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Rate Monitoring
Steven Petlick
CAS Underwriting Cycle Seminar
October 5, 2009
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

What is the reinsurance pricing actuary to do?

Effect of economic crisis on price monitor

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
ab
Rate Monitor for XYZ Insurance Company
Casualty Excess of Loss Treaty
Slide 4
2001
2002
2003
2004
2005
2006
2007
2008
Rate Change
0
+10%
+35%
+9%
+3%
-1%
-9%
-10%
Rate monitoring from the
perspective of the reinsurance
pricing actuary
ab
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
ab
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
ab
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
ab
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
ab
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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Economic Crisis Effect on Rate
Monitors
Slide 24
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
Most rate monitors calculate rate changes based on
change in premium per exposure

Exposures are typically estimated at time of policy
renewal and premium is calculated based on
exposure base

Rate monitors are typically created using actual
premium and estimated exposures at time of pricing

For many types of policies, premium is not adjusted if
exposure base turns out different than that assumed
at time of pricing

In most cases, rate monitors are not adjusted
Economic Crisis Effect on Rate
Monitors
Slide 25
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
This can result is distortions in rate monitors if
exposure estimates are materially incorrect

During current economic crisis, many exposures
were overestimated, in particular for classes like
Construction (sales), Manufacturing (sales)

This may have resulted in overstatement of rate
decreases during 2008 and possibly 2009
Economic Crisis Effect on Rate
Monitors
ab
Example: Renewal rate change
Portfolio of 20 risks with 2007 premium of $1.76m and
exposure of $37.1m (could be sales)
Portfolio renews in 2008 with premium of $1.66m and
exposure of $37.9m
Rate change = -7.80%
Company provides this information to reinsurer for
1/1/2009 treaty renewal
Assumed rate change for 2009 is +1.5%
Slide 26
Economic Crisis Effect on Rate
Monitors
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Actual exposure for 2008 comes in on average 10.8%
below projected. Since premium does not change,
effective rate change becomes +3.40% (as opposed
to original -7.80%.)
Does the company go back and adjust their rate monitor
for the revised exposure? Probably not.
When 1/1/2010 renewal is done, the rate monitor
should “self-adjust”; i.e.. the 2009 monitor should
reflect the revised exposure and the effective 2009
rate change will be much higher, all other things
being equal.
Slide 27
Economic Crisis Effect on Rate
Monitors
ab
Example: Reinsurance treaty Effective 1/1/2009
Using 2008 rate change of -7.8% (2009 assumption
+1.5%), indicated loss ratio = 87.6%
Using “real” 2008 rate change of +3.4% (2009
assumption +1.5%), indicated loss ratio = 78.1%
This would have a major impact on the reinsurance
underwriting decision
Slide 28
Economic Crisis Effect on Rate
Monitors
ab
Example: Renewal Effective 1/1/2010
“Real” rate change for 2009 is +1.5%; however,
company does not go back and correct exposures
used in 2008 rate monitor, so understated premium
per exposure is used. With “real” 2009 premium per
exposure (that is, reflecting reduced exposure), the
2009 rate change appears to be +13.8%. (+2% rate
change is assumed for 2010.) Indicated loss ratio is
86.5%.
Slide 29
If 2008 exposures are corrected, and 2008 rate change
of +3.4% is used, along with real rate change of
+1.5% for 2009 (and same +2% for 2010), indicated
loss ratio is ________
Economic Crisis Effect on Rate
Monitors
ab
Example: Renewal Effective 1/1/2010
86.5%
So the process self-corrected.
However, the underwriting decision for 2008
could have be affected. In addition, if the exposures
continue to drop, this process could be perpetuated
over multiple years.
Slide 30
Economic Crisis Effect on Rate
Monitors
ab
Caveats:
Slide 31
•
Just because exposure base falls short, does that
mean that actual exposure has fallen short? For
example, for a Construction risk, if sales decline, was
it due to less actual work or lower fees for the same
work? The latter may not represent a real drop in
loss exposure.
•
Is exposure auditable; i.e. can premium be adjusted
for audited exposure? (Example: Workers Comp.)
Economic Crisis Effect on Rate
Monitors
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Caveats:
•
Slide 32
Is the chosen exposure base the best measure of
exposure to loss? For example, for a Trucking risk,
exposure base may be number of units. In the
recession, the number of units may not change, but
the miles driven may be down.
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Conclusions
Summary:
Slide 33

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

Understand how exposure base is being used in the
rate monitor
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Conclusions
Summary:
Slide 34

Determine if company is making corrections to rate
monitor to account for revisions in exposure base

Incorporate assumptions on going forward exposure
base when projecting future rate movement