Abstract

Traditional spanning and step-down spanning tests are used to study whether or not small cap indexes in Asian and G7 countries could be separate asset classes of efficient portfolios for U.S. investors. Empirical tests on different index combinations show that the composition of a benchmark portfolio determines whether or not a small cap index could enlarge the original efficient frontier. The interaction among all assets in a portfolio is the key to the effectiveness and efficiency of a small cap index in efficient portfolios and constraints do not always reduce diversification benefits of a new asset. In addition, the time period the sample covered and length of holding time also influence the test results. Most small cap indexes of G7 countries are separate asset classes to the portfolio consisting of the popular indexes in G7 markets in our sample period. Moreover, pair-wise correlation is not an effective approach to search and study the diversification benefits. The step-down test results are consistent with empirical measures on risk and return of portfolios; this fact implies that the step-down approach, as an alternative method to correlation analysis, could be a powerful procedure to identify potential separate asset classes.