Stock vs. mutual insurers: Who should and who does charge more?

• We extend the Doherty and Garven (1986) model to mutual insurers and include frictions.
• Numerical implementation of the model to explain mutual and stock premiums.
• Comparison with empirical evidence from panel data set (Hausman–Taylor estimator).
• Empirically observed premiums are not consistent with normative findings.
• Results suggest considerable wealth transfers between stakeholder groups.

We contribute to the literature by developing a normative theory of the relationship between stock and mutual insurers based on a contingent claims framework. To consistently price policies provided by firms in these two legal forms of organization, we extend the work of Doherty and Garven (1986) to the mutual case, thus ensuring that the formulae for the stock insurer are nested in our more general model. This set-up allows us to separately consider the ownership and policyholder stakes included in the mutual insurance premium and explicitly takes into account the right to charge additional premiums in times of financial distress, restrictions on the ability of members to realize the value of their equity stake, as well as relevant market frictions. A numerical implementation of our model shows that, for the premiums of stock and mutual insurers to be equal, the latter would need to hold comparatively less equity capital. We then evaluate panel data for the German motor liability insurance sector and demonstrate that observed premiums are not consistent with our normative findings. The combination of theory and empirical evidence suggests that policies offered by stock insurers are overpriced relative to policies of mutuals. Consequently, we suspect considerable wealth transfers between the stakeholder groups.