Ruhm, David wrote:
> Duration is very relevant from the pricing perspective, because if the =
losses pay out quickly, the supporting capital can be released sooner. T=
he longer the losses take to pay out, the longer the surplus must be used=
to support the line, increasing the cost of capital. (Note - this entir=
e discussion of risk load has been based on the assumption that risk load=
is supposed to correspond to the cost of capital used to support the bus=
iness. Other valid views exist.) You are correct in pointing out that t=
he amount of surplus allocated to a policy year of business that's about =
to be written is not proportional to the duration; but the line's surplus=
(for the "accounting" purposes you referred to) is proportional to durat=
in because it includes surplus from earlier years, corresponding to the r=
eserves from those years. The connection is that, at steady-state, the l=
ine surplus equals the one-year-prospective-pricing surplus times the dur=
ation, because as the single year runs off, it
> produces a declining sequence of reserve values which are equal to the =
reserves for each of the prior years.
>
> All surplus allocation methods are subject to the "all surplus supports=
" criticism - practical questions / problems require that a reasonable me=
thod be found and applied. - David Ruhm
>
> -----Original Message-----
> From: Israel Krakowski [SMTP:IKRA0@allstate.com]
> Sent: Wednesday, July 01, 1998 12:59 PM
> To: casnet@lists.casact.org@inetgw
> Subject: RE: Allocating Surplus and Risk Loads -Reply
>
> I think some of the discussion here is at cross purposes. If you will r=
ecall
> Glenn's first comment suggested that surplus allocation was
> interchangeable with calculating a risk load--that is, it is primarily =
a pricing
> function. Now this may not be its only function, but for that particula=
r
> function it strikes me that a lot of the considerations below are not
> germane, since pricing is done before the policy is issued.
> Unfortunately Glenn himself, I believe, had conflated the issues. Thus
> from the risk load/pricing angle I don't see what relevance the duratio=
n is.
> It happens to be true that books of (P&C) business with longer duratio=
n
> tend to be more risky, but there is no necessary connection here. It ma=
y
> seem intuitive that a "longer" policy should have more surplus associat=
ed
> with it, but this is only form the "accounting" perspective where you'r=
e
> attempting to actually connect surplus with a particular policy/line or=
> whatever.
>
> Are there other uses for surplus allocation. Well there's monitoring pr=
ofit,
> but it seems to me that the correct surplus to allocate here is what wa=
s
> originally allocated for pricing purposes. The allocation described be=
low,
> 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 vulnerabl=
e 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 po=
int
> 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 ri=
sk
> changes. At first, the risk will include event risk. Examples of even=
t 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 cl=
aim
> is reported, the estimation risk should decrease. Hence there is more
> risk in the IBNR reserve than in the case plus Bulk reserve. (NOTE: T=
his
> 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 decr=
ease
> 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 t=
he
> 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 li=
ne at
> a point in time (i.e., the stock value). The faster the payout (or dur=
ation
> of reserve) the smaller the stock value will be in relation to the init=
ial
> amount. This also implies that a start-up may have small initial capit=
al
> requirements inherent in its balance sheet risks, but the capital
> requirements will steadily grow until it reaches a "steady state" or go=
ing
> 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 poli=
cy
> expiration, then that writer can release the supporting capital sooner,=
> increasing capital velocity. If this could be done, then the overall c=
apital
> requirements (surplus stock) would be much lower. The faster the
> capital velocity, the more flexible a company can be, and the slower th=
e
> capital velocity, the more locked-in the company will be.
>
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