Final answer:
Credit cards typically offer term life insurance which covers a specified period without cash value. Actuarially fair premiums are calculated based on the risk of the insured group. Charging a single premium for a mixed-risk group may lead to adverse selection and potential financial loss for insurers.
Step-by-step explanation:
The type of life insurance that credit cards typically offer is known as term life insurance. This type of insurance provides coverage for a specified period, or "term," and pays out a death benefit only if the policyholder dies during that time. Unlike whole life insurance, it does not have a cash value that can be used as an account. When considering a group of individuals for life insurance, actuaries calculate the actuarially fair premium, which is a premium that reflects the true risk of paying out the policy.
Lets take an example where there are two groups of 50-year-old men, one with a family history of cancer and one without. If 20% have a family history of cancer with a 1 in 50 chance of dying in the next year, and the other 80% have a 1 in 200 chance, the premiums would be different for each group if they were insured separately. The calculation for the actuarially fair premium would be based on the probability of death and the amount the insurance company would have to pay out.
Calculating premiums separately:
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- Group with family history of cancer: (1/50 chance of dying) x 200 men x $100,000 payout = $400,000 total risk. The fair premium would be $400,000 divided by 200 men, equalling $2,000 per person.
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- Group without family history of cancer: (1/200 chance of dying) x 800 men x $100,000 payout = $400,000 total risk. The fair premium would be $400,000 divided by 800 men, equalling $500 per person.
Calculating the premium for the entire group:
If the insurance company cannot differentiate between those with and without a family history of cancer, the premium would be averaged over the entire group. This could lead to issues like adverse selection, where those with higher risk are more likely to purchase insurance, driving up costs and potentially leading to losses for the insurance company.
If the insurance company charges the actuarially fair premium to the entire group rather than to each group separately, it will likely undercharge the high-risk group and overcharge the low-risk group, creating an imbalance and potentially financial losses if there are significantly more high-risk policyholders than expected.