2008 Seminar on Reinsurance
Reinsuring Commercial Umbrella
Brian E. Johnson, ACAS, MAAA
Agenda
•
Basic Review of Commercial Umbrella
–Umbrella vs Following Form Excess
–How is an Umbrella policy written and priced?
• Discuss
the more common ways an Umbrella portfolio
can be reinsured
–Quota Share (Cessions)
–Excess of Loss
–Things to consider
 Market
Slide 2
Trends
Basic Umbrella Review
 Sometimes
a primary insurance company will write an
excess liability policy.
 Excess
liability policies take two main forms
–Umbrella
–Following Form Excess
 Both
types of excess policies are written “on top” of
underlying policy usually with a requirement that the
insured maintain the underlying coverages.
 Other
than where noted, these two coverages can be
priced using similar methodologies.
Slide 3
Basic Umbrella Review
Slide 4

A Following Form Excess does just what it says. It
follows an underlying policy and provides for
additional limit. All the same coverages and
exclusions on the underlying policy are applicable to
the Following Form Excess policy.

An umbrella policy is a little different. In addition to
adding limits to an underlying policy (ies), it may
“drop-down” to cover losses not covered by the
underlying policy unless it is specifically endorsed to
follow the underlying in coverage.

An umbrella policy may also cover certain loss
adjustment expenses not covered by the underlying
policy (drop down coverage).
Basic Umbrella Review
Example of drop-down:
Tatooine Cantina buys a $1M GL policy that excludes
liquor liability. They also buy a $2M umbrella policy
on top of it (attaching at $1M). The umbrella does
not have the liquor exclusion. The bartender on duty
continues to serve alcohol to a patron after he was
visibly drunk. That patron gets into a bar fight and
cuts off the arm of another customer, Bob. Bob sues
Tatooine and wins $500K. Even though this loss is
below the $1M retention, the umbrella “drops down”
to pick up the loss.
Slide 5
Basic Umbrella Review
Slide 6

In commercial lines, excess or umbrella policies are
priced by applying factors to the premium of the
underlying policy. Manual or “net” premium could be
used.

These factors are derived from severity curves (ILFs)
but include a load for the insurers’ profit and
expenses.

Typically the first $1M of Umbrella is priced as a
percentage of the premium for the underlying lines
(these are called umbrella factors).

Additional layers are priced as a percent of the first
$1M of umbrella or a percent of each preceding
layer.
Basic Umbrella Review
Slide 7

In addition to the excess factors, there are usually
minimum premiums per $1M in limit and/or policy
applicable.

Quite often, the underwriter also has some flexibility
to apply discretionary credits/debits to the umbrella
factors or final umbrella premium.

An insurance company can write an umbrella policy
over their own underlying policies or over another
insurance company’s policies. (supported vs
unsupported).
Reinsuring an Umbrella Portfolio:
Quota Share
Slide 8

Typically reinsurance on umbrella policies is provided
on a proportional basis.

The quota share cession percentage can be the same
for all limits or vary by layer.

If there is enough credible information, a reinsurer
pricing this business would be able to do an ELR
analysis by trending umbrella premium and trending
and developing umbrella losses.

There will not be many losses in the layer. A loss
ratio analysis based on experience rating would not
be credible.
Reinsuring an Umbrella Portfolio:
Quota Share

There are a few important things that must be
considered in order to successfully experience rate
an umbrella portfolio.
– Historical individual umbrella losses with
attachment point for every loss (also excess vs
drop-down) and historical umbrella premium.
– Underlying rate changes
– Umbrella rate changes
 Changes in umbrella factors
 Changes in amount of discretionary pricing.
– Excess loss development factors
Slide 9
– Drift in limits distribution
Reinsuring an Umbrella Portfolio:
Quota Share

Another way to estimate the profitability of an
umbrella quota share (ELR) is to split the analysis into
two pieces:
– Using ground-up data, estimate the adequacy of
the underlying premium
– Estimate the adequacy of the umbrella factors in
comparison to some industry or reinsurance
company yardstick
– The theory is that the ELR of the umbrella policy
would be affected by both the adequacy of the
underlying premiums and excess factors.

Slide 10
Let’s illustrate this with an example.
Reinsuring an Umbrella Portfolio:
Quota Share
Cortana Re has been given a chance to reinsure a book of commercial
umbrella business written by Covenant Insurance. Covenant writes
either $1M limit or $2M limit umbrellas over their own $1M GL
policies. You have the following information about the account. You
also use a pareto distribution to develop the following limited severity
curve. Estimate the ELR on the Umbrella portfolio.
ERL on Covenant's GL policies:
Umbrella factor for 1st Mill:
Umbrella factor for 2nd Mill:
% umbrella policies at 1M:
% umbrella policies at 2M:
Slide 11
Limit
1,000,000
2,000,000
3,000,000
75%
20% of underlying $1M policy
75% of 1st Mill of umbrella
40%
60%
Avg Sev
16,000
19,084
21,555
Reinsuring an Umbrella Portfolio:
Quota Share
 Essentially
the Umbrella factors are the ratio of
umbrella premium to underlying premium:
premumb
premund
 Using
your severity curve, you promulgate an excess
loss factor for each layer:
lossumb
lossund
Slide 12
Reinsuring an Umbrella Portfolio:
Quota Share

A ratio of the two factors (umbrella adequacy factor)
multiplied by the underlying ELR equates to the
umbrella loss divided by the umbrella premium.
lossumb
lossund
lossund
X
premund
lossumb
=
premumb
premumb
premund

Slide 13
Using a simple Excel spreadsheet you can estimate
the weighted average adequacy factor and ELR for an
umbrella portfolio.
Reinsuring an Umbrella Portfolio:
Quota Share
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Slide 14
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
1,000,000 1,000,000
xs
xs
Underlying 1,000,000
Umbrella layer:
1st
2nd
GL ISO % of underlying:
19.3%
12.9%
ISO Total Limits:
19.3%
32.2%
Cortana % of underlying:
20.0%
15.00%
Cortana Total Limits:
20.0%
35.00%
Umbrella Limits Dist:
40.0%
60.0%
Umbrella Adequacy Factor:
93.3%
ERL on Covenant's GL policies:
75.0%
Umbrella ELR:
69.9%
Based on ISOTruncated Pareto with client specific exposure distribtions
Cumulative of (1)
Given
Cumulative of (3)
Given
= wtg average of (2) / wtg average of (4)
Given
= (6) x (7)
Reinsuring an Umbrella Portfolio:
Quota Share
Slide 15

In practice, umbrella policies are typically written
over multiple underlying coverages (i.e. GL, AL, and
EL).

The analysis for these situations is the same with
multiple underlying ELRs and umbrella factors.
Reinsuring an Umbrella Portfolio:
Quota Share
Umbrella layer:
GL ISO % of underlying:
CAL ISO % of underlying:
Avg ISO % of underlying:
XYZ % of underlying:
Premium Dist:
Umbrella Adequacy Factor:
GL L&ALAE Ratio:
AL L&LALAE Ratio:
Avg. AL/GL L&ALAE Ratio:
UMB ELR on 1st $5M:
Slide 16
1,000,000
xs
Underlying
1st
13.17%
11.08%
12.60%
16.01%
58.37%
73.2%
72.2%
91.1%
77.4%
56.6%
1,000,000
xs
1,000,000
2nd
3.93%
3.91%
3.93%
8.01%
22.14%
1,000,000
xs
2,000,000
3rd
2.29%
2.22%
2.27%
4.00%
7.54%
1,000,000
xs
3,000,000
4th
1.55%
1.48%
1.53%
2.00%
3.38%
1,000,000
xs
4,000,000
5th
1.14%
1.07%
1.12%
1.00%
8.57%
Reinsuring an Umbrella Portfolio:
Quota Share

Some things to consider if using this method:
–You must consider the proper method to load for
excess ALAE versus ground-up ALAE
–You must factor in the effect of discretionary pricing
 You
must also factor in the effects of the minimum
premiums.
–The “actual” excess factor obtained because of your
minimum premiums may be far greater than the
filed excess factors.
–This is sometimes very hard to do because it
requires the cedant to keep premiums by layer in
the system.
Slide 17
Reinsuring an Umbrella Portfolio:
Quota Share

The reinsurer must also be very aware of shifting
limits (or attachment) points.
– Some layers may be more or less adequate than
others.
– A shift to higher or lower limit umbrella policies
may affect the adequacy factor.
Slide 18

Once an ELR is determined the reinsurer can
determine what commission can be paid the cedant.

There must also be some consideration what load to
add for “drop-down” coverage.
Reinsuring an Umbrella Portfolio:
Excess of Loss

Another way to reinsure an umbrella portfolio is
reinsure it on an excess of loss basis.

This type of treaty can come in two varieties:
– A cedent decides to include their umbrella
portfolio into their mainframe XOL treaty. Typically
the limit and attachment points are with respect to
first dollar i.e. $5M xs $1M
– A cedent who writes unsupported umbrellas may
choose to keep a fixed retention on every umbrella
regardless of the attachment.

Slide 19
One of the biggest concerns is how a shift in limits or
attachment points could change the expected loss in
your reinsured layer.
Reinsuring an Umbrella Portfolio:
Excess of Loss
Let’s start with a scenario where every umbrella has the same
attachment point, limits vary and the excess of loss cover is $4.0M xs
$1.0M from the ground:
Limited
Prem
Limit Attachment
Distr. XS Factor
Limit
Severity
500,000
18,147
4,500,000
1,000,000
25.0%
95.3%
1,000,000
21,623
1,500,000
1,000,000
10.0%
100.0%
3,000,000
1,000,000
35.0%
100.0%
1,500,000
23,604
5,000,000
1,000,000
30.0%
91.5%
2,000,000
24,946
Wavg:
96.3%
2,500,000
25,940
3,000,000
26,719
3,500,000
27,353
4,000,000
27,884
4,500,000
28,338
5,000,000
28,733
5,500,000
29,081
6,000,000
29,391
Given an umbrella ELR of 65%
the rate we would charge would
be 63% plus load.
Slide 20
Reinsuring an Umbrella Portfolio:
Excess of Loss
Slide 21
Reinsuring an Umbrella Portfolio:
Excess of Loss
Let’s look at a scenario where the umbrella attachment points and limits
vary and the excess of loss cover is $4.0M xs $1.0M with respect to the
ground:
Prem
Limit Attachment
Distr. xs factor
4,500,000
500,000
25.0%
1,000,000
1,500,000
10.0%
100.0%
3,000,000
1,500,000
35.0%
100.0%
1,500,000
3,000,000
30.0%
100.0%
Wavg:
91.8%
Slide 22
67.2% =(28733-21622)/(28733-18147)
Reinsuring an Umbrella Portfolio:
Excess of Loss
Slide 23
Reinsuring an Umbrella Portfolio:
Excess of Loss
Let’s look at a scenario where the umbrella attachment points and limits
vary and the excess of loss cover is $4.0M xs $1.0M with respect to the
umbrella:
Prem
Limit Attachment
Distr. xs factor
4,500,000
500,000
25.0%
1,000,000
1,500,000
10.0%
3,000,000
1,500,000
35.0%
50.7% =(28338-25939)/(28338-23604)
1,500,000
3,000,000
30.0%
28.0% =(28338-27884)/(28338-26718)
Wavg:
38.3%
Slide 24
48.4% =(28733-23604)/(28733-18147)
0.0%
Reinsuring an Umbrella Portfolio:
Excess of Loss
Slide 25
Reinsuring an Umbrella Portfolio:
Excess of Loss
 In
order to properly rate the XOL on umbrella business
the reinsurer will need data that may not be readily
available from the cedant.
–A matrix distribution of limits by attachments
–Historical information on how limits and
attachments have shifted over time
A
shift in the limits or attachment points could make
the average expected loss cost increase or decrease
significantly.
 In
some cases it may make more sense to charge a
schedule of rates which vary by attachment and limit
as opposed to a single rate.
Slide 26
Reinsuring an Umbrella Portfolio:
Excess of Loss
 The
reinsurer may also want to rethink the appropriate
load (for parameter risk) needed to write this type of
cover.
 Using
an XOL load typically used when reinsuring
primary policies may not be appropriate.
 There
must also be some consideration what load to
add for “drop-down” coverage.
Slide 27
Reinsuring an Umbrella Portfolio:
Market Trends

Like the rest of the market the rates have been
decreasing.
– Decreasing manual rates
– Decreasing discretionary mods
– Decreasing umbrella factors
– Increased use of umbrella credits
– Umbrella on E&S business hit the hardest
Slide 28

More companies trying to purchase auto carve-outs
for their umbrella portfolio.

Companies are looking at the option of moving from
an umbrella quota share to an XOL.
Reinsuring an Umbrella Portfolio:
Market Trends

Continued deterioration of terms and conditions
– Little to no referral guidelines
– Decreasing minimums per million
Slide 29

Increase in the umbrella limits primary companies
are willing to write.

More primary companies are willing to attach higher
(write the excess umbrellas as opposed to lead
umbrella) where it is perceived rates per million are
more adequate.

Increase in the number of companies willing to offer
SAM in the umbrella for certain classes (i.e. social
services)
Reinsuring an Umbrella Portfolio:
Market Trends

More risks, typically written in the E&S markets, are
being written in the standard umbrella market at
standard umbrella rates.

Actuaries and UWs need to make sure they
understand the underlying umbrella form.
– While there is a standard ISO form most
companies use a hybrid form
– Recently the umbrella forms have been broadening

Slide 30
Actuaries should also make sure umbrellas are
properly endorsed to reduce the chance of dropdown coverages (i.e. a driver is excluded on the
underlying but not on the umbrella)