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Rate Monitoring
Steven Petlick
Seminar on Reinsurance
May 20, 2008
Rate Monitoring
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Table of Contents
Slide 2

Rate monitoring from the perspective of the
reinsurance pricing actuary

The effect of new business

The effect of changes in “quality” of book of business

What is the reinsurance pricing actuary to do?

Conclusions
Rate monitoring from the
perspective of the reinsurance
pricing actuary
ab
Standard Pricing Methodology includes:
Slide 3

Trend historical losses to prospective treaty period

Put historical premiums at rate level of prospective
treaty period; i.e. put them “on level”

During hard market periods, rate increases can turn
dirt into gold

Opposite holds true in soft market periods
Rate monitoring from the
perspective of the reinsurance
pricing actuary
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Rate Monitor for XYZ Insurance Company
Casualty Excess of Loss Treaty
Slide 4
2000
2001
2002
2003
2004
2005
2006
2007
Rate Change
-2%
0
+10%
+35%
+9%
+3%
-1%
-9%
Rate monitoring from the
perspective of the reinsurance
pricing actuary
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What would you do?
I would immediately get back to the
client with questions:
Slide 5

Are the rate changes written or earned?

Are they adjusted for exposure changes?

Are they adjusted for changes in limits/ attachments/
deductibles/ SIRs?

Do they include new business or are they measured
on renewals only? (most common)
Rate monitoring from the
perspective of the reinsurance
pricing actuary
Slide 6
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
Do they include the effect of commission changes?

Do they reflect changes in terms and conditions?

What types of increases/ decreases are they
observing on lost business?

How are the rate changes actually calculated?
The Effect of New Business
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Suppose you are trending and onleveling a 2007 loss
ratio for a reinsurance treaty incepting at 1/1/2009.
(In reality you would likely use at least 5 historical
years, but, for simplicity, we will consider only 2007.)
Assume the following:
2007 Ultimate Loss Ratio = 60%
Expected Annual Trend = 6%
Renewal Rate Changes = 2008 -10%, 2009 -10%
Slide 7
The Effect of New Business
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If you assume that these rate changes apply to
the entire book of business (i.e. new business
rate adequacy = renewal rate adequacy) then
your projected 2009 loss ratio would be:
60% x 1.06 / (1-.10) X 1.06/(1-.10) = 83.2%
Slide 8
The Effect of New Business
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Now suppose that you believe that new
business is less adequately priced than
renewal business. How would this affect
your projection?
In order to answer this, you would need a few
more pieces of information:
Slide 9

Expected renewal retention rate

Projected premium growth
The Effect of New Business
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Simulation Model for New Business Effect
Initial Assumptions
Slide 10

2007 base portfolio of 100 policies with
premium of $50mm and loss ratio of 60%

Renewal rate changes of -10% for 2008 and
2009

Renewal retention rate of 80%
The Effect of New Business
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Simulation Model for New Business Effect
Initial Assumptions
Slide 11

New business for 2008 and 2009 will
consist of 20 new policies with same average
premium as renewal book

“New business differential” values of 0, -10%
and -20%
The Effect of New Business
ab
What is “new business differential?”
It is defined as the difference in rate adequacy
between new business in the portfolio as
compared to the renewal book for the same
period. It is NOT the rate change on new
business.
More about this later.
Slide 12
The Effect of New Business
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Simulation model operation:
Slide 13

Base year 2007 portfolio is simulated:
premium is generated from uniform
distribution on 0-$1000; loss ratio from
normal, mean 60%, SD 10%

Each policy is either renewed or non-renewed
for 2008 according to the renewal retention
probability (80%)

If a policy is renewed, the premium reflects
the renewal rate change (-10%)
The Effect of New Business
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Simulation model operation:
Slide 14

For renewed policies, the loss ratio reflects
assumed loss trend of 6% and renewal rate
change

20 new business policies are generated
using same uniform distribution reduced for
renewal rate change

Loss ratio for new business policies is
simulated using renewal loss ratio adjusted
for new business differential
The Effect of New Business
ab
Previous results assume that the base book of
business carries a loss ratio of 60%, and after
lost (i.e. non-renewed) business the renewed
book is unchanged (i.e. base at 60%.) The
reality is that there may be a bias in the
quality of the lost business, and in the soft
market we might expect “better” business to
be leaving. Companies report that lost
business frequently moves at rate reductions
of 20-30% or more!
Slide 15
The Effect of New Business
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We next assumed that the expected retention
rate for an individual policy varies according
to the loss ratio of the policy. For this
simulation, we assume that for each point of
loss ratio variation from the mean, the
probability of renewal varies by one
percentage point from the expected renewal
retention rate. For example, if the base loss
ratio for the book of business is 60%, and the
renewal retention rate is 80%, a policy with a
loss ratio of 62% would have a probability of
renewal of 82%.
Slide 16
The Effect of New Business:
Results of Simulation
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Loss Ratio
80% Retention Rate
98.0%
96.0%
94.0%
92.0%
90.0%
88.0%
86.0%
84.0%
82.0%
2009 Base Case
2009 Vary Ret
0
Slide 17
-10%
-20%
New Business Differential
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The Effect of New Business
We next ran the simulations assuming a
renewal retention of only 60%; not unheard
of for some E&S writers.
Slide 18
The Effect of New Business:
Results of Simulation
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Loss Ratio
60% Retention Rate
102.0%
100.0%
98.0%
96.0%
94.0%
92.0%
90.0%
88.0%
86.0%
84.0%
82.0%
2009 Base Case
2009 Vary Ret
0
-10%
-20%
New Business Differential
Slide 19
What is the reinsurance pricing
actuary to
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How do we estimate the “new business
differential? Typically, such a quantity is not
included in reinsurance submissions
Slide 20

Ask the ceding company if they have
attempted to estimate the effect of new
business/ lost business on their portfolio

Some rate monitors will already include these
effects: e.g. ratio of actual to benchmark
What is the reinsurance pricing
actuary to
Slide 21
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
Look for ways to extract this information from
the data that is provided: e.g. if you can
identify new business in current bordereau of
policies, then compare price per million for
like limits, attachments, classes, etc.

If you cannot identify new business, then look
at changes in price per million from year to
year, again for like limits, attachments,
classes, etc. This can at least give you an
indicator of the total (new + renewal) rate
change – compare to the rate change
provided in the submission
What is the reinsurance pricing
actuary to

Slide 22
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Compare the rate change that the ceding
company provides to that of similar portfolios
and to industry benchmarks (CIAB,
MarketScout.) If they are very different and
you have no way of estimating the new
business effect, then you might assume that
the differences are at least partially
attributable to new business/ lost business.
What is the reinsurance pricing
actuary to
New
Year
Slide 23
Adjusted
Written
Renewal
Rate
Business
Exposure
Rate
Premium
Retention
Change
Differential
Inflation
Change
2003
40,000
80%
2004
40,000
80%
15.0%
0%
0.0%
15.0%
2005
40,000
80%
29.0%
0%
0.0%
29.0%
2006
40,000
80%
10.0%
0%
0.0%
10.0%
2007
49,470
80%
2.0%
-5%
0.0%
0.3%
2008
44,409
80%
-10.0%
-10%
0.0%
-11.8%
2009
43,054
80%
-8.0%
-10%
0.0%
-10.2%
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Conclusions
Summary:
Slide 24

Always understand how rate monitors in reinsurance
submissions are computed

In addition, ask the client if new business is being
included in the rate monitor

If not, request information that would enable you to
estimate the new business effect

Initiate a discussion regarding lost business; do they
measure how much of a decrease business is leaving
for?
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Conclusions
Summary:

Slide 25
Engage the client in a conversation regarding the
effect of lost business on the quality of their
remaining book of business – this is difficult, as
there is no objective way to measure this