What is the effect of adding members to a risk pool on expected payouts and insurer risk?

What is the effect of adding members to a risk pool on expected payouts and insurer risk?

• A. Lowers expected payout and increases insurer risk
• B. Increases expected payout and lowers insurer risk
• C. Increases both expected payout and insurer risk
• D. Has no effect on expected payout or insurer risk

Answer: (B)

Pooling more members changes two things at once: the total amount the insurer expects to pay out tends to rise with more insured individuals, while the uncertainty around that total falls on a relative basis due to diversification. Each added member brings another potential claim, so the overall expected payouts grow roughly in proportion to the pool size. At the same time, the variability of total claims becomes more predictable as the numbers get large—the individual risks diversify, and the law of large numbers makes the total payout more stable. So the best choice captures both effects: higher expected payouts, but lower insurer risk thanks to diversification.

Pooling more members changes two things at once: the total amount the insurer expects to pay out tends to rise with more insured individuals, while the uncertainty around that total falls on a relative basis due to diversification. Each added member brings another potential claim, so the overall expected payouts grow roughly in proportion to the pool size. At the same time, the variability of total claims becomes more predictable as the numbers get large—the individual risks diversify, and the law of large numbers makes the total payout more stable. So the best choice captures both effects: higher expected payouts, but lower insurer risk thanks to diversification.