Richard, you are correct that the EPD by definition cannot be negative. The
problem being considered is given an acceptable EPD ratio, what surplus is
required to lower the EPD ratio to that threshold. Of course if the EPD
ratio with no surplus is already lower than the threshold, such as in
David's example, the "needed surplus" will be negative.
In David's example, if the company holds surplus of n, the deficit in case
of a loss is ($20,000-n). Thus, the "needed surplus" to achieve a 5% EPD
ratio will be N, such that:
[ (20,000 - N) * 99% ]
------------------------------- = 5%
(990,000)
Solving for N gives $-30,000.
As mentioned, an unrealistic example, but an insurer that reserves very
conservatively could have an EPD ratio lower than the threshold with no
additional capital.
"Ruhm, David" <David.Ruhm@AIG.com> on 01-07-99 11:44:57 AM
To: "'CASNET'" <casnet@lists.casact.org>
cc: (bcc: Daniel Greer/USFG)
Subject: RE: Excess Policyholder Deficit Examples
Consider a $1,000,000 loss having 99% probability (1% probability of zero
loss). Expected loss equals $990,000. Let assets equal $980,000 which
means surplus is ($10,000) which is less than zero. The EPD is 99% x
$20,000 = $19,800. The EPD ratio is EPD / Expected Loss = 19,800 /
990,000
= 2%, which is less than a 5% criterion. To lower the EPD ratio even
further, just increase the probability of loss toward 100% and move the
assets closer to the expected loss. (Not a realistic example, as Glenn
pointed out, but it does the job.) - David Ruhm
> -----Original Message-----
> From: Richard A. Derrig [SMTP:rad@shore.net]
> Sent: Thursday, January 07, 1999 11:28 AM
> To: Meyers, Glenn G.
> Cc: casnet@lists.casact.org
> Subject: RE: Excess Policyholder Deficit Examples
>
> Glenn: Where do I go wrong? Is not the EPD in the case of a fixed loss L
> (fully funded by a risk-free security) zero? If funding is a variable
then
> EPD should be positive if default risk is non-zero.
>
> Richard A. Derrig, Ph.D.
> Senior Vice President, Auto Insurers Bureau
> 101 Arch Street
> Boston, MA 02110
> Phone: (617) 439-4542
> Fax: (617) 439-6789
> Email: rad@shore.net
>
> > -----Original Message-----
> > From: Meyers, Glenn G. [mailto:GMeyers@iso.com]
> > Sent: Tuesday, January 05, 1999 9:27 AM
> > To: 'CASNet'
> > Subject: Excess Policyholder Deficit Examples
> >
> >
> > Yesterday's posting yielded a large number of both private and public
> > responses. I would like to think a bit before I react to them. (This
> is
> > one reason why I like e-mail discussions.)
> >
> > I did receive a request for some EPD examples. This I can provide now.
> > Attached is an Excel 97 spreadsheet I created for this purpose. It
uses
> > macros with Solver to calculate the surplus implied by the probability
> of
> > ruin criteria, and by the EPD criteria.
> >
> > <<Gamma Example for CASNET.xls>>
> >
> > A single point mass provides the ultimate example. Suppose an
> > insurer as a
> > fixed loss L. Then the EPD for a surplus of -p*L is p.
> >
> > Glenn Meyers
> > Insurance Services Office, Inc.
> > Internet: gmeyers@iso.com <mailto:gmeyers@iso.com>
> > Voice:(212) 898-5938
> > Fax: (212) 898-6060
> >
> >
> >
>
>
>
> Visit the CAS Web Site at http://www.casact.org
> ===============================================
> To subscribe or unsubscribe from CASNET:
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> Type in the body join casnet to subscribe
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