Risk pooling and the law of large numbers

What is risk pooling?

Risk pooling is the basic mechanism of insurance. Many people facing a similar risk each pay a modest, known premium into a common fund, and the fund pays the large, uncertain losses of the few who suffer them. No single member could afford to carry a house fire or a family death alone, but a pool of thousands can absorb it easily.

The law of large numbers explains why pooling works. For one person, whether a loss happens this year is close to unpredictable. For a large group of similar, independent risks, the proportion who suffer a loss becomes stable and can be estimated from experience. The bigger the pool, the closer actual claims come to the expected figure, and the less the insurer needs to charge as a margin for uncertainty.

How risk pooling works

A simple example

Suppose 10,000 people each face a 1 in 1,000 chance of a ₹10 lakh loss in a year.

Each member pays about ₹1,000 plus a loading for expenses, commission, capital and profit, instead of carrying a ₹10 lakh exposure alone. With only 100 members the expected number of losses would be 0.1, and a single claim would wipe out ten years of premiums, which is why small pools are unstable. The figures are illustrative.

Conditions for a pool to work

• Many similar risks. Members should face broadly comparable chances of loss, or be priced by risk class through underwriting.
• Independence. One member's loss should not cause another's. Floods, earthquakes and pandemics break this condition because they hit many members at once. Insurers manage such accumulation through catastrophe reinsurance, and IRDAI's reinsurance regulations require insurers to buy adequate catastrophe protection backed by catastrophe modelling approved by their boards.
• Honest entry. If mainly high-risk people join, the pool's actual experience diverges from its pricing. This is adverse selection.
• Measurable losses. The insurer needs to know when a loss has occurred and how large it is.

Pools beyond a single insurer

Some risks are too large or rare for one company's pool. Indian insurers therefore also pool risk together. IRDAI's reinsurance regulations define an insurance pool as a joint underwriting arrangement in which participating insurers take a predetermined share of all business written. Examples in India include the Indian Market Terrorism Risk Insurance Pool, set up in 2002, and the India Nuclear Insurance Pool, set up in 2015, both managed by GIC Re. Reinsurance itself is pooling at a global scale: reinsurers spread risks from many countries and lines so that no single event overwhelms them.

What risk pooling means for distribution

• Pricing depends on the pool you build. The claims experience of the customers a channel brings in feeds directly into the insurer's loss ratio and future pricing. A channel that brings a broad, well-disclosed mix of customers helps keep premiums affordable for all of them.
• Group business is pooling made simple. In group term insurance and group health, the employer or affinity group provides a ready-made pool. Larger groups are priced more on their own experience, while small groups are priced closer to the insurer's book rates.
• Mass schemes show the principle at work. Government schemes such as PMJJBY keep premiums low by covering very large numbers of account holders through banks and post offices, so enrolment volume matters to their viability.
• Explaining premiums to customers. Many customers feel their premium is "wasted" in a claim-free year. A clear explanation is that the premium bought protection, and that in a pool the claim-free majority is what pays for the families who did need it.
• Persistency sustains the pool. When healthy customers lapse and less healthy ones stay, the pool deteriorates. Good renewal service is part of keeping a book balanced.