BAS Sixth Annual Case Competition

Presented by Joan Dai, Annie Chen, Daniel He, Roy Kim

1

BAS Sixth Annual Case Competition

Team 14

Background

2

BAS Sixth AnnualCase Competition

Team 14

BackgroundUnexpected demographic shifts in pension plan• Retirement Increase

• Early retirement• Postponed retirement

• Creeping Active Termination

3

BAS Sixth Annual Case Competition

Team 14

Problem

Asset and liability mismatch

LiabilitiesAssetsLiabilities

Assets

4

BAS Sixth Annual Case Competition

Team 14

• Binomial Confidence Intervals• Bootstrap Estimates• Exponential Moving Average

• Final Funding Status Report

Agenda

5

BAS Sixth Annual Case Competition

Team 14

Rate Analysis

6

BAS Sixth Annual Case Competition

Team 14

Rate Analysis

Second YearFirst Year

Active Terminated

Retired

7

Terminated Vested

BAS Sixth Annual Case Competition

Team 14

Rate Analysis• Hypothesis tests of previous assumption rates

• Graphically shown with standard 95% confidence intervals

8

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

Team 14

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

9

BAS Sixth Annual Case Competition

Team 14

CAL Case Competition

TeamActive Retirement

Active Termination

Terminated Vested

Active Retirement Active Termination Terminated Vested 11

Rate Derivation

12

BAS Sixth Annual Case Competition

Team 14

Rate Derivation• Assume original assumption is not credible

• Based only on participants’ behavior

13

BAS Sixth Annual Case Competition

Team 14

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

14

BAS Sixth Annual Case Competition

Team 14

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

. . .

15

BAS Sixth Annual Case Competition

Team 14

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

16

BAS Sixth Annual Case Competition

Team 14

Rate Synthesis

17

BAS Sixth Annual Case Competition

Team 14

Rate SynthesisObjectives

• Reduce noise• Predict the trend

Techniques• Exponential moving average

18

BAS Sixth Annual Case Competition

Team 14

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

Team 14

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

20

BAS Sixth Annual Case Competition

Team 14

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

21

BAS Sixth Annual Case Competition

Team 14

Rate Synthesis

22

BAS Sixth Annual Case Competition

Team 14

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

23

BAS Sixth Annual Case Competition

Team 14

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

24