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Chris,
Good question but I think you need to be more specific regarding the
quota-share reinsurance:
For ceding company: Vertical sharing will have no effect on ceding
company's entire portfolio(regardless of the correlation and ER of the
Portfolio).
For assuming company: It might and might not effect the exposure ratios
depends on 1) the correlation between the assumed business and the existing
business, 2) the exposure ratio between the assumed business and the
existing business.
An interesting fact from the assuming company's point of view(see example
below from Ben Walden, 96 #11), the equation of ER as a function of quota-
share % has the characteristics of a second degree polynomial with upward
concavity. This implies a possibility of two solutions for every Exposure
Ratio(notice that at both 83% and 0%, the ER is 0.1), and also an unique
solution at the absolute minimum. Thus, an additional question can be asked
from this example, what is the quota-share % in order to minimize the ER for
the reinsurer?
Another interesting fact about stone's paper is that this concept does not
have to apply to reinsurance or Cat risk specifically. It is really a way
to derive UW profit load (from the d factor) using the stability constraint
embedded in the ER. I looked at this paper as an extension to Ferrari's
paper on total rate of return. UW profit margin piece in the total rate of
return from Ferrari's paper can be derived using a stability(or
profitability and survival) constraint in stone's paper with probability and
std given. For example, calculate the total rate of return on economic
premium if the insurer wants to make sure that its surplus and premium will
be enough to cover losses and expenses with less than X% of probability.
---Yin
> -----Original Message-----
> From: Pam Kaplan [SMTP:PKaplan@scpie-ahi.com]
> Sent: Wednesday, March 31, 1999 2:05 PM
> To: studygroup10@lists.casact.org
> Subject: RE: Stone - Does vertical sharing reduce ER of portfolio?
>
> From a reinsures standpoint, it is good as they can do more separate
> vertical sharing treaties and hence reduce risk so eggs are not all in
> one basket. I know this is discussed but not sure it is the question
> asked here. The impact on the ceding company's ER would not matter
> (unless you consider multiple insurer's less risk, which they are).
>
> Also I know it mentions that you have a greater number of reinsures
> able to handle the risk if it is partitioned into smaller sections.
> These ideas may help if the question relates to the industry's capacity
> or ER.
>
> So are we supposed to read in too much or not enough into these types of
> questions? Is this paper on the syllabus next year? Let's get it
> tossed off or get clarifications and corrections added so we don't waste
> our precious study time.
>
>
>
> -----Original Message-----
> From: ben.walden@milliman.com
> [mailto:ben.walden@milliman.com]
> Sent: Wednesday, March 31, 1999 11:38 AM
> To: chrisheim@email.msn.com
> Cc: studygroup10@lists.casact.org
> Subject: Re: Stone - Does vertical sharing reduce
> ER of portfolio?
>
> I agree this is a confusing concept - here is my
> interpretation.
>
> Vertical sharing (quota-sharing) of a risk will not
> lower the total exposure ratio of the risk itself. However, vertical
> sharing will reduce the impact an added risk has on the exposure ratio
> of a portfolio.
>
> In other words, vertical sharing of a risk will reduce
> the exposure ratio for the portfolio relative to taking the entire risk.
>
>
> See study manual question A19. (96 #11).
> The original portfolio has a SD of 100 and a mean of
> 1000, for an ER of 10%.
> If a risk is added with a SD of 50 and a mean of 100,
> the new portfolio ER is (100^2 + 50^2)^1/2 / (1000+100) = .1016
> If only 83% of this risk is taken, the portfolio ER is
> lower, (100^2 + 41.666^2)^1/2 / (1000+83.33) = .1000
> Taking even lower shares of this risk will further
> reduce the new portfolio exposure ratio.
>
> Hope this helps.
>
> Ben W
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Chris,
Good question but I think =you need to be more specific regarding the quota-share =reinsurance:
For ceding company: =Vertical sharing will have no effect on ceding company's entire =portfolio(regardless of the correlation and ER of the =Portfolio).
For assuming company: =It might and might not effect the exposure ratios depends on 1) the =correlation between the assumed business and the existing business, 2) =the exposure ratio between the assumed business and the existing =business.
An interesting fact from the =assuming company's point of view(see example below from Ben Walden, 96 =#11), the equation of ER as a function of quota- share % has the =characteristics of a second degree polynomial with upward =concavity. This implies a possibility of two solutions for every =Exposure Ratio(notice that at both 83% and 0%, the ER is 0.1), and also =an unique solution at the absolute minimum. Thus, an additional =question can be asked from this example, what is the quota-share % in =order to minimize the ER for the reinsurer?
Another interesting fact =about stone's paper is that this concept does not have to apply to =reinsurance or Cat risk specifically. It is really a way to =derive UW profit load (from the d factor) using the stability =constraint embedded in the ER. I looked at this paper as an =extension to Ferrari's paper on total rate of return. UW profit margin =piece in the total rate of return from Ferrari's paper can be derived =using a stability(or profitability and survival) constraint in stone's =paper with probability and std given. For example, calculate the =total rate of return on economic premium if the insurer wants to make =sure that its surplus and premium will be enough to cover losses and =expenses with less than X% of =probability.
---Yin
-----Original Message-----
From: Pam Kaplan [SMTP:PKaplan@scpie-ahi.com]
Sent: Wednesday, March 31, 1999 2:05 PM
To: studygroup10@lists.casact.org
Subject: = RE: Stone - Does vertical sharing =reduce ER of portfolio?
From a reinsures standpoint, it =is good as they can do more separate
vertical sharing treaties and =hence reduce risk so eggs are not all in
one basket. I know this =is discussed but not sure it is the question
asked here. The impact on =the ceding company's ER would not matter
(unless you consider multiple =insurer's less risk, which they are).
Also I know it mentions that you =have a greater number of reinsures
able to handle the risk if it =is partitioned into smaller sections.
These ideas may help if the =question relates to the industry's capacity
or ER.
So are we supposed to read in =too much or not enough into these types of
questions? Is this paper =on the syllabus next year? Let's get it
tossed off or get =clarifications and corrections added so we don't waste
our precious study time.
= -----Original Message-----
= From: ben.walden@milliman.com
[mailto:ben.walden@milliman.com]
= Sent: Wednesday, March 31, 1999 11:38 =AM
= To: =chrisheim@email.msn.com
= Cc: =studygroup10@lists.casact.org
= Subject: =Re: Stone - Does vertical sharing reduce
ER of portfolio?
= I agree this is a confusing concept - here =is my
interpretation.
= Vertical sharing (quota-sharing) of a risk will =not
lower the total exposure ratio =of the risk itself. However, vertical
sharing will reduce the impact =an added risk has on the exposure ratio
of a portfolio.
= In other words, vertical sharing of a risk will =reduce
the exposure ratio for the =portfolio relative to taking the entire risk.
= See study manual question A19. (96 #11).
= The original portfolio has a SD of 100 and a mean =of
1000, for an ER of 10%.
= If a risk is added with a SD of 50 and a mean of =100,
the new portfolio ER is (100^2 =+ 50^2)^1/2 / (1000+100) =3D .1016
= If only 83% of this risk is taken, the portfolio =ER is
lower, (100^2 + 41.666^2)^1/2 / =(1000+83.33) =3D .1000
= Taking even lower shares of this risk will =further
reduce the new portfolio =exposure ratio.
= Hope this helps.
= Ben W