Format: (210.00 x 297.00 mm); Date: Mar 13, 2008 16:49:21; Output Profile: SPOT ISO Coated v2 (ECI); Preflight: Failed
WO R K I N G PA P E R S E R I E S
NO 883 / MARCH 2008
ASSESSING THE BENEFITS
OF INTERNATIONAL
PORTFOLIO
DIVERSIFICATION IN
BONDS AND STOCKS
by Roberto A. De Santis
and Lucio Sarno
WO R K I N G PA P E R S E R I E S
N O 8 8 3 / M A R C H 20 0 8
ASSESSING THE BENEFITS
OF INTERNATIONAL PORTFOLIO
DIVERSIFICATION IN BONDS
AND STOCKS 1
by Roberto A. De Santis 2 and Lucio Sarno 3
In 2008 all ECB
publications
feature a motif
taken from the
10 banknote.
This paper can be downloaded without charge from
http://www.ecb.europa.eu or from the Social Science Research Network
electronic library at http://ssrn.com /abstract_id=1105383.
1 This paper was partly written while Lucio Sarno was a Visiting Scholar at the International Monetary Fund. We are grateful for constructive
comments at various stages of this paper to Lorenzo Cappiello, John Cochrane and Robert Engle. The authors alone are responsible for
the views expressed in the paper and for any errors that may remain.
2 Corresponding author: European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany; Tel: +49 69 1344 0;
e-mail: [email protected]
3 University of Warwick and Centre for Economic Policy Research (CEPR). Contact address: Finance Group,
Warwick Business School, University of Warwick, Coventry CV4 7AL,
United Kingdom; e-mail: [email protected]
© European Central Bank, 2008
Address
Kaiserstrasse 29
60311 Frankfurt am Main, Germany
Postal address
Postfach 16 03 19
60066 Frankfurt am Main, Germany
Telephone
+49 69 1344 0
Website
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Fax
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All rights reserved.
Any reproduction, publication and
reprint in the form of a different
publication, whether printed or
produced electronically, in whole or in
part, is permitted only with the explicit
written authorisation of the ECB or the
author(s).
The views expressed in this paper do not
necessarily reflect those of the European
Central Bank.
The statement of purpose for the ECB
Working Paper Series is available
from the ECB website, http://www.ecb.
europa.eu/pub/scientific/wps/date/html/
index.en.html
ISSN 1561-0810 (print)
ISSN 1725-2806 (online)
CONTENTS
Abstract
4
Non-technical summary
5
1 Introduction
7
2 A factor pricing model of
exchange rates, bonds and stocks
2.1 Setup
2.2 Uncovered interest rate parity
2.3 Uncovered return parity for
equities and bonds
2.4 Equity and bond returns equilibrium
2.5 The full parity system
10
10
11
11
12
12
3 Empirical implementation
3.1 GMM estimation and
restrictions to test comovement
3.2 Stochastic discount factor
3.3 Risk premia
13
4 Data
15
5 Empirical results
5.1 The base case
5.2 The US discount factor
5.3 The model with time-varying risk premia
5.4 Performance of global
and domestic portfolios
5.5 Time-varying comovement from the 1980s
17
17
18
19
6 Concluding remarks
23
References
25
Tables and figures
29
European Central Bank Working Paper Series
41
13
14
15
20
22
ECB
Working Paper Series No 883
March 2008
3
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ECB
Working Paper Series No 883
March 2008
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Working Paper Series No 883
March 2008
27
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)#(((* #!-'' 28
ECB
Working Paper Series No 883
March 2008
ECB
Working Paper Series No 883
March 2008
29
Australia
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
US
8.40
5.67
7.97
11.06
8.61
8.57
14.06
8.31
5.71
10.47
4.88
0.43
8.88
5.85
8.04
9.22
10.49
5.34
7.85
stock
3.23
3.14
3.56
2.94
3.96
3.26
3.07
3.10
2.92
3.11
4.37
4.03
3.23
1.29
1.85
3.95
0.24
2.15
2.81
bond
Mean
(annualized, %)
1.98
0.20
0.40
-1.31
0.79
0.99
-0.53
0.74
0.26
0.89
0.39
-2.31
0.20
4.13
1.03
0.21
-0.10
1.96
-
FX
11.84
15.40
14.60
15.40
13.73
16.85
31.06
17.62
18.47
17.50
21.26
17.87
16.51
15.03
21.19
18.63
23.18
13.49
13.87
stock
6.43
4.12
4.38
4.22
5.76
5.21
3.85
4.68
4.34
5.41
6.15
4.80
4.30
4.02
3.88
6.02
4.13
5.42
6.07
bond
Std deviation
(annualized, %)
9.27
10.17
10.18
10.91
6.00
10.05
11.14
10.02
10.16
9.88
10.36
11.09
10.15
9.16
10.32
10.50
11.42
9.08
-
FX
-0.46
-0.56
-0.80
-1.05
-1.10
-0.43
-0.34
-0.56
-0.90
-0.34
0.29
-0.02
-0.97
-0.34
-0.92
-0.54
-0.17
-0.69
-0.77
stock
-0.19
-0.37
-0.22
-0.08
-0.16
-0.56
-0.01
-0.26
-0.44
-0.35
0.29
-0.65
-0.32
0.19
-0.24
0.24
-0.16
-0.08
-0.31
bond
Skewness
-0.17
-0.25
-0.30
-0.05
-0.02
-0.22
-0.40
-0.26
-0.24
-0.36
-0.45
0.76
-0.21
-0.38
-0.25
-0.40
-0.50
-1.03
-
FX
3.12
3.89
5.04
5.84
7.28
3.50
4.09
3.78
5.82
4.61
3.59
3.16
4.97
3.69
5.07
4.16
3.74
3.94
4.57
stock
3.13
2.63
2.47
3.16
3.51
3.60
3.95
2.44
2.74
3.98
4.59
6.21
2.68
3.58
4.20
4.41
3.16
3.62
3.73
bond
Kurtosis
2.85
3.75
3.75
3.07
3.11
3.68
4.04
3.65
3.77
3.86
4.43
6.25
3.75
3.63
3.59
3.97
4.68
6.83
-
FX
This table shows summary statistics for monthly annualized local currency denominated log asset returns for 19 countries and annualized log foreign exchange (FX) excess returns
for 18 currencies. The exchange rate returns are excess returns for borrowing in dollars, converting to the foreign currency, lending at the foreign interest rate, and converting the
proceeds back to dollars. The stock and bond indices are total market returns from Datastream, the interest rates are for one-month Eurocurrency deposits from the Bank for
International Settlements. The stock and bond returns are excess returns over the same country’s one-month interest rates. The data are monthly observations from January 1991
through May 2007.
Table 1
Summary statistics of excess log equity, bond and exchange rate returns
Table 2
Correlation between asset return differentials and changes in the exchange rate
This table shows monthly correlation coefficients between (i) exchange rate returns and equity returns differentials; (ii)
exchange rate returns and bond returns differentials; (iii) equity returns differentials and bond returns differentials; (iv)
exchange rate returns and interest rate differentials for a set of 18 countries vis-à-vis the US. The foreign exchange rate
is defined as units of US dollars per domestic currency. The stock indices are total market returns from Datastream, the
bond price indices are total market returns on 7-10 year maturity benchmarks, the interest rates are for one-month
Eurocurrency deposits from the Bank for International Settlements. ‘FX’ denotes excess returns for borrowing in US
dollars, converting to the domestic currency, lending at the domestic interest rate, and converting the proceed back to
dollars. The stock and bond returns are excess returns over the same country’s one-month interest rate. The data are
monthly observations from January 1991 through May 2007.
Australia
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
30
ECB
Working Paper Series No 883
March 2008
FX and equity
returns differentials
FX and bond
returns differentials
Equity and bond
returns differentials
FX and interest rate
differentials
-0.069
-0.186
-0.221
-0.288
-0.005
-0.307
-0.285
-0.351
-0.330
-0.301
-0.155
-0.078
-0.410
0.024
-0.169
-0.266
-0.295
-0.357
0.053
-0.357
-0.321
-0.295
0.148
-0.368
-0.218
-0.356
-0.319
-0.285
-0.130
-0.203
-0.346
0.029
-0.240
-0.287
-0.210
-0.376
0.146
0.214
0.200
0.303
0.160
0.205
0.312
0.435
0.407
0.281
0.482
-0.098
0.358
0.107
0.357
0.458
0.468
0.375
0.151
0.065
0.069
0.077
0.035
0.013
-0.115
0.006
0.064
-0.132
-0.117
0.137
0.072
0.162
-0.057
-0.106
-0.072
-0.124
ECB
Working Paper Series No 883
March 2008
31
Australia
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
s.e.
(0.002)
(0.003)
(0.003)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.003)
(0.003)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.003)
(0.002)
Constant
0.002
-0.001
0.000
0.000
0.001
0.001
0.001
0.001
-0.002
0.000
0.000
-0.001
0.001
0.003
0.001
0.000
-0.001
0.001
-0.799
-0.555
0.942
-0.571
-0.615
-0.338
-0.321
-0.479
-1.312
0.554
-0.172
0.084
-0.980
-0.496
-0.446
0.142
0.360
-0.470
FX /
Equity
First equation
(0.280)
(0.142)
(0.255)
(0.203)
(0.149)
(0.198)
(0.156)
(0.167)
(0.528)
(0.380)
(0.172)
(0.234)
(0.257)
(0.300)
(0.133)
(0.265)
(0.321)
(0.212)
s.e.
0.003
0.001
0.001
-0.001
0.002
0.001
0.000
0.001
0.000
0.001
0.001
0.000
0.001
0.001
0.001
0.001
0.001
0.001
Constant
(0.003)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.003)
(0.002)
(0.002)
(0.002)
(0.001)
s.e.
-2.786
-1.639
-1.745
-1.687
-0.979
-1.220
-1.096
-1.572
-1.561
-1.199
-0.367
-1.603
-1.409
-2.113
0.418
-0.899
-0.679
-0.584
FX /
Bond
Second equation
(1.427)
(0.579)
(0.518)
(0.546)
(0.788)
(0.426)
(0.386)
(0.510)
(0.632)
(0.474)
(0.328)
(0.608)
(0.520)
(1.169)
(0.554)
(0.343)
(0.410)
(0.473)
s.e.
-0.001
-0.002
0.000
0.003
0.002
0.001
0.005
0.000
-0.002
0.003
-0.007
-0.006
0.000
0.000
-0.001
0.000
0.001
-0.002
Constant
(0.003)
(0.003)
(0.002)
(0.002)
(0.002)
(0.003)
(0.005)
(0.002)
(0.002)
(0.003)
(0.004)
(0.004)
(0.002)
(0.002)
(0.004)
(0.002)
(0.003)
(0.001)
s.e.
3.732
-0.518
0.208
1.183
-1.236
-0.202
3.042
2.248
0.777
-1.508
3.339
-0.314
1.881
0.970
-1.253
1.260
1.113
0.645
Equity /
Bond
Third equation
(1.736)
(0.905)
(0.416)
(0.450)
(0.648)
(0.402)
(0.615)
(0.558)
(0.709)
(0.593)
(0.839)
(0.485)
(0.614)
(0.635)
(0.972)
(0.346)
(0.468)
(0.428)
s.e.
0.053
0.102
0.089
0.580
0.207
0.103
0.627
0.342
0.161
0.223
0.514
0.158
0.130
0.287
0.287
0.431
0.722
0.203
J-Stat
The results refer to the estimation of system (14) by one stage GMM estimation with the optimal weighting matrix being the unity matrix. The instruments used in the system are:
lagged one-period earnings yields and lagged one-period change in earnings yields in both the domestic country and the US for stocks; lagged one-period excess bond returns and
lagged one-period change in excess bond returns in both the domestic country and the US for bonds. Standard errors are reported in parenthesis. J-Stat denotes the p-value of the Jstatistic to test the null hypothesis that the overidentifying restrictions are satisfied. Excess returns are expressed vis-à-vis the US. The data are monthly observations from January
1991 through May 2007.
Table 3
Model with similar risk premia across country pairs
Table 4
Model with similar risk premia across country pairs:
Testing the hypothesis of ‘no diversification gains’
This table presents confidence intervals for the Wald test on the coefficients reported in Table 4. L stands for lower
estimate of the 95% confidence interval. U stands for upper estimate of the 95% confidence interval. The restrictions to
test the null hypothesis of no diversification gains in system (14) are: Eˆ 0 Dˆ 0 Jˆ 0 0 , Dˆ 1 1 0 , Eˆ1 Jˆ1 0 . The pvalue for this test is obtained from a Wald test statistic, distributed asymptotically as chi-square. The data are monthly
observations from January 1991 through May 2007.
FX / Equity
D̂ 1
Australia
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
32
ECB
Working Paper Series No 883
March 2008
FX / Bond
Ê 1
Equity / Bond
Jˆ1
Test of ‘no
diversification
gains’
L
U
L
U
L
U
p - value
-1.348
-0.833
0.443
-0.969
-0.908
-0.726
-0.626
-0.807
-2.348
-0.191
-0.509
-0.375
-1.485
-1.083
-0.706
-0.378
-0.267
-0.885
-0.250
-0.277
1.442
-0.174
-0.322
0.049
-0.015
-0.151
-0.277
1.299
0.164
0.544
-0.475
0.091
-0.186
0.661
0.989
-0.055
-5.583
-2.775
-2.760
-2.757
-2.524
-2.055
-1.854
-2.572
-2.799
-2.127
-1.009
-2.796
-2.428
-4.405
-0.668
-1.571
-1.482
-1.511
0.011
-0.503
-0.729
-0.616
0.566
-0.385
-0.339
-0.573
-0.323
-0.270
0.275
-0.411
-0.391
0.179
1.504
-0.227
0.125
0.342
0.329
-2.292
-0.608
0.302
-2.506
-0.989
1.836
1.154
-0.613
-2.671
1.695
-1.264
0.678
-0.273
-3.158
0.583
0.195
-0.194
7.134
1.257
1.023
2.064
0.034
0.585
4.248
3.342
2.166
-0.346
4.983
0.636
3.085
2.214
0.652
1.937
2.031
1.484
0.849
0.000
0.000
0.136
0.010
0.000
0.000
0.010
0.901
0.000
0.000
0.000
0.896
0.183
0.000
0.000
0.001
0.089
Table 5
The US SDF and estimated expected excess returns
The results refer to the estimation of system (16) by one stage GMM estimation with the optimal weighting matrix
being the unity matrix. The instruments used to construct the managed portfolios are: lagged one-period change in
earnings yields in both the domestic country and the US for stocks; lagged one-period change in bond yields in both the
domestic country and the US for bonds. Standard errors are reported in parenthesis. J-Stat denotes the p-value of the Jstatistic to test the null hypothesis that the overidentifying restrictions are satisfied. Estimated market premia and US
risk free rate are annualized values. The data are monthly observations from January 1991 through May 2007.
US risk free
rate
US equity
US bond
Foreign
equity
Foreign
bond
Foreign
currency
deposit
J-stat
Australia
4.206
7.935
2.848
8.182
3.272
1.974
0.210
Austria
4.246
7.935
2.848
5.538
3.099
0.208
0.381
Belgium
4.228
7.935
2.848
7.867
3.551
0.408
0.262
Switzerland
4.215
7.935
2.848
11.050
2.908
-1.289
0.390
Canada
4.203
7.935
2.848
8.720
4.040
0.837
0.189
Denmark
4.225
7.935
2.848
8.166
3.239
0.955
0.306
Finland
4.216
7.935
2.847
13.825
3.137
-0.568
0.290
France
4.223
7.935
2.848
8.034
3.095
0.701
0.303
Germany
4.219
7.935
2.848
5.487
2.852
0.279
0.831
Ireland
4.219
7.935
2.848
10.367
3.096
0.888
0.305
Italy
4.208
7.935
2.848
4.980
4.361
0.390
0.583
Japan
4.152
7.935
2.848
0.695
4.116
-2.446
0.138
Netherlands
4.223
7.935
2.848
8.842
3.194
0.212
0.578
New Zealand
4.253
7.935
2.848
5.317
1.361
3.912
0.689
Norway
4.230
7.935
2.848
7.600
1.837
1.010
0.108
Spain
4.209
7.935
2.848
9.053
3.920
0.201
0.687
Sweden
4.201
7.935
2.848
10.571
4.032
-0.095
0.704
UK
4.219
7.935
2.848
5.242
2.079
1.942
0.391
ECB
Working Paper Series No 883
March 2008
33
34
ECB
Working Paper Series No 883
March 2008
Australia
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
8.281
7.789
8.083
8.144
7.932
8.272
7.574
8.037
8.094
8.247
7.720
8.147
8.263
8.469
8.510
7.975
8.003
8.248
Risk premia
on US
equities
2.938
2.833
2.917
2.903
2.861
2.941
2.879
2.973
2.954
2.907
2.973
3.056
2.933
2.836
2.996
2.954
2.870
2.942
Risk premia
on US
bonds
7.870
5.336
8.237
11.514
8.134
8.718
14.119
8.777
5.731
10.650
5.164
0.641
9.164
4.976
7.937
9.325
10.996
5.847
Risk premia
on foreign
equities
(adjusted)
(1)
8.234
4.977
7.972
10.979
8.462
8.252
13.398
8.283
5.279
10.241
4.848
0.615
8.665
5.297
7.703
8.845
10.666
5.526
(2)
Risk premia
on foreign
equities
-0.332
0.373
0.300
0.606
-0.293
0.500
0.835
0.532
0.469
0.458
0.333
0.030
0.539
-0.306
0.270
0.523
0.392
0.340
Covariance
between
stock returns
and FX
(3)
3.691
3.123
3.573
3.011
3.864
3.219
3.143
3.137
2.876
3.112
4.540
4.333
3.196
1.299
1.903
3.842
4.021
2.060
Risk premia
on foreign
bonds
(adjusted)
(1)
3.740
3.109
3.548
3.019
3.928
3.200
3.141
3.139
2.869
3.097
4.592
4.343
3.195
1.342
1.894
3.807
4.000
1.981
(2)
Risk premia
on foreign
bonds
-0.039
0.018
0.031
-0.003
-0.058
0.025
0.007
0.002
0.011
0.020
-0.037
0.000
0.006
-0.042
0.011
0.044
0.030
0.081
Covariance
between
bond returns
and FX
(3)
-0.011
-0.017
-0.015
-0.018
-0.009
-0.019
-0.040
-0.020
-0.021
-0.020
-0.025
-0.022
-0.018
-0.015
-0.026
-0.023
-0.029
-0.013
Variance
differentials
(equities)
-0.014
-0.012
-0.012
-0.013
-0.008
-0.012
-0.012
-0.012
-0.012
-0.013
-0.014
-0.013
-0.012
-0.010
-0.012
-0.015
-0.016
-0.012
Variance
differentials
(bonds)
Estimated mean market premia are annualized values. The risk premia are obtained from estimating a BEKK GARCH(1,1) model for each country relative to the US. Note that (1) is
approximately equal to the sum of (2) and (3), because (2) and (3) are the covariance terms, while (1) is the log of one minus the covariance terms. Returns’ variances differentials
needed to estimate the full system (14) are reported (in mean) in the last two columns. The data are monthly observations from January 1991 through May 2007.
Table 6
Time varying risk premia
ECB
Working Paper Series No 883
March 2008
35
0.07
-0.33
-0.93
-1.74
-1.26
-1.12
-1.44
-1.60
-1.79
-1.33
-0.35
-1.09
-1.60
-3.34
0.86
-1.16
-0.66
-0.70
(0.21)
(0.15)
(0.24)
(0.22)
(0.18)
(0.31)
(0.31)
(0.30)
(0.28)
(0.58)
(0.35)
(0.41)
(0.29)
(0.46)
(0.21)
(0.21)
(0.38)
(0.27)
-0.21
-0.17
1.06
-0.78
-0.79
-0.86
-0.30
-0.98
-0.40
0.75
-1.09
-0.33
-1.43
-1.32
-0.59
-0.30
0.50
-0.15
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
(0.48)
(0.64)
(0.43)
(0.97)
(2.04)
(0.63)
(0.49)
(0.44)
(0.60)
(1.09)
(0.55)
(0.67)
(0.50)
(0.85)
(0.53)
(0.45)
(0.73)
(0.91)
FX and
Bond
Australia
FX and
Equity
0.71
1.07
1.30
-1.67
-0.50
1.92
-1.12
3.09
-1.13
0.27
2.29
2.92
0.47
-1.21
1.49
-0.25
-1.51
1.13
(0.46)
(0.71)
(0.36)
(1.35)
(0.99)
(0.56)
(0.77)
(1.00)
(0.65)
(1.17)
(0.55)
(0.98)
(0.50)
(0.54)
(0.52)
(0.59)
(1.06)
(1.10)
Equity and
Bond
-0.10
0.78
-5.98
2.97
1.70
0.17
-22.15
5.50
-10.54
5.68
0.09
7.51
-7.27
-1.90
0.34
-0.70
-5.71
-2.57
(0.96)
(2.09)
(1.92)
(1.05)
(3.35)
(3.87)
(7.42)
(5.39)
(3.93)
(4.31)
(1.99)
(3.86)
(4.39)
(0.73)
(0.88)
(0.68)
(2.13)
(1.95)
Foreign
equity risk
premia
-0.63
-0.82
3.29
-1.88
-5.94
-2.87
-3.99
2.08
3.98
-2.77
-1.40
-6.04
-3.35
2.79
-3.79
0.64
0.10
0.84
(0.75)
(2.06)
(1.44)
(1.30)
(1.97)
(2.43)
(2.07)
(3.81)
(1.24)
(1.71)
(1.40)
(2.88)
(1.92)
(1.33)
(2.45)
(1.20)
(1.66)
(1.62)
Domestic
equity risk
premia
10.41
-8.10
17.86
48.48
-72.62
51.10
-3.69
3.78
-11.60
-15.67
-28.36
-10.32
-6.07
-3.29
3.01
3.09
12.62
2.66
(2.88)
(4.16)
(4.82)
(14.76)
(16.37)
(21.95)
(1.31)
(2.67)
(3.01)
(101.2)
(19.69)
(8.81)
(6.43)
(1.38)
(6.37)
(3.16)
(5.70)
(0.80)
Foreign
bond risk
premia
-0.35
-45.20
-9.21
15.20
7.68
-41.22
8.70
-24.10
-6.57
-23.10
-13.08
9.82
30.97
7.75
-6.85
-15.28
-36.72
-10.07
(1.84)
(32.30)
(3.48)
(9.89)
(12.63)
(18.37)
(2.63)
(7.18)
(13.50)
(36.86)
(14.54)
(9.38)
(11.24)
(2.33)
(4.08)
(7.29)
(12.98)
(3.14)
Domestic
bond risk
premia
0.79
-0.14
-1.19
0.54
10.02
1.63
3.64
9.60
-5.51
-4.25
2.43
1.79
4.59
-0.40
2.43
-1.39
-0.30
-1.59
(0.59)
(0.91)
(1.05)
(0.90)
(3.20)
(1.49)
(2.53)
(2.87)
(1.37)
(2.82)
(1.69)
(1.30)
(1.57)
(0.53)
(1.53)
(1.04)
(1.17)
(1.12)
Variances
(equity)
3.80
-6.17
8.02
4.81
3.00
-3.83
-0.85
1.68
-5.37
-22.67
-1.43
-3.03
-2.38
-1.02
-2.51
-6.79
2.34
3.37
(1.26)
(3.17)
(2.16)
(3.71)
(5.53)
(2.88)
(1.45)
(2.24)
(1.98)
(7.84)
(2.50)
(6.09)
(2.68)
(1.25)
(1.77)
(3.92)
(5.82)
(1.53)
Variances
(bond)
0.03
0.12
0.02
0.10
0.03
0.08
0.09
0.14
0.01
0.39
0.13
0.03
0.54
0.26
0.07
0.09
0.08
0.05
J-stat
The results refer to the estimation of system (14) by one stage GMM estimation with the optimal weighting matrix being the unity matrix. The estimated coefficients of the system of
equations are reported in the first column for each variable. Standard errors are reported in parenthesis. Estimated constant terms are not reported. For methodology and sample
period, see text in Table 4. In addition to the instruments indicated in Table 4, we use also lagged one-period risk premia. The data are monthly observations from January 1991
through May 2007.
Table 7
Model with time varying asset-specific risk premia across country pairs
Table 8
Model with time varying asset-specific risk premia across country pairs:
Testing the hypothesis of ‘no diversification gains’
This table shows confidence intervals for the Wald test on the coefficients reported in Table 8. L stands for lower
estimate of the 95% confidence interval. U stands for upper estimate of the 95% confidence interval. The restrictions to
test the null hypothesis of no diversification gains in system (14) are: Eˆ 0 Dˆ 0 Jˆ 0 0 , Dˆ 1 1 0 , Eˆ1 Jˆ1 0 . The pvalue for this test is obtained from a Wald test statistic, distributed asymptotically as chi-square. The data are monthly
observations from January 1991 through May 2007.
FX and Equity
D̂ 1
Australia
Austria
Belgium
Switzerland
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Spain
Sweden
UK
36
ECB
Working Paper Series No 883
March 2008
FX and Bond
Ê 1
Equity and Bond
Jˆ1
Test of ‘no
diversification
gains’
L
U
L
U
L
U
p - value
-0.616
-0.462
0.586
-1.205
-1.147
-1.465
-0.905
-1.555
-0.944
-0.398
-1.781
-1.122
-1.994
-2.230
-0.991
-0.705
-0.244
-0.685
0.202
0.113
1.526
-0.349
-0.442
-0.264
0.314
-0.396
0.153
1.892
-0.392
0.472
-0.861
-0.410
-0.184
0.105
1.248
0.377
-1.720
-1.764
-1.821
-2.784
-2.919
-2.089
-2.762
-2.685
-3.921
-2.506
-1.204
-2.040
-2.843
-7.335
-1.040
-2.009
-1.919
-1.638
1.857
1.109
-0.039
-0.695
0.406
-0.142
-0.123
-0.521
0.346
-0.162
0.513
-0.138
-0.355
0.655
2.752
-0.313
0.591
0.246
-1.030
-3.589
-1.415
0.472
-2.261
-0.501
1.004
1.209
-2.025
-2.406
1.140
-2.624
0.824
-2.429
-4.308
0.601
-0.318
-0.194
3.281
0.566
0.917
2.508
-0.152
1.451
4.832
3.379
2.558
0.139
5.041
0.380
3.013
1.437
0.974
1.993
2.458
1.604
0.002
0.000
0.000
0.648
0.056
0.554
0.004
0.605
0.025
0.000
0.045
0.000
0.456
0.289
0.077
0.007
0.001
0.010
ECB
Working Paper Series No 883
March 2008
37
Portfolios B and C are constructed using respectively information from the models with similar risk premia and with time varying asset-specific risk premia across country pairs.
Portfolios
Excess returns
Sharpe ratio
Information ratio
Estimated
Treynor ratio
Jensen’s alpha
Black-Treynor ratio
(annualized, %)
(annualized)
(annualized)
(annualized, %)
(annualized, %)
(annualized, %)
Beta
US stocks and bonds
5.33
0.72
0.00
1.00
5.33
0.00
0.00
US stocks only
7.85
0.57
0.32
1.70
4.61
-1.22
-0.72
US bonds only
2.81
0.46
-0.32
0.30
9.43
1.22
4.10
Two-country portfolios
US and Australia
6.56
0.71
0.22
0.99
6.64
1.29
1.31
US and Austria
4.97
0.65
-0.06
0.71
6.99
1.18
1.66
US and Belgium
5.75
0.74
0.08
0.79
7.24
1.51
1.90
US and Switzerland
5.51
0.72
0.03
0.76
7.28
1.48
1.95
US and Canada
6.21
0.71
0.21
1.04
5.94
0.64
0.61
US and Denmark
6.12
0.76
0.15
0.86
7.15
1.56
1.82
US and Finland
6.68
0.63
0.18
1.01
6.61
1.29
1.28
US and France
5.89
0.71
0.11
0.89
6.60
1.13
1.27
US and Germany
4.95
0.59
-0.07
0.89
5.56
0.21
0.23
US and Ireland
6.51
0.76
0.23
0.93
7.02
1.57
1.69
US and Italy
5.17
0.56
-0.02
0.82
6.33
0.81
1.00
US and Japan
2.62
0.30
-0.41
0.80
3.27
-1.65
-2.06
US and Netherlands
5.79
0.73
0.10
0.87
6.64
1.14
1.31
US and New Zealand
6.52
0.72
0.19
0.90
7.21
1.70
1.88
US and Norway
5.66
0.61
0.05
0.92
6.12
0.73
0.79
US and Spain
6.06
0.67
0.13
0.94
6.42
1.03
1.09
US and Sweden
6.22
0.62
0.13
1.03
6.06
0.75
0.73
US and UK
5.52
0.72
0.04
0.86
6.41
0.93
1.08
Fully (A) and partially (B and C)
diversified portfolios
A - Portfolio (all 19 countries)
6.04
0.64
0.09
0.79
7.63
1.82
2.30
B - Portfolio (13 countries as in Table 5)
5.93
0.62
0.08
0.81
7.34
1.62
2.01
C - Portfolio (11 countries as in Table 9)
5.73
0.61
0.05
0.80
7.20
1.49
1.87
Global benchmarks
D - MSCI World and Lehman Global
4.01
0.55
-0.31
0.83
4.82
-0.42
-0.51
E - MSCI World (stocks only)
5.46
0.42
0.01
1.42
3.83
-2.14
-1.50
F - Lehman Global (bonds only)
2.55
0.50
-0.37
0.24
10.80
1.29
5.47
Table 9
In-sample performance of domestic, global and diversified portfolios, Jan. 1991 – May 2007
38
ECB
Working Paper Series No 883
March 2008
2.77
11.65
12.26
12.27
4.92
4.92
11.65
12.26
12.27
2.77
A - Portfolio (all 19 countries)
B - Portfolio (13 countries)
C - Portfolio (11 countries)
D - MSCI World and Lehman Global
D - MSCI World and Lehman Global
A - Portfolio (all 19 countries)
B - Portfolio (13 countries)
C - Portfolio (11 countries)
US stocks and bonds
(annualized)
(annualized, %)
Panel 1
(annualized)
Information ratio
Estimated
Beta
Panel 2
1.40
1.46
1.47
0.63
Diversified and global portfolios
0.00
1.11
1.23
1.14
1.01
1.00
0.00
1.00
1.30
1.29
1.34
0.48
1.78
1.79
1.75
-0.63
1.23
1.31
1.23
0.73
Diversified, global and domestic portfolios
0.73
Global benchmark MSCI World and Lehman Global
1.30
1.29
1.34
0.73
0.48
Domestic benchmark (US stocks and bonds)
Sharpe ratio
Excess returns
US stocks and bonds
Portfolios
9.51
9.96
9.39
3.79
4.92
10.50
10.00
10.76
4.86
2.77
(annualized, %)
Treynor ratio
5.62
6.21
5.84
-0.83
0.00
8.58
8.86
9.11
2.12
0.00
(annualized, %)
Jensen’s alpha
4.59
5.04
4.48
-1.13
0.00
7.73
7.22
7.99
2.09
0.00
(annualized, %)
Black-Treynor ratio
Portfolios B and C are constructed using respectively information from the models with similar risk premia and with time varying asset-specific risk premia across country pairs. We
run the models over the period January 1991 and May 2001 in order to select the countries based on the structural test to form the portfolios to be held over the subsequent six-year
period June 2001-May 2007. Portfolio B is formed by stocks and bonds of Belgium, Canada, Denmark, Finland, France, Germany, Ireland, Italy, New Zealand, Norway, Spain,
Sweden and US. Portfolio C is formed by stocks and bonds of Austria, Belgium, Switzerland, Denmark, Finland, Germany, Italy, New Zealand, Spain, Sweden and US.
Table 10
Out-of-sample performance of domestic, global and diversified portfolios, June 2001 – May 2007
Figure 1
The US Stochastic Discount Factor
estimated using the approach of Brandt-Cochrane-Santa Clara (2006)
Panel A: The figure shows the scatter plot of the US SDF estimated on a country pair basis. The US SDF on the vertical
axis is estimated vis-à-vis the UK. Theoretically, if all the points were on the 45-degree line, the SDF estimated on a
country pair basis would be sufficient to price all assets. Correlation coefficients are reported in parentheses.
2.2
Australia - (0.86)
2.0
Austria - (0.81)
Belgium - (0.79)
1.8
Canada - (0.83)
1.6
Denmark - (0.90)
1.4
Finland - (0.77)
1.2
France - (0.89)
Germany - (0.87)
1.0
Ireland - (0.89)
0.8
Italy - (0.82)
0.6
Japan - (0.63)
0.4
Netherlands - (0.81)
New Zealand - (0.93)
0.2
Norway - (0.95)
0.0
-0.2
-0.2
Spain - (0.86)
Sweden - (0.82)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Switzerland - (0.71)
Panel B: The US SDF estimated on a country pair basis vis-à-vis the UK
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1990
1992
1994
1996
1998
2000
2002
2004
2006
ECB
Working Paper Series No 883
March 2008
39
Figure 2
Assessing the Degree of Comovement over Time
The figure shows the time-varying p-value from the Wald test: Eˆ 0 Dˆ 0 Jˆ 0 0 , Dˆ 1 1 0 , Eˆ1 Jˆ1 0 . The p-values
are calculated by estimating the system (14) using a 10-year moving window and testing the above restrictions month
by month starting from January 1980 for Germany, the Netherlands and the UK; from December 1980 for Switzerland;
and from January 1982 for Japan. The Chi Square is reported on the vertical axis.
Germany
The Netherlands
150
150
125
125
100
100
75
75
50
50
25
25
0
1989
1993
1997
2001
2005
0
1989
1993
UK
150
125
125
100
100
75
75
50
50
25
25
1993
1997
2001
2005
2001
2005
Japan
150
125
100
75
50
25
0
1989
40
ECB
Working Paper Series No 883
March 2008
1993
1997
2001
2005
Switzerland
150
0
1989
1997
0
1989
1993
1997
2001
2005
European Central Bank Working Paper Series
For a complete list of Working Papers published by the ECB, please visit the ECB’s website
(http://www.ecb.europa.eu).
836 “Reporting biases and survey results: evidence from European professional forecasters” by J. A. García and
A. Manzanares, December 2007.
837 “Monetary policy and core inflation” by M. Lenza, December 2007.
838 “Securitisation and the bank lending channel” by Y. Altunbas, L. Gambacorta and D. Marqués, December 2007.
839 “Are there oil currencies? The real exchange rate of oil exporting countries” by M. M. Habib and
M. Manolova Kalamova, December 2007.
840 “Downward wage rigidity for different workers and firms: an evaluation for Belgium using the IWFP
procedure” by P. Du Caju, C. Fuss and L. Wintr, December 2007.
841 “Should we take inside money seriously?” by L. Stracca, December 2007.
842 “Saving behaviour and global imbalances: the role of emerging market economies” by G. Ferrucci and
C. Miralles, December 2007.
843 “Fiscal forecasting: lessons from the literature and challenges” by T. Leal, J. J. Pérez, M. Tujula and J.-P. Vidal,
December 2007.
844 “Business cycle synchronization and insurance mechanisms in the EU” by A. Afonso and D. Furceri,
December 2007.
845 “Run-prone banking and asset markets” by M. Hoerova, December 2007.
846 “Information combination and forecast (st)ability. Evidence from vintages of time-series data” by C. Altavilla
and M. Ciccarelli, December 2007.
847 “Deeper, wider and more competitive? Monetary integration, Eastern enlargement and competitiveness in the
European Union” by G. Ottaviano, D. Taglioni and F. di Mauro, December 2007.
848 “Economic growth and budgetary components: a panel assessment for the EU” by A. Afonso and
J. González Alegre, January 2008.
849 “Government size, composition, volatility and economic growth” by A. Afonso and D. Furceri, January 2008.
850 “Statistical tests and estimators of the rank of a matrix and their applications in econometric modelling”
by G. Camba-Méndez and G. Kapetanios, January 2008.
851 “Investigating inflation persistence across monetary regimes” by L. Benati, January 2008.
852 “Determinants of economic growth: will data tell?” by A. Ciccone and M. Jarocinski, January 2008.
853 “The cyclical behavior of equilibrium unemployment and vacancies revisited” by M. Hagedorn and I. Manovskii,
January 2008.
854 “How do firms adjust their wage bill in Belgium? A decomposition along the intensive and extensive margins”
by C. Fuss, January 2008.
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855 “Assessing the factors behind oil price changes” by S. Dées, A. Gasteuil, R. K. Kaufmann and M. Mann,
January 2008.
856 “Markups in the euro area and the US over the period 1981-2004: a comparison of 50 sectors”
by R. Christopoulou and P. Vermeulen, January 2008.
857 “Housing and equity wealth effects of Italian households” by C. Grant and T. Peltonen, January 2008.
858 “International transmission and monetary policy cooperation” by G. Coenen, G. Lombardo, F. Smets and
R. Straub, January 2008.
859 “Assessing the compensation for volatility risk implicit in interest rate derivatives” by F. Fornari, January 2008.
860 “Oil shocks and endogenous markups: results from an estimated euro area DSGE model” by M. Sánchez,
January 2008.
861 “Income distribution determinants and public spending efficiency” by A. Afonso, L. Schuknecht and V. Tanzi,
January 2008.
862 “Stock market volatility and learning” by K. Adam, A. Marcet and J. P. Nicolini, February 2008.
863 “Population ageing and public pension reforms in a small open economy” by C. Nickel, P. Rother and
A. Theophilopoulou, February 2008.
864 “Macroeconomic rates of return of public and private investment: crowding-in and crowding-out effects”
by A. Afonso and M. St. Aubyn, February 2008.
865 “Explaining the Great Moderation: it is not the shocks” by D. Giannone, M. Lenza and L. Reichlin,
February 2008.
866 “VAR analysis and the Great Moderation” by L. Benati and P. Surico, February 2008.
867 “Do monetary indicators lead euro area inflation?” by B. Hofmann, February 2008.
868 “Purdah: on the rationale for central bank silence around policy meetings” by M. Ehrmann and M. Fratzscher,
February 2008.
869 “The reserve fulfilment path of euro area commercial banks: empirical testing using panel data” by N. Cassola,
February 2008.
870 “Risk management in action: robust monetary policy rules under structured uncertainty” by P. Levine,
P. McAdam, J. Pearlman and R. Pierse, February 2008.
871 “The impact of capital flows on domestic investment in transition economies” by E. Mileva, February 2008.
872 “Why do Europeans work part-time? A cross-country panel analysis” by H. Buddelmeyer, G. Mourre and
M. Ward, February 2008.
873 “The Feldstein-Horioka fact” by D. Giannone and M. Lenza, February 2008.
874 “How arbitrage-free is the Nelson-Siegel model?” by L. Coroneo, K. Nyholm and R. Vidova-Koleva,
February 2008.
875 “Global macro-financial shocks and expected default frequencies in the euro area” by O. Castrén, S. Dées and
F. Zaher, February 2008.
42
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March 2008
876 “Are sectoral stock prices useful for predicting euro area GDP?” by M. Andersson and A. D’Agostino,
February 2008.
877 “What are the effects of fiscal policy shocks? A VAR-based comparative analysis” by D. Caldara and C. Kamps,
March 2008.
878 “Nominal and real interest rates during an optimal disinflation in New Keynesian models”
by M. Hagedorn, March 2008.
879 “Government risk premiums in the bond market: EMU and Canada” by L. Schuknecht, J. von Hagen and
G. Wolswijk, March 2008.
880 “On policy interactions among nations: when do cooperation and commitment matter?” by H. Kempf and
L. von Thadden, March 2008.
881 “Imperfect predictability and mutual fund dynamics: how managers use predictors in changing systematic risk”
by G. Amisano and R. Savona, March 2008.
882 “Forecasting world trade: direct versus “bottom-up” approaches” by M. Burgert and S. Dees, March 2008.
883 “Assessing the benefits of international portfolio diversification in bonds and stocks” by R. A. De Santis and
L. Sarno, March 2008.
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March 2008
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Format: (210.00 x 297.00 mm); Date: Mar 13, 2008 16:49:19; Output Profile: SPOT ISO Coated v2 (ECI); Preflight: Failed