2004 2005 ALM 2030 2050 50 JEL Classification: H55, G11 Key words: 2 H16 007 102-0073 4-1-7 FAX: 03-5211-1082, E-mail: kitamura@nli-research.co.jp E-mail: nakasima@nli-resaech.co.jp E-mail: usuki@nli-research.co.jp 1
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 2050. 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
1.1 2004 1 2017 18.3 100 1 50 50 2 P P 2000 1 (2005) 2 3
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) 3 2006 4 4 ( ) 5 4 1 4
Sharpe and Tint(1990) ALM (2004) (2005) p15 P 2 ALM 3 4 1.2 2004 6 P P 7 15 20 24 2.80 3.27 0.58 0.66 1.8 2.1 1 1% 2.8 3.1 1979 2003 1973 2003 8 9 10 5 3.2 3.7 0.05 11 P 1999 2003 6 (2005) 7 (2005) 8 NOMURA-BPI TOPIX CITI MSCI-KOKUSAI 9 10 5
11 2 2 2029 257.9 P 50% 50 (2004) P 12 1 13 14 P 3.2 50 11 12 13 14 6
2 2 2029 P 2023 15 2029 3 3.0 16 17 18 10 30 4 19 3.2 15 16 10 1.2720 2.0030 2.362005 7 29 17 18 20 30 19 7
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
(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 25 1981 2005 x y x y xy λ = 0.439 (0.0056) λ = 0.644(0.105) σ = 0.013 σ = 0.018 22 x y x θ, θ x y θ x = 0.01 θ y = 0.011 ri () t r() t = µ + σ ε () t (5) i i i r i i µ, σ i y i 1 2 1 2 21 (3) AR(1)Congressional Budget Office (2002) AR(1) VAR(2) 22 10
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 1970 2003 CITI 1985 ρ xy = 0.3 11
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) + 0.003) (8) (8) 0.003 0.3 25 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 24 1 2 3 25 ct () ct () 12
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 393000 P 231000 m () t zt () 2016 0.0019 26 13
( 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 50 2010 2050 Ft () 0 50( φ 0.5 )2050 2051 29 2100 τ F τ φ 50 30 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 28 2023 50.2 3.9 2015 5.2 2030 4.5 2050 29 2050 30 φ() t 50 31 (2004) 65 2 3 1 14
3-1 A P1 P3 P P3 52 P1 2025 50 P1 P3 5 P1 50 30 30 50 30 B P1 P3 3-2 A A 5 15 30 50 3 P 2023 11 5 2011 2011 595 2043 50 5050 32 3.2 P3 3.374.1 2015 5.8 2030 4.4 2050 1 2.6 2015 2.7 2030 0.1 2050 2015 2030 2050 0.1 33 95 5.3 2015 8.5 2030 8.7 2050 95 57.6 32 50 50% 50 33 15
φ( τ ) φ( τ ) ψ () t ψ () t 16
(15) φ( τ ) τ (11) (14) 17
(15) φ( τ ) τ (11)(14) 18
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3-1 A B P1P3 P 2 1 50.7 3.9 2015 5.5 2030 50% P3 P1 5 3.0 2015 3.5 2030 3 2023 P3 2030 P1 2050 P1 50 50 3.0% ) 34 4 5 35 1 P4 0.3 2050 P5 1.0 2050 50 50 50 3-2 B 50 50% 34 35 2 1 2 3 + 5050 20
43.1 ( 143.9 ( 3)50%2030 50 50 A (=3.0 ) 2.0 2 10 36 37 38 3-2 C P (P2-2 P2-5)P2-1 τ φ( τ ) ψ () t P2-2 P A P3 P2015 2030 1 9 502050 P2-12015 2030 A P12050 1.5 2.0 50 36 (=)1.89 50 2.26 25 1.72 20 0.21 10 37 4.8-2.02.8 1973 2003 CITI 1985 38 21
2 C 1 A P2-4 P2 P2-5 P3 P2-5 11.2 2015 0.7 2030 2.6 2050 P3 1.0 2.5 (2005) p.17 100 2015 2 2050 1 5 39 50 50 P3 P 3-1 A 5 50 2015 50 3-2 (1)(2) (3)(3) (4) 3-3 P 1 40 1% 19.3 10 12 50% 18.3 1 39 (2005) 4 10 40 50% 22
23
P P 2 P 2006 4 P P P 2 P P 2 P 24
5.1. g k t 15 41 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) 43 108 J ( tgk,, ) d( t, g, k) J (, tgk, ) Jt ( 1, gk, 1) (1 dtgk (,, )) (19) t J (, tgk, j (, tg)) Ttgk (,, ) 60 65 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) 41 2015 59 2018 60 2021 61 2024 62 2027 63 64 42 2 43 25
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) 20 20 20 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= 15 2 3 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 2 2 3 H 1 δ 1 ( t) 1 2 3 H 3 H( tgk,, ) ( Otgk (,, ) H( tgk,, ) H( tgk,, )) (1 δ ( t)) BK () t PK () t 1 44 (26) jt () (2005)225 5 51 2002 1 jt () 26
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 46 108 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 5 46 47 (34) (35) (36) t + 96 t + 95 1 27
48 5.2. Otgk (,, ) ( 14 1 ) 2100 2150 49 δ L (, tgk, ) 2001 2005 2002 7 2025 5 5 1 2000 2010 2025 3 1 δ 2 (, tgk, ) 2000 2001 5 50 2002 1999 2001 2003 (1999) p142-143 35 2003 35 2003 35 50 δ 3 (, tgk, ) 2002 2 51 2003 2003 Hm (, t g, k ) (1999) p144 2025 2025 Wtgk (,, ) 2001 2000 5 1 R(, tgk, ) 1985 2000 2000 52 5 1 20 59 59 κ (, tg) 2000 60 48 5 100 5 95 2100 2105 5 1 49 2100 2100 2100 1.7038 2150 2.0402 50 5 1 51 2000 15 54 5 52 2000 8 4 2 1984 1985 28
53 Ik ( ) 2001 2000 1 20 1 ht () 2004 0.354 2017 18.3 J (, tgk, ) ( 12 ) Ptgk (,, ) ( 12 ) Ptgk (,, ) 54 5.3. 1981 2005 (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 56 25 57 OLS (37)(39) a OLS (37)(40) x x a y x 53 54 75 2000 55 Dickey-Fuller Hayashi(2000) p575 5 1 1 56 50 57 3 3 25 29
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) pp5-10 2003 Vol.29, pp1-59 1993 No.25 pp 7-33 2004 20042004 Vol.32 pp1-29. (2000) 11. 2002 2005 31 2005 16 2001 2003 28, pp.101-112. 1998Vol.50 No.3 pp.249-258. 1999 30