Risk Pooling

Risk Pooling in Health Financing

Risk pooling is the part of health financing that decides how prepaid money is held and shared, so that people who stay healthy in a year help pay for those who need costly care. The World Health Organization (WHO) treats it as one of three financing functions, between raising revenue and purchasing, and it applies to tax-funded services as much as to insurance funds. The design of pools sets how far a given amount of prepaid money can be redistributed towards people with high need, which is what financial protection and equity of access depend on. Revenue raising is covered under health system financing.

Pooling as a financing function

The World Health Report 2010 defines pooling as the accumulation and management of financial resources so that the financial risk of paying for health care is borne by all members of the pool and not by the individuals who fall ill. Funds must be prepaid before illness occurs, through taxes or insurance, if they are to be pooled. A payment made by a patient at the point of use is therefore never pooled for that episode, which is why out-of-pocket costs are counted apart from pooled spending.

Kutzin, writing for WHO in 2013, stresses that every health financing system, whether or not it is called insurance, includes collection, pooling and purchasing. A tax-funded national health service pools risk across its whole population without selling a policy, while a scheme labelled health insurance can pool poorly if its membership is narrow.

Who subsidises whom in a pool

Mathauer, Saksena and Kutzin, in a 2019 review by WHO staff, state that risk pooling effectively means that the healthy subsidise the sick and, because of their lower health risks, the young subsidise the old. Without pooling, sicker people would pay more because payments would follow need. The authors name de-linking contributions, whether taxes or premiums, from health risk as the central objective of pooling.

Redistribution by income is a separate matter, set by contribution rules rather than by the pool itself. The World Health Report 2010 describes covering people who cannot afford to contribute through cross-subsidisation, either from general government revenues or by setting insurance contributions higher for people who can pay. Community rating breaks the link between premium and risk without tying the premium to income.

Why a larger pool has steadier costs

Arrow observed in 1963 that the law of large numbers gives insurance a range of increasing returns, so that insurers have to be above a certain size. The reason lies in how the mean and variance of total claims grow with membership.

$$E(S_N) = N\mu, \qquad \operatorname{Var}(S_N) = N\sigma^2, \qquad CV(S_N) = \frac{\sigma}{\mu\sqrt{N}}$$

where $S_N$ is total annual claims in a pool of $N$ members, $\mu$ and $\sigma^2$ are the mean and variance of one member's annual claims, assumed independent and identically distributed, and $CV(S_N)$ is the coefficient of variation, the standard deviation of total claims divided by expected total claims. Grinstead and Snell give the first two results for an independent trials process, so the relative swing in claims shrinks as members join. If each member has one episode of cost $C$ with probability $p$ or none, then $\mu = pC$, $\sigma^2 = p(1-p)C^2$ and the coefficient of variation is $\sqrt{(1-p)/(Np)}$.

Independence is the assumption that fails most often. The variance of a sum includes twice the covariance of its parts, so when an epidemic or a new high-cost technology raises many members' costs together, adding members does not remove the extra variance. Pools therefore still need reserves, and small ones may buy stop-loss or reinsurance cover.

Nature and structure of pooling arrangements

Mathauer and colleagues describe pooling along two design aspects. The nature of pooling is whether coverage is voluntary or compulsory, with automatic coverage counted as compulsory. The structure of pooling is whether there is one pool or several and, if several, whether they overlap territorially, compete for members or segment the population. For any given level of prepaid funds, these features determine its redistributive capacity.

Voluntary pools attract people with higher risks, so their costs exceed the population average and there are too few healthy members to redistribute from. The authors call the resulting cycle of rising premiums and curtailed benefits the death spiral of voluntary insurance, worked through on the adverse selection page.

From more than 100 countries, the 2019 review proposes eight broad types of arrangement, the last two occurring alongside the first six. The table pairs each with the main consequence the authors attach to it.

Fragmentation and the transfers that offset it

Mathauer and colleagues define pools as fragmented when there are barriers to redistribution of available prepaid funds. The World Health Report 2010 reports strong evidence that fragmented pooling without risk equalisation can work against equity, because each pool has an incentive to enrol low-risk people and better-covered groups are unwilling to share their funds. Multiple pools with separate administrations are also inefficient.

Fragmentation is reduced by merging pools or by moving money between pools that stay separate. Thailand's Universal Coverage Scheme, introduced in 2002, replaced three schemes for poorer, older and voluntarily insured people and pooled their revenues with extra budget funding. Its funding per head has converged with the private employees' scheme, though civil servants still receive more.

The World Health Report 2010 states that all countries using competing insurers for mandatory coverage use some system of risk equalisation, and it describes funds in the Netherlands and Switzerland being transferred towards schemes that enrol high-risk people. Both sources describe effective transfers as creating a virtual single pool, and the report warns that this is administratively demanding. The transfer formula belongs to risk adjustment, and insurer behaviour when it is imperfect to cream skimming.

Worked example with two segmented pools and their merger

All numbers in this example are illustrative. A country of 100,000 people has two pools. Pool A covers 20,000 formal-sector employees through payroll contributions of USD 160 per member a year, and pool B covers the other 80,000 people from a government budget of USD 50 per person. Every member faces one type of hospital episode costing USD 1,000, with an annual probability of 4% in pool A and 8% in pool B, and episodes are independent.

1. Expected cost per member. Pool A expects 0.04 × 1,000 = USD 40 per member and pool B expects 0.08 × 1,000 = USD 80.

2. Separate pools. Pool A raises 20,000 × 160 = USD 3,200,000 against expected claims of 20,000 × 40 = USD 800,000, four times its expected cost. Pool B raises 80,000 × 50 = USD 4,000,000 against 80,000 × 80 = USD 6,400,000, covering 62.5% of expected cost (50 divided by 80). Its shortfall of USD 2,400,000 falls on patients as out-of-pocket payments or as care forgone.

3. Merger. Combined revenue is 3,200,000 + 4,000,000 = USD 7,200,000 and combined expected cost is 800,000 + 6,400,000 = USD 7,200,000, USD 72 per member each, so one common package is fully funded. The implicit transfer from former pool A members is 3,200,000 minus 800,000, or USD 2,400,000, exactly the old shortfall in pool B.

4. Equalisation without merger. If a central fund collects all contributions and pays each pool its expected cost, pool A pays in USD 3,200,000 and receives USD 800,000, a net transfer of USD 2,400,000 that matches the merger, provided the formula predicts expected cost correctly.

5. Volatility. The coefficient of variation of total claims is $\sqrt{0.96/800}$, or 3.46%, for pool A and $\sqrt{0.92/6400}$, or 1.20%, for pool B. In the merged pool the variance of total claims is the squared episode cost times 768 + 5,888 = 6,656, so the standard deviation is USD 81,584, or 1.13% of USD 7,200,000. Split pool B into 40 district pools of 2,000 people and each expects claims of USD 160,000 (2,000 × 80) with a coefficient of variation of $\sqrt{0.92/160}$, or 7.58%, so a reserve of two standard deviations is 15.2% of a year's expected claims against 2.4% for pool B as one pool.

6. Interpretation. The merger added no money and changed only whom the money could reach, since total revenue already matched total expected cost. Had revenue been lower, a merger would have spread the gap rather than closed it, which is why the 2019 review keeps the level of prepaid funding apart from pooling design. Merging cut the coefficient of variation from 3.46% for pool A and 1.20% for pool B to 1.13%, small next to the 7.58% of a district pool.

Pooling in economic evaluation and health technology assessment

Pooling arrangements decide who the payer is and how many there are, which bears on the perspective of an analysis. The NICE manual for technology appraisal (PMG36, section 4.2.9) states that NICE does not set the budget for the NHS and that the reference-case perspective on costs is that of the NHS and personal social services. Where several pools each pay for their own members, a technology's costs and savings can fall on different budgets, and a budget impact analysis may need results for each pool.

Moving costs between pools does not change the resources an intervention uses or the health it produces, so pooling does not by itself change its incremental cost-effectiveness ratio. It does change who bears the cost and, through exclusions and cost sharing, who is able to use the technology, which is the territory of distributional cost-effectiveness analysis. A model that assumes full coverage where much of the cost is paid out of pocket overstates access and misses catastrophic health expenditure.

Measuring how well a system pools

No single figure captures pooling, and fragmentation needs its own measures. The World Health Report 2010 frames coverage in three dimensions, the population covered, the services covered and the proportion of costs met from pooled funds, and Kutzin describes progress in simple terms as the per cent of that cube filled with pooled funds. Prepaid and out-of-pocket shares of spending show how much is pooled, not how fragmented it is.

Mathauer and colleagues propose comparing the share of the population covered by voluntary insurance with its share of expenditure, and report that in South Africa voluntary insurance accounted for 47% of health spending yet covered about 16% of the population. A count of pools on its own misleads, because pools joined by effective risk equalisation can act as one.

Risk pooling and neighbouring ideas

Health insurance is an institution with rules on enrolment, entitlement and payment that usually contains a pool, and the risk pool is the group whose costs are financed together. Risk adjustment links separate pools without merging them, and reinsurance protects a pool's upper tail, which matters most for small schemes such as community-based insurance. Moral hazard in health insurance is a response to coverage, separate from the sharing mechanism.

Common misreadings

Most errors about pooling come from judging a system by its labels or by one feature. Four recur in policy writing and in models.

1. Taking a scheme's name as evidence of pooling. A voluntary national insurance fund may pool little, while a tax-funded service pools across everyone.
2. Assuming a bigger pool always protects more. Size steadies claims, but a large pool with narrow benefits or heavy cost sharing still leaves households exposed.
3. Equating risk pooling with income redistribution. Flat premiums pool risk between healthy and sick members without any transfer between income groups.
4. Treating pooling as a cost-effectiveness argument. Pooling changes who pays and who can use a technology, not the resources it consumes or the health it produces.

Sources

• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973. https://www.aeaweb.org/aer/top20/53.5.941-973.pdf
• Grinstead CM, Snell JL. Introduction to Probability. 2nd ed. American Mathematical Society; 2003. Chapter 6. https://math.dartmouth.edu/~prob/prob/prob.pdf
• Kutzin J. Health financing for universal coverage and health system performance: concepts and implications for policy. Bulletin of the World Health Organization. 2013;91(8):602-611. https://doi.org/10.2471/BLT.12.113985
• Mathauer I, Saksena P, Kutzin J. Pooling arrangements in health financing systems: a proposed classification. International Journal for Equity in Health. 2019;18:198. https://doi.org/10.1186/s12939-019-1088-x
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Section 4.2.9. https://www.nice.org.uk/process/pmg36
• World Health Organization. The world health report: health systems financing: the path to universal coverage. Geneva: WHO; 2010. https://iris.who.int/handle/10665/44371