Investments, tenth edition

Portfolio

World

U.S. Only

Average monthly return (%)

.31

.21

Standard deviation (%)

4.90

4.63

 These results are instructive. First, we see that U.S. stocks make for a relatively low-risk 

portfolio. While the U.S. portfolio may lie inside the world efficient frontier, and thus may 

offer a lower Sharpe ratio than the world portfolio, it nevertheless may have lower volatil-

ity than the better-diversified world portfolio. 

 Things are more complicated when we recognize that the data do not support the 

validity of the world CAPM, and hence we cannot be certain that the world portfolio 

is the most efficient risky portfolio. We do observe that higher country standard devia-

tions tend to be rewarded with higher average returns. A passive investor may therefore 

wish to examine simple rules of thumb for including a small number of countries (via 

international index funds of various combinations) in an attempt to dull the effect of high 

individual-country standard deviations and yet improve the Sharpe ratio of the overall 

portfolio. In all three of these rules, we assume the perspective of a U.S. investor, using 

dollar-denominated returns. We include countries on the basis of market capitalization 

for two reasons: (1) the resultant portfolio will be at least reasonably close to the theo-

retically efficient portfolio, and (2) the weights of any foreign country will not be too 

large. We estimate the risk of progressively more diversified portfolios relative to the 

number of foreign countries included, and the total portfolio weight of the international 

component. 

 The three rules of thumb are to include country indexes in order of:

    1.   Market capitalization (from high to low).  This rule is motivated by a world CAPM 

consideration in which the optimal portfolio is capitalization weighted.  

   2.   Beta against the U.S. (from low to high).  This rule concentrates on diversifying the 

risk associated with investments in higher-risk countries.  

   3.   Country index standard deviation (from high to low).  This rule is motivated 

by the observation that higher country standard deviations (SDs) are correlated 

with higher average returns. It relies on diversification to mitigate individual-

country  risk.    

 These alternatives illustrate the potential risks and rewards of international diversifi-

cation. Results of this exercise appear in  Table 25.11  and  Figure 25.16 . First turn to panel 

A of  Figure 25.16 , which vividly shows how portfolio SD progresses as we diversify the 

U.S. portfolio using the three rules. Clearly, adding countries in order of beta (or covari-

ance with the U.S. market), from low to high, quickly reduces portfolio risk despite the 

fact that the standard deviations of all 12 included countries are higher than those of 

the U.S. However, once we have adequate diversification, adding these higher-volatility 

indexes eventually begins to increase portfolio standard deviation. Adding countries in 

order of standard deviation (but this time, from high to low to improve expected returns, 

which are correlated with volatility) incurs the greatest increase in portfolio SD, as we 

would expect.   

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