Insurance Company Capital Structure Swaps and Shareholder Wealth

utions to the insurer. We now consider examples where the insurer’s asset/loss correlation differs
from either the reinsurer or the policyholder, while all other estimates agree. If the reinsurer has
a lower asset/liability correlation, its assumption of these losses will decrease its risk and it may
charge relatively less for reinsurance. The solution to the optimal swap problem in these cases
is a corner solution and the standard model applies. Two simple scenarios in which correlation
estimates differ are presented in tables 6 and 7.
While not modeled analytically, differences in correlation estimates along with other valuation
differences (expected loss, volatility, etc.) change the magnitude of the effect of a swap, but not
the direction.
6.7 Swap Example Charts
Figures 2 through 4 illustrate the range of possible controlling shareholder effects from the swaps
discussed in the prior section. In these figures, we hold all values constant except the insider and
market value of liabilities, preserving the spread between the market and insider values when a
deviation exists. The graphs show the change in shareholder wealth resulting from swaps that issue
equity and reinsure losses on the left, to swaps that issue new policies and use cash proceeds to
retire equity on the right.
Figure 3 provides intuition for the counterintuitive results in table 4 (in which capital structure
swaps in either direction enriched controlling shareholders) and table 5 (in which capital structure
swaps in either direction diminished shareholder wealth). In the latter graphs, we can see that the
arbitrary swaps chosen for the numerical examples resulted in either destroying or adding value
no matter which swap was executed. From figure 3, we can see that interior extremes explain this
interesting result. In the case where both expected loss and volatility are overstated, managers can
increase controlling shareholder value by issuing equity and purchasing reinsurance, but at some
point, the dilution from issuing equity eliminates the gains from buying cheap reinsurance and
controlling shareholder value declines.
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