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De-Mystifying Reinsurance Pricing
STRIMA ConferenceBaton Rouge, LASeptember 26, 2006
Presented byMichael Petrocik, FCAS, MAAAChief Actuarial Officer – Specialty MarketsMunich Reinsurance America, Inc.
2
Actuarial Concepts 3
Comparison of Pricing Methods 19
Experience Rating 21
Exposure Rating 27
Final Steps 32
Agenda
3
Actuarial Concepts
Three Important Actuarial Pricing Concepts:
Loss development
Trending
Credibility
4
Loss Development
Loss development is the process of estimating the ultimate value of a body
of losses, based on the amount of reported or paid loss at a given point in
time.
The difference between the ultimate amount of losses and the
reported amount is called IBNR (Incurred but not reported)
Excess loss development estimates the ultimate value of losses in a
specific excess layer. This process is much more difficult than ground-up
development because…
Excess losses take much longer to reach maturity
Excess losses are much less frequent
5
Ground-Up Loss Development
General Liability
Ground-Up Reported Loss Development
$5 Million Policy Limit
12 Months
24 Months
36 Months
48 Months
60 Months
72 Months
84 Months
Ult Loss
1999 10,000 17,000 20,400 28,560 31,416 34,558 36,285 43,543
2000 9,000 17,100 22,230 26,676 28,010 29,130 36,704
2001 12,000 19,200 26,880 34,944 40,186 54,265
2002 8,000 12,000 19,200 21,120 31,502
2003 11,000 19,800 29,700 55,581
2004 12,000 20,400 53,120
2005 13,000 57,602
6
Ground-Up Loss Development
Age-to-Age Ratios 12-24 24-36 36-48 48-60 60-72 72-84
1999 1.700 1.200 1.400 1.100 1.100 1.050
2000 1.900 1.300 1.200 1.050 1.040
2001 1.600 1.400 1.300 1.150
2002 1.500 1.600 1.100
2003 1.800 1.500
2004 1.700
Avg A-A 1.702 1.391 1.255 1.105 1.072 1.050 1.200
Ult Factors 4.431 2.604 1.871 1.492 1.350 1.260 1.200
% of Ult 22.6% 38.4% 53.4% 67.0% 74.1% 79.4% 83.3%
7
Excess Loss Development
General Liability
Excess Reported Loss Development
$4 Mil xs $1 Mil Layer
12 Months
24 Months
36 Months
48 Months
60 Months
72 Months
84 Months
Ult. Loss
1999 1,000 2,700 3,510 6,143 7,985 7,985 9,183 14,693
2000 0 0 1,500 1,950 1,950 2,730 5,023
2001 1,500 1,800 4,320 7,776 14,774 29,319
2002 600 1,800 5,400 9,180 28,367
2003 0 1,500 3,750 19,705
2004 2,000 5,800 72,208
2005 1,000 33,199
8
Excess Loss Development
Age-to-Age Ratios 12-24 24-36 36-48 48-60 60-72 72-84
1999 2.700 1.300 1.750 1.300 1.000 1.150
2000 1.300 1.000 1.400
2001 1.200 2.400 1.800 1.900
2002 3.000 3.000 1.700
2003 2.500
2004 2.900
Avg A-A 2.667 2.369 1.701 1.557 1.079 1.150 1.600
Ult Factors 33.199 12.450 5.255 3.090 1.984 1.840 1.600
% of Ult 3.0% 8.0% 19.0% 32.4% 50.4% 54.3% 62.5%
9
Loss Development Comparison
General Liability
Percents of Ultimate
Ground-Up Excess
Age Development Development
12 22.6% 3.0%
24 38.4% 8.0%
36 53.4% 19.0%
48 67.0% 32.4%
60 74.1% 50.4%
72 79.4% 54.3%
84 83.3% 62.5%
10
Trending
Trending is the process of adjusting past years data to the conditions that
will
exist in the year being forecast.
Most forms of trending are an adjustment for inflation
There are two purposes for trending past experience years:
1. To restate the past as it would look if those events occurred during
the upcoming policy year
2. To put each of the past years on an equal basis in order to assist in
comparing them
11
Trending
There are three types of trend adjustments that are typically done during an
actuarial analysis.
Exposure trend – units that are denominated in dollars are adjusted
for subsequent inflation in that item
Loss severity trend – losses are adjusted for changes in the average
size of similar type claims
Loss frequency trend – the number of claims is adjusted based upon
changes in how often a claim occurs
12
Trend versus Development
Losses are adjusted by both loss development factors and trend factors.
Don’t each of these steps do the same thing?
No. Both processes are necessary to get a full forecast of the upcoming
year’s claims because…
Development takes the amount of known losses at a point in time to
their final, full (historical) value
Trending restates the historical value of losses at cost levels expected
to exist in the upcoming policy year
13
Leveraged Trend
Inflation (trend) affects different layers in very different ways. It is kindest to
the ground-up layer and harshest to the excess layer. The increased effect
on the excess layer is referred to as “leveraged trend.”
Leveraged trend is due to the interplay of limits and attachment points on
claim values. Let’s look at an example.
14
Leveraged Trend
Policy Limit $1,000,000
Attachment Point $100,000
Inflation Rate 20%
Before Inflation After Inflation
Total Ground Up Excess Total Ground Up Excess
50,000 50,000 0 60,000 60,000 0
95,000 95,000 0 114,000 100,000 14,000
250,000 100,000 150,000 300,000 100,000 200,000
15
Leveraged Trend
Before Inflation
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
1 2 3
Cla
im S
ize
Excess
Ground Up
After Inflation
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
1 2 3
Cla
im S
ize
Excess
Ground Up
Claims Size Claims Size
16
Leveraged Trend
Now let’s look at the inflation rate for each layer.
Before After Inflation
Total Claim 395,000 474,000 20.0%
Ground-Up Layer 245,000 260,000 6.1%
Excess Layer 150,000 214,000 42.7%
17
Credibility
Credibility is the process of assessing the predictive reliability of a body of
data used in experience rating.
The credibility process assigns a value between 0% and 100% to the
experience rating.
This value is used as a weight on the experience rate result when
calculating the final loss pick.
The remainder, or complement of credibility, is usually assigned to an
exposure rating estimate.
18
Credibility
Credibility is generally defined in terms of a number of expected claims or an
amount of exposure.
Although based on statistical tests, credibility always includes a significant
amount of judgment.
Many important factors can’t be quantitatively evaluated, like data
quality.
The relative value of the exposure rating estimate must also be
judgmentally considered.
19
Methods Used to Price Reinsurance
Experience Rating
Also known as “loss rating”
Price based on past claims experience
Exposure Rating
Price base on present hazard complexion of the risk
Natural catastrophe and terrorism models use exposure methods
20
Comparison of Methods
Experience Rating
Generally, the preferred method
Price based on past history of claims
Greater reliance on client’s experience
Exposure Rating
Typically used to supplement data that
is not fully credible
Price based on current hazard
composition of risk
Greater reliance on industry experience
21
Experience Rating
Experience rating bases the loss estimate on the client’s past history of
losses within the layer being reinsured.
Experience rating works best in situations where there are multiple claims
expected in a single year.
High layers and smaller coverages are challenging to rate.
Before analyzing, experience must be adjusted, if there have been changesin the claims environment (tort caps and immunities).
Natural catastrophe losses are not experience rated.
22
Experience Rating Data
Exposure Information – for each line of business, exposure units are needed
for each year of history, as well as an estimate for the upcoming year.
Common exposure units:
Auto – power units (number of vehicles)
Workers Comp – payroll
Property – total insured values
General Liability – net operating expenditures (NOE), population,
police, students
Professional Liability – NOE, population, students, doctors, occupied
beds
23
Experience Rating Data
Subject Premium – if premium is calculated for the reinsured layer, it can be
used in lieu of exposures.
If so, premium is needed for each historical year, as well as the
prospective year
Using premium is most typical in workers’ compensation
When using premium, a history of rate changes is also required so
that past premium can be adjusted to current rate levels.
24
Experience Rating Data
Loss Information – the key component of any experience rating analysis is
accurate, detailed loss information.
Losses are needed for each year being analyzed, in line of business
detail.
Reinsurers look to get information on all past losses. At a minimum, all
losses of at least half the attachment point are necessary.
Losses should be evaluated as recently as possible.
If possible, annual evaluations of each loss should be submitted. This
allows the reinsurer to create loss development factors unique to the
risk.
25
Experience Rating Data
Loss Information Detail
Line of business
Paid and outstanding amounts
Allocated loss adjustment expenses separate from loss
Occurrence dates
Policy limit
Brief claim description of large losses
Policy effective date, if policies are issued on various dates
Catastrophe losses identified
26
Experience Rating Steps
1. Adjust past exposure units for inflation, if necessary
2. Adjust past loss experience for claims inflation (trending)
3. Calculate how much of each trended claim falls into the layer being
priced
4. Develop claims in layer to ultimate value
5. Calculate ratio of losses to (trended) exposures
6. Select appropriate average loss ratio
7. Apply selected loss ratio to prospective exposures to yield expected
losses
27
Exposure Rating
Rather than use past history, exposure rating evaluates the current loss
complexion of the risk.
Detailed profiles of the current exposures insured define the loss
complexion.
Exposure rating is typically used to supplement places where experience
rating is not fully credible.
Exposure rating estimates losses in excess layers based upon relativities to
lower layers.
Relativities are applied to the experience rated estimate of a low
(ground-up) layer.
28
Exposure Rating Curves
Exposure rating relies upon loss severity curves which describe the amount
of losses expected at any given limit.
Loss severity curves are based on statistical fits to claims experience for
broad classes of business, rather than the client’s actual experience.
Profile information is used to fine tune curves.
29
Exposure Rating Curves
Sample Casualty Curve
Limit % of Losses Incremental Relativity
250,000 60.0% 60.0% 100.0%
500,000 70.0% 10.0% 16.7%
1,000,000 80.0% 10.0% 16.7%
2,000,000 90.0% 10.0% 16.7%
3,000,000 95.0% 5.0% 8.3%
4,000,000 98.0% 3.0% 5.0%
5,000,000 100.0% 2.0% 3.3%
30
Exposure Rating Data
The key exposure rating data are profiles of the insured exposures of each
line of business.
Auto – vehicles by weight class
Workers’ comp – payrolls by class of business
Property – total insured values by location
Also, distributions of construction types, occupancies and
protection classes
General and professional liability – exposures by class or hazard type
(low, medium and high hazard)
Policy limit distribution, if various limits apply
31
Exposure Rating Steps
1. Calculate loss estimate for base layer.
2. Select appropriate curve for line of business.
3. Adjust curve to applicable limit(s).
4. Modify curve based on profile of line of business.
5. Calculate relativity for the layer being priced.
6. Multiply base layer losses by relativity to yield losses for layer.
32
Final Steps
Expenses – costs other than claim payments
Allowances for reinsurer expenses are added to final loss pick.
Must include reinsurer’s expenses as well as any external expenses
(commission, TPA).
Usually a combination of percentage charges (commission, taxes) and
flat dollar amounts (overhead).
Reinsurer’s margin – return for capital used
Margins are based on target combined ratios or returns on equity.
Target margins reflect riskiness and cash flow dynamics.
Thank you very much for your attention.
Michael Petrocik, FCAS, MAAAMunich Reinsurance America, Inc.
© Copyright 2006 Munich Reinsurance America, Inc. All rights reserved. The Munich Re America name is a mark owned by Munich Reinsurance America, Inc.
The material in this presentation is provided for your information only, and is not permitted to be further distributed without the express written permission of Munich Reinsurance America. This material is not intended to be legal, underwriting, financial, or any other type of professional advice. Examples given are for illustrative purposes only.