=09You state that the longer a reserve is held=2C the greater the dollar co=
st of the capital needed to support it=2C which I agree with=2E But=2C the=
amount of capital doesn't necessarily need to be higher for the dollar cos=
t of capital to be higher=3B the length of time could be higher=2C holding =
the same amount for a longer period=2E The model I have in mind is that a =
dollar of reserves has a certain amount of capital =22attached=22 to it=2C =
starting from the day it is put up until it becomes a paid-loss dollar=2C a=
t which time the capital is released=2E If the reserve has a long duration=
=2C the capital is held longer=2C which increases the cost of capital =28bu=
t not the amount=29=2C which does imply a higher risk load=2E If=2C at som=
e point in time=2C we measure the amount of capital assigned to a line by t=
his process=2C the amount will be proportional to duration=2E The distinct=
ion is that each dollar of reserve doesn't get more capital assigned to it =
on the basis of duration=2C but the aggregated reserve for the line does=2C=
because it's a larger reserve as a consequence of the duration=2E
=09Fundamentally=2C this model is based on the concept of surplus' use as a=
cushion for adverse reserve development=2E Each reserve dollar is cushion=
ed by a certain amount of surplus=2E The amount of cushion needed for each=
dollar of outstanding loss is proportional to the risk of adverse excursio=
n=2C which is the reason to use the coefficient of variation of loss ratios=
as a measure of risk =28this assumes premium adequacy=29=2E
=09The loss portion of the unearned premium reserve needs surplus too=2C be=
cause=2C practically speaking=2C the company is =22on the hook=22 for those=
exposures since they have been written=2E Furthermore=2C the risk is high=
er since the accidents are as yet unknown =28e=2Eg=2E=2C a hurricane could =
still happen to exposures associated with the UPR=2C but not with loss rese=
rves=29=2E On the other side=2C the UPR contains a surplus-generating prof=
it =28and acq'n expense=29 component=2C so that as each dollar of UPR gets =
earned=2C a few cents of surplus are generated=2E This =22on-the-fly=22 su=
rplus automatically cushions the loss portion of the UPR=2C lessening the a=
mount of balance-sheet surplus needed for allocation=2E
=09All of these concepts are consistent with your formula=2C with which I a=
gree=2C to the extent that it is used to allocate surplus for the purpose o=
f calculating risk loads for prospective pricing=2E The calculations under=
lying the crucial=2C enigmatic =22Marginal Surplus=22 factor are a ripe fie=
ld for discussion=2E I have read some of your work in this area=2C enjoyed=
it=2C and recommend it to anyone interested in surplus allocation=2E - Dav=
id Ruhm
-----Original Message-----
From=3A=09Meyers=2C Glenn G=2E =5BSMTP=3AGMeyers=40iso=2Ecom=5D
Sent=3A=09Tuesday=2C June 30=2C 1998 9=3A50 AM
To=3A=09'CASNet'
Subject=3A=09RE=3A Allocating Surplus and Risk Loads
David and Brad=3A
On the surface I don't agree with allocating surplus in proportion to
the loss portion of the unearned premium reserve for startup business=2E
The loss reserve number by itself does not say how long the reserve must
be held and the longer you hold the reserve=2C the greater the =28dollar=29=
cost of the capital needed to support it=2E
Looking a little deeper and remembering a version of Murphy's law -
Constants aren't - I can see a way to wiggle out of this one by varying
the constant of proportionality with duration=2E
Actually=2C I prefer formulas with less wiggle room=2E At the very least
you learn something when things go wrong=2E Let me expose a formula to
the virtual arrows of CASNet=2E
Allocated Surplus for a line of insurance is proportional to=3A
Expected Loss times
Duration times =
Marginal Surplus of the line =28which implicitly allows for covariance and
parameter uncertainty=2E=29
I will tighten this up by stating that the constant of proportionality
should be the same for all lines - in defiance of Murphy=2E
I will leave some wiggle room in my definition of total surplus=2E My
favorite surplus formula is to make it a function of the insurer's
aggregate variance=2E But I do not want to make a hard stand here=2E
=
Glenn Meyers
Insurance Services Office=2C Inc=2E
Internet=3A gmeyers=40iso=2Ecom =
Voice=3A=28212=29 898-5938 =
Fax=3A =28212=29 898-6060 =
=09----------
=09From=3A Ruhm=2C David =5BSMTP=3ADavid=2ERuhm=40aig=2Ecom=5D
=09Sent=3A Monday=2C June 29=2C 1998 10=3A16 AM
=09To=3A 'Meyers=2C Glenn G=2E'
=09Cc=3A 'casnet=28a=29lists=2Ecasact=2Eorg'
=09Subject=3A RE=3A Allocating Surplus and Risk Loads
=09Glenn=2C
=09=09In fact=2C I have worked through the math somewhat
extensively=2C since I built a surplus allocation model for a prior
employer which was based on these concepts =28including the duration
concept=29=2E
=09=09I respectfully disagree with your claim that there would
be a problem with a startup or growing line of business=2C as long as you
are also allocating surplus in proportion to the loss portion of the
unearned premium reserve=2E If one does not include this additional loss
element in the allocation process=2C your point does appear valid=2E Does
this seem correct to you=3F - David Ruhm
=09----------
=09From=3A Bradford S=2E Gile =5BSMTP=3Akgecorp=40ix=2Enetcom=2Ecom=5D
=09Sent=3A Monday=2C June 29=2C 1998 9=3A45 PM
=09To=3A Meyers=2C Glenn G=2E
=09Cc=3A 'Ruhm=2C David'=3B 'casnet=40lists=2Ecasact=2Eorg'
=09Subject=3A Re=3A Allocating Surplus and Risk Loads
=09The basic ideas that I have been following are=3A
1=2E=09Surplus allocated to a given line should be proportional to loss
duration=2C because surplus should not be released until the last loss
dollar has ben paid=2E
2=2E=09Volatility in losses and=2For pricing inaccuracy =28parameter risk=29=
must be reflected=2E I suggest the simple idea that surplus should be
directly proportional to the =28historical=29 coefficient of variation on
loss ratios=2E
=09If these measures are adopted=2C I fail to see how a percentage of
loss reserves=2C including unearned premium=2C can be reasonable for
volatile long-tailed lines=2E
=09Brad Gile
Visit the CAS Web Site at http=3A=2F=2Fwww=2Ecasact=2Eorg
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