Bonus-malus: when does claiming insurance for a small loss cost more than the future premium?
The insurer may cover 1.2 million soum of damage to a vehicle. But if the claim is paid, the discount built up for claim-free years is lost, and over the next five years the premium becomes 1.4 million soum more expensive in total. The logic of bonus-malus, a table of hypothetical coefficients and the threshold for the decision "pay it myself or claim on the insurance".
The van of the "Tez yetkaz" courier service touched a post while reversing in the yard, and its bumper cracked. The repair costs 1 200 000 soum. The van is insured, and the dispatcher Laylo wants to call the insurer right away. The director Bahodir stops her: "Let's do the sums first."
Key rules
- Bonus-malus is a system that links the premium to the policyholder's own history: for claim-free years the premium decreases (bonus), after a claim is paid it increases (malus). It is most often found in motor insurance
- Premium = base premium × coefficient. The base premium depends on the type of vehicle and other factors, while the coefficient depends only on your history
- When a claim is paid, the discount is lost not for one year but for several: because the coefficient comes down the ladder slowly, returning to the previous level takes years
- That is why with a small loss the question is not "will the insurer pay?" but "is the payout bigger than the extra premium in the future?"
- The decision threshold: if the payout amount is greater than the sum of the premium differences in the coming years, claiming pays off; if it is smaller, cover the loss yourself
- You do the calculation on the assumption that the base premium does not change and there will be no new loss: state this assumption openly
- The exact coefficients, the steps of the ladder and which losses trigger a "malus" differ for each type of insurance and contract: ask about the policy terms before signing
Example: a bumper for 1.2 million soum
Hypothetical rules (compiled by the author): the starting coefficient is 1.00; for each claim-free year it decreases by 0.05, but does not fall below 0.70; after the year in which a claim was paid it increases by 0.15. "Tez yetkaz" has driven four years without a claim, and its current coefficient is 0.80. The base premium is 2 000 000 soum a year.
| Year | A: we pay ourselves (coeff.) | A: premium | B: we claim (coeff.) | B: premium | Difference (B − A) |
|---|---|---|---|---|---|
| 1 | 0.75 | 1 500 000 | 0.95 | 1 900 000 | 400 000 |
| 2 | 0.70 | 1 400 000 | 0.90 | 1 800 000 | 400 000 |
| 3 | 0.70 | 1 400 000 | 0.85 | 1 700 000 | 300 000 |
| 4 | 0.70 | 1 400 000 | 0.80 | 1 600 000 | 200 000 |
| 5 | 0.70 | 1 400 000 | 0.75 | 1 500 000 | 100 000 |
| Total | 7 100 000 | 8 500 000 | 1 400 000 |
In year 6 option B also falls to 0.70 and the difference disappears. So claiming results in 1 400 000 soum of extra premium in total over five years.
Decision: - loss of 1 200 000: claiming loses 200 000 soum, so we pay for the repair ourselves; - if the loss were 2 000 000: claiming gains 600 000 soum, so we claim on the insurance; - the threshold in this example is 1 400 000 soum.
Note: if you look only at the first year (difference 400 000), a 1.2 million payout looks very attractive. This is exactly where the mistake is made. The calculation has not taken the time value of money into account: the differences in future years are somewhat smaller in today's money, so in practice the threshold is slightly below 1.4 million.
Test yourself
5 questions on this topic: pick an option or reveal the answer.
During the year an insurance company collected 500 mln soums of insurance premiums and paid out 350 mln soums of insurance claims. What is the loss ratio (claims paid / premiums collected × 100%)?
According to the insurer's statistics, the probability that one such rural house is completely destroyed by fire within a year is 0.003. The house is insured for 80 000 000 soum. Taking into account only this risk and only total loss, and without adding the insurer's expenses and profit, what is the expected loss (risk part of the net premium = probability × sum insured)?
During the year an insurance company earned 800 mln soum of insurance premiums, paid 520 mln soum of insurance claims and incurred 200 mln soum of operating expenses. What is the combined ratio ((claims + expenses) / premiums)?
An insurance agent collected 240 mln soum of premiums for the insurer during the year. The agent's contract provides for commission of 7% of the premiums collected (hypothetical term). How much commission does the insurer pay the agent?
A bakery's insurance contract for its tandoor oven sets an unconditional deductible of 1 500 000 soums. In an insured event the loss was 9 000 000 soums. How much does the insurer pay?
Answered: 0 / 50 of 5 correct
All tests →See also
Sources
- Fundamentals of insurance (general concepts) · bonus-malus system: a premium discount for claim-free periods, an increase in the premium after a claim is paid; general knowledge. The exact coefficients and how they are applied depend on the type of insurance, the contract and the rules in force
- Example, company name, base premium, coefficients and calculations · compiled by the author, hypothetical; not actual insurance terms