Small Caps in International Equity Portfolios: The Effects of Variance Risk

Abstract

Small capitalization stocks are known to have asymmetric risk across bull and bear markets. This paper investigates how variance risk affects international equity diversification by examining the portfolio choice of a power utility investor confronted with an asset menu that includes (but is not limited to) European and North American small equity portfolios. Stock returns are generated by a multivariate regime switching process that is able to account for both non-normality and predictability of stock returns. Non-normality matters for portfolio choice because the investor has a power utility function, implying a preference for positively skewed returns and aversion to kurtosis. We find that small cap portfolios command large optimal weights only when regime switching (and hence variance risk) is ignored. Otherwise a rational investor ought to hold a well-diversified portfolio. However, the availability of small caps substantially increases expected utility, in the order of riskless annualized gains of 3 percent and higher. These findings are robust to a number of modifications concerning the coefficient of relative risk aversion, the investment horizon, short-sale possibilities, and the exact structure of the asset menu.