You idea of allocating surplus (or calculating risk load) in proportion
to the loss reserve is conceptually different from allocating surplus in
proportion to the duration - although in some cases the two could be
close.
Let me explain. The loss reserve should (at least in theory) be the
same until the claim is paid. There is nothing in the loss reserve that
indicates how long the supporting capital must be held. It indicates
only how much loss should be paid.
Now as you pay the claims, you reduce the loss reserve on the paid
claims to zero and if you work through the math, the duration and the
loss reserve (for the current and prior years) should be directly
proportional ASSUMING THE UNDERLYING EXPOSURE HAS BEEN CONSTANT OVER
TIME. In general, exposure is increasing. This could be really bad for
a startup line of business.
If given the choice between allocating surplus in proportion to the
duration or the loss reserve, I would choose duration.
Glenn Meyers
Insurance Services Office, Inc.
Internet: gmeyers@iso.com
Voice:(212) 898-5938
Fax: (212) 898-6060
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From: Ruhm, David [SMTP:David.Ruhm@aig.com]
Sent: Friday, June 26, 1998 11:07 AM
To: 'CASNET'
Subject: RE: Allocating Surplus and Risk Loads
Three comments in reply to Glenn Meyers' comments on surplus
allocation:
1) Mr. Meyers makes a good point that surplus allocation
is primarily a pricing tool. In addition, it is also commonly used in
the related, but retrospective, function of profitability analysis.
When a company uses a surplus allocation method to calculate
profitability (such as ROE), it makes sense for the company to
prospectively price using a pricing model that is based on the same
measure of profitability and that uses the same method of surplus
allocation. Management's ability to aim for company targets is enhanced
by use of such a "parallel" pricing model.
2) Mr. Meyers indicates that the "real purpose" of
allocating surplus is risk load calculation. In fact, there may not be
a singular ("real") purpose to allocation of surplus, but rather several
practical applications.
3) Mr. Meyers makes the point that longer-tailed lines
require surplus to be held longer, and that risk load should therefore
be directly related to loss duration. This seems correct. One way of
accounting for this is to allocate part of the surplus in proportion to
loss reserves. An adjustment factor can also be included for the line's
volatility of reserve development to ultimate. - David Ruhm
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