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Review of Capital Allocation for Insurance Companies
ARIA Paper by Stewart C. Myers and James R. Read, Jr.
PCAS Review by Paul J. Kneuer, FCAS
The CAS must thank Doctors Myers and Read for their intriguing article. They have
developed a practical algorithm for a previously subjective problem. Regulators often
require a way to measure at least the indirect cost of an insurer’s Surplus in ratemaking.
This article offers a well-defined solution, together with a theoretical and philosophical
explanation. There are practical problems with any approach to pricing administration in
a largely free economy and with the most common theoretical context for administered
rate regulation. But these issues are outside of the author’s scope.
The Authors’ Proposal
Profit targets or premium levels for regulated insurance products often reflect the
amount of Surplus that an insurer commits to support the business under review and the
cost of committing that Surplus. The authors suggest the following algorithm to
appropriately reflect the cost of committing Surplus to a particular insurance product:
1. Compute the total expected default value of an insurer or of a group of insurers.
This would be for the entire industry in an administered pricing state, such as
Massachusetts.
2. Compute the insurers’ marginal default value in respect of each product segment
(the partial derivatives of the overall default value with respect to an increase in
the amount of expected losses for each product.)
The authors show the novel and intriguing result that when the quantity of (expected
losses x marginal default value) for each product is summed over all products, the result
is equal to the overall expected default value. This is a surprising result. There are
diversification benefits in combining risky but partly uncorrelated ventures, so the
marginal cost of adding more of a product is generally less than the average cost. The
by-line costs usually do not “add up.” (This is the financial root of all insurance.) The
new contribution here is to multiply these marginal values by the current amount of
expected losses in each product category. Since these results do “add up”, they can be
used as an allocation base.
3. Allocate the overall Surplus among products in proportion to (marginal default
value x expected losses.)
In the Myers-Cohn pricing approach commonly used in Massachusetts, regulators
recognize that the allocated Surplus earns investment profits in addition to operating
returns and that these investment profits are currently subject to two rounds of taxation:
once paid by insurers corporately, and then paid again by the owners of the insurers.
Regulated rates must allow a provision for the cost of this second taxation, or else they
are confiscatory.
4. Load the premiums by a pre-tax provision of (Allocated Surplus x Return on
Assets x Time Factor x Tax Rate). A sample calculation is shown on page two of
the following exhibit, assuming a one-year maturity and that the authors’
algorithm provided a 50% surplus-to-expected-loss ratio.
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