The Bonus-Malus system was designed to differentiate insurance premiums based on the individual behavior of persons specified in the insurance contract. In theory, this system supports actuarial fairness and encourages preventive behavior.
However, when the system is fully imposed through regulation, with no link to actual actuarial calculations, it creates a systemic risk that cannot be mitigated. Discounts and penalties no longer reflect real risks but are applied mechanically, which can lead to suboptimal behavior and financial instability.
What does imposed mean? Link to heading
An imposed Bonus-Malus system means that:
- BM classes (including coefficients) are set by the authority, not derived from the insurer’s own experience.
- The applied discount is not proportional to individual risk but to a uniform scale position.
- All insurers are required to follow the same rules, regardless of portfolio structure.
As a result, the Bonus-Malus system becomes an administrative redistribution mechanism, not an actuarial tool for risk selection and pricing.
The core issue is not the existence of BM classes per se, but the imposition of externally fixed coefficients, which decouple price from real risk and prevent market adaptation.
A partial solution under an imposed system? Link to heading
Indeed, aware of the risk induced by the system, actuaries may set a higher profit margin (or adjustment factor) as a backup plan. However, they will never be able to fully mitigate the risk across all classes. For example, they can set a profitable level in the class with the best discount, but not across all classes. Thus, they can only calibrate fairly in one class, but cannot defend themselves impartially against the system as a whole.
Some insurers will incur losses, but in the long term, only profitable insurers will remain, which means that ultimately, through an imposed system, policyholders end up paying more than the fair premium — even if only some of them.
Causal Link to heading
analysis
To better understand this, we will use a simplified example where exposure, location, and the Bonus-Malus system are the only variables explaining claim frequency.
Exposure, location, and the Bonus-Malus system are confounding variables. These are variables correlated with both the explanatory and dependent variables, and can distort the estimated relationship between them.
First, we can model the relationship between the confounding variables and behavior, as shown in the left figure below. Then, we can model the relationship between the confounding variables and the outcome, as in the middle figure. Alternatively, we can model both sets of relationships, as shown in the figure on the right.
For a more detailed explanation, a doubly robust model such as the one on the right is required. However, in this context, if the Bonus-Malus system is not properly calculated but merely adopted as is, the modeling effects will be negatively influenced, potentially leading to incorrect or distorted results.
Illustrative example Link to heading
Let’s assume the authority imposes a maximum 50% discount for the best Bonus class. However, from its own experience, the actuary determines that the actuarially justified discount is only 25%.
To compensate for this discrepancy, the insurer adjusts the base premium upward, e.g., by 50%. Thus, if the actuarial premium was 100, the new starting premium becomes 150.
Then:
- Clients in the class with the maximum discount (−50%) will pay
150 × (1 − 0.50) = 75— exactly the correct price:100 × (1 − 0.25).
But:
- A client in a class with only a 5% imposed discount will pay
150 × (1 − 0.05) = 142.5, maintaining the distortion dictated by the imposed system. - Any new client will enter the system at a base premium of 150, maintaining the 2:1 ratio imposed by the system.
The distortion propagates systemically, affecting all intermediate classes, and fairness in pricing appears only through recalibration — not across the entire system.
This premium recalibration affects balance, fairness, competition, and trust in the pricing system and doesn’t even guarantee a profit for the insurer. Without recalibration, the insurer will surely lose money on the best Bonus class — where most policyholders should be.
Thus, the issue is not recalibration, but the imposition of a system that requires recalibration.
By enforcing a uniform system:
- Drivers with low actual risk may end up subsidizing higher risks in the same BM class.
- Insurers cannot finely differentiate risks, losing a key tool for selection and pricing.
- Ultimately, good policyholders pay more than they should, and high-risk ones pay less than their actual cost.
This is a form of uncontrolled cross-subsidization that erodes the predictive function of the premium.
Systemic risk and instability Link to heading
By distorting actuarial pricing:
- The market loses efficient risk allocation.
- Insurers can no longer build correct pricing across all levels.
- Since the system progresses yearly, adjustments must be continuous, aligned with current segmentation.
- Effect duplication between classes: a person should receive the final premium based on all explanatory variables, without duplicating effects.
- System duplication with other cascading discounts (e.g., pensioner discount or identification of high-risk policyholders).
- Renewal can become illogical, creating the illusion of higher premiums even without claims.
- Reinsurers will charge a premium on imposed systems, recognizing all the issues above.
- Insurers’ ratings may be downgraded or even capped.
What alternatives exist? Link to heading
- The system may be imposed only at the conceptual level (e.g., defining the classes), but the coefficients must remain at the discretion of actuaries, with transparency and supervision.
- Allow actuarial adjustments within the regulated grid.
- Fully integrate the system into the pricing model at the time of tariff calculation, via a complete unified model.
Conclusion Link to heading
The full imposition of a Bonus-Malus system may seem fair at first glance, but in the long run, it leads to inefficiency, antiselection, and systemic risk. For a sustainable market, it is essential that premiums reflect actual risk, not just an administrative position in a table. Bonus-Malus must remain an actuarial tool, not a political one. It is a good example of a policy that fails.
Our core concern in causal analysis is the causal question itself — it governs what data to analyze, how to analyze it, and to which populations our inferences apply.
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