Are there other uses for surplus allocation. Well there's monitoring profit,
but it seems to me that the correct surplus to allocate here is what was
originally allocated for pricing purposes. The allocation described below,
where surplus is released over time, I would call an accounting use. It
would be helpful e.g. if a regulator wanted the surplus allocated to
his/her state and such and such a line. On the other hand it vulnerable to
the "all the surplus is available to pay the losses for each policy"
argument.
>>> "Blanchard, Ralph S" <ralph.s.blanchard@travelers.com> 07/01/98
07:13am >>>
I agree with David Ruhm's analysis of this situation. The discussion
to-date seems to have confused two items, the surplus assigned to a
policy, which is a flow, and the surplus associated with a line at a point
in time, which is a stock amount.
The amount assigned to a policy should be a function of the risk
associated with writing the policy, and will change over time as the risk
changes. At first, the risk will include event risk. Examples of event risk
include:
. Catastrophe risk
. Large loss risk (such as a fire at a major resort leading to a
large number of suits and injured parties)
. High frequency risk as was seen in 1984 for WC, when an
expanding economy led to an increased use of inexperienced workers
and higher WC accident rate.
After the policy has "expired", the event risk will be essentially over, but
the estimation risk is still there. Therefore the surplus requirement should
drop but not go away once the losses move from the Unearned Premium
Reserve to the loss reserve. There is still some "event" type risk in the
IBNR reserve, as the events have occurred for policy trigger purposes
but the details are not available for estimation purposes. Once the claim
is reported, the estimation risk should decrease. Hence there is more
risk in the IBNR reserve than in the case plus Bulk reserve. (NOTE: This
line of reasoning can be found in an earlier paper by Bob Butsic, which
dealt with profitability pricing loads.)
Given the above conceptual framework, surplus supporting a policy
should start out at its highest at inception, and should gradually decrease
as risk disapates.
Note that the above framework would NOT necessarily give you the
same surplus loads by line. A WC policy for which losses take 10 years
to pay out may have the same paid loss duration as a GL policy, but the
risks could be totally different. The WC policy may have risk similar to an
annuity, while the GL policy may incorporate the far greater risks of the
tort system. The statement that surplus should strictly be a function of
duration breaks down most obviously when life insurance products are
considered. The surplus needed to support most life insurance reserves
is typically much less than the surplus needed to support casualty
reserves, even if the durations are similar.
After surplus is notionally assigned to a policy, the amounts assigned to
historic policies can be stacked up to get the total assigned to the line at
a point in time (i.e., the stock value). The faster the payout (or duration
of reserve) the smaller the stock value will be in relation to the initial
amount. This also implies that a start-up may have small initial capital
requirements inherent in its balance sheet risks, but the capital
requirements will steadily grow until it reaches a "steady state" or going
concern level.
One useful concept for capital management is the velocity of capital. If
the writer of a long tail line can eliminate the risk sooner after policy
expiration, then that writer can release the supporting capital sooner,
increasing capital velocity. If this could be done, then the overall capital
requirements (surplus stock) would be much lower. The faster the
capital velocity, the more flexible a company can be, and the slower the
capital velocity, the more locked-in the company will be.
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