changes over time, affecting the return to a U.S. investor on an investment in German
securities. The variability of the exchange rate for each currency converted to dollars
is shown in the column titled “Exchange Risk.” As discussed in the last section, the
exchange risk and the within country risk are usually relatively independent (in this
period they were negatively correlated for many countries) and standard deviations are
not additive. Thus total risk to the U.S. investor is much less than the sum of exchange
risk and within country risk. For example, the standard deviation of German stocks in
marks is 20.41%. The standard deviation of changes in the mark dollar exchange rate
is 10.55%. However, the risk of German stocks in dollars when both fluctuations are
taken into account is 20.13%. It should be emphasized that the variability of exchange
rates is calculated by examining the variability of each currency in dollars. Thus the
total risk is measured from a U.S. investor’s point of view.
As shown in Exhibit 11.6 over the 1990–2000 time period, the standard deviation
of an index of the U.S. equity market was less than the standard deviation of other mar-
ket indexes when the standard deviation of returns was calculated in its own currency
(domestic risk). When the effect of exchange risk is taken into account, the higher risk
of foreign markets was even more pronounced. These results are not atypical. Solnik
(1988), Kaplanis and Schaefer, and Eun and Resnick (1989) find the same results for
different periods.
For long-term bonds, the standard deviation of the U.S. bond index is about aver-
age when the standard deviation of each index is calculated in its own currency.
When returns are adjusted for changes in exchange rates and all returns are expressed
in dollars, the risk for the U.S. bond index is much lower than for any foreign index.
This illustrates the importance of exchange rate fluctuations on returns and risk. Fi-
nally, for short-term bonds (Exhibit 11.8) the effect of exchange rates is even more
dramatic. The exchange rate risk is by far the largest component of total risk. When
the standard deviation is calculated for a U.S. investor, the standard deviation of U.S.
T-bills is much less than the standard deviation for non-U.S. investments. For the
case of T-bills and perhaps bonds, although the relatively low correlation strongly
suggests that international diversification pays, the higher standard deviation sug-
gests it may not.
Exhibit 11.9 shows the combination of a value-weighted index of non-U.S. markets
and the corresponding U.S. index. The numbers in the table are standard deviations of
this combination when various percentages are invested in the international portfolio.
When considering equities the minimum risk is achieved with 74% in the U.S. port-
folio and 26% in the market-weighted world portfolio (excluding U.S. securities), and
total risk is reduced by 3.7% compared with exclusive investment in the U.S. market.
The risk reduction for long-term bonds is much less dramatic because the relative risk
of a non-U.S. market-weighted international bond portfolio is much higher and the
correlation slightly higher. Nevertheless a slight risk reduction is achieved. Finally, for
T-bills some international diversification lowers risk (slightly less than 1%). Because
of exchange risk the standard deviation of a value-weighted non-U.S. international
short-term bond portfolio is dramatically higher than the standard deviation of U.S. T-
bills. In this time period, however, the correlation of U.S. T-bills and a value-weighted
index of foreign T-bills was about zero. Thus, even with the high standard deviation,
a modest amount of international diversification lowered risk.
These results were derived using data from 1990 to 2000. An interesting question to
analyze is whether the results are unique to the period examined or if we can safely gen-
eralize them. The conclusions depend on the correlation between the world portfolio
11 • 10 INTERNATIONAL DIVERSIFICATION