where
R- N is the expected return on the non-U.S. securities in dollars
R
US is the expected return on U.S. securities
N is the standard deviation of the non-U.S. securities in dollars
US is the standard deviation of U.S. securities
N,US is the correlation between U.S. securities and non-U.S. securities
RF is the risk-free rate of interest
Although this equation is written from a U.S. investor’s point of view, a similar
equation holds true for investors in any country considering foreign investment. The
reader would simply redefine the symbols presently subscripted U.S. to the country
of interest.
Note that in Exhibit 11.13 the return required on a foreign investment is, for most
markets, considerably less than the return on the U.S. investment. For an assumed
U.S. expected return of 12%, Austrian securities would have to have an expected re-
turn of less than 9.04% for it not to pay to invest in Austrian securities at all. Diver-
sification into Canada and Spain requires higher expected returns than diversification
into other countries and Hong Kong would have to have an expected return above
U.S. securities. For Canadian securities this result is caused by high correlation of the
U.S. and Canadian markets. For Spain and Hong Kong it is primarily very high stan-
dard deviation that makes diversification less attractive. Thus, the expected return in
these markets must be higher or almost as high as the U.S. market for diversification
to pay.
11 • 16 INTERNATIONAL DIVERSIFICATIONU.S. Return
Country 12% 16%
Australia 9.99 12.66
Austria 9.04 11.07
Belgium 9.53 11.88
Canada 11.36 14.94
France 10.19 12.98
Germany 10.35 13.24
Hong Kong 12.46 16.76
Italy 9.36 11.60
Japan 9.95 12.58
Netherlands 10.05 12.75
Spain 11.44 15.07
Sweden 10.98 14.30
Switzerland 10.08 12.79
United Kingdom 10.45 13.41
Equally Weighted
Index (Non-U.S.)
Value-Weighted
Index (Non-U.S.) 10.17 12.95Exhibit 11.13. Minimum Returns on Foreign Markets Necessary for International
Diversification to Be Justified.