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.

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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.

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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.