Lu Yi MSc Candidate Simon Fraser University

Transcription

1 Lu Yi MSc Candidate Simon Fraser University 1

2 DB Plan DC Plan risks Employer risks Employees risks risks 2

3 Between employers and employees Across different generations: Different age groups have different risk profiles Employer risks Employees in different age groups Benefits of risk sharing discussed in Bovenberg et al. (2007), Gollier (2008), Blommestein et al. (2009), Cui et al. (2011) 3

4 Target Benefit: e.g. 1% of Final Average Earnings * Service Contribution: e.g. 15% of salary Employer Contribute Target Benefit Plan $$$ Benefit Employees Affordability test Triggers and actions 4

5 At each valuation point: Affordability test: whether the target benefit is affordable Funded ratio = Assets Liabilities Triggers: whether we should take action Immediate action: e.g. funded ratio 100% Delayed action: e.g. funded ratio corridor Upper bound: 110% Lower bound: 90% Actions: what adjustment to make Benefits (past and/or future accruals) Contributions Investment strategy 5

6 Distribution of benefit adjustments by size Without Corridor With Corridor (90%-110%) 6

7 Use value-based ALM approach Hoevenaars and Ponds (2007) Soer (2012) Lekniute, Beetsma, and Ponds (2014) Quantify value transfer when moving between designs 7

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9 Entry age: 30 Retirement age: 65 Age at death: 85 Stationary population: 100 people at each age at all times Past service is recognized at plan inception The pension fund is assumed to be liquidated after 25 years 9

10 z t+1 = v + Bz t + Σε t+1 where ε t+1 ~N 0, I State variables: 1-month T-bill yield 15-year zero coupon bond yield Inflation rate TSX stock return in excess of the 1-month T-bill rate Dividend yield 10

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12 Age\t C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

13 Age\t C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

14 Age\t C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

15 Age\t C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

16 Age\t C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

17 Age\t C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

18 Age\t V 6 V 7 V 30 V 64 V 65 V C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0,

19 Pricing kernel based on Ang and Piazzesi (2003) as in Hoevenaars and Ponds (2007) M t+1 = e (δ 0+δ 1 z t λ t Σ Σλ t +λ t Σ ε t+1 ) One period stochastic discount factor 19

20 Pricing kernel based on Ang and Piazzesi (2003) as in Hoevenaars and Ponds (2007) M t+1 = e (δ 0+δ 1 z t λ t Σ Σλ t +λ t Σ ε t+1 ) Short rate 20

21 Pricing kernel based on Ang and Piazzesi (2003) as in Hoevenaars and Ponds (2007) M t+1 = e (δ 0+δ 1 z t λ t Σ Σλ t +λ t Σ ε t+1 ) Time varying market risk premium 21

22 Pricing kernel based on Ang and Piazzesi (2003) as in Hoevenaars and Ponds (2007) M t+1 = e (δ 0+δ 1 z t λ t Σ Σλ t +λ t Σ ε t+1 ) Time varying market risk premium λ t = λ 0 + Λ 1 z t 22

23 Pricing kernel based on Ang and Piazzesi (2003) as in Hoevenaars and Ponds (2007) M t+1 = e (δ 0+δ 1 z t λ t Σ Σλ t +λ t Σ ε t+1 ) Economic Value of P t+k V t P t+k = E t [M t+k P t+k ], where M t+k = M t+1 M t+2 M t+k 23

24 Age\t V 6 V 7 V 30 V 64 V 65 V 85 M C 24,30 R C 23,30 -C 24,31 R C 0,30 -C 1,31 -C 20,50 -C 21,51 -C 23,53 -C 24,54 R C 0,64 B 1,65 B 20,84 B 21, B 0,65 B 1,66 B 20, B 0, V x = E(CF x,0 + σ r+l e 1 t=1 M t CF x,t ) 24

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26 Calibrated simple asset model based on Canadian market data Modeled operation of Canadian target benefit plan designs Applied value-based ALM method developed by Hoevenaars and Ponds (2007) Created Shiny app to demonstrate value shift between generations of plan members App can help plan actuaries to visualize and understand the impact of each design element 26

27 Asset model (Lekniute et al. (2014)) More options for affordability test, triggers and actions (Sanders (2006)) Separate surplus and deficit options (Kocken (2008) and Soer (2012)) 27

28 Ang, A., & Piazzesi, M. (2003). A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics, 50(4), doi: /S (03) Blommestein, H. J., Janssen, P., Kortleve, & N., Yermo, J. (2009). Evaluating the Design of Private Pension Plans: Costs and Benefits of Risk-Sharing. OECD Working Papers on Insurance and Private Pensions, No. 34, OECD Publishing. doi: / Bovenberg, L., Koijen, R., Nijman, T., & Teulings, C. (2007). Saving and Investing Over The Life Cycle and The Role of Collective Pension Funds. De Economist, 155, No. 4. doi: /s Cui, J., Jong F., & Ponds, E. (2011). Intergenerational Risk Sharing within Funded Pension Schemes. Journal of pension economics and finance, 10(01), doi: /ssrn Cochrane, J.H., & Piazzesi, M. (2005). Bond Risk Premia. The American Economic Review, 95(1), doi: / Gollier, C. (2008). Intergenerational Risk-sharing and Risk-taking of A Pension Fund. Journal of Public Economics, 92(5), doi: /j.jpubeco

29 Hoevenaars, R.P. (2008). Strategic asset allocation & asset liability management. PhD Dissertation. Universiteit Maastricht. Retrieved from Hoevenaars, R.P. and Ponds, E. Valuation of Intergenerational Transfers in Funded Collective Pension Schemes (2007). Available at SSRN: Kocken, T. Curious Contracts: Pension Fund Redesign for the Future. Uitgeverij Tutein Nolthenius in s-hertogenbosch, The Netherlands (2006). ISBN , 242 pages Lekniute, Z., Beetsma, R.M., & Ponds, E.H. (2014). A Value-based Approach to the Redesign of US State Pension Plans. doi: /ssrn Sanders, B. (2016). Analysis of Target Benefit Plan Design Options. Retrieved from Slagmolen, C. (2010). Economic Scenarios for an Asset and Liability Management Study of a Pension Fund. University of Groningen. Retrieved from Soer, M. (2012). Fairness between generations in the new Dutch pension agreement. University of Groningen. Retrieved from 29

30 Thank you! 30

31 x t y t 180 inf t s t div t μ σ

32 1 y t (0) 180 y t (0.116) inf t (0.6387) s t (0.3838) div t (0.2779) y t 1 y t 180 inf t s t div t R (0.1982) (0) (0.4422) (0.4383) (0.0011) (0.6870) (0.868) (0.0037) (0.6379) (0.1842) (0.4903) (0.243) (0.0195) (0.0052) (0) (0.0122) (0.809) (0.1395) (0.8299) (0)

33 y t 1 y t 180 inf t s t div t

34 1 y t 180 y t inf t s t div t 1 y t y t inf t s t div t

35 y 1 y 180 inf s div Σλ 0 y y inf s div

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37 Simple plan design to study t=0 F0 F 0 : Initial Fund B 0 : Initial Benefit C 0 : Initial Contribution F 1 : F 0 + C 0 B 0 (1 + Asset Return) t=1 F1 Target Accrued Liability FR = F 1 TAL 1 Triggers and Actions C 1, B 1 Target Accrual rate Valuation rate Valuation method 37

38 Risk-Neutral distribution: π s = M s E M π(s) Risk-Neutral pricing: P x = 1 R f Σπ s x(s) If M(s) = E(M) in all scenario => risk free 1 R f Σπ s x(s) = 1 Σπ s x(s) Rf If m(s) E(m) 1 R f Σπ s x s < 1 Σπ s x(s) Rf 38