Insurance Company Capital Structure Swaps and Shareholder Wealth

Wt=2 = EM,t=0
Et=2
EM,t=1
Where Wt=2 is the shareholder wealth at t = 2 and Ejt is the j value of equity at time t. Equation
12 represents the proportion of total equity market value before the swap (held by the controlling
shareholders) to total equity market value after the swap (held by both controlling shareholders
and noise traders). Thus the ratio reflects the smaller proportion of total equity market value held
by the controlling shareholders after the swap has occurred. This ratio is then multiplied by the
total t = 2 equity value to represent the terminal wealth of the controlling shareholders. New
shareholders have been added, and the controlling shareholders now hold a smaller portion of the
total equity than they held before the swap occurred. Managers will engage in the swap only when
the optimal t = 2 wealth exceeds the t = 0 wealth.
When the firm issues new policies and uses the proceeds to retire equity, the initial wealth of
controlling shareholders is the ratio of market value of equity at t = 2 to the market value of equity
at t = 0, multiplied by the t = 0 insider value of the firm’s equity:
Wt=0 = EM,t=1
EI,t=0
EM,t=0
Equation 13 represents the proportion of total equity market value after the swap to total equity
market value held before the swap, and reflects the ratio of total equity held by the controlling
shareholders. This ratio is then multiplied by the total t = 0 insider equity value to represent the
wealth of the controlling shareholders prior to the swap. The controlling shareholders hold a larger
portion of the equity after the swap than they held before the swap occurred. Again, managers
will engage in the swap only when the the t = 2 wealth exceeds the t = 0 wealth.
For firms issuing equity and using proceeds to purchase reinsurance, the change in controlling
shareholder wealth as a function of expected losses is:
17
(12)
(13)