Expense Recognized at Issue

A hypothetical insurer writes one annual policy cohort on January 1 with total written premium of $400,000. It recognizes a $48,000 acquisition expense immediately, at issue. Premium is earned uniformly over the policy year, with no cancellation. Calculate the written-basis ratio at issue, the expense-to-earned-premium ratio for the first six months, and the full-year earned-basis ratio.

Method. Keep the expense recognition period explicit. The $48,000 is recognized at issue; it is not spread over the six-month or full-year periods unless the problem says to do so.

Written-basis ratio at issue.

$$ \frac{\$48{,}000}{\$400{,}000}=0.12=12.00\%. $$

First six months. Six months of coverage earn \(6/12\) of the premium:

$$ P^E_{\text{first six months}} =\frac{6}{12}(\$400{,}000)=\$200{,}000. $$

All $48,000 of acquisition expense was recognized at issue, so the expense-to-earned-premium ratio for that period is:

$$ \frac{\$48{,}000}{\$200{,}000}=0.24=24.00\%. $$

Full policy year. The full $400,000 premium is earned during the year. The expense was still recognized only once, at issue:

$$ \frac{\$48{,}000}{\$400{,}000}=0.12=12.00\%. $$

Check and interpretation. The first-six-month ratio is higher because the full acquisition expense is compared with only half the policy's premium. Over the full term, total earned premium equals written premium, so the ratio returns to 12.00%. The common mistake is to assume that an expense incurred at issue must be divided only by premium earned at issue; the correct denominator depends on the period and question being measured.

Common Denominator Traps

  • Using the wrong premium total. Written premium is not automatically earned premium for the same calendar year. Calculate the earned portion from the coverage periods or an explicitly applicable earning assumption.
  • Changing both numerator and denominator without labeling the result. A written-basis numerator and an earned-premium denominator can describe a deliberate measure, but it is not the same ratio as expenses incurred in the period divided by earned premium in that period.
  • Assuming the ratios must match. They match only when the premium bases match, or when the numerator is zero. Differences can result from premium growth, seasonality, policy terms, and expense timing.
  • Treating a special earning identity as universal. The half-current, half-prior formula depends on uniform annual writing and straight-line earning. If those assumptions fail, calculate the earned premium from the actual or stated earning pattern.
Key takeaway: Name the numerator and denominator before calculating an expense ratio. Use written premium to measure expenses relative to premium written, or earned premium to relate expenses to premium recognized for coverage provided. Explain any timing mismatch rather than treating the two ratios as interchangeable.

Check Your Understanding

For each problem, state the premium basis used and keep the expense recognition period clear.

  1. A hypothetical insurer writes two annual policies in one year: $90,000 on January 1 and $150,000 on October 1. Premium earns uniformly over 12 months. Calendar-year expenses are $24,000. Calculate written premium, earned premium, and both expense ratios. (Answer: Written premium = $240,000; earned premium = $127,500; written-basis ratio = 10.00%; earned-basis ratio = 18.82%.)
  2. A hypothetical portfolio has $500,000 of written premium in the prior year and $700,000 in the current year. Policies are annual, level-premium, and written uniformly throughout each year; premium earns straight-line, with no adjustments. Current-year expenses are $90,000. Calculate current-year earned premium and the two ratios. (Answer: Earned premium = $600,000; written-basis ratio = 12.86%; earned-basis ratio = 15.00%.)
  3. A hypothetical $240,000 annual policy is written on April 1. It earns uniformly over its 12-month term, and a $30,000 acquisition expense is recognized at issue. What is the policy's written-basis ratio, and what is the expense-to-earned-premium ratio for the first three months of coverage? (Answer: Written-basis ratio = 12.50%; first-three-month earned premium = $60,000; first-three-month ratio = 50.00%.)
  4. A hypothetical insurer reports $80,000 of expenses incurred during a year. Its written premium is $640,000 and earned premium is $500,000. Calculate both ratios and explain which is larger. (Answer: Written-basis ratio = 12.50%; earned-basis ratio = 16.00%; the earned-basis ratio is larger because its denominator is smaller.)
  5. A hypothetical annual-policy portfolio has $900,000 of written premium in each of two successive years. Policies are written uniformly, earn level premium straight-line, and have no cancellations. Current-year expenses are $108,000. Calculate current-year earned premium and both ratios; state whether the difference is due to premium growth. (Answer: Earned premium = $900,000; both ratios = 12.00%; there is no difference because written premium is level between the two years.)

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