A “square‐root rule” for reinsurance? Evidence from several national markets

Using a game‐theoretic model of insurance markets, Powers and Shubik in 2001 derived a mathematical expression for the optimal number of reinsurers for a given number of primary insurers. Subsequently in 2005, Powers and Shubik showed analytically that, for large numbers of primary insurers, this expression is effectively a “square‐root rule”, i.e. the optimal number of reinsurers in a market is given asymptotically by the square root of the total number of primary insurers. In this paper, we test the accuracy of the square‐root rule empirically.

The numbers of primary insurers and reinsurers existing in a range of 18‐20 different national insurance markets over a period of 11 years are used.

The empirical results are consistent with the square‐root rule. In addition, we find that the number of reinsurers may also be associated with the market's willingness to pay for risk. When the market's perception of risk is high, there is a greater supply of reinsurance to provide capacity to primary insurers.

An empirical model is presented that deals explicitly with the number of insurers and reinsurers in a market. This is of value to government policymakers and insurance regulators.