Inheritance Gains in Notional Defined Contributions Accounts (NDCs)

Transcription

1 Company LOGO Actuarial Tachrs and Rsarchrs Confrnc Oxford th July 211 Inhritanc Gains in Notional Dfind Contributions Accounts (NDCs) by

2 Motivation of this papr In Financial Dfind Contribution (FDC) systms, th pnsion balancs of dcasd prsons ar normally inhritd by th individual s survivors. In DB pay-as-you-go pnsion systms if sombody dis bfor th rtirmnt ag his/hr survivors do not gt anything. A Notional Dfind Contribution (NDC) pnsion systm is a pay-as-you-go schm that dlibratly mimics a FDC systm. What will happn if somon dis bfor rciving any bnfit undr this modl? What will happn to th notional capital accumulatd by th individual? Inhritanc Gains in NDC s 1/18

3 Aim of this papr To analys whthr a survivorship dividnd SD (inhritanc gains) should b includd as an xtra rturn in th notional rat of NDC s. To quantify th ffcts of not considring th survivorship dividnd. Inhritanc Gains in NDC s 2/18

4 Contnts 1. Introduction 2. NDC pnsion systms and Inhritanc gains 3. Th modl 4. An xampl 5. Main conclusions Nxt stps in th rsarch 3/18

5 1. Introduction From th NDC s pnsion schms only Swdn applis a Survivorship Dividnd. Th survivorship dividnd, SD, at a spcific ag, masurs th portion of th accrditd account balancs of participants rsulting from th distributions, on a birth cohort basis, of th account balancs of participants who do not surviv to rtirmnt. Should it b applid to all th NDC s systms? What is th ffct of th possibl applications of a SD on futur pnsionrs? Is thr any financial-actuarial basis to SD? What happns if SD is not applid? Inhritanc Gains in NDC s 4/18

6 2. NDC pnsion systms and Inhritanc Gains A notional account is a virtual account rflcting th individual contributions of ach participant and th fictitious rturns that ths contributions gnrat ovr th cours of th participant s working lif. Whn th individual rtirs, h or sh (hncforth, h) rcivs a pnsion that is drivd from th valu of th accumulatd notional account, th xpctd mortality of th cohort rtiring in that yar, and, possibly, a notional imputd futur indxation rat. Th notional modl combins PAYG financing with a pnsion formula that dpnds on th amount contributd and th rturn on it. Inhritanc Gains in NDC s 5/18

7 2. NDC pnsion systms and Inhritanc Gains Th amount on th notional account (K) Notional rat for contributions Crditd Actuarial Divisor (A d ) contributions = Pnsion=K/A d Ag Inhritanc Gains in NDC s K Lif xpctancy + Notional rat for pnsionrs 6/18

8 2. NDC pnsion systms and Inhritanc Gains K= Notional Capital x r 1 θ x x= x y x x r 1 i= x (1+ r i ) = P x r & a λ x r x x r y x θ x Whr: : ag of ntry in th labour markt : ag of rtirmnt : salary at ag x : contribution rat at ag x P x r λ & a& x r : pnsion at x r : lif annuity at x Inhritanc Gains in NDC s 7/18

9 2. NDC pnsion systms and Inhritanc Gains Italy Latvia Poland Swdn Rat of contribution 2%-33% 14% 12.22% 16% Rat of rturn on contributions Rtirmnt ag 5-yar avrag GDP growth 65 (man) 6 (woman) Growth rat covrd wag bill Growth rat covrd wag bill Growth rat covrd contribution pr participant + ABM + Inhritanc gains 62/62 65/6 65/65 Standard formula Pnsion formula Survivor contingncy 1.5% rat of rturn Tn-yar rvision mortality Standard formula Standard formula Standard formula 1.6% rat of rturn Annual rvision mortality Rat for pnsions Inhritanc Gains in NDC s RPI RPI RPI+ 2% wag growth RPI+ (wag growth-1.6%) 8/18

10 2. NDC pnsion systms and Inhritanc Gains NDC s hav strongr immunity against political risk than traditional DB PAYG systms. + NDC s crat no fals xpctations about th pnsions to b rcivd in th futur. NDC s ncourag actuarial fairnss and stimulat th contributors intrst in th pnsion systm. - Som charactristics shard with th traditional DB PAYG or capitalizd systm. (dmographic chang, problm of th minimum rtirmnt ag ) Inhritanc Gains in NDC s 9/18

11 Growth rat salary = g Growth population = γ (1+g)(1+γ)=(1+G) 3. Th modl Ag Contributors Wags X X +1 X +2 t=1 t t=1 t N t,1) N,t) = N,1) (1 + γ) 1 y t 1,1) y,t) = y,1) (1 + g) N + 1,1) N + 2,1) N N t 1 + 1,t) = N + 1,1) (1 + γ) t 1 + 2,t) = N + 2,1) (1 + γ) X +A-1 N + A-1,1) xr = x + A P + A,1) Inhritanc Gains in NDC s

12 Growth rat salary = g Growth population = γ (1+g)(1+γ)=(1+G) θ θ θ t t and t (1+ G) A 1 = θ y t+ 1 (t 1) =... A 1 +k, t) y N Inhritanc Gains in NDC s 3. Th modl Aftr «w-x -A» yars- STEADY STATE +k, 1) 64 Incom 44from7 contributions k, t) N = w-x r Incom from7 contributions k, 1) = w-x + A, 1) + A+ k, 1) Spnding on pnsions A-1 w-x A-1 P t 1 k k N (1+ G) (1+ λ) Spnding on pnsions 1+ λ 1+ G P + A, t) N + A+ k, t) x : ag of ntry in th labour markt x r = x + A P : ag of rtirmnt, t) y,t) : Salary at ag x, momnt t N,t) : Popl aliv at ag x, momnt t k : avrag pnsion at x in t θ t : contribution rat at momnt t = 1/18

13 Growth rat salary= g Growth population = γ (1+g)(1+γ)=(1+G) 64 Incom 44from 7contributions θ t A 1 y +k, t) N 3. Th modl +k, t) = w-x A-1 P + A, t ) N + A+ k, t) G 3 Spnding on pnsions 1+ λ k θ A 1 a N + k, A+ k+ t) + k, A+ k+ t) + λ & a& x y + A N + A,t) Accrditd contribution rat (1 G) A k Including dad popl θa = θt Inhritanc Gains in NDC s x : ag of ntry in th labour markt x r = x + A P : ag of rtirmnt, t) y,t) : Salary at ag x, momnt t N,t) : Popl aliv at ag x, momnt t : avrag pnsion at x in t θ t : contribution rat at momnt t 11/18

14 Growth rat salary= g Growth population = γ (1+g)(1+γ)=(1+G) 3. Th modl Survivorship dividnd at th rtirmnt ag, momnt t: D ac K A,t) A 1 ac Containing CAPITAL from dcasd A k θa N + k, A+ k+ t) y + k, A+ k+ t) (1+ G) A 1 A k = θa y + k, A+ k+ t) (1 G) N + A,t) A,t) + ac K + A,t) K i + A,t) ac ac i D + A,t) = K + A,t) K + A,t) Inhritanc Gains in NDC s 12/18

15 Growth rat salary= g Growth population = γ (1+g)(1+γ)=(1+G) 3. Th modl A 1 With NO Survivorship dividnd P i + A, t ) A k θa y (1 G) + k, A+ k+ t) + w-x A-1 λ k λ N 1+ + A+ k, t) && a x + A 1+ G Spnding on pnsions = 64 Incom 44 from7 contributions 4448 θ A 1 * t y +k, t) N +k, t) θ a = θ ac D * + A,t) t (1+ ) θa > i K + A,t) θ * t Inhritanc Gains in NDC s 13/18

16 4. An xampl Tim t aftr raching th stady stat Assumptions: g = 1%; γ= % ; λ =% θ = θ t a = 17% Inhritanc Gains in NDC s 14/18

17 4. An xampl K ac Assumptions: g = 1%; γ= % ; λ =% Accumulatd Dividnd, momnt t aftr raching th stady stat K i P P + A, t ) No SD A, t ) with SD 2.8 Ag 49.39% Inhritanc Gains in NDC s 15/18

18 4. An xampl Assumptions SD P K ac K i 65 with SD P 65 no SD % chang g = 1%; γ= % ; λ =% g = 1%; γ= 2% ; λ =% g = 1%; γ= 4%; λ=% For an individual who is now 65 and blongs to th initial group with x r -x working yars Inhritanc Gains in NDC s 16/18

19 5. Main conclusions Financial actuarial basis Th survivorship dividnd has a strong financial-actuarial basis which suggsts that th aggrgat contribution rat to apply is th sam as th on accrditd to th individual contributor. In th countris that hav not distributd th survivorship dividnd this bcoms a hiddn way of accumulating financial rsrvs in ordr to compnsat for th incras in longvity. Inhritanc Gains in NDC s 17/18

20 6. Nxt stps in th rsarch Snsitivity analysis: Diffrnt arning profils. Diffrnt individual working livs. Diffrnt mortality tabls. Application of th SD to NDC systm that currntly do not apply it. Inhritanc Gains in NDC s 18/18

21 Company LOGO Actuarial Tachrs and Rsarchrs Confrnc Oxford th July 211 Inhritanc Gains in Notional Dfind Contributions Accounts (NDCs)