Gains from Portfolio Diversification into Less Developed Countries' Securities: A Comment

The thesis that there are gains from international diversification has been made several times in the professional literature as a reading of several of Errunza's citations clearly illustrates. The diversification argument that is presented consists essentially of indicating that (1) both the derived efficient frontier and optimal portfolio depend upon, among other things, the covariances of returns between securities and (2) intracountry covariances are indeed higher than intercountry convariances.1 Ergo, the presumption that international diversification results in a more desirable mean-variance efficiency locus-optimal portfolio. This argument has considerable intuitive appeal. However, a more general as well as more rigorous delineation would have been to structure the argument in terms of optimal portfolio choice in a two-parameter equilibrium capital market with homogenous expectations. This in turn would imply that (1) the mean-variance portfolio decision rule would exhibit the separation property-i.e., the decision with regard to the composition of the risky assets in the portfolio would be independent of the decision with regard to the proportion of the risky assets in the portfolio; (2) the investment opportunity set consists of two assets-i.e., the market portfolio consisting of all risky assets and the riskless asset; and (3) any portfolio which includes only a subset of the market portfolio would be characterized by having some diversifiable or residual risk, and hence, by definition, would be inefficient. If the argument for international diversification were presented in this manner, an important limitation of Errunza's empirical procedure would have been transparent. The procedure employed by Errunza to generate the efficiency locus was via a quadratic programming algorithm of Boles, et al. The utilized data inputs were historical (19571971; 1959-1972) means, variances, and co-variances of quarterly and annual returns of various countries' national stock price indices adjusted for U.S. exchange rate fluctuations.2'3 This procedure incorporates a crucial assumption about the set of investor expectations which concommittantly may lead to implications that conflict with our prior portfolio choice discussion. Specifically, as indicated, the set of investor beliefs about a country's returns, variances, and covariances is identical to the historical magnitudes of these variables.4 Thus, the estimated gains from portfolio diversification A la Errunza's procedure hold precisely only for individuals having this specific expectations generator. Hence, depending upon the particular sequence of history, there may be little, if any, correspondence between the risky Errunza portfolio and the portfolio of all risky marketable assets, or for that matter, with the risky portfolio generated by a different expectations generator under ceteris paribus Errunza conditions.5 Indeed, Tables 1 and 2 of Errunza aptly illustrate the first point above. Further, there is no presumption, particularly given capital market equilibrium, of any correspondence between historical mean-variance portfolio dominance of period 1 and ex ante mean-variance portfolio efficiency of period 2.6,7 Accordingly, two useful and interesting exercises would have been to assess the stationarity of the intercountry pairwise covariances and the serial correspondence la portfolio composition between