Understanding the Benefits of Risk Pooling and Diversification in Property Insurance Markets
By Xuesong You and Carolyn Kousky
The foundation of insurance lies in the pooling and diversification of risk. Risk pooling allows policyholders to replace the risk of a devastating loss with a much smaller and more predictable annual payment. Diversification helps prevent insurers from experiencing losses that would leave them insolvent, instead making their annual claims payouts more stable and predictable. The mathematics that enable these powerful benefits of insurance, however, are harder when risks are correlated—when many policyholders suffer losses simultaneously—and when losses can be catastrophic. In this post, we will illustrate how risk pooling and diversification, when achieved, translate into lower premium costs for the policyholders who ultimately bear these costs. We explain why ensuring the benefits of pooling and diversification is critical to a well-functioning insurance market.
The Fundamental Challenge
When individuals make regular payments for an insurance contract, they expect insurers to fulfill their promise of paying claims when losses occur. To meet that commitment, a risk pool (by which we mean the “book of business” or all the policies held by either a private or public insurer) must be managed carefully to maintain a sufficient level of claims-paying ability. Insurers cannot just have funds available to pay for the average annual loss (the amount expected any year), but must have access to funds to cover very severe loss years. Private insurers, for example, are typically disciplined by regulators and rating agencies to keep insolvency risk very low. To obtain a financial strength rating of A, AA, and AAA from S&P—indicating very high capacity to meet financial commitments—an insurer must demonstrate that it can withstand 1-in-250-year, 1-in-333-year, and 1-in-500-year events, respectively. This means it must be able to pay claims for an event that has only a 0.4% (1/250), 0.3% (1/333), or 0.2% (1/500) chance, respectively, of occurring in any given year [1]. State insurance regulators have their own solvency regulations in addition to rating agencies. And Government-Sponsored Enterprises (GSEs), such as Fannie Mae and Freddie Mac, have specific rating requirements for property insurers as a condition for a mortgage's eligibility on the secondary market, adding another layer of market discipline around solvency. But ever more robust claims-paying ability comes at a cost: the more capital an insurer must hold to manage its risk pool, the higher the premiums policyholders ultimately pay.
The Benefit of Pooling Independent Risks
Independent risks, in this context, refer to insurance policies where the risk of loss to one policyholder is not related to the risk of loss of another policyholder. For instance, if one home has a kitchen fire, it does not imply other homes will: these are independent risks. In contrast, if one home burned in a wildfire, it is very likely neighboring homes did as well: these risks are not independent; they are correlated.
Pooling, or bringing together, a large number of independent risks underpins insurance since it reduces the extra capital an insurer must hold to survive an extremely severe loss year. This benefit can be illustrated by comparing two portfolios of different sizes: Portfolio A with 20 independent annual policies and Portfolio B with 200 independent policies (use the interactive tool below to explore different scenarios). For simplicity, let’s assume all policies have the same loss distribution: a 10% chance of a $100 loss in any given year and a 90% chance of a zero loss.
To survive a 1-in-100-year disaster, that is, for the insurer to be able to pay all policyholder claims for potential losses in 99% of years (keeping the probability of insolvency below 1%), an insurer holding Portfolio A must hold $600 in reserve (or otherwise have access to this amount of funds to pay claims through instruments such as reinsurance). That is 200% above the expected annual loss of $200 (=10%*$100*20), meaning that an insurer with Portfolio A must charge 3 times the expected loss per policy to meet their solvency target.
When more risks are added into the pool, as in Portfolio B, the amount needed for the same 1-in-100-year disaster target is $3,000. This is larger in absolute terms, since there are now more policies in the pool, but smaller in relation to each policy. So the amount the insurer has to have on hand in relative terms has gone down and is now only 1.5 times the total annual expected loss of $2,000 (= 10%*$100*200). Therefore, an insurer with Portfolio B needs to charge policyholders only 1.5 times the expected loss per policy—not 3 times as before—to have the same level of claim-paying ability as Portfolio A. This is what happens when a large number of independent risks are pooled: the extreme loss becomes less likely and is replaced with a more certain, smaller loss. This, in turn, allows the insurer to charge consumers less.
Consumers thus benefit from the pooling of independent risks. This effect compounds as more independent risks are added to the pool: As the pool of independent risk grows (slide up the policy count for Portfolio B), the chance of a severe loss gets smaller. This means the amount the insurer needs to charge can get closer to the expected loss of the policy. This is the powerful mathematics behind insurance.
When Pooling Breaks Down
This benefit of risk pooling, however, is only fully realized when risks are independent and do not occur together. If everyone in the pool were to be hit by the same event simultaneously, the pool would need enormous sums of capital to pay everyone’s loss. This is one of the key challenges with insuring natural disasters: a single wildfire, for example, can destroy an entire neighborhood, confounding risk pooling and requiring substantial funds. When one disaster can impact many homes simultaneously, it means the risk of burning across homes is correlated, not independent.
To illustrate how insuring correlated risks undermines the benefits of risk pooling and can be more costly, consider a portfolio of 200 policies, each with a 10% probability of a $100 loss and a 90% probability of no loss (similar to Portfolio B described above), but now with a correlation of 0.3 (you can use the interactive tool below to explore different scenarios). The correlation is a measure of whether when one home suffers a loss, another does, too. A correlation of zero would mean they were completely independent. A correlation of 100%, or 1, would mean when one burned, for example, the other always would also burn. In reality, correlation between properties in a disaster is somewhat less than 1 and is based on the hazard, landscape, and built environment.
To manage this pool of correlated risks against the same 1-in-100-year disaster, it now requires holding $9,900 in reserve (versus $3,000 when the policies were independent), even though the expected total loss remains the same at $2,000. This correlation thus effectively increases the capital requirements by 345% above expected loss.
Correlation also wipes out the benefits of adding more policies to a portfolio. Holding the same assumptions above, but now slide up the policy count from 200 to 3,000. As can be seen, adding correlated policies to a portfolio does not produce diversification benefits. In relative terms, the additional capital needed to withstand a 1-in-100 year disaster because of the correlation remains significantly high at 362% above expected loss. In absolute terms, adding more risks, or growing the pool or an insurer's portfolio, thus only serves to scale up the insurer’s financial responsibility: it no longer produces the cost savings for policyholders that diversification would typically provide.
Implications for Consumer Premiums
The varying levels of capital that insurers must hold have important implications for consumer costs. If we assume for illustration that the insurer meets all their capital needs through premiums charged to policyholders, as can be seen below, the premium cost per policy is lowest when risks are independent and the pool is sufficiently large (which allows for effective risk pooling and diversification).
For example, in the case where all policies have the same loss distribution (as above, a 10% chance of a $100 loss in any given year and a 90% chance of a zero loss) and are independent, the insurer would only need to charge a premium of $11.27 per policy to cover the potential costs of a 1-in-100-year disaster, assuming a pool size of 3,000 policies. This amount is closest to the expected loss of $10 (= 10%*$100).
However, as the correlation between risks increases, the premium costs rise significantly. With a low correlation of 0.05, the premium already nearly doubles to $22.23 per policy. At a correlation of 0.5, the premium increases to $69.81, and at a correlation of 0.8, it reaches $96.23—close to the full potential loss of $100 that could occur if the risk materializes. This is why disaster insurance can be so much more expensive than non-disaster insurance: the correlation drives up needed premiums for the insurer to maintain their ability to pay claims.
These charts demonstrate that the benefits of risk pooling operate on the principle that combining a large number of independent risks reduces uncertainty. When individuals come together to form a larger, more diversified risk pool, as is done in a formalized insurance market, the financial burden shared among them becomes significantly lower. This means that each participant needs to contribute less in premium costs to ensure that claims-paying commitments can be met, even in a severe disaster year. Understanding this dynamic is important not only for insurers managing solvency, but for understanding why certain risks like natural disasters remain costly to insure, whether through private insurers or public programs.
For disaster risks where individual policyholders do not face independent risks, premiums are going to be more expensive, even if those correlations are small. In the extreme, insurers will need to limit the number of policies they write in a correlated geography to maintain greater independence across their portfolio. Using tools like global reinsurance, which expands the risk pool to include independent risks from other countries, can create diversification among risks that are locally correlated, thereby expanding the ability of insurers to cover disaster risks and making it a necessity for a healthy disaster insurance market.
Endnotes
[1] As of 2026, there are 199 U.S. homeowners insurers (those that wrote positive premiums in homeowners insurance) rated by S&P, all of which hold a financial strength rating of A or above.