change fluctuations is clearest for long- and short-term bonds. Although we will not
present the tables, the correlation coefficients are somewhat lower when we calculate
the correlation between returns assuming exchange risk is fully hedged away. Ex-
change movement increases the correlation among countries’ returns. The average
correlation coefficient between two countries is 0.46 assuming exchange risk is
hedged away for the countries shown in Exhibit 11.3. This contrasts with 0.48 when
exchange risk is fully borne. Similarly, Kaplanis and Schaefer found an average cor-
relation of 0.37 when including the effect of exchange risk and 0.32 when exchange
risk was fully hedged. Risk in international stock portfolios is normally reduced if ex-
change risk is hedged away and always reduced in bond markets.
The effect on expected return is less clear. Exhibits 11.10 and 11.11 show that dur-
ing the 1990–2000 period, exchange movements caused losses to U.S. investors for
most countries. The same table in the 1970s would have shown mostly gains. Also,
the loss to the U.S. investor is the gain to the foreign investor, so that a different table
would hold if we expressed returns in, for example, Swiss francs. Thus the effect of
eliminating exchange gains or losses on expected return varies from country to coun-
try and period to period.
One way to determine whether international diversification will be a useful strat-
egy in the future is to analyze how low expected returns in foreign countries would
have to be for an investor not to gain via international diversification.
11.7 RETURN EXPECTATIONS AND PORTFOLIO PERFORMANCE. Most of the lit-
erature on domestic and international diversification tells us that history is a much
better guide in forecasting risk than it is in forecasting returns. If we accept the his-
torical data on risk as indicative of the future, for any assumed return on the U.S.
market we can solve for the minimum return that must be offered by any foreign mar-
ket to make it an attractive investment from the U.S. standpoint.
We did this under two assumptions: that the U.S. market would return 12% and
that it would return 16%. These numbers were selected because 16% is approxi-
mately the return for the U.S. equity market in the 1990s and 12% is roughly the his-
torical long-term return on U.S. equities. The calculations used the correlation coef-
ficients shown in Exhibit 11.3 and the standard deviations shown in Exhibits 11.6
through 11.8, and a risk-free rate of 6%. These numbers are shown in Exhibit 11.13.
The basic formula to determine these numbers is as follows:
Hold non-U.S. securities as long as^7
(11.1)RNRF
sN
7RUSRF
sUS
rN,US11.7 RETURN EXPECTATIONS AND PORTFOLIO PERFORMANCE 11 • 15(^7) From Chapter 4 the first-order conditions are
SettingZNequal to zero and eliminating ZUSresults in the preceding equation as an equality. Increasing
R
- Nwould cause ZNto be greater than zero. For a more detailed derivation see Elton, Gruber, and Rentz-
ler (1987).
This analysis assumes foreign securities cannot be shorted. If they can be shorted, then markets for
which Equation (11.1) doesn’t hold are candidates for short sales.
RUSRFZNrN,USsUSsNZUSs^2 USRNRFZNs^2 NZUSrN,USsUSsN