Selecting Which Premium Components Are Adjustable

Why the Adjustable Base Matters

An experience adjustment changes a risk’s prospective premium in response to its experience. But the same adjustment factor can produce different charged premiums depending on which premium components it applies to. A plan may apply the factor to the entire prospective premium base, or only to a defined subset such as an experience-rated loss component. Components excluded from the adjustment remain at their prospective amounts.

This is a design choice, not an arithmetic detail. Applying the same factor to a larger base creates a larger dollar change. Therefore, a premium calculation should identify both the factor and the premium components to which it applies. The examples below use hypothetical insurance products and invented figures.

Definition: Let $P_0$ denote the prospective premium before an experience adjustment. Divide it into an adjustable component $A$ and a nonadjustable component $N$, so that $P_0=A+N$. If $R$ is the experience adjustment factor, applying it to the total base gives $P=RP_0$. Applying it only to the selected component gives $P=RA+N$. At $R=1$, both methods produce the prospective premium $P_0$.

The labels “adjustable” and “nonadjustable” describe the plan’s treatment of premium components; they do not prescribe which items must go in either group. Depending on the plan’s purpose and construction, the prospective base might include expected losses, expenses, taxes, assessments, or other amounts. A component should be included in $A$ only if the plan intends the experience factor to modify it. The rest belongs in $N$.

In the calculations that follow, $R$ is a multiplier: $R=1.10$ increases the applicable base by 10%, while $R=0.90$ decreases it by 10%. The examples treat $R$ as given or calculate it from a stated rule. They focus on the effect of choosing the adjustment base, rather than on setting plan parameters.

Two Premium Calculations

For a total-premium adjustment, the entire prospective premium changes in the same proportion:

P_{\text{total}}=R(A+N)=RP_0.

For a selected-component adjustment, only $A$ changes:

P_{\text{selected}}=RA+N.

The difference between these results is especially clear by subtracting the selected-component premium from the total-premium premium:

P_{\text{total}}-P_{\text{selected}} =R(A+N)-(RA+N) =(R-1)N.

Thus, if $R>1$, adjusting the total base produces a higher premium than adjusting only $A$, by $(R-1)N$. If $R<1$, the total-base premium is lower by $(1-R)N$. The results coincide when $R=1$ or $N=0$. This comparison assumes the same prospective components and the same factor in both calculations.

Worked Example: Applying a Debit to Two Different Bases

A hypothetical commercial policy has a prospective premium of $90,000. The plan designates $72,000 as adjustable and $18,000 as nonadjustable. The experience factor is $R=1.10$. Calculate the premium under both methods, then check the difference.

Method: calculate each premium using its stated adjustment base. First verify the decomposition: $A+N=\$72{,}000+\$18{,}000=\$90{,}000=P_0$.

Total-premium adjustment: Apply the factor to all $90,000:

P_{\text{total}}=1.10(\$90{,}000)=\$99{,}000.

Selected-component adjustment: Apply the factor to $72,000, then add the unchanged $18,000:

P_{\text{selected}}=1.10(\$72{,}000)+\$18{,}000 =\$79{,}200+\$18{,}000 =\$97{,}200.

Check: The difference is $\$99{,}000-\$97{,}200=\$1{,}800$. The formula gives $(R-1)N=0.10(\$18{,}000)=\$1{,}800$, as required. The common mistake is to multiply the full $90,000 by 1.10 even though $18,000 was specified as nonadjustable.

Component Choices and the Effective Premium Change

A component-only adjustment does not change the whole premium by the same percentage as $R$. If $A$ and $N$ are nonnegative and sum to $P_0$, the premium change is

P_{\text{selected}}-P_0=(R-1)A.

Relative to the original premium, the percentage change is therefore

\frac{P_{\text{selected}}-P_0}{P_0} =(R-1)\frac{A}{P_0}.

The ratio $A/P_0$ is the adjustable share of the prospective premium. For example, if 70% of the base is adjustable and the factor is 0.90, the premium decreases by $10\%\times70\%=7\%$, not 10%. By contrast, a total-premium adjustment changes the full premium by $R-1$, assuming no other premium changes.

A plan’s component definitions should be operational: the calculation should make clear what amounts are included in $A$, what amounts are included in $N$, and how the amounts are determined. Otherwise, two calculations using the same factor may still produce different results because they use different adjustment bases.

Worked Example: Separating Loss and Expense Components

A hypothetical policy has a $90,000 prospective premium consisting of $60,000 for an experience-rated loss component, $24,000 for expenses, and $6,000 for a fixed charge. The plan adjusts the loss component and $12,000 of the expenses; the remaining $12,000 of expenses and the $6,000 fixed charge are unchanged. The factor is $R=0.85$. Calculate both premiums and the percentage reduction from the prospective premium.

Method: identify the adjustable and unchanged amounts before applying the factor. The adjustable amount is $A=\$60{,}000+\$12{,}000=\$72{,}000$. The unchanged amount is $N=\$12{,}000+\$6{,}000=\$18{,}000$. Check that $A+N=\$90{,}000$.

Total-premium adjustment:

P_{\text{total}}=0.85(\$90{,}000)=\$76{,}500.

The dollar decrease is $\$90{,}000-\$76{,}500=\$13{,}500$, or $15\%$ of the prospective premium.

Selected-component adjustment:

P_{\text{selected}}=0.85(\$72{,}000)+\$18{,}000 =\$61{,}200+\$18{,}000 =\$79{,}200.

The dollar decrease is $\$90{,}000-\$79{,}200=\$10{,}800$. As a percentage of the prospective premium, that is $\$10{,}800/\$90{,}000=0.12$, or 12%. Check: the adjustable share is $\$72{,}000/\$90{,}000=0.80$; multiplying the 15% factor reduction by 80% gives a 12% premium reduction. The common mistake is to treat every expense as unchanged—or, conversely, to apply the factor to every expense—without following the stated component selection.

How the Choice Connects Experience to Premium

The adjustment base also determines how strongly a change in experience affects the charged premium. To show this connection, suppose a plan uses an experience factor of the form

$$ R(q)=1+Z(q-1), $$

where $q$ is the ratio of actual losses to expected losses for the experience period, and $Z$ is a fixed factor between 0 and 1. This is an illustrative linear rule, not a universal experience-rating formula. It assumes the ratio and $Z$ are defined for the same basis and that the resulting $R$ is used without additional limits or adjustments.

Substituting this rule into each premium calculation gives

P_{\text{total}}=P_0[1+Z(q-1)], \qquad P_{\text{selected}}=A[1+Z(q-1)]+N.

The following justification shows why selecting a smaller base reduces the premium’s response to a change in $q$. Hold $A$, $N$, and $Z$ fixed. For the total-premium method, subtract the premium at $q=1$ from the premium at $q$:

P_{\text{total}}(q)-P_{\text{total}}(1) =P_0[1+Z(q-1)]-P_0 =P_0Z(q-1).

For the selected-component method, the corresponding change is

P_{\text{selected}}(q)-P_{\text{selected}}(1) =A[1+Z(q-1)]+N-(A+N) =AZ(q-1).

The same experience departure $q-1$ is multiplied by $P_0Z$ in the first case and $AZ$ in the second. Since $A\leq P_0$ when $N\geq0$, the selected-component adjustment has no greater dollar response under these assumptions. This is a mathematical comparison, not a judgment that one design is always preferable.

Worked Example: Comparing Premium Response to a Change in Loss Experience

A hypothetical account has expected losses of $200,000. Its prospective premium is $125,000, divided into $80,000 adjustable and $45,000 nonadjustable. Use $R(q)=1+Z(q-1)$ with $Z=0.50$. Calculate the selected-component and total-premium charges when actual losses are first $150,000 and then $170,000. State the premium change under each method.

Method: calculate $q$, then $R$, then each premium. At $150,000 of actual losses,

q_1=\frac{\$150{,}000}{\$200{,}000}=0.75, \qquad R_1=1+0.50(0.75-1)=1-0.125=0.875.

The charges are

P_{\text{total},1}=0.875(\$125{,}000)=\$109{,}375,

P_{\text{selected},1}=0.875(\$80{,}000)+\$45{,}000 =\$70{,}000+\$45{,}000 =\$115{,}000.

At $170,000 of actual losses,

q_2=\frac{\$170{,}000}{\$200{,}000}=0.85, \qquad R_2=1+0.50(0.85-1)=1-0.075=0.925.

The new charges are

P_{\text{total},2}=0.925(\$125{,}000)=\$115{,}625,

P_{\text{selected},2}=0.925(\$80{,}000)+\$45{,}000 =\$74{,}000+\$45{,}000 =\$119{,}000.

Check: The total-premium charge rises by $\$115{,}625-\$109{,}375=\$6{,}250$; the selected-component charge rises by $\$119{,}000-\$115{,}000=\$4{,}000$. The change in the factor is $0.925-0.875=0.05$, so the expected premium changes are $0.05(\$125{,}000)=\$6{,}250$ and $0.05(\$80{,}000)=\$4{,}000$, respectively. A common mistake is to compare only the two factors and conclude that both premiums change by the same percentage of their full prospective premium.

Choosing and Communicating the Adjustment Base

The component choice should follow the plan’s intended treatment of premium, not a desire to make the arithmetic look simpler. A full-base adjustment links every included dollar to the experience factor. A selected-component adjustment links only the designated portion, while retaining the stated amounts of excluded components. In either case, the prospective premium at $R=1$ remains the reference amount.

When setting out a calculation, use this sequence:

State the prospective premium.
Identify $P_0$ and verify the amounts of its components sum to it.

Identify the adjustment base.
State which components make up $A$ and which remain in $N$, if the adjustment is component-specific.

Apply the factor to the correct amount.
Use $RP_0$ for a total-base adjustment or $RA+N$ for a selected-component adjustment.

Check against the reference and the stated design.
At $R=1$, the charge should equal $P_0$; any amount designated unchanged should not be multiplied by $R$.

The central exam trap is to focus on the numerical factor and overlook its base. Before calculating, translate the plan description into an equation. This makes the intended connection between experience and premium explicit and helps prevent a correct factor from being applied to the wrong dollars. This distinction is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.

Check Your Understanding

For each hypothetical plan, identify the adjustment base and calculate the requested charge. Dollar answers are to the cent where applicable.

A $48,000 prospective premium has $30,000 adjustable and $18,000 unchanged. With $R=1.12$, calculate the total-premium and selected-component charges. (Answer: $53,760 total-premium charge; $51,600 selected-component charge.)
A $200,000 prospective premium has $140,000 adjustable and $60,000 unchanged. With $R=0.92$, calculate both charges. (Answer: $184,000 total-premium charge; $188,800 selected-component charge.)
A plan uses $R(q)=1+0.25(q-1)$. Actual losses are $300,000 and expected losses are $250,000. If $A=\$90,000$ and $N=\$30,000$, calculate the factor and selected-component premium. (Answer: $q=1.20$, $R=1.05$, and premium $=\$124,500$.)
A $160,000 prospective premium has $100,000 adjustable and $60,000 unchanged. The factor is $R(q)=1+0.40(q-1)$; actual losses are $225,000 and expected losses are $250,000. Calculate the factor and the total-premium and selected-component charges. (Answer: $q=0.90$, $R=0.96$, $153,600 total-premium charge, and $156,000 selected-component charge.)
A $110,000 prospective premium has 55% of its base adjustable. With $R=1.08$, calculate the selected-component premium and compare its dollar increase with that under a total-premium adjustment. (Answer: $A=\$60,500$, $N=\$49,500$, selected-component premium $=\$114,840$, an increase of $4,840; total-premium increase $=\$8,800$.)

What You'll Learn