not present in pure domestic investment—country selection and exchange expo-
sure.^12
The decision concerning how much to invest in each country depends on the fac-
tors discussed earlier, namely, intercountry correlation, the variance of return for
each country’s securities, and the expected return in each country. There is good ev-
idence that the past standard deviations and correlations are useful in predicting the
future.
Recently a number of researchers have also found predictable in returns. Harvey
(1995), Solnick (1998), and Campbell and Hammo (1992) find predictability in many
country’s returns. The predictability is low with 1% to 2% of the variation in returns
explained by past variables. However, Kandel and Stambaugh (1996) provide evi-
dence that even with this low explanatory power, improvement in portfolio allocation
can be achieved. What variables seem to predict returns? Lagged returns, price lev-
els (dividend price, earnings price, and book price ratios), interest rate levels, yield
spreads, and default premiums have all been used. How is this done?
There are several ways to estimate the coefficients in a multi-index model. For ex-
ample, we could estimate the relationship between return in a country (e.g., France)
and some of the variables that have been found to predict return. Performing this
analysis we could find the relationship
Return 1 1 (return in the prior period) (interest rate in the prior period)
The coefficients,1, 1, and , are estimated by running a time series regression.
To forecast return in the next period, one simply substitutes the current value of this
period’s return and interest rates in the right side of the equation.
These predictions of return plus past values of correlations and standard deviations
can be used as input to the portfolio optimization process.
A second possibility for predicting expected returns is to utilize a valuation model.
For example, the infinite constant growth model states that
Estimates of next period’s dividend could be obtained by estimating earnings and
estimating the proportion of earnings paid out as dividends (the payout rate). The
payout ratio for a country portfolio is very stable over time, and forecasts of earnings
are widely available and at an economy level quite accurate. Estimates of growth
rates in earnings are also widely available internationally. Thus valuation models are
a feasible way to estimate expected returns.^13
One of the few studies that examines some alternative ways of estimating expected
return is Arnott and Henriksson (1989). They forecast the relative performance of
Expected returnDividend
PriceGrowth(^1)
2
(^1)
2
11.9 MODELS FOR MANAGING INTERNATIONAL PORTFOLIOS 11 • 23
(^12) Technically the amount to invest in any security should depend on securities selected in other coun-
tries. Thus our treatment of first selecting each portfolio within a country and then doing country selec-
tion is nonoptimal. However, it captures much of practice. Furthermore, intercountry factors are rela-
tively unimportant in determining each securities’ return, so this assumption may be a simplification that
improves performance.
(^13) Testing of the accuracy of forecasts produced by these models is unavailable, so all we can do is to
suggest types of analysis; we cannot report results.