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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)
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 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
Drawbacks– Over-Simplified
– May Lack Diagnostic Detail
– Depends on the Past Repeating Itself
– No Feedback Between Rate Action & Premium
– “Wishful Thinking” Risk
Loss r
ati
o M
od
elin
gSIMPLECO.com 2000 Strategic Plan (REVISION 2)
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 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
– Still Provides Point Estimate
– Allows for Different Conditions
– Works Well for Relatively Stable Lines
Drawbacks– Over-Simplified
– May Lack Diagnostic Detail
– Depends on the Past Repeating Itself
– No Feedback Between Rate Action & Premium
– “Wishful Thinking” Risk
– Can Struggle with Large Losses
– Does not Separate Business & Liability Risk
Fre
qu
en
cy &
Severi
ty M
od
elin
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
ty M
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
elin
gAdvantagesAdvantages
– Provides Diagnostic Detail
– Allows Different Trend Factors
– Still Provides Point Estimate
– Allows for Different Conditions
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
e M
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
e M
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
2000 2001 2002 2003 2004Written Premium 1,000 1,100 1,210 1,331 1,464 % Growth 10% 10% 10% 10%
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