Insurance Company Capital Structure Swaps and Shareholder Wealth

Ej is value of equity, Aj is current value of assets and Lj is expected value of loss liabilities.
The function N (•) is a draw from the standard normal distribution function.
ln
d1 =
Aj
Lj
+ 0.5V 2
j t
√
√ , d2 = d1 − Vj t
t
Vj
V 2
j = σ 2 jA + σ 2 jL − 2ρjALσjAσjL
j takes the value of M for market value of equity and I for insider value of equity, σjk is the
standard deviation of the variable k (either A for assets or L for losses) under j, and t is time to
policy expiration. Note that V 2
j is the instantaneous variance of the portfolio of long assets and
short liabilities, and for simplicity, probability distributions for assets and liabilities are stable over
time. 8
4.2 The Swap
If managers believe that reinsurance will add value for the firm, they may be able to enrich con-
trolling shareholders by purchasing reinsurance with the proceeds of a new equity issue. However,
a firm can use excess cash to adjust to a desired capital structure without incurring flotation costs.
Alternatively, managers could enrich controlling shareholders by selling more policies, using the
proceeds to reduce outstanding equity and thereby increase leverage if they believed that they
could sell policies at a sufficient premium or retire equity at a sufficient discount. Managers need
not retire equity to make such a swap worthwhile if they chose instead to use policy-generated cash
to finance new projects or increase capital levels to satisfy regulators.
When the manager chooses to undertake a capital structure swap, they will essentially increase
or reduce the expected value of the loss reserves by some proportion α. When 0 < α < 1, the
manager is purchasing reinsurance funded by an equity issue. When α > 1, the manager is issuing
8 Some may suggest that these models require continuous trading and publicly tradable securities. First, as already
shown, Rubinstein (1976) derives the option pricing model in a discrete time framework. Second, while it may not
seem obvious at first, loss reserves are increasingly tradable. There has been a liquid reinsurance market in the
developed world for decades, constantly swapping risks and trading risk for cash. In addition, the past decade has
seen the proliferation of loss securitization, in which losses are bundled and sold to investors in exchange for LIBOR
plus risk premium coupons. Thus, these constraints should not apply to use of an option pricing model in this context.
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