マクロ経済スライド下における積立金運用でのリスク

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1 ALM JEL Classification: H55, G11 Key words: 2 H FAX: , kitamura@nli-research.co.jp nakasima@nli-resaech.co.jp usuki@nli-research.co.jp 1

2 Risk Analysis of Pension Reserve Investment with Macro Economy Indexation under the 2004 Public Pension Reform By Tomoki Kitamura, Kunio Nakashima, and Masaharu Usuki Abstract The 2004 public pension reform, by introducing a fixed premium system and macro economy indexation, has intimately linked pension reserve investment policies with benefit levels and financial soundness. Thus, we developed a stochastic ALM simulation model in which the length of benefit adjustment period and replacement ratio (ratio of standard benefits to standard wages) are endogenous variables, and analyzed how pension investment performance affects the replacement ratio and funding ratio (reserve assets divided by annual benefit payments). The results show that if the pension reserve is invested in accordance with the current asset allocation policy set by the Ministry of Health Labor and Welfare, it is possible to avert a financial crisis until 2030, while the funding ratio could deteriorate substantially by Moreover, if we accept certain conditions such as a longer benefit adjustment period, even an asset allocation consisting exclusively of low-risk domestic bonds can achieve the goals of a 50% replacement ratio and financial soundness. However, if we reduce the expected return on domestic bonds to the current market yield, a riskier asset allocation is needed to achieve the same investment performance, increasing the downside risk for the funding ratio. For all asset allocation policies we analyzed, the funding ratio and financial soundness are vulnerable to poor investment performance, suggesting that further pension reform may be necessary in the near future. Considering that plan design and pension investment decisions strongly influence each other, our results imply the need to coordinate asset allocation policy, pension plan design, and the financial and actuarial recalculation process with utmost care when the Government Pension Investment Fund begins the revision of asset allocation policies in the future. JEL Classification: H55, G11 Key words: public pension, macro economy indexation, investment of public pension reserve, asset allocation, risk management 2

3 P P (2005) 2 3

4 3 P P P P P ALM Asset Liability Management ALM 2 4 P (1993) (1999)1999 (1999)1999 (2003) (2002)(2004) 2004 (2003) Lee et al.(1998)congressional Budget Office(2002) 5 ALM Sharpe(1990) ( )

5 Sharpe and Tint(1990) ALM (2004) (2005) p15 P 2 ALM P P % P (2005) 7 (2005) 8 NOMURA-BPI TOPIX CITI MSCI-KOKUSAI

6 P 50% 50 (2004) P P

7 P

8 2-1 P A 1 B 2 C 5 P ALM x() t ( ) dx() t = θ λ x() t dt + σ dw () t (1) x x x x yt () ( ) dy() t = θ λ y() t dt + σ dw () t (2) y y y y 20 θx, θy, λx, λy, σx, σ y Wx, Wy ρ θ, θ λ, λ xy σ, σ t x y 1 1 Gourieroux and Jasiak(2001) p251 (1) x y x y 20 x() t yt () Vasicek x() t yt () (2000) p826 8

9 9

10 (2) 1 exp( λx) 1 exp( λx) x() t = θx + exp( λx) x( t 1) + σx ε x() t (3) λx 2λx 1 exp( λy) 1 exp( λy) yt () = θy + exp( λy) yt ( 1) + σ y ε () t λ y 2λ y (4) y 21 ε x () t ε y () t 0 ρxy λ, λ σ, σ, ρ x y x y xy λ = (0.0056) λ = 0.644(0.105) σ = σ = x y x θ, θ x y θ x = 0.01 θ y = ri () t r() t = µ + σ ε () t (5) i i i r i i µ, σ i y i (3) AR(1)Congressional Budget Office (2002) AR(1) VAR(2) 22 10

11 ε r () t 0 1 ρ i xr i ρ 23 yr i α() t β () t τ ( τ < t ) at () bt () yt () 3 ( ) ( ) ( ) 1 3 yt ( ) 1 + yt ( 1) 1 + yt ( 2) 1 + yt ( 3) 1 zn () t z () t x( t 1) + y() t n zn () t x() t 1 3 x() t zn () t x( t 1) > 0, and z ( t) > 0, and x( t 1) > z ( t ) x( t 1) 0, and z ( t) 0 x( t 1) < 0, and z ( t) < 0, and x( t 1) > z ( t ) at () zn (), t at () 0, xt ( 1), n n n bt () xt ( 1), bt () 0, zn () t 1 xt ( 1) zn () t x( t 1) > z n ( t) at () zn () t 1 at () bt () 1 xt ( 1) n n (6) (7) 23 i r x xr i ρ j 4 wj r j σ i σ x cov( ab, ) a b ρ xr = cov( r, ) /( ) cov(, ) /( ) cov(, ) /( ) i i x σσ i x = wjrj x σσ i x = w j j rj x σi σx cov( rj, x), σ x, σ j CITI 1985 ρ xy =

12 zn () t x( t 1) > z n ( t) bt () 1 xt ( 1) at () 1 xt ( 1) bt () z () t ct () ct () ct () 2 1 H 1 () t 2 H 2 () t 3 H 24 3 () t M () t mt () M()/ t M( t 1) mt () 3 mt () ct () c ( t) max(0, m( t) ) (8) (8) α() t max( at ( ),0) + max( at ( ) ct ( ),0) if τ > t α () t at () if τ t β () t max( bt ( ),0) + max( bt ( ) ct ( ),0) if τ > t β () t bt () if τ t (9)(10) τ > t ct () max ct () ct () τ t 2-2 (9) (9) (9) ct () at () > 0 ct () α() t at () 0 ct () at () bt () (6) (7) n (9) (10) H (), t H (), t H () t ct () ct () 12

13 at () α() t ct () at () > 0 ct () α() t at () 0 ct () ct () φ() t φ() t φ() t Hm () t Pm () t zt () xt () + yt () 26 Pm ( t 1) (1 + α( t)) (1 + α( t)) φ() t = φ( t 1) H ( t 1) (1 + zt ( )) (1 + zt ( )) m At () Ut () Gt () B() t Kt () (5) i r() t i (11) A() t = (1 + r()) t A( t 1) + U() t + G() t B() t K() t (12) i At () Gt () B() t Kt () P i F() t t Hm () t P m () t zt ()

14 ( PV ) () B t U t K t 27 At () F() t ( PV ) () ( PV ) ( PV ) ( PV ) ( PV ) () F() t A() t B () t K () t + U () t (13) ψ ( t) ψ ( t) t 1 ψ ( t) At ( 1) ψ () t B() t + K() t τ 28 φ() t 50 φ() t Ft () 0 50( φ 0.5 ) τ F τ φ τ φ τ F { φ F } (14) τ min τ, τ,2051 (15) τ min{ t = 2010, L,2100; φ( t) 0.5} φ τ min{ t = 2010, L,2100; F( t) 0} F 31 τ φ( τ ) ψ () t 3 (16) 27 ( PV ) () ( PV ) () ( PV ) () B t U t K t φ() t (2004)

15 3-1 A P1 P3 P P3 52 P P1 P3 5 P B P1 P3 3-2 A A P P %

16 φ( τ ) φ( τ ) ψ () t ψ () t 16

17 (15) φ( τ ) τ (11) (14) 17

18 (15) φ( τ ) τ (11)(14) 18

19 (15) φ( τ ) τ (11)(14) 19

20 3-1 A B P1P3 P % P3 P P P P % ) P P B 50 50%

21 43.1 ( ( 3)50% A (=3.0 ) C P (P2-2 P2-5)P2-1 τ φ( τ ) ψ () t P2-2 P A P3 P P A P (=) CITI

22 2 C 1 A P2-4 P2 P2-5 P3 P P (2005) p P3 P 3-1 A (1)(2) (3)(3) (4) 3-3 P % % (2005) % 22

23 23

24 P P 2 P P P P 2 P P 2 P 24

25 5.1. g k t He (, t g, k ) 2 H 2 (, t g, k ) Hm (, t g, k ) H 2 (, t g, k) Otgk (,, ) δ L (, tgk, ) 2 δ 2 (, tgk, ) 42 ( ) ( ) δ ( ) δ ( ) H2 tgk,, Otgk,, L tgk,, 2 tgk,, He () t (17) (17) kh () t [ 2 m ] (18) H() t H(, tgk, ) H (, tgk, ) e g k= 15 Hm (, t g, k ) (2000) t kj (, t g) J ( tgk,, ) d( t, g, k) J (, tgk, ) Jt ( 1, gk, 1) (1 dtgk (,, )) (19) t J (, tgk, j (, tg)) Ttgk (,, ) kj (, t g) 1 Ttgk (,, ) Ttgk (,, ) Tt ( 1, gk, 1) (1 dtgk (,, )) (20) f () t 60 Ttg (,,60) ft ( ) H( t 1, g,59) (1 dtg (,,60)) e 1 T d J ( t, g, k ( t, g)) T( t 1, g, k ( t, g) 1) (1 d( t, g, k ( t, g))) j j j W( t, g, k) (,, ) I( g, k) ( ) (21) W t g k 1 zt Wtgk (,, ) Wt ( 1, gk, 1) (1 + zt ( )) Igk (, )/ Igk (, 1) R(, tgk, ) Ptgk (,, (, tg)) R(, tgk, ) Rt ( 1, gk, 1) j (22) β ( t)

26 W( t, g, k) ( β ()) ( ) L h () ( β ()) () L Rt ( 1, gk, 1) 1 + t + W tgk,,, k= 21,, k t Rtgk (,, ) Rt ( 1, gk, 1) 1 + t, k= kh t + 1,, kj( tg, ) 1 (23) (23) Ptgk (,, (, tg)) κ( t, g, k ( t, g)) (23) j Ptgk (,, (, tg)) Rtgk (,, (, tg)) κ (, tgt, g), k ( t, g)) (24) (12)U t (22)W t, g, k () ( ) H t g k ht ( ) e (,, ) j j j (18) Ut kh () t () ht () Wtgk (,, ) H e (, tgk, ) (25) g k= 15 (19) J ( tgk,, ) (,, ) j( t) 44 B() t P t g k 108 (26) g k= k (, t g) B() t j() t P(, t g, k) J(, t g, k) P( t, g, k) α ( t) j Ptgk (,, ) Pt ( 1, gk, 1) (1 + α()) t (27) (12) Kt () 3 H 3 () t 1 H 1 () t BK () t H 3 () t c g 2 c H (, t g, k) 2 3 δ 3 ( g, k) 2 j 60 c 3 g k= H () t H (, t g, k ) δ ( g, k ) (28) 1 H 1 () t 60 1 g k = 20 H () t H (, t g, k) 1 (29) H1 (, t g, k ) O H 1 δ 1 ( t) H 3 H( tgk,, ) ( Otgk (,, ) H( tgk,, ) H( tgk,, )) (1 δ ( t)) BK () t PK () t 1 44 (26) jt () (2005) jt () 26

27 P ( n ) K () t 45 ( n) ( n) K K P () t P ( t 1) (1 + β ()) t ( n) K K + α + K P ( t) 0.95 P ( t 1) (1 ( t)) 0.05 P ( t) (30) t k () t O K δ () t B () t K K B () t P () t O (, t g, k ) () t (31) 108 K K δ g k= k () t K Kt () (18)(28) (31) e 3 1 e 3 m K K() t ( H () t + H ())/( t H () t + H () t + H () t + H ()) t B () t (32) Gt () δ () K G t Gt () δ () t Kt () (33) G (13) F() t B ( ) () t PV PV t+ 96 ( + ) j j= t i (34) B ( ) () t B ( j )/1 µ B() t θ ( = 1.0%) θ ( = 1.1%) x (26) B() t J (, tgk, ) P( t, g, k) α() t β () t θ x θ y µ i K ( PV ) () t i PV t+ 96 j δ j t G µ = i (35) ( K ) () t (1 ()) t K( j)/(1 + ) δ G () t K ( j ) (30) α () t θx β () t θ y 47 PV t+ 95 j + µ j= t i (36) ( U ) () t U( j)/(1 ) y 45 α() t β () t (34) (35) (36) t + 96 t

28 Otgk (,, ) ( 14 1 ) δ L (, tgk, ) δ 2 (, tgk, ) (1999) p δ 3 (, tgk, ) Hm (, t g, k ) (1999) p Wtgk (,, ) R(, tgk, ) κ (, tg)

29 53 Ik ( ) ht () J (, tgk, ) ( 12 ) Ptgk (,, ) ( 12 ) Ptgk (,, ) (3) x() t AR(1) x() t = a + b x( t 1) + c ε () t (37) ( λ ) x x x x 1 exp 1 exp( ) 1/2 x λx ax θx, bx exp ( λx), cx σx (38) λ λ (4) x yt () yt () = a + b yt ( 1) + c ε () t (39) ( λy) y y y y 1 exp 1 exp( λ ) 1/2 y ay θy, by exp ( λy), cy σ y (40) λy λy b = 1 b = 1 Dickey-Fuller 55 y OLS (37)(39) a OLS (37)(40) x x a y x Dickey-Fuller Hayashi(2000) p

30 λ = exp( b ), σ = (2ln( b ) /(1 b ) c x x x x x λ = exp( b ), σ = (2ln( b ) /(1 b ) c y y y y y 2 x 2 y (41) Congressional Budget Office 2002Uncertainty in Social Security's Long-Term Finances: A Stochastic Analysis Gourieroux C and J Jasiak 2001Financial EconometricsPrinceton Hayashi F (2000)EconometricsPrinceton Lee, D., M.W. Anderson, and S. Tuljapurkar 2003Stochastic Forecasts of the Social Security Trust Fund, Report prepared for the Social Security Administration Sharpe W (1990) Asset Allocation in Managing Investment Portfolios-Dynamic Processeds J. Magin and D. Tuttle Warren, Gorham, and Camont Sharpe W and L G Tint 1990Liabilities: A New ApproachJournal of Portfolio Management 16(2) pp Vol.29, pp No.25 pp Vol.32 pp1-29. (2000) , pp Vol.50 No.3 pp

Public Pension and Immigration The Effects of Immigration on Welfare Inequality The immigration of unskilled workers has been analyzed by a considerab

Public Pension and Immigration The Effects of Immigration on Welfare Inequality The immigration of unskilled workers has been analyzed by a considerable amount of research, which has noted an ability distribution.