Investments, tenth edition

  Realistic Benefits from International Diversification 

 While recent realized returns can be highly misleading estimates of expected future returns, 

they are more useful for measuring prospective risk. There are two compelling reasons for 

this. First, market efficiency (or even near efficiency) implies that stock prices will be 

difficult to predict with any accuracy, but no such implication applies to risk measures. 

Second, it is a statistical fact that errors in estimates of standard deviation and correlation 

from realized data are of a lower order of magnitude than estimates of expected returns. 

For these reasons, using risk estimates from realized returns does not bias assessments of 

the potential benefits from diversification. 

  Figure 25.12  shows the efficient frontier using realized average monthly returns on the 

stock indexes of the 25 developed countries, with and without short sales. Even when 

the (ex post) efficient frontier is constrained to preclude short sales, it greatly exagger-

ates the benefits from diversification. Unfortunately, such misleading efficient frontiers are 

still presented in articles and texts on the benefits of diversification.  

 A more realistic description of diversification is achievable only when we input rea-

sonable equilibrium expected returns. Absent superior information, such expected returns 

are best based on appropriate risk measures of the assets. The capital asset pricing model 

(CAPM) suggests using the beta of the stock against the world portfolio. To generate