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89
Nominal Yield Curves
Real Yield Curves
0.12
0.031
0.03
0.11
0.029
0.1
0.028
0.027
0.09
0.026
0.08
0.025
0.024
0.07
0.023
0.06
0.022
0.05
0
1
2
3
4
5
6
7
8
9
10
0.021
0
1
2
3
4
5
6
7
8
9
Iljxuh 4= Ihdvleoh vkdshv ri wkh qrplqdo dqg uhdo |lhog fxuyhv iru wkh
65
prgho1
8:
10
(A1) Realized and fitted Inflation under Independence
(A2) Realized and fitted GDP growth under Independence
0.18
0.15
0.16
0.14
0.1
0.12
0.1
0.05
0.08
0.06
0
0.04
0.02
-0.05
0
-0.02
55
60
65
70
75
80
85
90
95
100
-0.1
55
60
(B1) Realized and fitted Inflation with Joint estimation
65
70
75
80
85
90
95
100
95
100
(B2) Realized and fitted GDP growth under Joint estimation
0.18
0.15
0.16
0.14
0.1
0.12
0.1
0.05
0.08
0.06
0
0.04
0.02
-0.05
0
-0.02
55
60
65
70
75
80
85
90
95
100
-0.1
55
60
(C1) Realized and fitted Inflation under Joint Estimation with Yields
65
70
75
80
85
90
(C2) Realized and fitted GDP growth under Joint Estimation with Yields
0.18
0.15
0.16
0.14
0.1
0.12
0.1
0.05
0.08
0.06
0
0.04
0.02
-0.05
0
-0.02
55
60
65
70
75
80
85
90
95
100
-0.1
55
60
65
70
75
80
85
90
Iljxuh 5= Uhdol}hg dqg wwhg lq dwlrq dqg uhdo JGS jurzwk1
8;
95
100
(A2) Long-term Real Yields using GDP and Inflation
0.16
0.14
0.14
0.12
0.12
0.1
0.1
yield (%)
yield (%)
(A1) Short-term Yields using GDP and Inflation
0.16
0.08
0.08
0.06
0.06
0.04
0.04
0.02
55
60
65
70
75
80
85
90
0.02
55
95
60
(B1) Short-term Yields using GDP and Inflation; gamma = 1
65
70
75
80
85
90
95
(B2) Long-term Real Yields using GDP and Inflation; gamma = 1
0.16
0.16
0.14
0.14
0.12
0.12
0.1
0.1
yield (%)
0.08
0.06
0.08
0.06
0.04
0.04
0.02
0.02
0
-0.02
55
60
65
70
75
80
85
90
0
55
95
60
(C1) Short-term Yields using GDP, Inflation and Yields
65
70
75
80
85
90
95
(C2) Long-term Real Yields using GDP, Inflation and Yields
0.16
0.16
0.14
0.14
0.12
0.12
0.1
0.1
yield (%)
0.08
0.06
0.08
0.06
0.04
0.04
0.02
0.02
0
-0.02
55
60
65
70
75
80
85
90
0
55
95
60
65
70
75
80
85
90
Iljxuh 6= Dfwxdo dqg wwhg vkruw dqg orqj qrplqdo dqg uhdo udwhv1
8<
95
(A) Term premium - 2 year bond
(B) Term premium - 5 year bond
0.01
0.02
0
0
-0.02
-0.01
-0.04
-0.02
-0.06
-0.03
-0.08
-0.1
-0.04
-0.12
-0.05
-0.14
Unrestricted
Risk Neutrality
Adjusted
-0.06
-0.07
55
60
65
70
75
80
85
90
Unrestricted
Risk Neutrality
Adjusted
-0.16
-0.18
55
95
60
(C) Actual and Model ex-post 1-year excess returns - 2 year bond
65
70
75
80
85
90
95
(D) Actual and Model ex-post 1-year excess returns - 5 year bond
8
25
Actual
Model
Actual
Model
20
6
15
ercentage excess returns
percentage excess returns
4
2
0
10
5
0
-5
-2
-10
-4
-15
-6
55
60
65
70
75
80
85
90
95
-20
55
60
65
(E) Short horizon inflation risk premium
70
75
80
85
90
95
(F) Long horizon inflation risk premium
0.01
0.05
0
0
-0.01
-0.05
-0.02
-0.03
-0.1
-0.04
-0.15
-0.05
-0.06
-0.2
-0.07
Unrestricted
Risk Neutrality
Adjusted
-0.08
-0.09
55
60
65
70
75
80
85
90
95
Unrestricted
Risk Neutrality
Adjusted
-0.25
-0.3
55
60
65
70
75
80
85
90
95
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lq dwlrq dqg uhdo JGS1
93
(A) Term premium - 2 year bond
(B) Term premium - 5 year bond
0.03
0.15
0.02
0.1
0.01
0.05
0
-0.01
0
-0.02
-0.05
-0.03
-0.04
-0.1
-0.05
Unrestricted
Risk Neutrality
Adjusted
-0.06
-0.07
55
60
65
70
75
80
85
90
Unrestricted
Risk Neutrality
Adjusted
-0.15
-0.2
55
95
60
65
70
75
80
85
90
95
(D) Actual and Model ex-post 1-year excess returns - 5 year bond
(C) Actual and Model ex-post 1-year excess returns - 2 year bond
25
8
Actual
Model
Actual
Model
20
6
15
ercentage excess returns
percentage excess returns
4
2
0
10
5
0
-5
-2
-10
-4
-15
-6
55
60
65
70
75
80
85
90
95
-20
55
60
65
(E) Short horizon inflation risk premium
70
75
80
85
90
95
(F) Long horizon inflation risk premium
0.02
0.1
0.05
0
0
-0.02
-0.05
-0.04
-0.1
-0.15
-0.06
-0.2
Unrestricted
Risk Neutrality
Adjusted
-0.08
-0.1
55
60
65
70
75
80
85
90
95
Unrestricted
Risk Neutrality
Adjusted
-0.25
-0.3
55
60
65
70
75
80
85
90
95
Iljxuh 8= H{0dqwh whup suhpld dqg lq dwlrq ulvn suhpld hvwlpdwhg xvlqj
lq dwlrq dqg uhdo JGS1 Frh!flhqw ri ulvn dyhuvlrq h{rjhqrxvo| vhw @ 41
94
(A) Term premium - 2 year bond
(B) Term premium - 5 year bond
0.04
0.1
0.05
0.02
0
0
-0.05
-0.02
-0.1
-0.15
-0.04
-0.2
-0.06
-0.25
Unrestricted
Risk Neutrality
Adjusted
-0.08
-0.1
55
60
65
70
75
80
85
90
Unrestricted
Risk Neutrality
Adjusted
-0.3
-0.35
55
95
60
(C) Actual and Model ex-post 1-year excess returns - 2 year bond
65
70
75
80
85
90
95
(D) Actual and Model ex-post 1-year excess returns - 5 year bond
8
25
Actual
Model
Actual
Model
20
6
15
ercentage excess returns
percentage excess returns
4
2
0
10
5
0
-5
-2
-10
-4
-15
-6
55
60
65
70
75
80
85
90
-20
55
95
60
65
(E) Short horizon inflation risk premium
75
80
85
90
95
(F) Long horizon inflation risk premium
0.1
0
0
ercentage term remium
0.02
-0.02
-0.04
-0.06
-0.1
-0.2
-0.3
-0.08
-0.1
55
70
Unrestricted
Risk Neutrality
Adjusted
60
65
70
75
80
85
90
95
-0.4
-0.5
55
Unrestricted
Risk Neutrality
Adjusted
60
65
70
75
80
85
90
95
Iljxuh 9= H{0dqwh whup suhpld dqg lq dwlrq ulvn suhpld hvwlpdwhg xvlqj
lq dwlrq/ uhdo JGS dqg |lhogv1
95
(A) Actual nominal term structure
(B) Fitted nominal term structure
0.14
0.16
0.12
0.14
0.12
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
6
4
0.02
100
95
90
85
2
80
75
70
65
60
55
5
0.02
100
0
95
90
85
80
75
70
65
60
55
0
i
(C) Fitted real term structure
0.03
.025
0.02
.015
0.01
.005
0
005
100
5
95
90
85
80
75
70
65
60
55
0
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vwuxfwxuh xqghu mrlqw hvwlpdwlrq ri JGS/ lq dwlrq/ vkruw dqg orqj |lhogv1
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96
Iljxuh Ohjhqgv=
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prgho1
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duh wwhg wr lq dwlrq dqg uhdo frqvxpswlrq vhulhv1 Wkh vdph vhw ri eholhiv duh xvhg wr frpsxwh
fruuhvsrqglqj fxuyhv lq wkh wzr sdqhov
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Sdqho +D,
vkrzv wwhg dqg uhdol}hg lq dwlrq dqg JGS jurzwk zkhq rqo| lq dwlrq dqg frqvxpswlrq duh
xvhg wr hvwlpdwh wkh sdudphwhuv ri wkh prgho dqg wkh wzr surfhvvhv duh hvwlpdwhg lqghshq0
ghqwo|1 +Wdeoh 4, Sdqho +E, vkrzv wkh vdph vhulhv xqghu d mrlqw hvwlpdwh iru wkh wzr surfhvvhv
+Wdeoh 5, dqg Sdqho +F, vkrzv wkh vdph vhulhv zkhq dovr |lhogv duh xvhg1 +Wdeoh 6,
Iljxuh 6= Dfwxdo dqg wwhg vkruw dqg orqj qrplqdo dqg uhdo udwhv1
Sdqhov
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duh hvwlpdwhg xvlqj hlwkhu JGS dqg lq dwlrq/ rqo|1 Sdqho +E4, vkrzv wkh vdph vhulhv exw
dvvxplqj wkdw wkh frh!flhqw ri ulvn dyhuvlrq lv @ 4= Sdqho +F4, vkrzv wkh vdph vhulhv zkhq
sdudphwhuv duh hvwlpdwhg xvlqj uhdo JGS/ lq dwlrq dqg vkruw dqg orqj |lhogv1 Sdqhov +D5,0+F5,
vkrz wkh 80|hdu dfwxdo dqg wwhg qrplqdo dqg uhdo udwh xqghu dqdorjrxv dvvxpswlrqv1
Iljxuh 7= H{0dqwh whup suhpld dqg lq dwlrq ulvn suhpld hvwlpdwhg xvlqj
lq dwlrq dqg uhdo JGS1 Sdqho +D, vkrzv wkh rqh0|hdu h{0dqwh whup suhplxp rq d wzr |hdu
erqg iru wkh fdvhv zkhuh +l, lv dv hvwlpdwhg +xquhvwulfwhg,/ +ll, zkhuh lv vhw htxdo wr }hur
+ulvn qhxwudolw|,> dqg +lll, wkh whup suhplxp lv dgmxvwhg iru wkh eldv1 Sdqho +E, vkrzv wkh
rqh0|hdu h{0dqwh whup suhplxp rq d yh |hdu erqg1 Sdqhov +F, dqg +G, vkrz wkh h{0srvw
dfwxdo uhwxuq dqg prgho jhqhudwhg uhwxuq iru wkh 5 |hdu dqg 8 |hdu erqg1 Sdqhov +H, dqg
97
+I, vkrz wkh hvwlpdwhg lq dwlrq ulvn suhplxp lq fdvhv +l, 0 +lll, deryh iru wkh vkruw dqg orqj
krul}rq/ uhvshfwlyho|1
Iljxuh 8= H{0dqwh whup suhpld dqg lq dwlrq ulvn suhpld hvwlpdwhg xvlqj
lq dwlrq dqg uhdo JGS zlwk @ 41
Sdqho +D, vkrzv wkh rqh0|hdu h{0dqwh whup suhplxp
rq d wzr |hdu erqg iru wkh fdvhv zkhuh +l, lv dv hvwlpdwhg +xquhvwulfwhg,/ +ll, zkhuh lv vhw
htxdo wr }hur +ulvn qhxwudolw|,> dqg +lll, wkh whup suhplxp lv dgmxvwhg iru wkh eldv1 Sdqho
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wkh h{0srvw dfwxdo uhwxuq dqg prgho jhqhudwhg uhwxuq iru wkh 5 |hdu dqg 8 |hdu erqg1 Sdqhov
+H, dqg +I, vkrz wkh hvwlpdwhg lq dwlrq ulvn suhplxp lq fdvhv +l, 0 +lll, deryh iru wkh vkruw
dqg orqj krul}rq/ uhvshfwlyho|1
Iljxuh 9= H{0dqwh whup suhpld dqg lq dwlrq ulvn suhpld hvwlpdwhg xvlqj
lq dwlrq/ uhdo JGS/ vkruw dqg orqj |lhogv1
Sdqho +D, vkrzv wkh rqh0|hdu h{0dqwh whup
suhplxp rq d wzr |hdu erqg iru wkh fdvhv zkhuh +l, lv dv hvwlpdwhg +xquhvwulfwhg,/ +ll, zkhuh
lv vhw htxdo wr }hur +ulvn qhxwudolw|,> dqg +lll, wkh whup suhplxp lv dgmxvwhg iru wkh eldv1
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vkrz wkh h{0srvw dfwxdo uhwxuq dqg prgho jhqhudwhg uhwxuq iru wkh 5 |hdu dqg 8 |hdu erqg1
Sdqhov +H, dqg +I, vkrz wkh hvwlpdwhg lq dwlrq ulvn suhplxp lq fdvhv +l, 0 +lll, deryh iru wkh
vkruw dqg orqj krul}rq/ uhvshfwlyho|1
Iljxuh := Dfwxdo dqg wwhg whup vwuxfwxuh ri qrplqdo dqg uhdo whup vwuxf0
wxuh xqghu mrlqw hvwlpdwlrq ri JGS/ lq dwlrq/ vkruw dqg orqj |lhogv1
Sdqho +D, sorwv
wkh wlph vhulhv ri uhdol}hg whup vwuxfwxuh iurp 4<93 wr 4<<91 Sdqho +E, vkrzv wkh wlph vhulhv
ri wwhg whup vwuxfwxuh zkloh Sdqho +F, vkrzv wkh wlph vhulhv ri uhdo udwhv1
98