## Reinsurer Diversification: A Risk Metric Approach to Diversification

Christopher Klein, Global Head of Business Intelligence

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In many instances, a common and useful approach to risk management issues involves establishing metrics and monitoring actions in light of certain benchmarks. Risk metrics are generally easier to understand and capture important summary information as opposed to trying to deal with, for example, a comparison of entire probability distributions.

Suppose that a ceding company has determined that its financial condition is such that it could withstand surplus impairment of up to USD100 million and remain on course. The ceding company could absorb that level of surplus blow without triggering any rating agency or regulatory actions that might hurt its ability to do business, and the company is confident that it will remain adequately capitalized for its business. In this case, the ceding company might want to measure its credit risk as the probability of defaults on recovery amounts in excess of USD100 million, which could be labeled a “risk of ruin” metric.

In a similar vein, another metric is the expected value or average value of default amounts that are in excess of a particular level, in this case USD100 million. This can be called the “expected deficit” metric. Or, the cedent could monitor and control the expected value of losses resulting from reinsurer defaults, calculated as outlined earlier. And, there may be some ceding companies that would choose to limit the probability of any default at all within its reinsurance program.

The following table provides the values for the risk measures under three of the reinsurance placement examples set forth above. The risk of ruin probability for the program with a single Aaa rated reinsurer is clearly 1.0 percent; for the program with three Aaa rated reinsurers, the risk of ruin is the sum of the probabilities from Table 4 for the two defaults or all default cells (the only cases with loss exposure over USD100 million). For the program with Aaa, Aa, and A reinsurers the risk of ruin probability is also the sum of the probabilities for two defaults or all default (Table 5). Expected deficits are calculated as the product of probabilities multiplied by values exposed in excess of USD100 million, so the expected deficit of the single Aaa case is 1 percent multiplied by USD100 million. With the diversified programs, the deficits are calculated similarly, but recall that in the two default cases the probability is multiplied by USD33.3 million, the amount in excess of USD100 million. The expected loss and probability of any default are straightforward.

This table again shows that diversifying the purchase, even to companies with lower credit quality, reduces the risk of severe impact as measured by Risk of Ruin or Expected Deficit. But there is no free lunch, however. Diversification raises the probability that there is some non-zero default amount. There is no difference in the expected loss (average default amount) between programs involving either one or three Aaa rated reinsurers, but the expected loss value goes up when reinsurers of lower credit quality are added.

The major rating services, A.M. Best and Standard & Poor’s (S&P), include reinsurance recoverables in their calculation of risk based capital. However, they do not provide an objectively calculated credit for diversification of the reinsurance pool.

Credit for counterparty diversification is a qualitative judgment by the rating agencies. For example, S&P may take a negative view on a cedent that has unsecured reinsurance recoverables from a single counterparty and a positive view of a cedent with a multi-reinsurer panel. In certain circumstances, this judgment could make a difference to the final rating assigned.

**Earlier Installments**

**Reinsurer Diversification: Roots and Benefits >>**

**Reinsurer Diversification: Case Studies >>**

Additional Contributor

- Sean Mooney, Chief Economist