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
-----Original Message-----
From: Meyers, Glenn G. [SMTP:GMeyers@iso.com]
Sent: Friday, June 26, 1998 9:35 AM
To: casnet@lists.casact.org@inetgw
Subject: Allocating Surplus and Risk Loads
I would like to comment on the allocation of surplus discussion.
First - I hope that most of us would agree that the allocation of
surplus is a pricing tool, and is not directly connected to the safety
of the insurance policy that is "supported" by the allocated surplus.
To quote Chuck McClenehan "A monoline auto company with $100 million of
surplus is not the same as a multiline company with $100 million of
surplus allocated to its auto line."
Second - The real purpose of allocating surplus is to calculate a risk
load. Conversely, you can allocate surplus in proportion to your
favorite risk load. That is to say allocating surplus (as it is used)
is equivalent to a risk load formula.
The difference between the approaches is that pricing by allocating
surplus is a "top-down" method and the risk load approach is a
"bottom-up" method. There are probably some insights that the surplus
allocaters can gain from looking at risk loads.
I like to view risk load as the cost of marginal surplus. I offer three
ideas related to some of the knottier problems involved in allocating
surplus.
1. You have to hold surplus longer to support long tailed lines.
Therefore the risk load should depend (among other things) on a factor
times the duration of the losses - - at least as a first approximation.
2. Marginal surplus methods can account for correlations between
lines. Suppose, for example, you assume that the total needed surplus
is a function of the variance. If Y is the random loss of the policy in
question and X the random loss for the rest of the insurer's business,
then the marginal variance is Var[Y] + 2Cov[X,Y].
You can also treat correlations between losses and
assets by marginal methods.
3. You can treat "surplus substitutes", such as reinsurance, very
much the same as surplus. For example, you can calculate the marginal
cost of reinsurance.
I suspect there are some things that the surplus allocaters can tell us
riskies.
Here are some papers for those who want more information on marginal
surplus risk loads.
Rodney Kreps - "Reinsurer Risk Loads from Marginal Surplus Requirements"
- 1990 PCAS
Glenn Meyers - "The Competitive Market Equilibrium Risk Load Formula for
Catastrophe Ratemaking" 1996 PCAS. This is available on the CAS web
site under "Publications"
Glenn Meyers
Insurance Services Office, Inc.
Internet: gmeyers@iso.com
Voice:(212) 898-5938
Fax: (212) 898-6060
Visit the CAS Web Site at http://www.casact.org
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