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CAS 2008 Spring Meeting
Joint Meeting CIA/SOA/CAS
A Survey of P&C Predictive
Modeling Applications
Gaétan Veilleux, FCAS, MAAA
June 18, 2008
What is Predictive Modeling?
A statistical process which estimates the value of an
observed item (dependent variable) based upon the
values of other explanatory variables.
2
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P&C Predictive Modeling applications
Generalized Linear Models (GLM)
Data mining and other methods
– Artificial neural networks
– Classification and regression trees (CART)
– Multivariate adaptive regression splines (MARS)
– Cluster analysis
– Principal components analysis / factor analysis
3
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Generalized linear models
E[Y] = μ = g-1(X.β + ξ)
Var[Y] = φ.V(μ) / ω
Consider all factors simultaneously
Allow for nature of random process
Provides diagnostics
Robust and transparent
Increasingly a global standard
4
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Insurance applications of GLMs
Ratemaking
Underwriting
Marketing
Retention
Expense analysis
Claims management
Risk management / reinsurance
Sales channel
Reserving
5
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Applications
Ratemaking
– Revise existing rating factor relativities with
multivariate analysis
– Introduce new rating variables or underwriting tiers
– Re-define territorial boundaries
– Re-define vehicle classifications
– Unbundle homeowners by-peril
– Understand effect of proposed rate changes at
renewal (including moderator algorithms)
– Define rating plan that optimizes profit while retaining
required volume
6
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Ratemaking objective
Age
Sex
Vehicle
Rating Plan
Premium
Area
Claim
Limit
7
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Modeling the cost of claims
Age
Sex
Vehicle
Area
Model
Expected
cost of
claims
Claim
Limit
8
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Modeling the cost of claims
BI
Freq
x
Amt
= Cost 1
PD
Freq
x
Amt
= Cost 2
MED Freq
x
Amt
= Cost 3
COL
Freq
x
Amt
= Cost 4
OTC
Freq
x
Amt
= Cost 5
9
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GLM output (significant factor)
200000
1.2
180000
1
154%
138%
0.8
160000
140000
105%
73%
0.6
120000
72%
58%
100000
45%
0.4
39%
80000
31%
Exposure (years)
Log of multiplier
93%
84%
60000
0.2
5%
40000
0%
0
20000
0
-0.2
1
2
3
4
5
6
7
8
9
10
11
12
13
Vehicle symbol
P value = 0.0%
Onew ay relativities
Approx 95% confidence interval
Parameter estimate
10
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Age - sex interaction
Example job
Run 5 Model 3 - Small interaction - Third party material damage, Numbers
155%
1
138%
300000
0.8
250000
63%
63%
200000
46%
40%
0.4
28%
19%
24%
20%
150000
0.2
13%
Exposure
Log of multiplier
0.6
6%
0%
-2%
100000
-6%
0
-11%
-18%
-19%
50000
-0.2
-0.4
0
17-21
22-24
25-29
30-34
35-39
40-49
50-59
60-69
70+
P level = 0.0%
Rank 6/6
Age of driver.Sex of driver
Approx 2 SEs from estimate, Sex of driver: Female
Approx 2 SEs from estimate, Sex of driver: Male
Unsmoothed estimate, Sex of driver: Female
Unsmoothed estimate, Sex of driver: Male
Smoothed estimate, Sex of driver: Female
Smoothed estimate, Sex of driver: Male
11
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Impact analysis
Example job
Age of driver
7000
180%
170%
160%
6000
150%
140%
5000
120%
110%
100%
3000
Loss ratio
Count of records
130%
4000
90%
80%
2000
70%
60%
1000
50%
40%
0
30%
0.450 0.500
0.600 0.650
0.750 0.800
0.900 0.950
1.050 1.100
1.200 1.250
1.350 1.400
1.500 1.550
1.650 1.700
1.800 1.850
1.950 2.000
2.100 2.150
2.250 2.300
2.400 2.450
Ratio: Risk Premium / Current premium
tariff
17-21
22-24
25-29
30-34
35-39
40-49
50-59
60-69
70+
Claims / Earnedprem
12
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Applications
Underwriting
– Provide guidelines on debits/credits
– Produce scorecards to automate some elements of
risk selection
Marketing
– Improve direct mail conversion rate for most profitable
risks
13
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Scoring
Distribution of score
2500
160%
140%
2000
100%
1500
80%
1000
60%
Actual loss ratio
Number of policies
120%
40%
500
20%
0
0%
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
Score based on expected loss ratio
Number of policies
Actual loss ratio
14
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Applications
Retention
– Understand effect of capping rate changes at renewal
– Develop lifetime customer value model
Expense analysis
– Vary acquisition costs by other criteria
Claims management
– Develop fraud scorecard
– Advise how TPAs affect claim costs
– Analyze the drivers of claim cost and hence loss
control
15
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Applications
Risk management / reinsurance
– Determine which risks to cede
Sales channel
– Align compensation with expected profitability
Reserving
– Provide additional method to assist reserving
actuaries with ultimate projections
– Identify predictors of “serious” claims
16
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P&C Predictive Modeling applications
Generalized Linear Models (GLM)
Data mining and other methods
– Artificial neural networks
– Classification and regression trees (CART)
– Multivariate adaptive regression splines (MARS)
– Cluster analysis
– Principal components analysis / factor analysis
17
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Data Mining
aka Knowledge Discovery in Databases (KDD)
Broad range of methods
Good at discovery, weak at estimation
Many (most) are not being applied to P&C insurance
ACM SIGKDD International Conference on
Knowledge Discovery & Data Mining
– Evolutionary spectral clustering by incorporating temporal smoothness
– Making generative classifiers robust to selection bias
– Nonlinear adaptive distance metric learning for clustering
18
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Data Mining – 5 Common Techniques
Artificial neural networks
– Non-linear predictive models that learn through
training
– Resemble biological neural networks in structure
Decision trees
– Tree-shaped structures that represent sets of
decisions
– These decisions generate rules for the classification
of a dataset
19
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Data Mining – 5 Common Techniques (2)
Genetic algorithms
– Optimization techniques
– Genetic combination, mutation, and natural selection
Nearest neighbor
– Classification of each record based on a combination
of the classes of the k record(s) most similar to it in a
historical dataset
Rule induction
– Extraction of useful if-then rules from data based on
statistical significance
20
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Artificial Neural Networks
ID
–
–
–
structural components for a GLM
Variables
Binning
Interactions
Input
Hidden
Output
Fraud detection
– Staged accidents
– Other PM techniques
21
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Classification and Regression Trees - CART
Decision tree based method
Binary recursive partitioning
Brute force non-parametric method
Response is discontinuous
Doesn’t capture strong linear relationships well
N = 100,000
Applications
Variable selection
Binning
Identify predictors of “serious” claims
Area = {1, 2, 3}
Area = {others}
N = 41,127
N = 58,873
Density <50
Density >100
N = 11,245
N = 2,743
Density 50-100
N = 44,885
22
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Multivariate Adaptive Regression Splines MARS
Multivariate non-parametric regression procedure
Brute force
Response is continuous
Piece-wise linear segments to describe non-linear
relationships
Applications
Variable selection
Binning
23
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Cluster Analysis
Seek to identify homogeneous subgroups
Average linkage or centroid methods
No good literature explaining which is best
Minimize within-group variation and maximize
between-group variation
Applications
Vehicle symbols
Segmenting/Tiering
Fraud detection
24
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Principal Components/Factor Analysis
Reduce number of variables
Detect structure
Consecutive factors are independent of (orthogonal
to) each other
Applications
Economic models s/a trend
Transform/reduce variables
25
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ISO Innovative Analytics - Risk Analyzer
Modeling Techniques Employed
Variable Selection – univariate analysis, transformations, known
relationship to loss
Sampling
Regression / general linear modeling
Sub models/data reduction – neural nets, splines, principal
component analysis, variable clustering
Spatial Smoothing – with parameters related to auto insurance
loss patterns
26
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Quotes
“Prediction is very difficult, especially if it's about
the future.”
- Nils Bohr, Nobel laureate in Physics
"I have seen the future and it is very much like the
present, only longer."
- Kehlog Albran, The Profit
"A good forecaster is not smarter than everyone
else, he merely has his ignorance better
organized."
- Anonymous
27
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watsonwyatt.com
CAS 2008 Spring Meeting
Joint Meeting CIA/SOA/CAS
A Survey of P&C Predictive
Modeling Applications
Gaétan Veilleux, FCAS, MAAA
June 18, 2008
watsonwyatt.com
SOA/CAS Spring Meeting
Application of Predictive Modeling in
Life Insurance
Jean-Felix Huet, ASA
June 18, 2008
Predictive Modeling
Statistical model that relates an event (death) with a number of
risk factors (age, sex, YOB, amount, marital status, etc.)
Age
Sex
Y.o.B.
Model
Married
Expected
mortality
Amount
etc.
1
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Application of Predictive Modeling In Life
Insurance
Predictive Modeling techniques offer an alternative way to analyze
mortality experience compared to Traditional “One-Way” analysis
One way analysis looks at a single risk factor at a time
However, a Predictive Modeling Approach will allow for interactions
between all risk factors when analyzing the true impact of the factor
under investigation
E.g. Annuitants with larger benefit amounts tend to show lighter
mortality than others, but this could also be influenced by the
underlying mix of gender, occupation, duration, marital status, etc.
In this presentation we will show the impact of analyzing various
risk factors using Predictive Modeling techniques versus traditional
one-way analysis.
2
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Current Approach of Mortality Analysis
Focus on limited risk factors that impact mortality
– Age, Sex, may extend to other factors (i.e. amount, marital status, and
geographical location)
– Company experience is sub-divided into categories to examine the relationship
of actual to expected mortality experience (A/E ratio). This ratio is typically
applied to a standard table varying by age and sex
Limitations
– Mortality is simultaneously impacted by all risk factors and has to be analyzed
with all factors together
– The subdivision process is limited by the credibility of the experience
developed for each sub category. Based on the lack of data it may not be
possible to identify and evaluate all factors impacting mortality.
– The current approach does not quantify the impact of each risk factor on the
mortality result.
Describe a more sophisticated mathematical approach to be used to identify the risk
factors affecting the mortality of the selected block of business, and assign weights
to each factor in order to develop the mortality experience assumption
3
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Generalized Linear Models (GLMs)
Special type of predictive modelling
A method that can model
–
a number
as a function of
– some factors
For instance, a GLM can model
– Motor claim amounts as a function of driver age, car type, no
claims discount, etc …
– Motor claim frequency (as a function of similar factors)
Historically associated with non-life personal lines pricing (where
there was a pressing need for multivariate analysis)
In this presentation we will be applying GLM techniques to the
analysis of the mortality experience for a block of annuity
business
4
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How to Read the Graphs
Generalized Linear Modeling Illustration
All graphs show relative Qx of
Annual Income Effect
different categories of one factor
against a base level identified by
“0%” label. Qx for other levels are
“x%” higher than the base level.
Colors
– Green: GLM results
– Orange: “One-way” relatives are
the relative death rates for the
factor before considering other
factors simultaneously.
– Blue: 95% confidence interval.
Tight confidence interval
indicates statistical significance.
Exposure
– The amount of exposure for a
category is indicated by the bar
on the x-axis.
0.06
1600000
0%
0
1400000
Log of multiplier
1200000
-0.12
1000000
-14%
-17%
-0.18
800000
600000
-0.24
400000
-0.3
-29%
-0.36
200000
0
<= 30K
<= 50K
<= 75K
<= 100K
> 100K
Income
Oneway relativities
Approx 95% confidence interval
Unsmoothed estimate
Smoothed estimate
5
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Exposure (years)
-6%
-0.06
Example 1: Effect of Annuity Amount
Generalized Linear Modeling Illustration
Income Effect
0.06
1600000
0%
0
1400000
Log of multiplier
1200000
-0.12
1000000
-15%
-0.18
800000
-18%
600000
Exposure (years)
-6%
-0.06
-0.24
400000
-0.3
200000
-29%
-0.36
0
<= 30K
<= 50K
<= 75K
<= 100K
> 100K
Income
Oneway relativities
Approx 95% confidence interval
Unsmoothed estimate
Smoothed estimate
Results show evidence of reduced mortality with increased benefits
6
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Example 2: Impact of age/sex
Generalized Linear Modeling Illustration
Run 1 Model 2 - GLM - Significant
3
1319%
1133%90000
1033%
865%
809%
756%
80000
672%
593%
591%
521%
495%
461%
444%
70000
411%
398%
369%
1.8
351%
332%
306%
294%
265%
255%
60000
228%
218%
195%
186%
164%
160%
1.2
138%
133%
119%
50000
106%
102%
85%
85%
70%
69%
56%
56%
44%
43%
0.6
40000
31%
30%
20%
17%
9%
5%
0%
-5%
-8%
-12%
30000
-14%
-17%
-20%
-23%
0
-25%
-30%
-30%
-33%
-35%
-35%
-36%
-36%
-40%
-41%
20000
-45%
-46%
-50%
-51%
-54%
-57%
-57%
-57%
-57%
-0.6
-60% -58%
-60%
-60%
-64%
10000
-68%
-1.2
Exposure (years)
96
90
>
Twoway mapping of Mage and Msex
93
<=
87
84
81
78
75
72
69
66
60
63
M
57
91
96
>
88
85
82
79
76
73
70
67
64
61
0
58
55
Log of multiplier
2.4
Oneway relativities
Restricted factor
A mortality table is fitted using experience data and the variation of
mortality by age is fixed in subsequent analysis of other risk factors
7
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Example 3: Calendar Year Trend
Generalized Linear Modeling Illustration
Run 1 Model 2 - GLM - Significant
0.1
700000
0.08
Log of multiplier
5%
4%
500000
4%
0.04
400000
2%
0.02
300000
1%
0%
0
200000
-0.02
100000
Exposure (years)
600000
0.06
0
-0.04
2002
2003
2004
2005
2006
2007
Unsmoothed estimate
Smoothed estimate
Calendar year
Oneway relativities
Approx 95% confidence interval
Mortality improvements 1% per annum over previous six years
8
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Example 4: Effect of Joint Life Status
Generalized Linear Modeling Illustration
Joint Survivor Status
0.08
2500000
0.06
3%
2000000
0.02
1500000
0%
0
1000000
-0.02
Exposure (years)
Log of multiplier
0.04
-4%
-0.04
500000
-0.06
0
-0.08
Single Life
Oneway relativities
Joint Life Primary
Approx 95% confidence interval
Joint Life Surviving Spouse
Unsmoothed estimate
Smoothed estimate
Evidence of “broken heart syndrome” which may influence pricing
9
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Example 5: The Selection Effect
Generalized Linear Modeling Illustration
Run 1 Model 2 - GLM - Significant
0.01
3000000
0%
0
2500000
2000000
-3%
-0.03
1500000
-0.04
-0.05
1000000
Exposure (years)
-0.02
-0.06
500000
-0.07
0
-0.08
<=5
5+
Duration
Approx 95% confidence interval
Smoothed estimate
Selection effect is not conclusive
10
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Example 6: Geographic Region Effect
Generalized Linear Modeling Illustration
Geographic Region
0.4
180000
0.3
160000
17%
7%
0.1
16%
15%
0%
0%
0%
0
140000
120000
8%
7%
7%
2%
100000
-2%
80000
-0.1
Exposure (years)
0.2
Log of multiplier
Log of multiplier
-0.01
60000
-14%
40000
-0.2
20000
0
-0.3
1
2
3
4
5
6
7
8
9
10
11
12
13
Region
Oneway relativities
Approx 95% confidence interval
Unsmoothed estimate
Some regions were found to be statistically significant ( 4, 7 and 13 ).
However, we excluded this factor mainly because of the wide confidence
interval for the other regions.
11
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How to Derive Mortality Assumptions
Mortality Table
based on 2007 and income < 35K
Age
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
Female
0.00795
0.00892
0.00978
0.01025
0.01003
0.00913
0.00836
0.00830
0.00878
0.00956
0.01040
0.01129
0.01230
0.01350
0.01483
0.01613
0.01726
0.01842
0.01989
0.02201
0.02471
Male
0.00955
0.01077
0.01201
0.01307
0.01373
0.01387
0.01394
0.01438
0.01518
0.01617
0.01721
0.01835
0.0197
0.02138
0.02338
0.02562
0.02802
0.03059
0.03337
0.0364
0.03969
Calendar year
Income
Joint Status
Factor level
Loading
Factor level
Loading
2002
2003
2004
2005
2006
2007
5.00%
4.00%
4.00%
2.00%
1.00%
0.00%
35K
50K
75K
100K
>100K
0.00%
-6.00%
-15.00%
-18.00%
-29.00%
Factor level Loading
Joint Life Alive
Surviving Spouse
Single
-4.00%
3.00%
0.00%
Mortality Assumption @
2007 level, income > 100K
Married with Joint Life Status
Female
55
0.00542
56
0.00608
57
0.00667
58
0.00699
59
0.00683
60
0.00622
61
0.00570
62
0.00565
63
0.00599
64
0.00652
65
0.00709
66
0.00769
67
0.00838
68
0.00920
69
0.01011
70
0.01099
71
0.01177
72
0.01255
73
0.01356
74
0.01500
75
0.01684
Mortality Assumption for female, 55, income>100K,
Married with joint life @2007 level = 0.00795
*(1+0%)*(1-29%)*(1-4%) = 0.00542
12
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Summary
GLM techniques are widely used in P&C for pricing purposes,
but its application in Life Insurance may not be as well
established.
By using GLM techniques in the analysis of annuitant mortality,
we were able to identify the true impact of various risk factors
while allowing for the interactions between these factors.
We demonstrated that for some risk factors, the application of
GLM showed significantly different mortality patterns when
compared to results of traditional analysis.
The advantage of additional knowledge on the mortality
characteristics of the annuity block will allow management to
make better pricing decisions and to gain business advantage
over competitors.
13
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watsonwyatt.com
CIA/SOA/CAS
Life 2008 Spring Meeting
Applications of Predictive Modeling
in Employee Benefits
Ron Littler, FSA
June 18, 2008
Applications of Predictive Modeling
in Employee Benefits
Predictive Modeling techniques are used to value employee
benefits, measure risks associated with benefit plans and model
alternative plan designs.
Valuation techniques in use include binomial lattice modeling and
Monte Carlo simulation.
Monte Carlo simulation is typically employed to determine the
probability of threshold outcomes (eg, VaR), assess the impact of
funding and investment policies and various plan designs.
There is increasing application of option pricing techniques to
pension obligations, eg there are emerging markets for plan
buyouts and longevity trading.
2
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Valuation Example - Share-Based Compensation
3
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Valuation Models – Share-Based Compensation
The Black-Scholes ‘model’ is the traditional and most widely used
method for valuing share options.
– Unlike tradable share options, employee share options are longer-term,
typically have performance conditions and are non-transferable.
– Consequently, Black-Scholes does not effectively reflect the impact of
anticipated employee exercise behavior and performance conditions.
A binomial model tends to produce a more realistic estimate of the
option’s true value.
– The method divides the option’s term into small time increments,
enabling the model to take into account most revelant assumptions
about an option grant’s features.
In some cases, Monte-Carlo simulation is required to fully capture
particular design features.
4
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Binomial Model
Scenario: Stock price will either increase by 10% or decrease by 5%
each time period.
S2=121
S1=110
S0=100
S2=104.5
S1= 95
S2=90.25
Let’s look at an option granted with a $100 exercise price.
5
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Binomial Model
The option will have the following payoffs at each “node”:
21
Probability = 25%
4.5
Probability = 50%
0
Probability = 25%
10
0
0
Grant
Hold
Exercise
Option Value = 25% x 21 + 50% x 4.5 + 25% x 0 = $7.50
6
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Binomial Model – Early Exercise
The option will have the following payoffs at each “node”:
10
Probability = 50%
0
4.5
Probability = 25%
0
Probability = 25%
0
Grant
Exercise or Hold
Exercise
Option Value = 50% x 10 + 25% x 4.5 + 25% x 0 = $6.13
7
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Valuation Models – Share-Based Compensation
Black-Scholes
Lattice
Monte Carlo
Easy
Moderate
Difficult
No
Yes
Yes
Relative P&L Expense
Generally highest
Generally lower than
B-S
Generally lower than
B-S
Assumption Flexibility
Not flexible
Very flexible
Very flexible
Ability to handle
performance features
No
Yes, but may be
limited
Yes
Ease to set up
Ability to capture unique
features of employee
awards
8
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Pension Funding, Investing and Design
9
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Modeling the impact of investment policy on
pension risk
Inflation?
Cash contributions?
Interest rates?
Income/expense?
Investment returns?
Balance sheet impact?
Future economic environment is uncertain
Financial results are uncertain
The purpose of an integrated asset/liability study is to:
– Simulate the future economy by generating thousands of possible
scenarios (stochastic modeling)
– Develop financial results for each scenario for potential asset
allocations
– Summarize results by calculating key risk measures
– Evaluate risk/reward tradeoff of different asset allocations through
efficient frontier framework and summary statistics
– Implement decisions into investment policy and assets
– Identify other (non-investment) risk management opportunities
10
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Stochastic Simulations – One Scenario
Future Discount Rates
Investment Returns
100.00%
14.00%
75.00%
Annual Returns (%)
Discount Rate (%)
50.00%
10.00%
6.00%
25.00%
0.00%
-25.00%
-50.00%
2.00%
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 11
-75.00%
Year 12
Year 1
Year
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 9
Year 10
Year 11
Year 12
Year
Cash Contributions
Pension Expense/(Income)
50
75
Expense/(Income) ($M)
Cash Contributions ($M)
25
50
C
25
0
(25)
C
(50)
(75)
(100)
0
(125)
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 11
Year 1
Year 12
Year 2
Year 3
Year 4
Year 5
Year 6
Year
Year 7
Year 8
Year 11
Year 12
Year
11
Copyright © Watson Wyatt Worldwide. All rights reserved
Stochastic Simulations – Many Scenarios
Future Discount Rates
Investment Returns
100.00%
14.00%
75.00%
Annual Returns (%)
Discount Rate (%)
50.00%
10.00%
6.00%
25.00%
0.00%
-25.00%
-50.00%
2.00%
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 11
Year 12
-75.00%
Year 1
Year
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 9
Year 10
Year 11
Year 12
Year
Cash Contributions
Pension Expense/(Income)
50
75
Expense/(Income) ($M)
Cash Contributions ($M)
25
50
C
25
0
(25)
C
(50)
(75)
(100)
(125)
0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year
Year 8
Year 9
Year 10
Year 11
Year 12
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 11
Year 12
Year
12
Copyright © Watson Wyatt Worldwide. All rights reserved
Measuring Risk of Pension Obligation
13
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Watson Wyatt’s Pension Risk Index
One way to quantify the additional risk the pension fund implies
for a company’s core business is a value-at-risk (VaR)
measure developed by Watson Wyatt called the Pension Risk
Index (PRI).
The VaR is the dollar reduction in the pension fund’s funded
position under adverse financial market conditions (95th
percentile worst outcome) given the plan’s asset allocation,
liability structure and sensitivity to interest rates.
The VaR is calculated using Watson Wyatt’s capital market
assumptions and proprietary asset/liability modeling
technology. The dollar value of this outcome is then compared
with the market capitalization of the plan sponsor.
14
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Pension Risk Index for the FORTUNE 1000
Distribution of Pension Risk Index Values, 2003-2006
15
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Analyzing Policy Decisions
16
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Simulated Investment Performance:
Comparison of Balanced and Life Cycle Funds
Motivation of simulation – DOL proposed regulation for
individual account plans; also (implicit) comparison of DC and
DB plan investment approaches
Assumes steady contributions of 6% of earnings over a 40
year career, with earnings, starting at $40,000 at age 25,
growing 4% annually thereafter through age 50 and flat
thereafter– best case scenario of no plan leakages and
continual work profile.
Assumes stochastic asset real returns based on 1960 – 2004
experience; investment expenses are not included.
Assumes equity/bond/cash mixes of average Balanced and
Life Cycle funds in the marketplace.
17
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Simulated Investment Performance:
Comparison of Balanced and Life Cycle Funds
Table shows distribution of account balance outcomes
(inflation-indexed) at end of career.
Overall mean is $529K for balanced fund vs. $515K for life
cycle; life cycle outcome is higher in first two deciles.
Balanced fund outperforms life cycle 57.3 percent of the time.
But standard deviation for balanced fund, particularly in the
age 55 to 65 period (not shown), is much higher than for life
cycle fund.
Interpretations – life cycle fund makes more sense for
individual account investor with shortening horizon, but longer
investment horizon of DB plan sponsor (balanced fund) gives a
higher expected return.
18
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Simulated Investment Performance:
Comparison of Balanced and Life Cycle Funds
Terminal Wealth at 65 ($1000)
Median
Decile
Overall
Balanced Fund
Standard Deviation
Mean
Lifecycle
Fund
Balanced Fund
Lifecycle
Fund
Balanced Fund
Lifecycle
Fund
1
194.5
200.7
187.8
194.9
32.1
30.3
2
260.5
263.3
260.1
262.9
15.9
15.3
3
313.9
312.6
313.4
312.5
15.1
13.7
4
363.9
360.4
364.3
360.4
14.9
14.0
5
417.9
410.9
418.2
411.2
16.5
15.5
6
479.0
468.3
479.5
468.8
19.1
17.9
7
553.3
537.0
553.8
537.9
24.1
22.3
8
650.8
627.8
652.5
629.7
33.4
31.5
9
796.0
764.7
802.7
770.2
57.5
53.8
10
1136.2
1082.4
1254.6
1202.4
391.2
377.2
447.5
438.6
528.7
515.1
324.8
307.2
19
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Summary
Valuation models such as Black-Scholes are inadequate for
many contingent obligations.
Lattice models and Monte Carlo simulation offer more flexibility
than Black-Scholes or other closed form solutions.
Applications of predictive modeling for employee benefits
include valuation and the determination of risks inherent in the
plans.
Predictive modeling can be used to help illustrate the impact of
policy decisions by plan sponsors.
20
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