lios has been consistently found. Thus the risk characteristics of international funds
that have been found in the past are likely to be found in the future. It is hard, how-
ever, to develop a convincing economic case that the U.S. market will outperform or
underperform other markets consistently in the future. Thus, once again, we believe
the relevant way to utilize mutual fund data to examine the reasonableness of inter-
national diversification is to examine the proportions to invest in the United States
and an international portfolio at various levels of assumed differences between re-
turns in the United States and returns in other countries. Exhibit 11.16 shows the op-
timal investment proportions for a portfolio of the S&P index and the typical inter-
national fund.
In calculating the proportions, the standard deviations shown in Exhibit 11.14 for
the S&P index and the average international fund were used as well as the average
correlation coefficient. An expected return of 12% was assumed for the S&P index
and a 6% riskless lending and borrowing rate.
Using data for the typical fund in the 10-year sample shows that international di-
versification pays as long as the return on the international portfolio is no less than
1 % below the return on the S&P index.^10 With equal expected return, the optimum
is 80% United States and 20% international.
11.9 MODELS FOR MANAGING INTERNATIONAL PORTFOLIOS. Prior sections
present analysis that suggests that a portfolio of international equities should be a part
of an optimum portfolio. Furthermore, examining the performance of international
funds shows that the analysis is confirmed by actual performance. The conclusions
were less clear for international bond funds.
(^1)
4
11.9 MODELS FOR MANAGING INTERNATIONAL PORTFOLIOS 11 • 21
15-Year Data Optimal 10-Year Data Optimal
Return on International Portfolio
Proportions Proportions
Relative to U.S. Portfolio U.S. International U.S. International
+3 27% 73% 40% 60%
+2 40% 60% 53% 47%
+1 53% 47% 66% 34%
0 68% 32% 80% 20%
–1 85% 15% 96% 4%
–2 99% 1% 100% 0%
–3 100% 0% 100% 0%
Rfthe return on the riskless and 6%,
RS&Pthe total return on the Standard & Poor’s index 12%.
Exhibit 11.16. Optimal Investment Proportions.
(^10) One consideration an investor in an international portfolio needs to be aware of is that there is some
evidence that international managers underperform domestic managers. At a number of conferences the
authors have listened to industry speakers who specialize in evaluating international portfolios. They es-
timate a U.S. manager of a portfolio of foreign securities (such as Japanese) underperforms the foreign
(Japanese) manager. The estimates we have heard range from 2% to 4%. The underperformance may well
hold. Estimates of the exact amount should be treated with some skepticism.