RE: Allocating Surplus and Risk Loads -Reply

Ruhm, David ( (no email) )
Wed, 1 Jul 1998 13:28:52 -0400

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Duration is very relevant from the pricing perspective=2C because if the lo=
sses pay out quickly=2C the supporting capital can be released sooner=2E T=
he longer the losses take to pay out=2C the longer the surplus must be used=
to support the line=2C increasing the cost of capital=2E =28Note - this e=
ntire discussion of risk load has been based on the assumption that risk lo=
ad is supposed to correspond to the cost of capital used to support the bus=
iness=2E Other valid views exist=2E=29 You are correct in pointing out th=
at the amount of surplus allocated to a policy year of business that's abou=
t to be written is not proportional to the duration=3B but the line's surpl=
us =28for the =22accounting=22 purposes you referred to=29 is proportional =
to duratin because it includes surplus from earlier years=2C corresponding =
to the reserves from those years=2E The connection is that=2C at steady-st=
ate=2C the line surplus equals the one-year-prospective-pricing surplus tim=
es the duration=2C because as the single year runs off=2C it produces a dec=
lining sequence of reserve values which are equal to the reserves for each =
of the prior years=2E

All surplus allocation methods are subject to the =22all surplus supports=22=
criticism - practical questions =2F problems require that a reasonable met=
hod be found and applied=2E - David Ruhm

-----Original Message-----
From=3A=09Israel Krakowski =5BSMTP=3AIKRA0=40allstate=2Ecom=5D
Sent=3A=09Wednesday=2C July 01=2C 1998 12=3A59 PM
To=3A=09casnet=40lists=2Ecasact=2Eorg=40inetgw
Subject=3A=09RE=3A Allocating Surplus and Risk Loads -Reply

I think some of the discussion here is at cross purposes=2E If you will rec=
all
Glenn's first comment suggested that surplus allocation was
interchangeable with calculating a risk load--that is=2C it is primarily a =
pricing
function=2E Now this may not be its only function=2C but for that particula=
r
function it strikes me that a lot of the considerations below are not
germane=2C since pricing is done before the policy is issued=2E
Unfortunately Glenn himself=2C I believe=2C had conflated the issues=2E Thu=
s
from the risk load=2Fpricing angle I don't see what relevance the duration =
is=2E
It happens to be true that books of =28P=26C=29 business with longer durat=
ion
tend to be more risky=2C but there is no necessary connection here=2E It ma=
y
seem intuitive that a =22longer=22 policy should have more surplus associat=
ed
with it=2C but this is only form the =22accounting=22 perspective where you=
're
attempting to actually connect surplus with a particular policy=2Fline or
whatever=2E

Are there other uses for surplus allocation=2E Well there's monitoring prof=
it=2C
but it seems to me that the correct surplus to allocate here is what was
originally allocated for pricing purposes=2E The allocation described belo=
w=2C
where surplus is released over time=2C I would call an accounting use=2E It=

would be helpful e=2Eg=2E if a regulator wanted the surplus allocated to
his=2Fher state and such and such a line=2E On the other hand it vulnerabl=
e to
the =22all the surplus is available to pay the losses for each policy=22
argument=2E =

=3E=3E=3E =22Blanchard=2C Ralph S=22 =3Cralph=2Es=2Eblanchard=40travelers=2E=
com=3E 07=2F01=2F98
07=3A13am =3E=3E=3E
I agree with David Ruhm's analysis of this situation=2E The discussion
to-date seems to have confused two items=2C the surplus assigned to a
policy=2C which is a flow=2C and the surplus associated with a line at a po=
int
in time=2C which is a stock amount=2E

The amount assigned to a policy should be a function of the risk
associated with writing the policy=2C and will change over time as the risk=

changes=2E At first=2C the risk will include event risk=2E Examples of ev=
ent risk
include=3A
=09=2E Catastrophe risk
=09=2E Large loss risk =28such as a fire at a major resort leading to a
large number of suits and injured parties=29
=09=2E High frequency risk as was seen in 1984 for WC=2C when an
expanding economy led to an increased use of inexperienced workers
and higher WC accident rate=2E

After the policy has =22expired=22=2C the event risk will be essentially ov=
er=2C but
the estimation risk is still there=2E Therefore the surplus requirement sh=
ould
drop but not go away once the losses move from the Unearned Premium
Reserve to the loss reserve=2E There is still some =22event=22 type risk i=
n the
IBNR reserve=2C as the events have occurred for policy trigger purposes
but the details are not available for estimation purposes=2E Once the clai=
m
is reported=2C the estimation risk should decrease=2E Hence there is more
risk in the IBNR reserve than in the case plus Bulk reserve=2E =28NOTE=3A =
This
line of reasoning can be found in an earlier paper by Bob Butsic=2C which
dealt with profitability pricing loads=2E=29

Given the above conceptual framework=2C surplus supporting a policy
should start out at its highest at inception=2C and should gradually decrea=
se
as risk disapates=2E =

Note that the above framework would NOT necessarily give you the
same surplus loads by line=2E A WC policy for which losses take 10 years
to pay out may have the same paid loss duration as a GL policy=2C but the
risks could be totally different=2E The WC policy may have risk similar to=
an
annuity=2C while the GL policy may incorporate the far greater risks of the=

tort system=2E The statement that surplus should strictly be a function of=

duration breaks down most obviously when life insurance products are
considered=2E The surplus needed to support most life insurance reserves
is typically much less than the surplus needed to support casualty
reserves=2C even if the durations are similar=2E

After surplus is notionally assigned to a policy=2C the amounts assigned to=

historic policies can be stacked up to get the total assigned to the line a=
t
a point in time =28i=2Ee=2E=2C the stock value=29=2E The faster the payout=
=28or duration
of reserve=29 the smaller the stock value will be in relation to the initia=
l
amount=2E This also implies that a start-up may have small initial capital=

requirements inherent in its balance sheet risks=2C but the capital
requirements will steadily grow until it reaches a =22steady state=22 or go=
ing
concern level=2E

One useful concept for capital management is the velocity of capital=2E If=

the writer of a long tail line can eliminate the risk sooner after policy
expiration=2C then that writer can release the supporting capital sooner=2C=

increasing capital velocity=2E If this could be done=2C then the overall c=
apital
requirements =28surplus stock=29 would be much lower=2E The faster the
capital velocity=2C the more flexible a company can be=2C and the slower th=
e
capital velocity=2C the more locked-in the company will be=2E

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