Insurance Company Capital Structure Swaps and Shareholder Wealth

Under the Merton-Margrabe exchange option valuation model, we will substitute equation 7
into equations 14 and 15 to generate the following optimization formulas.
∂Wt=2
∂Lt=1
∂Wt=2
∂Lt=1
= EM,t=1 [EM,t=1N (d2,t=2) − Et=2N (d2M,t=1)] = 0 (16)
= −EM,t=1N (d2,t=2) − Et=2N (d2M,t=1)
EM,t=0
= 0 (17)
When issuing equity to purchase reinsurance, the manager will find the value of losses that
solves equation 16. When retiring equity with proceeds of new insurance policy sales, the manager
will find the value of losses solving equation 17. To confirm that we have maximized shareholder
wealth, we confirm that the second derivative is negative.
5 Comparative Statics
Comparative statics on the preceding swap valuation models show that managers may be able to
increase the wealth of controlling shareholders by engaging in capital structure swaps. We now
propose two hypotheses about the value-enhancing nature of capital structure swaps, demonstrate
their validity with numerical examples and then test whether these value-enhancing swaps actually
occur in practice.
Given our theory, increasing liabilities to retire equity will benefit the controlling shareholders
when managers exploit risk preferences of policyholders, comparative advantage in provision of
real-services and tax effects. This is only possible when insurers can charge a relatively high price
for insurance policies, which is not possible under perfect competition. However, in the face of
information asymmetry, regulatory constraints and bankruptcy costs, disequilibrium can exist. In
fact, Doherty and Garven (1995) and prior literature show that underwriting returns appear to
follow a second-order autoregressive process. This creates an “underwriting cycle” in which prices
and profitability rise and fall over time. If information asymmetry, transaction costs and other
frictions prevent the capital markets from fully incorporating the increased profitability for firms
in the high-profit phase of the cycle, then managers may be able to increase shareholder wealth by
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