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Bond Business School
12-1-1991
International diversification of investment
portfolios: U.S. & Japanese perspectives
Cheol S. Eun
Bruce G. Resnick
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Eun, Cheol S. and Resnick, Bruce G., "International diversification of investment portfolios: U.S. & Japanese perspectives" (1991).
School of Business Discussion Papers. Paper 67.
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"International Diversification of Investment PorHolios:
US & Japanese Perspectives"
Cheol S Eun
&
Bruce G Resnick
DISCUSSION PAPER NO 18
December 1991
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INTERNATIONAL DIVRESIFICATION OF INVESTMENT PORTFOLIOS:
U.S. AND JAPANESE PERSPECTlVES*
by
Cheol S. Eun ** and Bruce G. Resnick***
July 1991
*The authors are grateful to Salomon Brothers, Inc. for providing the bond data in this study.
**The Wharton School, University of Pennsylvania, Philidephia, PA 19104-6367, U.S.A.
College of Business and Management, University of Maryland, College Park, MD 20742,
U.S.A.'
!
***School of Business, Bond University, Gold Coast, QLD 4229, Australia and School of
Business, Indiana University, Bloomington, IN 47405, U.S.A, :
INTERNATIONAL DIVERSIFICATION OF INVESTMENT PORTFOLIOS:
U.S. AND JAPANESE PERSPECTIVES
Abstract
In this paper, we analyze the gains from international diversification of investment
portfolios from the Japanese as well as the U.S. perspectives. The major findings of the paper
include: First, the 'potential' gains from international, as opposed to purely domestic,
diversification are much greater for U.S. investors than for Japanese investors. For U.S.
investors, the gains accrue not so much in terms of lower risk as in terms of higher return, and the
opposite holds for Japanese investors. Second, using various 'ex ante' international investment
strategies designed to control parameter uncertainty, U.S. investors can realize substantial gains
from international diversification in out-of-sample periods. Japanese investors, however, can gain
little. Third, hedging exchange risk generally allows the U.S., but not Japanese, investors to
benefit more from international diversification. For U.S. investors, the international bond
diversification with exchange risk hedging offers a superior risk-return trade-off than the
international stock diversification, with or without hedging.
INTERNATIONAL DIVERSIFICATION OF INVESTMENT PORTFOLIOS:
U.S. AND JAPANESE PERSPECTIVES
I.
Introduction
Reflecting the trend toward a greater integration of world capital markets, international
diversification of investment portfolios has recently received widespread attention at both the
academic and practitioner levels. Originally, Grubel (1968) extended the concept of modern
portfolio analysis, pioneered by Markowitz (1952) and Tobin (1958), to global markets. He
argued that international portfolio diversification is the source of an entirely different world welfare
gain, distinguishable from both the gains from trade and the productivity gains from international
factor movements. This insight provided the stimulus for a series of studies, such as Levy and
Sarnat (1970), Solnik (1974), and Lessard (1976), which collectively established a convincing case
for international portfolio diversification.
More recent studies, including Eun and Resnick (1988) and Jorion (1985), have shown i)
that hedging foreign exchange risk can potentially increase the gains from international
diversification, and ii) that it is important to control parameter uncertainty in order to capture the
potential gains from international diversification. In other words, investors can substantially
benefit from international diversification when they properly control foreign exchange and
parameter uncertainties. When neither of these uncertainties are controlled, however, investors
may not be able to realize enough of the potential benefits to justify international investment.
Instead, they should invest domestically.
It is pointed out that the previous literature was mostly focused on international
diversification of stock portfolios. Despite the fact that the international bond market is at least as
large as the international stock market in tenos of market capitalization value and is perhaps more
integrated than the latter, international diversification of bond portfolios has received much less
attention. This seems to mirror the fact that, in general, more empirical work has been done
applying modem portfolio theory to the equities market than the fixed-income market. Moreover,
the empirical studies of international bond diversification that have been done are still preliminary
and not in complete agreement with one anotheLFor example. Levy and Lerman (1988) show in
an ex post study that a U.S. investor who diversified across world bond markets could have earned
more than twice the mean rate of return on a U.S. bond portfolio, at the same risk level.
Similarly, Jorion (1987) showed that over the ten year period ending May 1987, a world valueweighted index of government bonds produced superior risk-return performance in comparison to a
U.S. government bond index. Additionally, he showed that a hedged equal-weighted index would
have produced about the same mean return as the U.S. government bond index, but with less than
half the volatility. In contrast, Burik and Eunis (1990) claim that the risk and return characteristics
on non-dollar bonds raise questions regarding their role in diversified portfolios of U.S. investors.
They claim that U.S. investors receive no reliable compensation for bearing the currency risk
inherent in foreign bonds. Moreover, while hedging can reduce the volatility due to exchange rate
changes, the additional costs reduce expected return materially. They conclude that foreign bonds
are a diversification opportunity many U.S. investors can afford to pass up.
In addition, most of the previous literature examined the issue from the viewpoint of U. S.
investors. Relatively little is known about international portfolio diversification from the
perspective of non-U.S. investors. As a result, it is not clear at present whether or not and to what
extent the general findings of the literature are applicable to non-U.S. investors.
In this study, we analyze the gains from international diversification from the Japanese as
well as the U.S. perspective, and make comparisons between the results obtained. Our analysis
2
encompasses both the international stock and bond markets. As is well known, Japan emerged as
the world's largest creditor nation during the 1980s, heavily investing in financial securities of
other nations. Specifically, the main objectives of the paper are to: i) evaluate the 'potential' gains
from international diversification from the Japanese and U.S. perspectives; ii) analyze the effect of
exchange rate uncertainty on international bond and stock portfolios, and iii) evaluate the out-ofsample period performance of a1temative 'ex ante' investment strategies designed to control for
parameter uncertainty, both with and without exchange risk hedging.
The organization of the paper is as follows. In Section II, we conduct an ex post analysis
of the gains from international diversification of bond and stock portfolios from U.S. and Japanese
perspectives, without considering the problem of parameter uncertainty. In Section III, we
investigate the effect of exchange rate uncertainty. In Section IV, we evaluate the performance of
various ex ante diversification strategies. Section V offers a summary and concluding remarks.
ll.
The Gains from International Diversification: An Ex Post Analysis
In this section, the potential gains from international diversification are determined by
solving for the optimal international (tangency) portfolios and then comparing their risk-return
characteristics to those of domestic portfolios. Seven major markets are considered: Canada
(CA), France (FR), Germany (GE), Japan (JA), Switzerland (SW), the United Kingdom (UK), and
the United States (US).l In solving the optimal international portfolios, monthly return data for
national bond and stock market indices from the period of 1978.1 through 1989.12 are used. The
stock market return data are from Morgan Stanley Capital International Perspective and the bond
market data are returns on Salomon Brothers World Government Bond Indices which are
comprised of intermediate term bonds.
From the historical return data, we first computed the mean, standard deviation and
3
correlation matrix in terms of both the U.S. dollar and the Japanese yen. The results are presented
in Table I. A few points are noteworthy. First, stocks have higher mean returns than bonds in
both the dollar and the yen; in fact, the highest return bond market, i.e., Japan, has a lower return
than the lowest return stock market, Switzerland. Of course, risk tends to be higher for the stock
markets than for bonds markets. It is also noted that in both numeraire currencies, Japan
(Switzerland) registered the highest (lowest) return among international bond markets as well as
among stock markets. Second, the 'inter-correlatiollS' among bond and stock markets tend to be
somewhat lower than the 'intra-correlations' among stock markets or among bond markets.
Specifically, in terms of the dollar (yen), the average value of the inter-correlations among bond
and stock markets is .31 (.25) while the average value of intra-correlations is .51 (.37) for the
bond markets and .44 (.41) for the stock markets. It is noted, however, that the inter-correlation is
quite high between the bond and stock markets of the same country, with the exception of the
numeraire currency country, which most likely reflects the same currency factor. Third, the
correlation matrix confirms the well known fact that correlations tend to be high among the
continental European countries, i.e., France, Germany and Switzerland, and also between the two
North American countries, Canada and the U.S.
Additionally, Table I presents the mean return and standard deviation of each national bond
and stock index in the respective local currency numeraire. Comparison of the local currency
returns with the corresponding dollar returllS implies that over the sample period the dollar
appreciated against the Canadian dollar, French franc and British pound, and depreciated against
the West German mark, Japanese yen and Swiss franc. A similar comparison of the local currency
returns against the yen returns indicates that the yen appreciated versus all the others.
Using the parameter values provided in Table I as input data, we solved the optimal
international (tangency) portfolios for U.S. and Japanese investors. To simplify the analysis, we
4
assume that the monthly risk-free rate is zero. It is also assumed that investors can take short
positions and use the short sale proceeds. Table II presents the compositions of optimal
international portfolios. The optimal portfolios for U.S. investors ( or dollar-based investors) are
examined first. In the optimal international bond portfolio, the U.S. receives the highest weight,
62.54%, followed by France (44.88%), Japan (28.38%), ,and the U.K. (8.95%); both Canada and
Germany receive a weight of about 2 % while Switzerland receives a large negative weight, 48.96%. In the optimal stock portfolio, again the 'U.S. market receives the largest weight,
47.92%, followed by Japan (39.45%), U.K. (7.70%), Germany (5.50%) and France (5.09%);
Switzerland receives a minuscule weight, .06%, and Canada receives a negative weight, -5.79%.
In the optimal mixed portfolio of bonds and stocks, the largest positive weights are given to the
U.S. bonds (51.45%) and Japanese stocks (36.5%), followed by the French and German bonds and
U.S. stocks.
When the Japanese yen is used as the numeraire, on the other hand, the Japanese market
receives the largest weight in the optimal bond portfolio as well as the optimal stock portfolio.
This reflects the high returns and low risks, in terms of yen, of the Japanese securities? Apart
from the Japanese markets, the French and U.S. markets receive positive weights in the optimal
international portfolios of the Japanese investors. It is also noted that the German securities tend to
receive negative weights in the Japanese optimal portfolios, while the opposite is true in the U.S.
optimal portfolios. This, of course, reflects the effect of numeraire currency.
Table II also provides the risk-return characteristics of the optimal
in~ernational
portfolios,
together with those of the domestic portfolios. As can be expected, Table II shows that each
international portfolio has a higher Sharpe ratio (SHP), I.e., reward-to-variability, than the
corresponding domestic strategy. This, of course, implies that investors, both U.S. and Japanese,
can potentially benefit from international diversification; the potential gains, however, are much
greater for U.S. investors than for Japanese investors. 3
5
Table I
Summary Statistics of the Monthly Returns to Bonds and Stocks: 1978.1-89.12'
(In U. S. Dollar and Japanese Yen)
Stocks
Bonds
CA
FR
GE
JA
SW
UK
US
CA
FR
GE
JA
.36
Canada
047
045
.83
-.06
.02
Switzer.
.36
.68
U.K.
045
.37
France
Germany
(%)
SO
(%)
ME
(%)
SO
(%)
.39
.25
.25
.14
.35
.32
.35
.88
3.91
.58
4.99
.90
3.29
.89
.68
.81
.52
.30
.08
.58
.51
044
.58
.29
.03
.83
4.06
045
3.23
.91
1.68
.64
.89
.56
.35
.12
.50
.58
.38
.62
.28
.00
.79
4.64
Al
3.81
.55
1.61
.66
.51
.27
.05
.39
.34
.73
.36
.25
-.02
1.07
4.97
.61
1.74
.61
1.74
.54
.30
.10
043
,50
Al
.65
.28
-.04
.55
4.60
.16
3.50
.28
1.07
.33
.28
.31
.31
.34
.33
.62
.10
.94
5.26
.57
4.78
.97
2.98
.32
.86
3.20
.56
4.60
.86
3.20
.25
-.17
.21
040
.50
.23
.49
.38
.23
.27
.19
.17
042
.31
-.09
046
-.08
.24
-.04
.32
-.10
.56
.25
.43
-.18
.35
-.14
.54
-.15
.15
.21
.12
Switzer.
Al
.56
.58
-.10
.61
.25
.39
046
.52
.74
.04
U.K.
.44
.29
.26
-.09
.23
.63
.36
.67
044
.44
.18
U.S.
.64
.31
.22
-.23
.15
.29
.67
.80
Al
.40
.13
Japan
ME
(%)
.76
.26
Germany
SO
040
.59
France
ME
(%)
.34
.43
Canada
US
.27
.86
Stocks
UK
Local
040
.11
.83
043
.40
U.S.
SW
Yen
U.S. Dollar
Bonds
Japan
Dollar
i
_.
.02
.08
.37
-.11
.33
.39
.21
.18
.26
.14
.32
.20
040
.27
.22
.37
.60
.71
1.39
6.14
1.10
7.16
1.39
5.54
.61
043
.58
Al
2.06
7.73
1.66
7.13
2.13
6.56
.37
.76
048
044
.30
1.50
6.62
1.13
6.36
1.28
SAl
.34
.35
.20
2.13
6044
1.66
4041
1.66
4041
045
.38
1.33
5.90
.96
5.66
1.08
4.47
.53
1.69
6040
1.35
6.55
1.76
5.41
1.34
4.60
1.07
6.13
1.34
4.60
045
049
.62
'The upper-right (lower-left) triangle provides the correlation matrix in dollar (yen) terms. ME and SO, respectively, denote the mean return and standard deviation of returns.
Table III
Decomposition of the Variance of Bond/Stock Returns in U.S. Dollars'
(Monthly Data: 1978.1-89.12)
Components of Var(R;s)
Var(ej)
Var(R;s)
Var(R;)
Canada
15.29
10.82
1.72
2.67
.08
France
16.48
2.82
12.74
.60
.32
Germany
21.53
2.59
13.84
4.91
.19
Japan
24.70
3.03
15.13
6.09
.45
Switzer.
21.16
1.14
17.64
2.34
.04
U.K.
27.67
8.88
12.39
6.08
.32
U.S.
10.24
10.24
.00
.00
.00
Canada
37.70
30.58
1.72
5.37
.03
France
59.75
43.03
12.74
3.75
.23
Germany
43.82
29.27
13.84
.00
.71.
Japan
41.47
19.45
15.13
5.83
1.06
Switzer.
34.81
20.07
17.64
-3.76
.86
U.K.
40.96
29.27
12.39
-1.52
.82
U.S.
21.16
21.16
.00
l'he variances are computed using monthly percentage returns.
.00
.00
2Cov(Ri,ei)
AVar
Bonds
Stocks
Examination of the Table II indicates that for Japanese investors, the gains from
international diversification accrue in terms of lower risk, not in terms of higher return. For U.S.
investors, on the other hand, the gains accrue not so much in terms of a lower risk as in terms of a
higher return. Consider, for example, the case of stock investment. By holding the optimal
international portfolio instead of the U.S. stock market index, U.S. investors can substantially
increase the mean return from 1.34% to 1.72% and, at the same time, moderately reduce the risk
from 4.60% to 4.19%. Japanese investors, on
the other hand, can reduce the risk from 4.41 % to
3.65% at the cost of reducing the mean return from 1.66% to 1.55% by holding the optimal
international portfolio, rather than the Japanese stock market index.
m.
The Effect of Exchange Rate Uncertainty
Suppose that U.S. investors invest in the ith foreign market. Then the dollar rate of return,
R;$, is given by
= 1>.
.l'i + e. + 1>·e·
.I.'i
I
(I)
l'
where Ri is the local currency rate of return on the ith market and ei is the rate of appreciation of
the local currency against the dollar. 4
The variance of the dollar rate of return can be decomposed as follows:
Var(R;$) = Var (R;)
+
Var (eD
+
2Cov(R;,ei) + tSar,
(2)
where Ll.Var represents the contribution of the cross product term, R;ei' to the variance of the
dollar rate of return. Of course, the same formula will apply to the variance of the yen rate of
return, Var(R;I), when the variable ei is redefined as the rate of appreciation of the local currency
against the yen.
Table III presents the decomposition of the variance of dollar returns into different
components during the sample period of 1978.1 - 89.12, while Table
Iy presents the same
decomposition for Japanese yen. It is clear from examination of the tables that exchange rate
6
uncertainty substantially increases the risk of foreign investment, whether bonds or stocks,
regardless of the numeraire currency. However, it is also noted from the tables that the effect of
exchange rate uncertainty on the risk of foreign investment is much more significant for bond
investment than for stock investment. This is due to the fact that stocks have much higher
volatility of local currency returns than bonds. In fact, the variance of exchange rate changes is
always greater than that of local bond returns but less than that of local stock returns in both
numeraire currencies, with the sole exception of the Canadian bond in dollar terms.
Consider, for instance, the case of Swiss bonds. The Swiss bond market has a local
currency variance of only 1.14 percent squared but the variance becomes 21.16 percent squared in
terms of the U.S. dollar. This dramatic increase in variance reflects the variance of the exchange
rate, 17.64 percent squared, as well as the covariance of the exchange rate change with the local
bond market return, 2.34 percent squared. Examination of the tables shows that, more often than
not, the covariances between the exchange rate changes and local market returns add to the risk of
foreign investment. It is noted that the contribution of the cross product term to the risk of foreign
investment, AVar, is rather insignificant.
Considering that investors are likely to hold multi-currency portfolios, it is useful to extend
the above analysis to a portfolio context. The variance of dollar portfolio returns can be written as
follows:
Var~$) =
where
Xi
I:iI:jXiXjCov(R;,R)
+
I:iI:jXi:<.iCov(ei,ej)
+ 2I:iI:jXi:<.iCov(Ri,ej),
represents the fraction of wealth invested in the ilb bond or stock market. The exchange
rate uncertainty contributes to the overall risk of the portfolio through the second and the third
terms of equation (3).
To empirically examine the effect of fluctuating exchange rates on the portfolio risk, we
construct equally-weighted portfolios ofthe seven markets. Table V provides the variances of
portfolio returns and their decompositions. In the case of stock portfolios, exchange rate
7
(3)
Table IV
Decomposition of the Variance of Bond/Stock Returns in Japanese Yena
(Monthly Data: 1978.1-89.12)
Components of Var(R;r)
Var(R;r)
Var(R;)
Canada
24.90
10.82
14.75
-1.01
.34
France
10.43
2.82
8.58
-1.08
.11
Germany
14.52
2.59
9.86
2.02
.05
3.03
3.03
.00
.00
.00
Switzer.
12.25
1.14
10.43
.69
-.01
U.K.
22.85
8.88
11.42
2.93
-.38
U.S.
21.16
10.24
14.59
-3.91
.24
Canada
51.27
30.58
14.75
5.96
-.02
France
50.84
43.03
8.58
-.38
-.39
Germany
40.45
29.27
9.86
.68
.64
Japan
19.45
19.45
.00
.00
.00
Switzer.
32.04
20.Q7
10.43
1.16
.38
U.K.
42.90
29.27
11.42
2.45
.24
U.S.
37.58
21.16
14.59
liThe variances are computed using monthly percentage returns.
2.11
-.28
Var(e;)
2Cov(R;,e;)
AVar
Bonds
Japan
Stocks
Table V
Decompostiion of the Variance of Returns of the Equally-Weighted Portfolios"
(Monthy Data: 1978.1-89.12)
Components of Portfolio Risk
VarCRp)
E E (l/NiCov(Rj,R}
I
J
E E(l/NiCov(ej,e}
I
J
2 E E (llNiCov(Rj,e)
I
J
U.S. Dollar
Bonds
11.31
2.61
(23.2%)
6.03
(53.5%)
2.63
(23.3%)
Stocks
20.52
14.13
(69.9%)
6.03
(29.9%)
.05
(.2%)
Bonds & Stocks
12.49
5.01
(40.5%)
6.03
(48.7%)
1.34
(10.8%)
Japanese Yen
Bonds
7.48
2.61
(35.1 %)
5.55
(74.6%)
-.73
(-9.7%)
Stocks
19.92
14.13
(70.6%)
5.55
(27.8%)
.33
(1.6%)
Bonds & Stocks
10.38
5.01
(48.3%)
5.55
(53.6% )
-.20
(-1.9%)
'The portfolio variances are computed using the monthly percentage returns. The relative contribution of the
individual components to the total portfolio risk appear in parentheses.
uncertainty accounts for about 30% of portfolio risk in terms of both the dollar and the yen. It is
noted that the cross-covariances among local market returns and the exchange rate changes
contribute relatively little to the risk of stock portfolios. In the case of bond portfolios, on the
other hand, the exchange rate uncertainty accounts for about 77% of the variance of dollar
portfolio returns and 65% of the variance of yen portfolio returns. It is noted that the crosscovariance terms contribute significantly to the risk of dollar bond portfolio, but reduce the risk of
yen bond portfolio. In the case of mixed portfolios comprising both bonds and stocks, the
exchange rate uncertainty accounts for about 59 % (52 %) of the variance of dollar (yen) portfolio
returns.
The preceding analysis indicates that exchange risk is not very much diversifiable in the
context of multi-currency portfolios, and that hedging exchange risk can potentially increase the
gains from international diversification, especially in the case of bond investment. This
observation leads one to consider the use of foreign exchange forward contracts as a tool for
exchange risk management.
As an example, assume that the U.S. investor sells the expected foreign currency proceeds
forward. In dollar terms, it amounts to exchanging the uncertain dollar return
(1
+
E(R;»(l
+
e) - 1 for the certain dollar return (1
+ E(RD)(1 + fD
- I, where E(Ri) is the
expected rate of return on the i'h foreign stock market in terms of the foreign currency and 11 is the
forward exchange premium. The unexpected foreign currency proceeds, however, will have to be
converted into U.S. dollars at the uncertain future spot exchange rate. The dollar rate of return
under the hedging strategy is thus given by
R j H$ = [1
+
E(Rj )](1
+
f)
+
[R j
-
E(R)J (1
+
e) - 1,
(4a)
(4b)
Obviously, parameter uncertainty enters into implementing the hedging strategy described
8
by equation (4) through E(R;). To a degree, the success of the hedge depends on the accuracy of
the estimate of E(RJ. Poor estimates of E(RJ will result in poor hedging results. If one assumes
that E(Ru cannot be estimated with accuracy, then instead of hedging the expected foreign currency
proceeds, an alternative is to hedge only the principal and convert any return in the spot market on
the horizon date. This hedging strategy can be described by
(Sa)
(5b)
In what follows, we refer to the hedging arrangement described by equation (4) as 'back-end'
hedging and that described by equation (5) as 'front-end' hedging. The key advantage of front-end
hedging is that the hedging decision can be made separately from the parameter estimation. 5
Because the third term in equations (4b) and (5b) will be small in magnitude as will be the
fourth term in equation (4b), the following approximation results for both hedging strategies:
(6)
Equation (6) suggests that much of the effect of exchange rate changes on the risk of the foreign
stock market investment can be offset by means of the forward exchange contract. Moreover, the
empirical results presented in Tables IV and V generally suggest that
H
Var(R'$) < Var(R'$)
and Cov(R,f,Rjf) < Cov(R'$,RjJ
since fi is a constant. Additionally, since the forward exchange premium is known to be a nearly
unbiased predictor of the future change of the exchange rate, I.e.,
fi '"
E(e,), hedging offers the
potential of reducing risk without adversely affecting return. Tables IV and V suggest that the
analogous statements hold for the. yen-based investors as well. 6
9
IV.
Ex-Ante Portfolio Strategies
In this study the ex ante international portfolio strategies we examine, both with and without
forward exchange hedging, are the strategies developed by Jobson and Korkie (1980, 1981), Jorion
(1985, 1986) and extended by Eun and Resnick (1988). This literature has established that the
expected return vector is the critical input for successfully implementing modern portfolio theory,
Le., identifying the ex ante 'optima!' investment weights. Conventional estimation of the inverse
of the variance-covariance matrix is satisfactory. In lhis study we use the unbiased estimator (see
Jobson and Korkie),
(T - N - 2) S-1 ,
(T - 1)
(7)
where S is the usual N x N sample variance-covariance matrix.
Let us examine the unhedged strategies first, using the expected return equation
A
Ii
= (1 - w)
A
X+
w
1. Yo,
(8)
where a bar under a variable symbol denotes a vector, Y is the N x 1 ex post (historical) sample
mean-return vector of the N assets, 1. is a vector of ones, Yo denotes the mean return from the ex
post minimum-variance portfolio, and ~ represents the estimated shrinkage factor for shrinking the
elements of Y toward Yo. Equation (8) is a Bayes-Stein expression derived by Jorion for
estimating the ex ante expected-return vector to use in solving the portfolio problem. It is,
however, general enough to encompass other models. If ~ = 0, the resulting vector of estimated
expected returns is the ex post classical sample means. Coupling these estimates with
t- 1 results in
identifying the weights of the ex post (or historical) tangency portfolio as the ex ante 'optimal'
investment weights. This method implicitly assumes no estimation risk,in the classical sample
..estimates and is labeled the certainty-equivalence-tangency (CET) portfplio strategy. A second
10
strategy, which is due to the simulation results of Jobson and Korkie (1980, 1981) is to arbitrarily,
set ~ = 1. Combined with t·1, this strategy identifies as the optimal ex ante investment weights
those of the ex post minimum-variance portfolio (MVP). The MVP strategy implicitly assumes
that there is no useful asset-specific information in Y because it is not required as input to solve the
portfolio problem.
A third strategy is the Bayes-Stein strategy developed by Jorion, which uniquely estimates
the shrinkage factor according to the equation.
~ =
-'-(N_+_2,-'-)('-T_-~1).:....,
(N + 2)(T - I) + (X - Yol)' TS-'(T - N - 2)
ex -
--,Yol)'
where T represents the length of the time series of the sample observations and S is as defined
before. Using ~ in equation (8) and t·1, the Bayes-Stein (BST) optimal ex ante tangency portfolio
can be determined. Equation (8) can potentially result in a uniform improvement on the ex post
classical sample mean or Yo as estimates of the expected return because it relies on a more general
model that includes them as special cases. Whether using the Bayes-Stein estimates in -the portfolio
problem results in a more efficient ex ante optimal portfolio is an empirical question. A fourth
unhedged strategy is to construct an equally weighted (EQW) portfolio. This approach can be
viewed as a naive diversification strategy in the attempt to capture some of the potential gains from
international diversification. Alternatively, it can be viewed as if the investor believes there is no
useful information in the historical return data that can distinguish one asset versus another.
If the investor selects an unhedged strategy, realized returns are defined by equation (I).
To implement either the CET, MVP or the BST strategy requires obtaining a historical time series
sample of dollar (or yen) returns, R i $ (R,t) (i= I, ... , N), to calculate the Y , Yo, S, and ~ needed
for equations (7) and (8). If the investor selects a hedged (H) strategy, realized returns are defined
by (4) if a back-end hedging (BH) strategy is implemented and (5) if a front-end hedging (PH)
strategy is selected. Equation (6), which approximates equations (4) and (5), suggests that when a
11
hedged strategy is employed, the variability in R¥s (R¥i) will be primarily due to the variability in
the local currency return, 1<; (i= 1, ... ,N). This, in turn, suggests that for either the ex ante backend or front-end hedging strategy, the expected-return vector be estimated (using $ as the example
notation) as
(9a)
A
E<Ef)
= (1 -
where Y, Yo, S, and
A
w) X
W,
+
wI Yo
+
(9b)
1,
and thus R, are calculated from a historical time series of local currency
returns, R; (i = 1, ... ,N). The vector f is not estimated from historical data but rather contains as
elements the current market-determined forward exchange premiums.
Examination of equations (4) and (5) show that R¥s (i;eUS) is dependent on how E(R;) is
estimated. For both the BH and FH versions of the EQW(H) strategy, the E(R;) values are each
estimated as the grand mean of the Y elements. This is also done for the MVP(H) strategy. For
the CET(H) strategy, the E(R;) values are the respective Yj elements. In the BST(H) strategy, the
E(R;) values are the respective elements from the vector .R in equation (9a).7 In the next section,
we empirically test the unhedged and hedged ex ante international diversification strategies in the
dollar and yen numeraires and compare their performance results with one another and with
domestic investment in the United States (US) and, respectively, Japan (JA).
V.
Empirical Results
A.
The Data and Test Structure
We use the Morgan Stanley Capital International Perspective Stock Index Monthly return
data and the Salomon Brothers World Government Bond Index Monthly ,return data described in
Section II for the seven countries previously mentioned as the primary data. The stock data are in
12
the U.S. dollar numeraire and the bond data are provided in both the U.S. and the local currencies.
Using the U.S. and local currency bond returns, a corresponding time series of exchange rate
changes versus the dollar and the yen are constructed for each country via solving equation (1) for
The return data and exchange rate change data are used to test the performance of the ex
ante investment strategies discussed in Section IV. In conducting the tests, it is assumed that the
investor has a twelve-month investment holding period. To estimate the 'optimal'
ex ante investment-weight vector, it is assumed that the investor has knowledge of the 60 monthly
returns prior to the beginning of the holding period. For the hedging strategies, the twelve-month
forward premiums are calculated as of the inception date of the holding period from spot and
twelve-month forward exchange rates obtained from the Chicago Mercantile Exchange Statistical
Yearbook volumes. The twelve-month forward premiums are then converted to monthly premiums
to calculate the ex ante expected-return vector and the holding-period returns.
We attempt to examine the performance results for each strategy for thirty-six out-Df-sample
(overlapping) holding periods using the 144 months of data. The sample periods are structured as
follows: For the first holding period covering months 61 through 72, the estimation period covers
months 1 through 60. For the second holding period of months 63 through 74, the estimation
period covers months 3 through 62. Each subsequent pair of estimation and holding periods is
shifted forward in time by two months. This methodology was successful in constructing 36 outof-sample tests when the numeraire
curren~y
was the yen. For the dollar, however, only 29 out-
of-sample periods could be constructed. For the other seven, a CET tangency portfolio on the
positively sloped section of the ex post efficient frontier did not exist. 8 Consequently, since all
strategies could not be compared, those seven out-Df-sample test periods were eliminated.
B.
Test Results
Tabl VIII presents the performance results for bonds, stocks, ~d combined portfolios of
7
bonds and stocks from employing the various ex ante strategies in the twenty-nine out-Df-sample
13
holding periods using the dollar as the numeraire currency. For each strategy, the table shows the
average portfolio mean return and standard deviation stated in percentage per month. The table
also shows the average Sharpe (SHP) measure of portfolio performance. Table IX presents the
corresponding results for the thirty-six out-of-sample holding periods when the yen serves as the
numeraire currency.
Before we discuss the performance results for the alternative ex ante international
investment strategies, we briefly examine the portfolio weights that produce the performance
results. Tables VI and VII present the average portfolio weight vectors for each strategy, both
with and without hedging, for the U.S. and Japanese investors, respectively. A few points are
noteworthy. First, hedging exchange risk induces both U.S. and Japanese investors to substantially
reduce investment in their domestic market and increase investment in foreign markets, especially
in the Swiss market. Second, the portfolio weight vectors under hedging for U.S. and Japanese
investors look remarkably similar for all asset classes. The reason for this is that regardless of
which numeraire currency is used, a particular hedging strategy will identify a similar ex ante
optimal investment weight vector to the extent that the forward premiums or discounts are small
relative to the local currency mean returns, as they typically will be.
B.!.
U.S. Results
Panel A of Table VIII presents the performance results for the unhedged strategies.
Examination of the results show that for all asset classes the three international diversification
strategies cbntrolling estimation risk, I.e., MVP, EQW and BST, have higher average SHP values
than the corresponding U.S. strategy, and also the CET strategy which does not attempt to control
estimation risk. The only exception is the BST strategy for the mixed bond/stock diversification
that failed to outperform the U.S. strategy of 50% bonds and 50% stocks. This result shows that
as long as estimation risk is properly controlled, U.S. investors can actually realize gains from
international diversification.
Panel A of Table VIII also shows that for each of the international investment strategies, the
14
Table VI
Average Portfolio Weigbts
for Out-of-Sample Periods: U.S.'
A. Unhedged Approach
Tangency Portfolio
Minimum-Variance Portfolio
Bayes-Stein
Market
Bonds
Stocks
Bonds/Stocks
Bonds
Stocks
Bonds/Stocks
Bonds
Canada
.2769
-.2850
.3002/-.6523
-.0590
-.0393
-.2377/.0081
.0826
-.1241
-.1214/-.2598
France
-.3187
.0049
-2.1407/-.1382
.3680
-.0537
.1841
-.0282
-.1856/-.0853
Germany
.7337
-.0150
2.3896/-.5855
-.3390
.1016
-.2014/.1889
.0804
.0695
.0872/.1912
Japan
.8034
.3363
.029511.1988
.0617
.1838
-.2021/.1997
.3946
.2349
-.2536/.5624
-1.3536
.1303
-4.750412.8086
.3052
.1360
.01731.1833
-.4439
.1348
-1.4935/1.1936
U.K.
.0700
.1572
.2107/.7309
-.0013
.0652
-.02461.0734
-.0048
.0943
.1126/.2566
U.S.
.7883
.6712
.7811/.8177
.6644
.6064
.4724/.4195
.7071
.6188
.50911.4866
Switzer.
.1664/-.0632
Stocks
Bonds/Slocks
B. Hedged Approach
Tangency Portfolio
Bayes-Stein
Minimum-Variance Portfolio
Market
Bonds
Stocks
Bonds/Stocks
Bonds
Stocks
Bonds/Stocks
Bonds
Stocks
Canada··
-.0521
-.2130
-.0354/-.0394
-.0757
.0621
-.0797/-.0182
·.0601
-.0801
-.0539/-.0315
France
.1591
.0945
.14041-.0100
.2192
-.0089
.02051.0068
.0921
-.0122
.06621-.0103
Germany
.1720
-.0068
.1800/-.0305
.0070
.0540
.0809/~.0019
.1639
.0242
.1707/-.0169
Japan
.2159
.3823
.2006/.0647
.1825
.3055
.1541/.0581
.2021
.3639
.1769/.0689
Switzer.
.5277
.4805
.44881.0768
.6826
.3856
.7791/.0435
.6522
.5419
.57051.0850
U.K.
-.0019
.1972
.01001.0146
-.0253
.0953
-.0293/-.0311
-.0277
.0658
-.00471-.0095
.0096
.1062
-.02241.0396
-.0226
.0965
-.0498/.0384
-.0208
.0654
-.0527/.0322
U.S.
llEach. number represents the average of 29 out-of-sample values.
Bonds/Stocks
Table VII
Average Portfolio Weights
for Out-Qf-Sample Periods: Japan'
A. Unhedged Approach
Tangency Portfolio
Minimum-Variance Portfolio
Bayes-8tein
Market
Bonds
Stocks
Bonds/Stocks
Bonds
Stocks
Bonds/Stocks
Bonds
Canada
.0330
-.2555
.0741/-.1027
-.0396
-.0396
-.0550/-.0130
-.0061
-.1121
-.0103/-.0.427
France
.2297
.0772
.1817/-.0275
.2239
.0196
.1709/-.0235
.2470
.0415
.1855/-.0284
Germany
-.0717
-.0869
-.0113/-.0382
-.2684
.0078
-.21791.0597
-.1841
-.0189
-.1459/.0299
Japan
.9241
.6287
.8116/.1374
.7541
.5071
.6271/.1260
.8345
.5472
.7219/.1182
Switzer.
-.1882
.2617
-.3191/.1777
.2230
.2852
. 1298/.0549
.0276
.2814
-.0740/.1163
U.K.
-.0120
.1324
-.0467/.0773
-.0103
.0598
-.0164/.0141
-.0141
.0835
-.0227/.0326
U.S.
.0851
.2424
-.0436/.1293
.1173
.1600
.0083/.1348
.0952
.1775
-.0041/.1238
Stocks
Bonds/Stocks
B. Hedged Approach
Tangency Portfolio
Mimimum-Variance Portfolio
Bayes-Stein
Market
Bonds
Stocks
Bonds/Stocks
Bonds
Stocks
Bonds/Stocks
Bonds
Stocks
C~ada'_
-.0239
-.2189
.0085/-.0710
-.0990
.0310
-.0798/-.0327
-.0385
-.0942
-.0135/-.0696
France
.0217
.0796
.2621/.0039
.2528
-.0071
-.0865/.0086
-.1029
-.0281
-.1891/-.0200
Germany
.2844
-.0180
.3028/-.0592
-.0142
.0579
.0975/-.0019
.2702
.0270
.2718/-.0264
Japan
.3014
.3913
.2069/.1497
.1951
.3171
.1331/.1021
.2636
.3761
. 151l1.1639
Switzer.
.4505
.5105
.6605/-.0249
.6599
.4066
.8174/.0923
.7057
.5866
.5576/.2188
U.K.
.0645
.2164
-.0237/.0468
-.0273
.0859
-.0204/-.0334
-.0030
.0683
.0563/-.0037
U.S.
-.0986
.0390
-.1322/.0200
.0326
.1087
-.03821.0419
-.0951
.0642
8Each number represents the average'ot 36 out-of-sample values.
Bonds/Stocks
-.1310/.0343
Table VIII
Average Out-of-Sample Performance Results
of the Ex Aote Investment Strategies: U.S."
Bonds
Stocks
Bonds and Stocks
A. Unhedged
ME(%)
5D(%)
SHP
1.50
6.48
.32
1.65
4.98
.37
6.74
21.10
.31
MVP
ME(%)
SD(%)
SHP
1.20
2.61
..40
1.86
4.38
.51
2.23
4.71
.41
EQW
ME(%)
SD(%)
SHP
1.29
3/J7
.41
2.07
4.40
.55
1.68
3.08
.54
BST
ME(%)
SD(%)
SHP
1.3.3
3.92
.37
1.80
4.46
.48
3.77
14.68
.35
US
ME(%)
SD(%)
5HP
.91
2.67
.31
1.32
4.84
.33
1.11
3.14
.36
CET
B. Back-End Hedged
CET
ME(%)
SD(%)
SHP
.78
1.09
.74
1.77
4.78
.49
.88
1.27
.72
MVP
ME(%)
SD(%)
SHP
.73
.90
.87
1.72
4.39
.51
.86
1.12
.81
EQW
ME(%)
SD(%)
SHP
.83
1.37
.63
1.60
4.24
.53
1.21
2.37
.60
BST
ME(%)
SD(%)
SHP
.75
1.05
.75
1.79
4.58
.51
.90
1.21
.79
C. Front-End Hedged
CET
ME(%)
SD(%)
SHP
.79
1.10
.74
1.78
4.77
.49
.89
1.27
.72
MVP
ME(%)
SD(%)
SHP
.73
.92
.87
1.73
4.38
.51
.86
1.13
.81
ME(%)
SD(%)
SHP
.83
1.38
.63
1.61
4.23
.53
1.22
2.37
.60
EQW
BST
"In each
cell,
ME(%)
.76
1.80
SD(%)
1.06
4.56
.74
SHP
.51
the three numbers represent the average ot 29 out-ot-sample va!~es.
.90
1.22
.79
Table IX
Average Out-of-Sample Performance Results
of the Ex Ante Investment Strategies: Japan'
Bonds
Stocks
Bonds and Stocks
.92
1.15
2.66
.46
.93
2.00
.51
A. Unbedged
ME(%)
SD(%)
SHP
1.96
.53
1.34
4.57
.35
MVP
ME(%)
SD(%)
SHP
.65
1.47
.53
1.53
4.21
.47
EQW
ME(%)
SD(%)
SHP
.37
2.14
ME(%)
SD(%)
SHP
.78
1.59
1.18
4.38
.37
1,48
4.21
.45
ME(%)
SD(%)
SHP
.75
1.64.59
2.18
5.24
.44
1.46
2.97
.52
CET
BST
JA
.17
.59
.78
2.87
.32
1.07
2.13
.54
B. Back-End Hedged
CET
ME(%)
SD(%)
SHP
.59
1.28
.49
1.28
5.83
.26
.64
3.81
.21
MYP
ME(%)
SD(%)
SHP
.52
.89
.64
1.81
5.30
.40
.14
4.76
.04
EQW
ME(%)
SD(%)
SHP
.67
1.33
.52
1.89
5.40
.43
1.04
3.24
.38
BST
ME(%)
SD(%)
SHP
.04
4.85
.06
1.45
5.52
.30
4.47
.14
.44
C. Front-End Hedged
CET
ME(%)
SD(%)
SHP
.59
1.28
.49
1.28
5.80
.26
.64
3.80
.21
MYP
ME(%)
SD(%)
SHP
.52
.89
.64
1.81
5.28
.40
.15
4.72
.04
EQW
ME(%)
SD(%)
SHP
.67
1.33
.52
1.88
5.37
.43
1.04
3.23
.38
BST
ME(%)
.04
1.45
SD(%)
4.83
5.50
SHP
.06
.30
'In each celt. the three numbers represent the average ot 36 out-ot-sample values.
.44
4.46
.14
stock portfolio has a higher average SHP ratio than the corresponding bond portfolio. In addition,
the stock portfolio is found to have a higher average SHP ratio than the corresponding mixed
bond/stock portfolio. Considering the relatively low correlations between stocks and bonds, this
result is somewhat unexpected. This result implies that in the presence of estimation risk involving
different classes of assets, expanding the opportunity set to include both stocks and bonds will not
always allow the investor to realize a superior risk-return trade-off.
A few points are of interest from Panel B, which presents the back-end hedging strategy
results. First, the average SHP ratio of the international bond portfolio increases substantially with
hedging. For example, the average SHP ratio of the MVP (EST) strategy increases from .40 (.37)
without hedging to .87 (.75) with hedging. As a result, each of the hedged international bond
investment strategies has an average SHP ratio which is more than twice as large as the SHP ratio
of the U.S. bond strategy. In addition, the average SHP ratio of the mixed portfolio of bonds and
stocks also increases substantially with hedging, outperforming the corresponding U.S. strategy.
Second, examination of the average SHP values for the hedged stock strategies shows that
each of the international strategies outperforms the U.S. strategy. However, with the exception of
the CET(H) strategy, the average SHP values of the hedged strategies are just about the same size
as the corresponding values for the unhedged stock strategies. In other words, hedging
internationally diversified stock portfolios is not of much benefit to the U.S. dollar-based investors.
This, of course, is in sharp contrast to the case of bond investment. This different hedging result
appears to be attributable to the fact that exchange risk is much more significant a factor in bond
investment than in stock investment, as can be seen from examination of Table V.
Third, once exchange risk is hedged, for each strategy the international bond portfolio has a
higher average SHP value than the corresponding stock portfolio. This is in contrast to the
unhedged results in Panel A, where for each strategy the stock portfolio has a higher average SHP
value than the bond portfolio. It is also found that for the CET(H), MVP(H) and EQW(H)
strategies, the bond portfolio has a higher average SHP value than the corresponding mixed
15
portfolio of stocks and bonds. When the results for all three asset classes are considered, the
MVP(H) strategy emerges as the best overall strategy among all hedging strategies.
Panel C of Table
vm presents the performance results of the front-end hedging strategies.
Examination of the panel indicates that the results are very similar in all cases to those obtained for
the back-end hedging strategies. This suggests that a greater qu,antity risk associated with front-end
hedging may be largely diversifiable in the context of a multi-eurrency portfolio. Note that the
front-end and back-end versions of a particular hedging strategy have identical ex ante investment
weight vectors but that the realized returns are computed differently because the back-end approach
calls for hedging the entire expected terminal value, whereas the front-end approach only hedges
the principal investment against exchange risk. Since the results are similar, practical
considerations suggest that the easier, front-end hedging be used, rather than the back-end hedging
that is based on the estimation of the expected future foreign currency position. 9
B.Z. Japanese Results
Table IX provides the performance resuits of the alternative international investment
strategies for Japanese investors. Perhaps, the most striking finding of the table is that the yenbased investors could not go too far wrong by just investing in Japanese bonds. The average SHP
value for investing solely in the Japanese bond market is larger than that for all other unhedged
strategies, except the BST strategy which has the same average SHP value. Similarly, the Japanese
bond strategy outperforms all the hedged strategies, except the MVP(H) strategy for international
bond investment.
It is noted from Panel A of Table IX that with the exception of EQW strategy, the bond
portfolio has a higher average SHP value than either the stock portfolio or the mixed portfolio of
bonds and stocks. This is in contrast to the U.S. case, where the stock portfolio outperformed
both the bond and mixed portfolios. In addition, Panel A shows that it is difficult for Japanese
investors to substantially benefit from holding internationally diversified stock or mixed portfolios.
16
The Japanese stock or mixed investment strategies performed nearly as well, or better, than the
corresponding international strategies considered.
Examination of Panel B and C, shows that the back-end and front-end hedging essentially
produce the same results. Unlike the case for U.S. investors, however, hedging fails to allow the
Japanese investors to achieve a superior risk-return trade-off. This result appears to be attributable
to the fact that the hedging strategies call for reduced investment in the best performing Japanese
market and increased investment in such weak markets as the Swiss. It is noted that among the
unhedged strategies, the EQW strategy performed the worst for the same reason, Le., reduced
investment in the Japanese market.
VI.
Summary and Conclusions
As world capital markets have become more integrated, both individual and institutional
investors have begun to diversify their portfolios internationally. In this paper, we have evaluated
the 'potential' gains from international diversification from the perspectives of both U.S. and
Japanese investors, considering bonds as well as stocks. In addition, we have examined the extent
to which U.S. and Japanese investors can actually capture the gains from international
diversification under the conditions of exchange rate and parameter uncertainties. The major
findings of the paper are summarized as follows.
First, the ex post analysis of the gains from international diversification indicates that, in
the absence of parameter uncertainty, both U.S. and Japanese investors can potentially benefit from
international diversification; the magnitude of the potential gains, however, is much higher for
U.S. investors than for Japanese investors. For U.S. investors, the gains accrue not so much in
terms of a lower risk as in terms of a higher returns. For the Japanese investors, on the other
hand, the gains accrue mostly in terms of a lower risk.
Second, in the presence of a parameter uncertainty, U.S. investors can capture gains from
international diversification by using various ex ante international investment strategies designed to
17
control estimation risk. In contrast, Japanese investors could gain little from employing the ex ante
strategies. This appears mainly due to the fact that the potential gains are relatively modest to
begin with for the Japanese investors, reflecting the strong performance of the Japanese capital
markets.
Third, exchange rate uncertainty is an important component of foreign investment risk for
both V.S. and Japanese investors, especially for bond investment. Hedging exchange risk is found
to generally increase the benefits from international investment for V.S., but not Japanese,
investors. It was also found that for V.S. investors, the international bond portfolio with hedging
substantially outperformed the international stock portfolio, with or without hedging. This implies
that V.S. investors should seriously consider using bonds with hedging as a vehicle for achieving
international diversification. Currently, equities are a much more popular instruments for
international diversification.
18
FOOTNOTES
1.
It is in the currencies of these countries that forward contracts are readily available.
2.
French and Poterba (1990) suggest that national investors weight their home country assets
more heavily in internationally diversified portfolios out of choice rather then because of
institutional constraints. The results presented in Table IT suggest that a large weight in the
home country asset(s) is optimal as well.
3.
As one would expect, when there are less then perfect positive correlations between bonds
and stocks, the combined portfolio of stocks and bonds will have a superior SHP measure.
4.
Our analysis in this section draws on our earlier work, Eun and Resnick (1988).
5.
It can be seen from comparing (4b) and (5b) that if the last term of (4b), ECRJ (fce;), is
small, which is highly likely, then the dollar rate of return will be similar for both hedging
methods.
6.
In this study, we adopt the 'complete' hedge approach, with a hedge ratio of minus unity.
We do not consider cross-hedging because the cross-hedge ratio is quite variable over time.
A recent study by Kaplanis and Schaefer (1991) shows that the cross-hedge approach often
leads to poorer out-of-sample period results than the unitary approach. A complete hedging
strategy is in accord with the empirical findings of Adler and Simon (1986) and the
theoretical work of Eaker and Grant (1985). Other recent studies on hedging strategies
include Black (1989, 1990) and Celebuski, Hill and Kilgannon (1990).
7.
When the expected-return vector is estimated for the MVP, MVP(H), BST and BST(H)
strategies of combined investment in stocks and bonds, we found that better results obtained
when equations (8) and (9b) were calculated separately for the bond asset class and for the
stock asset class rather than together. The results presented in this study are calculated in
this manner. Additionally, it is noted that the 'MVP(H) strategy' is actually a misinformer
since the ex ante expected returns for all N securities will not be the same after the forward
premiums are added according to equation (9b) or in the combined bond and stock version
of this strategy when Yo is estimated uniquely for bonds and for stocks. Consequently, the
expected-return vector is required as input into the portfolio problem to frnd the ex ante
solution weights. The name, however, is retained for simplicity.
8.
Confer Alexander and Francis (1986, pp. 64-65).
9.
In addition to hedging over the full twelve month investment horizon using twelve-month
forward contracts, we also examined a 'roll-over' hedging strategy using the MVP(H) and
BST(H) models where we use one-month, three-month and six-month forward contracts that
are 'rolled-over' at expiration to allow for hedging the exchange risk over the twelve month
investment period. In general, the average SHP values tended to increase with the length of
the forward contract used to hedge the exchange risk for both the MVP(H) and BST(H)
strategies .
Fl
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