Simulation Analysis for Evaluating Risk-sharing Pension Plans

PBSS Webinar December 14, 2016 Simulation Analysis for Evaluating Risk-sharing Pension Plans Norio Hibiki Masaaki Ono Keio University Mizuho Pension Research Institute This slide can be downloaded from http://www.ae.keio.ac.jp/lab/soc/hibiki/profile_2/hibiki_pbsswebinar_20161214.pdf

Biography Norio Hibiki is a professor of the Faculty of Science and Technology at Keio University in Japan. He received his B.E., M.E., and Ph.D. degrees in administration engineering from Keio University in 1988, 1990, and 1994, respectively. His major field is financial engineering, and he is especially interested in portfolio optimization, financial risk management, asset and liability management in bank, pension fund and insurance company, and household financial engineering. He is a fellow of the Operations Research Society of Japan. Masaaki Ono is a Research Fellow at Mizuho Pension Research Institute, a Fellow of the IAJ and a Certified Pension Actuary. He graduated from the University of Tokyo with a Bachelor s degree in science. He has been a Vice President of the IAJ since 2013 and chairs its Pension and Health Committee. He used to be the IAJ delegate to the Pensions and Employee Benefits Committee of the IAA until 2015. As for the public activities, he is now an acting member of two subcommittees in the Labor and the SME policy fields. 1

Contents 2. Models concerning Corporate Pension Plan Overview: Plan Design Risk-sharing plan Evaluation of utility Analysis using the Monte Carlo simulation Base : Comparison of DB, DC, CB and risk-sharing plans Sensitivity of five parameters of risk-sharing plan Sensitivity of management fee 4. Backtesting From March 1995 to March 2015 (20 years) 5. Conclusion Keywords : Risk-sharing, Investment Risk, Simulation 2

Introduction The occupational pensions become more important to complement the public pension. However, the traditional occupational s have some weakness for their sustainability or stability of benefits. DB (defined benefit) plan: It is difficult for a sponsoring company to make additional payments of the contribution for lack of the plan asset under the worse investment condition. DC (defined contribution) plan: We have a problem concerning stability of the pension which supports the living expenses in retirement. Recently, occupational pensions with new types of risk-sharing functions have been proposed; DA (defined ambition) plan in the U.K., target benefit plan in Canada, FTK2 in the Netherland, risk-sharing DB plan in Japan 3

Previous Studies Hoevenaars & Ponds (2008) Kocken (2012) Kortleve (2013) Turner (2014) Hardy (2015) Valuing intergenerational transfers in collective s Examining two kinds of valuation techniques for pension liabilities in risk-sharing s Describing a new Dutch pension contract generically labeled defined ambition(da) plans Evaluating a number of hybrid s Hybrid DB plans in the Netherlands Nonfinancial DC plan in Sweden Cash balance plans in the United States, Canada and Japan Riester plans in Germany Reviewing target benefit plan, and evaluating the plans through simulations of economic variables to assess risks and benefits The plan design in practice is discussed mainly in a qualitative manner, and there are some researches about the plan designs discussed specifically and quantitatively. 4

Purpose and contribution of our paper We propose a risk-sharing design, which involves a mechanism of sharing the deficiency and surplus in accordance with the funding ratio, and evaluate it quantitatively using Monte Carlo simulation approach. We formulate the simulation model with five parameters to control the level of risk-sharing. We conduct the sensitivity of the five parameters, and suggest how those parameters affect the plan design. We find the benefits and the contributions of the risk-sharing plan are not only at the level intermediate between the DC and DB plans because of the risk-sharing features, but also superior to them in some cases. We implement the backtest using the historical data, and examine the actual effect on four s for twenty years in Japan. 5

Models of Pension Plan Risks shared by stakeholders investment risk interest rate risk: incorporated in the plan design longevity risk and inflation risk: excluded due to historical background in Japan Stakeholders A sponsoring company Active participants Retirees 6

Problem: Setting 20 years old 65 years old 79 years old Working period (funding period) benefit period Four kinds of s: DC, DB, CB, Risk-sharing (RS) Match the size of all plans to compare them each other Assumption Number of persons of each age = 1 Set the same initial actuarial liability of active participants Set the same initial actuarial liability for DC, CB and RS plans Initial plan asset = Initial actuarial liability (Funding ratio = 1) Receive benefit/pay contribution at the beginning of each year 7

Actuarial liability Benefit Contribution Plan asset Design of DC, DB and CB plans DC plan DB plan CB plan Calculate based on Calculate based on Equal to expected yield of real yield of 10- plan asset 10-year government year government bond bond Calculate based on actuarial liability Normal contribution Calculate based on portfolio return Real benefit = 1 at retirement age, and nominal benefit is fixed in benefit period Normal contribution (with 150% rule) + Amortization Calculated based on portfolio return Calculate based on actuarial liability Normal contribution (with 150% rule) + Amortization Calculated based on portfolio return 8

Risk-sharing Pension Plan (1) Sharing investment risk based on the actuarial liability and benefit calculated for the CB plan Risk-sharing design, which involves a mechanism of sharing the deficiency and surplus in accordance with the funding ratio Five parameters to control the level of risk-sharing Trigger parameters: Sharing parameters: 9

Risk-sharing Pension Plan (2) deficiency-sharing no-sharing surplus-sharing ex) 1.05 1.3 Funding ratio 10

Risk-sharing Pension Plan (3) Shared fraction of deficiency(+)/surplus(-) at period n 11

Risk-sharing Pension Plan (4) amortization normal contribution decumulation 12

Risk-sharing Pension Plan (5) benefit of CB plan 13

Risk-sharing Pension Plan (6) Actuarial liability of CB plan 14

Evaluation of utility 15

Evaluation measures 16

Evaluation measures(2) 17

Numerical Analysis (1) Numerical Analysis using the Monte Carlo simulation approach Base : Comparison of risk-sharing plan with DC, DB and CB plans Sensitivity of five parameters of risk-sharing plan 18

Numerical Analysis (2) Generating random samples of nominal rate of return, which are normally distributed Expected return, standard deviation and correlation These parameters are based on the parameters used in order to derive the new policy asset mix for the third medium-term plan published by Government Pension Investment Fund in Japan 19

Numerical Analysis (3) -Setting for sensitivity - 20

Base (1) - Comparison of DB, DC, CB and risk-sharing (RS) plans - Percentiles of the distribution of actuarial liability (Case Aa) Variability among four plans Calculate based on DB: Expected yield of 10-year government bond CB: Real yield of 10- year government bond RS: adjustment of CB DC: portfolio return 21

Base (2) - Comparison of DC, DB, CB and risk-sharing (RS) plans - Percentiles of the distributions of benefit in Case Aa 70 14 Variabilities among four plans 16 9 11 19 10 DC plan: Benefit is based on actuarial liabilities calculated using portfolio return. DB plan: Benefit is fixed to 1 at retirement. CB < RS: Benefit of RS plan is adjusted by the funding ratio. 22

Base (3) - Comparison of DC, DB, CB and risk-sharing (RS) plans - Percentiles of the distributions of contribution in Case Aa 40 0 40 30 0 DB and CB plans: Shapes of distributions are similar, and contributions do not become negative. Risk-sharing plan: Contributions can become negative, and it is possible to decrease cost of a sponsoring company. The 99th percentile 0-60 (except DC plan) 23

Base (4) - Comparison of DC, DB, CB and risk-sharing (RS) plans - Mean-CVaR diagram in Case Aa Distributions become stable when about forty years pass We evaluate means and CVaRs in the latter sixty years of the simulation period Relationship of CVaRs among four plans Benefit Contribution 24

Base (5) - Comparison of four plans: Mean-CVaR diagram - Return (A) Return (B) Return (C) Portfolio [b] Portfolio [a] 25

Base (6) - Comparison of DC, DB, CB and risk-sharing (RS) plans - CVaR of Benefit CVaR of Contribution The relationship of CVaRs of four plans is not dependent on the portfolio returns 26

Sensitivity (1) - Trigger parameters in Case Aa - 35 T(1) 35 T(2) 30 30 25 20 15 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 25 20 15 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 10 10 5 5 0 1 1.05 1.1 1.15 1.2 T(1) 0 1.2 1.3 1.4 1.5 1.6 T(2) The parameters T(1) and T(2) are related with the funding ratio which triggers the deficiency/surplus-sharing. The CVaR of the contribution is sensitive to T(1) due to deficiency-sharing, but the other measures are a little bit sensitive to T(1) and T(2). 27

Sensitivity (2) - Sharing parameters - benefit contribution Who share the fraction? mean CVaR mean CVaR K(i) 1 - K(i) K(0) -/+ + -/+ + sponsor participants/retirees K(1) -/+ + -/+ + sponsor K(2) +/- - +/- - retiree participants Case Aa 45 40 35 30 25 20 15 10 5 0 'mean' is dependent on portfolio return: high return / low return K(0) K(1) K(2) Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 0.25 0.5 0.75 1 K(0) 60 50 40 30 20 10 0 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 0.2 0.4 0.6 K(1) 35 30 25 20 15 10 5 0 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 0.25 0.5 0.75 1 K(2) 28

Sensitivity (3) - Sharing parameters in Cases Ba and Ca - Case Ba 60 50 40 30 20 10 0 60 50 40 30 20 10 K(0) K(1) K(2) 0 0.25 0.5 0.75 1 K(0) Case Ca Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 70 60 50 40 30 20 10 0 70 60 50 40 30 20 10 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 0.2 0.4 0.6 K(1) Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 40 35 30 25 20 15 10 5 0 40 35 30 25 20 15 10 5 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 0.25 0.5 0.75 1 K(2) Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 0 0.25 0.5 0.75 1 K(0) 0 0 0.2 0.4 0.6 K(1) 0 0 0.25 0.5 0.75 1 K(2) 29

Sensitivity (4) - Management fees for four plans in Case Aa - 30 25 20 15 10 5 0 DC plan DB plan Mean (Benefit) CVaR_95% (Benefit) Contribution (Constant ) 0 50 100 150 management fee (bp) 45 40 35 30 25 20 15 10 5 0 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 50 100 150 management fee (bp) 45 40 35 30 25 20 15 10 5 0 CB plan Risk-sharing plan Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 50 100 150 management fee (bp) 35 30 25 20 15 10 5 0 5 Mean (Benefit) CVaR_95% (Benefit) Mean (Contribution) CVaR_95% (Contribution) 0 50 100 150 management fee (bp) 30

Sensitivity (5) - Management fees for four plans - Sensitivity of the benefits and contributions to the management fee 31

Backtesting - Setting - Backtest period: From March 1995 to March 2015 (twenty years) Historical data Domestic stock (DS): TOPIX (Tokyo Stock Price Index) Domestic bond (DB): JPGBI (Citigroup Japan Government Bond Index) Foreign stock (FS): S&P500 (Standard & Poor's 500 Stock Index) Foreign bond (FB): USGBI (Citigroup USA Government Bond Index) Inflation rate: Wage growth rate, calculated using monthly labor survey 10-year government bond yield Dollar-yen exchange rate (center value of interbank spot rate) Japanese yen interest rate: one-year Euroyen TIBOR Dollar interest rate: one-year Eurodollar interest rate 32

Index(1995=1) Backtesting - Historical Data - Market Index 4.5 4 TOPIX Citi_JPGBI S&P500 Citi_USGBI 3.5 3 2.5 2 1.5 1 0.5 0 1995 2000 2005 2010 2015 10-year government bond yield 7 (%) 6 5 4 Yen/Dollar 150 140 130 120 110 100 90 80 Yen-Dollar exchange rate 70 1995 2000 2005 2010 2015 115 110 105 Wage growth rate 3 2 1 0 1990 1995 2000 2005 2010 2015 100 95 90 1990 1995 2000 2005 2010 2015 33

Backtesting - Result(1) - Portfolio weights (Constant rebalance strategy) Cumulative returns (on a yen basis) No hedge Perfect hedge mean 9% 8% 7% 6% 5% 4% 3% 2% Mean and standard deviation of annual rate of return b b a a 0% 10% 20% 30% standard deviation c c No hedge Perfect hedge 34

Backtesting - Result(2): No hedging strategy - Portfolio [a] Portfolio [b] Portfolio [c] Contribution contribution contribution contribution Benefit benefit benefit benefit 35

Backtesting - Result(3): Mean-CVaR diagram - mean 16 15 14 13 12 Benefit DC(c) DC(a) DC(b) DB Portfolio [a] Portfolio [b] Portfolio [c] RS(c) RS(a) RS(b) CB mean 6 4 2 0-2 -4 Contribution DC DB(b) DB(a) CB(b) DB(c) CB(a) CB(c) RS(b) Portfolio [a] RS(a) Portfolio [b] Portfolio [c] 11 8 10 12 14 CVaR(95%) -6 RS(c) 5.06 CVaR(95%) 5.065 Mean benefit among the four plans Mean contribution among the four plans CVaRs of benefits CVaRs of contributions 36

Conclusion In this paper, we design the risk-sharing using the five parameters which control the level of risk sharing. We implement the Monte Carlo simulation for a long-term period, and evaluate the uncertainty of benefits and contributions. Moreover, we compare the RS plan with the existing DC, DB, and CB plans, and we find the benefit and contribution of the RS plan are not only between the DC and DB plans, but also superior to them in some cases. In the future research, we compare the risk-sharing plan proposed in this paper with the intermediate plan which consists of the weighted plan of the DC and DB plans. In addition, we need to formulate the optimization model, which solve the problem to find the optimal parameter values of controlling the risk-sharing. 37

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Thank you for your attention Our paper can be downloaded from http://www.ae.keio.ac.jp/lab/soc/hibiki/profile_2/ho_2016.pdf This slide can be downloaded from http://www.ae.keio.ac.jp/lab/soc/hibiki/profile_2/hibiki_pbsswebinar_20161214.pdf 39

Appendix

Actuarial liability Actuarial liability of age x, period n, and scenario s DC and CB plan DB plan Actuarial liability of period n, and scenario s 41

Benefit Benefit of age x, period n and scenario s DC and CB plan DB plan Benefit of period n and scenario s 42

Contribution Contribution of period n and scenario s DC plan DB and CB plan Normal contribution without amortization Amortization 150% Rule Normal contribution 1.5 43

Plan asset Plan asset of period n, and scenario s DC plan DB and CB plan 44

Backtesting - Result(4): hedging strategy - Portfolio [a] Portfolio [b] Portfolio [c] Contribution contribution contribution contribution Benefit benefit benefit benefit 45

Backtesting - Result(5): Mean-CVaR diagram - mean mean 15 14.5 14 13.5 13 12.5 12 11.5 11 12.15 12.1 12.05 12 11.95 11.9 11.85 11.8 11.75 DC(c) Portfolio [a] Portfolio [b] Portfolio [c] DC(a) RS(a) RS(c) DC(b) RS(b) CB DB 6 8 10 12 14 DC(a) Benefit Portfolio [a] Portfolio [b] Portfolio [c] Benefit CVaR(95%) Benefit DC(b) RS(b) CB RS(c) 9 10 11 CVaR(95%) RS(a) mean 7 6 5 4 3 2 DC, CB(b) RS(b) Contribution Portfolio [a] Portfolio [b] Portfolio [c] CB(a) RS(a) DB(b) CB(c) RS(c) DB(a) DB(c) 0 4 8 12 16 20 CVaR(95%) Mean benefit among the four plans CVaRs of benefits: Mean contribution among the four plans CVaRs of contributions differ depending on the portfolios 46