and the U.S. index and the standard deviation of each index. As discussed earlier, the
correlations used in this analysis are very similar to the correlations other researchers
have found in other periods and somewhat higher than the correlations found in earlier
periods. The variability of return for foreign markets during this period is higher than
the variability of return that most other researchers have found.
Thus, the risk reduction shown in Exhibit 11.9 would hold if data from other pe-
riods were used and the results are likely to be robust across periods. Furthermore,
for stocks, rather substantial errors in selecting the optimal mix could be made and
risk would still be reduced. Therefore, using data from a prior period to decide on a
mixture of an international and domestic portfolio would likely result in a less risky
portfolio than pure domestic investment. For long-term bonds and T-bills, the risk re-
duction via international diversification is so small that errors in determining the risk-
minimizing mix of international and domestic portfolios could easily result in a port-
folio more risky than the domestic one held alone.
11.5 RETURNS FROM INTERNATIONAL DIVERSIFICATION. The decade of the 1990s
was an especially favorable time for U.S. markets relative to foreign markets. Exhibits
11.10 and 11.11 show the average annual returns from January 1990 to December 2000
on several international markets. The “Exchange Gain” column is the difference be-
tween the return in the assets home country and the assets return in the United States.^4
The average non-U.S. equity index had a return of 12.54% in its home country com-
pared with 16.17% for the U.S. market with an exchange loss averaging 2.212%,
when converted to dollars the average non-U.S. equity index returned 10.31%.
The column in Exhibit 11.10 that presents returns in U.S. dollars shows only three
countries, Hong Kong, Netherlands, and Sweden, that had returns above the United
11.5 RETURNS FROM INTERNATIONAL DIVERSIFICATION 11 • 11XValue-Weighted Index
Proportion in Long-Term
World Index (%) Stocks Bonds T-Bills
0% 13.59 7.90 0.35
10% 13.28 7.63 0.75
20% 13.12 7.45 1.38
30% 13.10 7.37 2.05
40% 13.23 7.39 2.72
50% 13.51 7.52 3.39
60% 13.93 7.75 4.06
70% 14.47 8.06 4.74
80% 15.12 8.46 5.42
90% 15.87 8.93 6.09
100% 16.70 9.45 6.77Exhibit 11.9. Risk from Placing XPercent in a World Index Excluding U.S. Securities
and the Rest in U.S. Index 1990–2000.
(^4) Earlier we showed that the expected return to a U.S. investor is not the sum of exchange gains and
losses and the return in the investor’s home country. Thus, column two includes not only the exchange
return but also includes all joint effects of the country and exchange return.