Final answer:
Charging an actuarially fair premium to the entire group rather than to each subgroup based on risk factors can lead to financial losses for an insurance company due to adverse selection.
Step-by-step explanation:
When an insurance company chooses to charge an actuarially fair premium to a group as a whole, rather than segmenting the group based on individual risk factors such as a family history of cancer, it may face financial challenges. If high-risk individuals (those with a family history of cancer, in the provided example) are underrepresented in the premium calculation, the insurance company will likely incur losses because the premiums collected will not fully cover the cost of the claims made by those high-risk individuals. Conversely, if the company raises premiums to cover the high-risk losses, it faces the risk of pricing out individuals with lower or average risk, who may elect not to purchase insurance at the higher rates. This effect is known as adverse selection and can undermine the insurance pool's sustainability by leading to a less healthy balance between high-risk and low-risk policyholders.