The way that a percentage of loss reserves is consistent with the duration concept is this: Loss reserves include prior accident years - for long-tailed lines, many of them. One can think of the accident years as stacked on top of each other, for visualization purposes. Since, for the same annual volume of business, the loss reserves are proportional to duration (assuming level writings, for now), duration is included. A longer-tailed line will have proportionately more surplus allocated to it.
If writings are not level, allocating in proportion to loss reserves still works, because the amount of variation being "cushioned" is proportional to the loss reserves. The "last dollar" rule holds, since the last dollar of reserves (which are assumed adjusted for adequacy) is paired to a proportional amount of surplus for its entire lifetime.
For calculating a risk load for pricing from this surplus allocation, it is true that just using loss reserves will not work - instead, one would use a level writings assumption, which is equivalent to multiplying by duration.
Maybe our conceptual difference is this: I'm assuming the same amount of surplus is appropriate for a dollar of loss reserves at age 24 as for the same dollar at age 60. Are you assuming something different, and is that the difference in our respective views? I considered using a decreasing linear function of age to represent this idea, but it wasn't clear that older reserves were less volatile with respect to ultimate. - David Ruhm
-----Original Message-----
From: Bradford S. Gile [SMTP:kgecorp@ix.netcom.com]
Sent: Monday, June 29, 1998 8:45 PM
To: Meyers, Glenn G.
Cc: Ruhm, David; 'casnet(a)lists.casact.org'
Subject: Re: Allocating Surplus and Risk Loads
The basic ideas that I have been following are:
1. Surplus allocated to a given line should be proportional to loss
duration, because surplus should not be released until the last loss dollar
has ben paid.
2. Volatility in losses and/or pricing inaccuracy (parameter risk) must be
reflected. I suggest the simple idea that surplus should be directly
proportional to the (historical) coefficient of variation on loss ratios.
If these measures are adopted, I fail to see how a percentage of loss
reserves, including unearned premium, can be reasonable for volatile
long-tailed lines.
Brad Gile
Meyers, Glenn G. wrote:
> David:
>
> 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
>
> ----------
> 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
>
> Visit the CAS Web Site at http://www.casact.org
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