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BAS Sixth Annual Case Competition
Presented by Joan Dai, Annie Chen, Daniel He, Roy Kim
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BAS Sixth Annual Case Competition
Team 14
Background
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BAS Sixth AnnualCase Competition
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BackgroundUnexpected demographic shifts in pension plan• Retirement Increase
• Early retirement• Postponed retirement
• Creeping Active Termination
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BAS Sixth Annual Case Competition
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Problem
Asset and liability mismatch
LiabilitiesAssetsLiabilities
Assets
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BAS Sixth Annual Case Competition
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• Binomial Confidence Intervals• Bootstrap Estimates• Exponential Moving Average
• Final Funding Status Report
Agenda
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BAS Sixth Annual Case Competition
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Rate Analysis
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BAS Sixth Annual Case Competition
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Rate Analysis
Second YearFirst Year
Active Terminated
Retired
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Terminated Vested
BAS Sixth Annual Case Competition
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Rate Analysis• Hypothesis tests of previous assumption rates
• Graphically shown with standard 95% confidence intervals
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Active Retirement RateAge Current55 0.0556 0.0557 0.0558 0.0559 0.0560 0.1061 0.1062 0.2063 0.3064 0.4065 1.00
BAS Sixth Annual Case Competition
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Rate Analysis• Hypothesis testing each age level with assumption rates as null
Reject Probability of at least this extremity is too small
Fail to Reject
Variation can be due to chance
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BAS Sixth Annual Case Competition
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CAL Case Competition
TeamActive Retirement
Active Termination
Terminated Vested
Active Retirement Active Termination Terminated Vested 11
Rate Derivation
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BAS Sixth Annual Case Competition
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Rate Derivation• Assume original assumption is not credible
• Based only on participants’ behavior
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BAS Sixth Annual Case Competition
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Rate Derivation• Method: Bootstrap simulation
• Sample Size: 750 from designated population• Resampling: 500 times• All Three Categories:
• Termination Rate• Active Retirement Rate• Terminated Vested Retirement Rate
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BAS Sixth Annual Case Competition
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Rate DerivationBootstrap Trials (Active Retirement Rate 2012 to 2013)
Age Trial 1 Trial 2 Trial 3 Trial 4 Trial 554 0.00 0.02 0.10 0.00 0.0555 0.00 0.00 0.05 0.05 0.1556 0.05 0.16 0.00 0.02 0.157 0.13 0.00 0.00 0.00 0.0058 0.00 0.00 0.25 0.00 0.0059 0.14 0.00 0.00 0.4 0.2560 0.11 0.09 0.16 0.2 0.0061 0.50 0.16 0.00 0.20 0.0062 0.10 0.75 0.20 0.00 0.2563 0.25 0.20 0.17 0.50 0.2964 0.50 0.25 0.00 0.33 0.0065 0.00 0.25 0.00 0.25 0.6766 0.66 0.50 0.22 1.00 0.0067 0.17 0.00 0.20 0.00 0.0068 0.16 0.50 0.43 0.16 0.5069 0.67 0.00 0.50 0.00 0.6770 1.00 1.00 0.60 1.00 0.7571 1.00 1.00 0.00 1.00 1.00
Bootstrap Result
Age Mean54 0.0255 0.0356 0.0657 0.0558 0.1159 0.1160 0.2461 0.2662 0.3263 0.2864 0.3165 0.3366 0.3667 0.2668 0.3369 0.3570 0.6971 0.97
. . .
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BAS Sixth Annual Case Competition
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Putting it all together• Assumption rates, fail-to-reject or reject• Bootstrap rates
Rate DerivationDerived Active Retirement Rates
2012 2013 2014 2015 201654 0.02 0.02 0.02 0.04 0.0855 0.05 0.05 0.05 0.05 0.0556 0.05 0.05 0.05 0.05 0.0557 0.05 0.05 0.05 0.05 0.0558 0.11 0.05 0.05 0.12 0.0559 0.11 0.05 0.19 0.05 0.1260 0.24 0.20 0.10 0.10 0.2261 0.26 0.10 0.28 0.25 0.3262 0.20 0.32 0.47 0.35 0.2063 0.30 0.30 0.30 0.30 0.3064 0.40 0.40 0.22 0.40 0.4065 0.33 0.19 0.37 0.29 0.1666 0.36 0.31 0.27 0.38 0.1467 0.26 0.22 0.24 0.42 0.5668 0.33 0.31 0.23 0.10 0.3669 0.35 0.30 0.22 0.45 0.2170 0.69 0.65 0.69 0.61 0.7371 0.97 0.99 0.92 0.97 0.99
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BAS Sixth Annual Case Competition
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Rate Synthesis
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BAS Sixth Annual Case Competition
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Rate SynthesisObjectives
• Reduce noise• Predict the trend
Techniques• Exponential moving average
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BAS Sixth Annual Case Competition
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Rate SynthesisAge 2012 – 2013 2013 – 2014 2014 – 2015 2015 – 2016 2016 – 2017
61 0.26 0.10 0.28 0.25 0.32
0.26
0.18
0.230.24
0.28
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
2012 - 2013 2013 - 2014 2014 - 2015 2015 - 2016 2016 - 2017
Tran
sitio
n Pr
obab
ility
Transition Years
Active Retirement, Age 61, 𝛼𝛼 = 0.5
𝛼𝛼 = 0.5 19
0.26
0.24 0.24 0.240.260.26
0.10
0.28
0.25
0.32
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
2012 - 2013 2013 - 2014 2014 - 2015 2015 - 2016 2016 - 2017
Tran
sitio
n Pr
obab
ility
Transition Years
Active Retirement, Age 61
𝛼𝛼 = 0.15 𝛼𝛼 = 1
BAS Sixth Annual Case Competition
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Rate SynthesisTable 2: Terminated-Vested
Retirement RatesAge Current Proposed Rate54 NA 0.0355 0.05 0.0556 0.05 0.0557 0.05 0.0558 0.05 0.0559 0.05 0.0760 0.10 0.1461 0.10 0.3262 0.20 0.2063 0.30 0.2064 0.40 0.2165 1.00 0.1166 NA 0.1667 NA 0.0468 NA 0.1669 NA 0.2070 NA 0.2171 NA 0.27
Table 1: Active Retirement Rates
Age Current Proposed Rate54 NA 0.0555 0.05 0.0556 0.05 0.0557 0.05 0.0558 0.05 0.0759 0.05 0.1060 0.10 0.1861 0.10 0.2862 0.20 0.2863 0.30 0.3064 0.40 0.3865 1.00 0.2366 NA 0.2467 NA 0.4468 NA 0.2769 NA 0.2870 NA 0.6971 NA 0.98
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BAS Sixth Annual Case Competition
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Rate SynthesisTable 3: Active Termination Rates, 25 - 44
Age Current Proposed Rate25 - 29 0.15 NA
30 0.15 0.1531 0.12 0.1232 0.12 0.1633 0.12 0.1234 0.12 0.1235 0.10 0.1036 0.10 0.1237 0.10 0.1038 0.10 0.1039 0.10 0.1040 0.09 0.1041 0.08 0.0742 0.07 0.0743 0.06 0.0744 0.05 0.06
Table 3: Active Termination Rates, 45 - 71
Age Current Proposed Rate45 0.05 0.0546 0.05 0.0647 0.05 0.0548 0.05 0.0549 0.05 0.0650 0.05 0.0651 0.05 0.0552 0.05 0.0553 0.05 0.0654 0.05 0.06
55 - 63 NA 0.0064 NA 0.01
65 - 69 NA 0.0070 NA 0.0171 NA 0.01
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BAS Sixth Annual Case Competition
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Rate Synthesis
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BAS Sixth Annual Case Competition
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Increased Early
Retirement
Increased Postponed Retirement
CreepingActive
Termination
Rate SynthesisFunding Status
Old Rates New Rates Net Difference
Normal Retirement Lump-Sum 2018 $327K $798K $473K
Increased Retirement
Increased Liability
Need for Increased
Assets
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BAS Sixth Annual Case Competition
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BAS Sixth Annual Case Competition
Team 14Index & Thank YouPresenters
Index1. Title Card2. Background: Title Card3. Background: Introduction4. Background: The Problem5. Background: Agenda6. Rate Analysis: Title Card7. Rate Analysis: Introduction8. Rate Analysis: Transition Pools9. Rate Analysis: Testing
10. Rate Analysis: 2012 – 2013 Experience
11. Rate Analysis 2013 – 2017 Experience
12. Rate Derivation: Title Card13. Rate Derivation: Introduction14. Rate Derivation: Method15. Rate Derivation: Results16. Rate Derivation: Combination
17. Rate Synthesis: Title Card18. Rate Synthesis: Method19. Rate Synthesis: Exponential
Smoothing20. Rate Synthesis: Trends21. Rate Synthesis: Tables 1 & 2
Proposal22. Rate Synthesis: Table 3 Proposal23. Rate Synthesis: Funding Status
Joan Dai Annie Chen Daniel He Roy Kim
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