Modeling asset and Liability cashflows in a dynamic setting: Basic tools and risk measures 2000 CAS DFA Seminar Robert J. Walling Paratus consulting limited

Modeling asset and Liability cashflows in a dynamic setting:

Basic tools and risk measures

2000 CAS DFA Seminar

Robert J. Walling

Paratus consulting limitedlondon - bloomington - Chicago - San Francisco - Boston

“Th

e g

ood

old

days”

SIMPLECO.com 2000 Strategic Plan

2000 2001 2002 2003 2004Written Premium 1,000 1,100 1,210 1,331 1,464 % Growth 10% 10% 10% 10%

% Earned in 1st Year 0.50 0.50 0.50 0.50 0.50

Earned Premium 975 1,050 1,155 1,271 1,398

Incurred Loss & LAE 702 725 791 864 936 Ratio to Earned Premium 72.0% 69.0% 68.5% 68.0% 67.0%

Incurred Underwriting Expense Ratio 350 363 393 433 476 Ratio to Written Premium 35.0% 33.0% 32.5% 32.5% 32.5%

Combined Ratio 107.0% 102.0% 101.0% 100.5% 99.5%

Poin

t esti

mate

mod

elin

gAdvantages

– Straight-forward

– Easy to Explain

– Point Estimate

Drawbacks– Over-Simplified

– May Lack Diagnostic Detail

– Depends on the Past Repeating Itself

– One Set of Economic Assumptions

– One Set of Investment Assumptions

– One Set of Market Assumptions

– No Feedback Between Rate Action & Premium

Scen

ari

o T

esti

ng

SIMPLECO.com 2000 Strategic Plan (REVISION 1)


% Earned in 1st Year 0.50 0.50 0.50 0.50 0.50

Earned Premium 975 1,050 1,155 1,271 1,398

Incurred Loss & LAE Ratio to Earned Premium - Adverse 73.0% 72.0% 71.0% 71.0% 71.0% Ratio to Earned Premium - Expected 72.0% 69.0% 68.5% 68.0% 67.0% Ratio to Earned Premium - Favorable 70.0% 68.0% 67.0% 66.5% 64.0%

Incurred Underwriting Expenses Ratio to Written Premium - Adverse 36.0% 35.5% 35.0% 34.5% 34.0% Ratio to Written Premium - Expected 35.0% 33.0% 32.5% 32.5% 32.5% Ratio to Written Premium - Favorable 34.0% 32.5% 32.0% 32.0% 31.5%

Combined Ratio - Adverse 109.0% 107.5% 106.0% 105.5% 105.0%Combined Ratio - Expected 107.0% 102.0% 101.0% 100.5% 99.5%Combined Ratio - Favorable 104.0% 100.5% 99.0% 98.5% 95.5%

Scen

ari

o T

esti

ng

Advantages– Straight-forward

– Easy to Explain

– Still Provides Point Estimate

– Allows for Different Conditions





– “Wishful Thinking” Risk

Loss r

ati

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gSIMPLECO.com 2000 Strategic Plan (REVISION 2)


% Earned in 1st Year 0.50 0.50 0.50 0.50 0.50

Earned Premium 975 1,050 1,155 1,271 1,398

Incurred Loss & LAE Expected Loss Ratio 72.0% 69.0% 68.5% 68.0% 67.0% Expected Loss Ratio Variance 4.0% 3.8% 3.8% 3.8% 3.7% Random Number 0.64 0.01 0.62 0.19 0.32 Ratio to Earned Premium - Simulated 73.4% 60.0% 69.7% 64.7% 65.2%

Incurred Underwriting Expenses Ratio to Written Premium - Simulated 35.0% 33.0% 32.5% 32.5% 32.5%

Combined Ratio - Simulated 108.4% 93.0% 102.2% 97.2% 97.7%

Loss r

ati

o m

od

elin

gAdvantages

– Straight-forward

– Easy to Explain



– Works Well for Relatively Stable Lines





– “Wishful Thinking” Risk

– Can Struggle with Large Losses

– Does not Separate Business & Liability Risk

Fre

qu

en

cy &

Severi

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od

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gXYZ Insurance Company - WC OutputRenewal & New BusinessDirect Underwriting Module

Description 2000 2001 2002 2003 20043. 'Losses:a. Initial Severity Mean

New 2,800 2,800 2,800 2,800 2,800 Renewal 2,800 2,800 2,800 2,800 2,800 Renewal (2) 2,800 2,800 2,800 2,800 2,800

b. Initial Severity Std. 200 200 200 200 200 c. Severity Trend 1.043 1.094 1.163 1.221 1.287 d. U/W & Rate Adjustmentse. Modeled Severity

New 3,074 3,099 3,185 3,217 3,694 Renewal 3,074 3,099 3,185 3,217 3,694 Renewal (2) 3,074 3,099 3,185 3,217 3,694

f. Initial Frequency MeanNew 0.373 0.373 0.373 0.373 0.373 Renewal 0.325 0.325 0.325 0.325 0.325 Renewal (2) 0.295 0.295 0.295 0.295 0.295

g. Initial Frequency Std. 0.017 0.017 0.017 0.017 0.017 h. Frequency Trend 1.000 1.000 1.000 1.000 1.000 i. U/W & Rate Adjustments 1.000 1.049 1.000 1.000 1.000 j. Modeled Frequency

New 0.38 0.37 0.39 0.36 0.38 Renewal 0.33 0.33 0.34 0.31 0.33 Renewal (2) 0.30 0.30 0.31 0.28 0.30

k. a Priori Ultimate Losses & ALAENew 13,293,589 21,638,252 25,267,946 23,265,222 17,939,731 Renewal 4,003,137 6,451,617 11,464,238 11,920,996 18,204,217 Renewal (2) 28,201,606 21,136,222 19,411,175 18,900,967 31,211,777 Modeled Cat LossesTotal 45,498,332 49,226,091 56,143,358 54,087,184 67,355,724

Accident Years (Modeled Direct Data)

Fre

qu

en

cy &

Severi

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od

elin

g3. Selected Severities & Frequency

Implied Severities

Current Level Factor

Implied Severities at

Current Implied

Frequencies Dir L/R

1990 1,144 1.0937 1,251 88.4%1991 1,409 1.0829 1,525 0.350 95.3%1992 2,447 1.0721 2,624 0.222 94.8%1993 2,244 1.0615 2,383 0.253 78.1%1994 2,652 1.0510 2,787 0.245 70.8%1995 2,811 1.0406 2,925 0.283 71.9%1996 2,891 1.0303 2,979 0.279 72.2%1997 2,853 1.0201 2,911 0.282 75.5%1998 2,426 1.0100 2,451 0.312 75.2%

Reasonability CheckSelected Severity Frequency Loss Cost Avg. Prem. Implied LR

a. New Business 2,800 0.373 1,045 1,100 0.9499 b. 1st Renewal 2,800 0.325 909 1,100 0.8260 c. 2nd & Subsequent Renewal 2,800 0.295 826 1,100 0.7509 d. Weighted Average Severity 2,800 0.308 864 1,100 0.7851 e. Selected Standard Deviation 200 0.017 f. Historic Standard Deviation 478 0.040

Fre

qu

en

cy &

Severi

ty m

od

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gAdvantagesAdvantages

– Provides Diagnostic Detail

– Allows Different Trend Factors



Drawbacks– Can be Over-Complicated

– Difficult to Parameterize with Limited Data

con

volu

tion

Mod

elin

gMHL Catastrophe Generator

Generated Losses - All CAT's0.72 0.36 0.48 0.48 0.42

19 15 16 16 16Countrywide

Prob # 0 1 2 3 4 0 1 2 3 4 Cat0 Cat1 Cat2 Cat3 Cat40.000 1 0.423 0.152 0.104 0.960 0.491 MA CO CA TX MO 87,741 108,286 65,886 479,377 153,020

0.000 2 0.656 0.931 0.175 0.402 0.665 OH TX FL LA OK 237,194 75,830 38,433 33,800 61,164

0.000 3 0.130 0.781 0.505 0.644 0.720 CO TX MO NY OK 24,864 39,630 61,566 119,156 66,083

0.000 4 0.634 0.825 0.180 0.078 0.430 NY TX FL CA MA 248,218 76,451 534,572 37,426 109,732

0.000 5 0.370 0.093 0.822 0.701 0.935 KS CA TX OK TX 9,547 32,812 357,342 29,941 1,233,224

0.001 6 0.879 0.819 0.882 0.483 0.543 TX TX TX MN MT 39,021 94,190 29,048 66,675 42,018

0.004 7 0.381 0.438 0.095 0.049 0.403 KS MA CA CA LA 31,000 241,297 97,910 62,768 33,057

0.009 8 0.607 0.024 0.341 0.845 0.772 NM AR KS TX TX 16,524 89,022 138,890 15,513 30,343

0.019 9 0.107 0.124 0.024 0.503 0.280 CA CA AR MO IL 47,489 277,227 75,869 83,523 52,176

0.036 10 0.036 0.396 0.391 0.955 0.610 AR LA LA TX NM 58,914 35,138 39,098 32,834 57,127

0.064 11 0.537 0.026 0.101 0.578 0.060 MT AR CA NE CA 45,415 92,898 48,639 108,704 11,851

0.105 12 0.363 0.423 0.192 0.339 0.225 KS MA FL KS GA 316,682 1,132,522 136,399 82,664 85,156

0.161 13 0.640 0.983 0.061 0.831 0.516 NY WI CA TX MO 91,957 35,688 217,262 28,752 14,073

0.231 14 0.663 0.821 0.487 0.117 0.443 OK TX MN CA MD 29,574 32,254 88,694 2,897 2,438,903

0.314 15 0.076 0.561 0.342 0.613 0.765 CA ND KS NV TN 14,217 46,942 61,298 284,148 57,689

0.406 16 0.274 0.623 0.776 0.002 IL NY TX AK 89,864 - 122,831 77,814 40,127

0.501 17 0.073 CA 29,739 - - - -

0.594 18 0.905 TX 616 - - - -

0.681 19 0.810 TX 153,283 - - - -

0.758 20 - - - - -

0.822 21 - - - - -

Random Number Generators Focal Points Claim Severities (000)

con

volu

tion

mod

elin

gAdvantages

- Lots of Detail

- Allows for Large Single Events

Drawbacks– Lots of Detail

Why

Enh

ance

Rat

e M

odel

ing?

• Key to Underwriting Cash Flows

• Imprecise Process at Many Companies

• Key Decision-Making Element

• Deterministic Approach Over-Simplified

• Somewhat Controllable

•Premium Growth does not Quantify

Underlying Exposure Changes

App

roac

hes

to R

ate

Mod

elin

g

•Inflation Only

•Demand Curves that Respond to U/W Cycle

•Competitive Need

•Indicated Rate Need

•Blended Approaches

•Retention Modeling

(F) UNDERWRITING GENERATOR

Current Market Condition:

(Phase 1: Mature Hard, 2: Immature Soft, 3: Mature Soft, 4: Immature Hard )

Probability of Entering PhaseCoverage Phase 1 2 3 4 m bXYZ Company - WC 1 80.0% 17.5% 2.5% 0% -30.0% 2.0%

2 0% 80.0% 17.5% 2.5% -40.0% 1.3%3 2.5% 0% 80.0% 17.5% -50.0% -1.5%4 17.5% 2.5% 0% 80.0% -40.0% 1.3%

Random Number 0.7443 0.7007 0.3240 0.7892 0.7693Market Position 2 2 2 2 2 2Market Rate Adjustment 0.0% 0.0% 0.0% 0.0% 0.0%

Organic Growth 5.0% 5.0% 5.0% 5.0% 5.0%Implied Rate Change 1.013 0.993 0.993 0.993 0.993 0.993Inflation 1.043 1.043 1.049 1.063 1.051 1.054Indicated Rate Level 1.000 1.072 1.258 1.125 1.062 0.898Indicated Weighting 0.0% 100.0% 100.0% 100.0% 100.0% 100.0%Total Implied Rate Change 1.056 1.072 1.258 1.125 1.062 0.898Allowed Change 1.056 1.072 1.200 1.125 1.062 0.898

Rat

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odel

ing

Assumptions:

- 4% Line Specific Inflation

- Market Demands –5% Rate Change to

Meet Growth Objectives

- Sufficient Data Available to Calculate

Indicated Rate Need

Rat

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odel

ing

Res

ults

-25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%

Indicated Rate Need

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

Impl

emen

ted

Rat

e L

evel

- Y

ear

1

Inflation OnlyDemand CurveIndicated Only

Inflation/Demand BlendIndicated/Demand Blend

Rat

e M

odel

ing

– A

ddit

iona

l Con

side

rati

ons

• Underwriting Cycle

• Jurisdictional Risk

• Retention Behavior

• New Business Success (Hit Ratios)

The

Und

erw

riti

ng C

ycle

?• Difficult to quantify

• Affects average rate charged or number of exposures written

• Everybody has a different opinion on what drives the cycle– Interest rates– Industry capacity

• When will it turn?

Und

erw

riti

ng C

ycle

Com

pone

nts

• Current perceived position

• Probability of turning

• Demand curve– Expected rate change based upon desired exposure

growth– Based upon competitive pressures– Unique for individual companies– May be unique by state

Juri

sdic

tion

al R

isk

Risk characteristics unique to individual states:

• Residual market burdens

• Rate “stickiness”

• Judicial climate

• Legislative climate

• Regulatory climate

• Implementation lag

Juri

sdic

tion

al R

isk

Com

pone

nts

• Allowable rate changes– Without going thru extensive filing support– Increases– Decreases

• Implementation lag– Includes systems

• Potential Regulatory “Shocks”

• As perceived by company

Juri

sdic

tion

al R

isk

Com

pone

nts

Mod

elin

g R

eten

tion

• Renewal Behavior Depends on:• Customer Characteristics• Change in Pricing on Renewal• Competitive Positioning

• Suggested Curve:• Has Flexible Shape• Accommodates GLM Estimation• Creates Actuarially Intuitive Scenarios

Mod

elin

g R

eten

tion

• Premium Retention can be modeled as:

where:

P1 = Proposed Rate Level

P0 = Current Rate Level

PM = Market Level

ii

m1

01

i

i

PP

PP1

1r

1st Prior 1st 2nd 3rd 4th 5thYear Year Year Year Year Year1998 1999 2000 2001 2002 2003

(A) PREMIUMS INPUT

1. Written Exposure Inputa. New Business 5,800 b. 1st Renewal 4,500 c. 2nd & Subsequent Renewal 33,300 d. Total 43,600

2. Average Annual Rate Inputa. New Business 1,100 1,179.68 1,415.62 1,592.45 1,690.70 1,518.59 b. 1st Renewal 1,100 c. 2nd & Subsequent Renewal 1,100

2a. Average Annual Rate Input - Total Marketa. New Business 1,100 1,147 1,203 1,279 1,343 1,416 b. 1st Renewal 1,100 c. 2nd & Subsequent Renewal 1,100

3. Exposure Growth Ratea. Enter Growth Objectives (1) Mature Hard 5.0% 5.0% 5.0% 5.0% 5.0%

(2) Immature Soft 5.0% 5.0% 5.0% 5.0% 5.0%(3) Mature Soft 5.0% 5.0% 5.0% 5.0% 5.0%(4) Immature Hard 5.0% 5.0% 5.0% 5.0% 5.0%

4. % of Premiums Earned in Year Writtena. New Business 60% 60% 60% 60% 60% 60%b. 1st Renewal 60% 60% 60% 60% 60% 60%c. 2nd & Subsequent Renewal 60% 60% 60% 60% 60% 60%

5. Renewal Ratioa. New Business 65% 68% 56% 57% 59% 73%b. 1st Renewal 72% 75% 62% 63% 65% 81%c. 2nd & Subsequent Renewal 78% 81% 68% 68% 71% 88%

Ben

efit

s of

Rat

e M

odel

ing

•Allows Pricing to be Dynamic to Market and Underwriting Conditions.

•Allows Reflection of Inflationary Pressures that are Impacting Losses and/or Exposures.

•Flexible Enough to Approximate Actual Company Rate Setting Processes.

•Allows for Balance of Adequacy and Marketability.

Why

Enh

ance

Und

erw

riti

ng E

xpen

se M

odel

ing? •Start-up Organization or Line of

Business or Distribution Channel with Initial Fixed Costs

•Some Lines of Business have Significant Fixed Costs

•Significant Growth/Shrinkage or Technology Changes may Require the Buying or Selling of Fixed Items

App

roac

hes

to U

nder

wri

ting

Exp

ense

Mod

elin

g •All Variable with Direct Written Premium

•Some Portion of General and Other Acquisition is Fixed

•Per Unit Cost (e.g. Policy Counts)

•“Sticky” Fixed Expenses (Shed some fixed expense elements once DWP increases/decreases by some amount)

Exp

en

se m

od

elin

gEXPENSECO.com 2000 Strategic Plan - U/W Expense Analysis


Incurred Underwriting Expenses - All Variable 360 396 436 479 527 Ratio to Written Premium - All Variable 36.0% 36.0% 36.0% 36.0% 36.0%

Incurred Underwriting Expenses - 50% Fixed 360 378 398 420 444 Ratio to Written Premium - 50% Fixed 36.0% 34.4% 32.9% 31.5% 30.3%

Incurred Underwriting Expenses - 50% Fixed but "Sticky" * 360 378 423 445 494 Ratio to Written Premium - 50% Fixed but "Sticky" 36.0% 34.4% 34.9% 33.4% 33.7%

* For each $200 in DWP growth, $25 of fixed expense is added.

U/W

Exp

ense

Mod

elin

g R

esul

ts

U/W

Exp

ense

Mod

elin

g B

enef

its

•Allows Companies to Focus on Operational Efficiency•Allows Companies to Incorporate Staffing Models into DFA•Allows Better Forecasts of U/W Expense Results in Growth/Decline Scenarios•Allows More Accurate Measurement of Expense Component of New Business Penalty

Documents

Modeling asset and Liability cashflows in a dynamic setting: Basic tools and risk measures 2000 CAS DFA Seminar Robert J. Walling Paratus consulting limited