Why Different Rates Are Not Automatically Unfair
Insurance rates need not be identical for every policyholder to be fair. Risks with different expected costs may reasonably receive different rates, provided the distinction is supported, applied consistently, and permitted under the governing rules. The difficult question is whether a rate difference reflects a meaningful difference in the risk being priced—or whether risks that are alike in relevant ways are being treated differently without a sound basis.
The word unfair discrimination has legal significance, but its precise meaning depends on the jurisdiction, product, and applicable rules. An actuarial review can identify unsupported differences and evaluate whether a classification is connected to expected costs. It cannot, by itself, decide every legal question. A conclusion about legality requires the applicable law and regulatory requirements.
“Similarly situated” is a crucial condition, not a casual description. A comparison is meaningful only after checking relevant differences such as coverage, limits, deductibles, exposure period, rating inputs, and applicable expenses. If those differ, a premium comparison may not isolate the treatment being examined. Conversely, risks with the same relevant characteristics should not receive different treatment merely because of a data, calculation, or implementation error.
What Makes a Rate Difference Supportable?
A cost-supported difference generally needs more than a plausible story. The actuary should be able to identify the rating distinction, show how it relates to expected costs, and assess whether the data and method are appropriate for the intended use. The result should also be applied as described in the rating plan. A factor that is reasonable in a model but implemented inconsistently can still produce unjustified differences in actual premiums.
For a simple illustration, suppose expected loss cost for group \(j\) is \(L_j\), fixed expense per policy is \(F\), and variable expenses are a proportion \(v\) of premium. Assume the same expense provisions apply to both groups, premiums are adequate on this basis, and there are no other adjustments. The indicated premium \(P_j\) satisfies \(P_j=L_j+F+vP_j\), so:
This model is deliberately simple; it is not a complete filing formula. Its value here is to make the comparison explicit. If the two groups have the same \(F\) and \(v\), then:
Thus, under these assumptions, a difference in indicated premium follows from a difference in expected loss cost. If the expected costs are equal, this model gives equal indicated premiums. A different result would need another supportable difference—such as a different expense provision—or further investigation. The equation does not establish that every observed cost difference is reliable or that a legally permissible distinction is automatically fair.
The justification is the premium balance itself: expected premium must cover expected losses, fixed expenses, and variable expenses. Moving the variable expense term to the left gives \(P_j(1-v)=L_j+F\); division by \(1-v\) yields the formula. Subtracting the two group formulas cancels the common fixed expense. If the expense assumptions differ, or if the product requires other provisions, that cancellation does not hold as written.
A Practical Review of a Questionable Difference
A disciplined review separates three questions: Are the risks genuinely comparable? Is the proposed distinction supported by appropriate cost evidence? Is the distinction applied correctly and allowed under the applicable rules? Evidence relevant to the second question may include exposure definitions, loss experience, model outputs, uncertainty, and the rationale for selecting the rating factor. The evidence should fit the decision being made; an observed difference alone does not prove a stable difference in expected costs.
Specify the coverage, policy period, relevant rating inputs, and treatment being compared. Do not treat different coverages or exposures as equivalent without adjustment.
Identify which expected cost component is believed to differ and how the rating distinction is intended to reflect that difference.
Check data definitions, methods, assumptions, uncertainty, and the conversion from indicated costs to charged rates. Recalculate key figures independently.
Confirm the factor is applied as documented and review the governing jurisdiction’s requirements before reaching a legal conclusion.
Worked Example: A Difference Supported by Expected Loss Cost
A hypothetical insurer compares two classes with the same coverage and expense provisions. Each class has 500 earned exposures. Over the observation period, Class A has $270,000 in losses and Class B has $330,000. Assume these data are appropriate for the comparison and the actuary’s selected prospective expected loss costs are the corresponding loss costs. Fixed expense is $75 per policy and variable expense is 10% of premium. Calculate the indicated premiums and assess the difference.
Method and assumptions. Calculate loss cost per exposure, then use \(P_j=(L_j+F)/(1-v)\). The example assumes equal exposure definitions, equal coverage, identical expenses, and no other premium components.
Step 1: Calculate loss costs. For Class A, \(L_A=\$270{,}000/500=\$540\) per exposure. For Class B, \(L_B=\$330{,}000/500=\$660\) per exposure. The difference is \(\$660-\$540=\$120\).
Step 2: Calculate Class A’s indicated premium. Add fixed expense: \(\$540+\$75=\$615\). The premium must also cover variable expenses equal to 10% of premium, so \(P_A=\$615/(1-0.10)=\$615/0.90=\$683.333\ldots\).
Step 3: Calculate Class B’s indicated premium. Add fixed expense: \(\$660+\$75=\$735\). Then \(P_B=\$735/0.90=\$816.666\ldots\).
Step 4: Compare and check. The indicated difference is \(\$816.666\ldots-\$683.333\ldots=\$133.333\ldots\). The formula also gives \(\$120/0.90=\$133.333\ldots\), confirming the calculation. Rounded to the nearest cent, the premiums are $683.33 and $816.67, a difference of $133.33.
Conclusion and common mistake avoided. Under the stated assumptions, the loss-cost difference supports a higher indicated premium for Class B. The common mistake is to use the $120 loss-cost difference as the final premium difference, ignoring variable expenses. This conclusion is conditional on the quality of the data and the assumptions; the arithmetic alone does not establish legal permissibility.
Worked Example: The Same Risks Receive Different Charges
A hypothetical rating system assigns two otherwise identical policyholders the same coverage, exposure, and rating inputs. Both have expected loss cost of $700, fixed expense of $80, and a 12% variable expense provision. The system charges one policyholder the base indicated premium and the other an additional 8% factor, although no cost or expense distinction has been documented. Calculate the difference and identify the actuarial concern.
Method and assumptions. First calculate the common indicated premium using \(P=(L+F)/(1-v)\). Apply the extra factor to that premium. Assume there is no separate documented adjustment or difference in policy terms.
Step 1: Calculate the common indicated premium. The amount before variable expenses is \(\$700+\$80=\$780\). Therefore, \(P=\$780/(1-0.12)=\$780/0.88=\$886.3636\ldots\).
Step 2: Calculate the second charge. An 8% increase is \(0.08\times \$886.3636\ldots=\$70.9090\ldots\). The adjusted charge is \(\$886.3636\ldots+\$70.9090\ldots=\$957.2727\ldots\).
Step 3: Compare and check. The charge difference is approximately $70.91, and \(\$886.36\times1.08=\$957.27\) to the nearest cent. The stipulated cost model indicates the same premium for both policyholders, so the extra factor is not supported by the stated cost information.
Conclusion and common mistake avoided. This is a potential unfair-discrimination concern requiring investigation, not a universal legal conclusion. The common mistake is to assume that a rating-system factor is justified merely because it is programmed into the system. The reviewer should verify the actual rules and investigate whether a legitimate difference was omitted from the problem’s assumptions or documentation.
Worked Example: A Frequency Difference Can Support Different Rates
A hypothetical product covers equipment with the same severity distribution in two risk groups. Expected claim severity is $5,000 in each group, but annual claim frequencies are 0.04 for Group A and 0.06 for Group B. Assume the frequency estimates are suitable prospective estimates, the groups have the same coverage and expenses, fixed expense is $40, and variable expense is 10% of premium. Calculate and compare indicated premiums.
Method and assumptions. For this example, expected loss cost is frequency multiplied by expected severity. Then use \(P_j=(L_j+F)/(1-v)\). The frequency and severity figures are assumed to be on the same annual exposure basis.
Step 1: Calculate expected loss costs. Group A has \(L_A=0.04\times \$5{,}000=\$200\). Group B has \(L_B=0.06\times \$5{,}000=\$300\).
Step 2: Calculate Group A’s premium. Add fixed expense: \(\$200+\$40=\$240\). Gross up for variable expenses: \(P_A=\$240/0.90=\$266.666\ldots\).
Step 3: Calculate Group B’s premium. Add fixed expense: \(\$300+\$40=\$340\). Gross up: \(P_B=\$340/0.90=\$377.777\ldots\).
Step 4: Compare and check. The premium difference is \(\$377.777\ldots-\$266.666\ldots=\$111.111\ldots\), which also equals the loss-cost difference of $100 divided by 0.90. Rounded to the nearest cent, the premiums are $266.67 and $377.78, a difference of $111.11.
Conclusion and common mistake avoided. A frequency difference can support different indicated rates when it is relevant and adequately substantiated. The common mistake is to compare rates without checking that frequency is annual and severity is per claim; multiplying quantities on incompatible time or exposure bases does not produce a valid loss cost.
Common Traps in Assessing Discrimination
- Equating equal treatment with equal rates. Different expected costs may support different rates. The relevant question is whether the distinctions are supported and permissible, not whether all policyholders pay the same amount.
- Calling every observed difference credible evidence. An experience difference may reflect limited data or random variation. The reviewer must assess the basis and limitations of the estimates before treating them as prospective costs.
- Comparing unlike policies. Coverage, limits, deductibles, and exposure periods can affect premiums. A comparison that ignores them may attribute a difference to the wrong cause.
- Stopping at the model output. A supportable indication does not guarantee that the filed or charged rate matches it. Check calculations, rating rules, and actual implementation.
- Confusing actuarial judgment with a legal determination. The actuarial analysis can describe cost support and identify concerns. The governing legal standard must be determined from the relevant jurisdiction and product rules.
Check Your Understanding
For each problem, state the calculation and the conclusion that follows from the facts given. Any legal conclusion remains subject to the applicable jurisdiction’s requirements.
- Two hypothetical classes have expected loss costs of $450 and $510 per exposure, respectively. Both have fixed expense of $30 and variable expenses of 10% of premium. Calculate the indicated premium for each class and the difference. (Answer: $533.33 and $600.00; the second is $66.67 higher.)
- Two otherwise identical risks have expected loss cost of $800, fixed expense of $100, and variable expenses of 20% of premium. One receives an additional 5% factor without any documented cost distinction. Calculate the base premium, the adjusted premium, and the difference; state the actuarial concern. (Answer: Base $1,125.00; adjusted $1,181.25; difference $56.25, a potential unsupported-differential concern.)
- In a hypothetical review, one group has 400 exposures and $240,000 in losses; another has 250 exposures and $150,000 in losses. Calculate the observed loss cost per exposure for each. If all other relevant characteristics are equal, do these figures alone establish a cost-supported rate difference? (Answer: $600 for each group; no rate difference follows from these loss costs alone, and their reliability as prospective estimates still requires assessment.)
- Two groups have annual claim frequencies of 0.03 and 0.05, each with expected severity of $4,000. Fixed expense is $50 and variable expenses are 10% of premium for both. Calculate each indicated premium and the difference. (Answer: $188.89 and $277.78; the second is $88.89 higher.)
- A reviewer finds different charged premiums for two policyholders with the same stated rating inputs. What additional checks are needed before concluding that the difference is unfair discrimination? (Answer: Verify that coverage, exposure, and other relevant terms are comparable; inspect the rating rules and calculation; identify any documented cost or expense distinction; assess supporting evidence; and apply the governing jurisdiction’s legal requirements.)