مزایای تنوع بخشی در بازارهای در حال ظهور منوط به محدودیت های پرتفوی

This paper examines the international diversification benefits subject to portfolio constraints—in particular, constraints on short selling. We show that the international diversification benefits remain substantial for U.S. equity investors when they are prohibited from short selling in emerging markets. This result is robust to investment restrictions on nonnative individuals. It is also unaffected by the fact that the U.S. equity index portfolio is not on the efficient frontier spanned by U.S. securities. The integration of world equity markets reduces, but does not eliminate, the diversification benefits of investing in emerging markets subject to short-sale constraints.

An important issue in international economics concerns the size of benefits from diversifying over securities in foreign countries, especially securities in emerging markets. In theory, if foreign securities do not perfectly correlate with U.S. securities, domestic investors gain from international diversification. However, the magnitude of the diversification benefits in general depends on various portfolio constraints, such as investors' ability to take short positions. Given the existence of derivative securities on stock market indices in developed countries, it is often feasible for institutional investors to take short positions on developed markets. Investors nonetheless face short-sale constraints in many emerging markets. In this paper, we study the impact of short-sale constraints on the existence and magnitude of international diversification benefits to U.S. equity investors. The existence of substantial diversification benefits of investing in emerging markets subject to short-sale constraints will underscore the importance of international diversification. Short-sale constraints have gained increasing attention in recent finance literature. Sharpe (1991) conjectures that departures from the CAPM might be small even in the extreme case where negative holdings are excluded. He postulates that institutional arrangements to improve investors' abilities to take negative positions facilitate the efficient allocation of risk in the economy. Hansen et al. (1994), He and Modest (1995), and Luttmer (1996) study how short-sale constraints and transactions costs affect consumption-based asset pricing models. For portfolio efficiency subject to short-sale constraints, Wang (1998) conducts Bayesian inference, Basak et al. (in press) develop an asymptotic test, and De Roon et al. (2001) carry out regression-based tests for mean–variance spanning. Ignoring short-sale constraints, many studies have documented low correlation across international markets and substantial diversification benefits. The early literature of Grubel (1968), Levy and Sarnat (1970), and Lessard (1973) finds low correlation among equity returns in industrial countries and concludes that the gain from international diversification is substantial. Harvey (1995) shows that securities in emerging markets promise U.S. investors both high expected returns and risk, as well as low correlation with securities in developed markets. Bekaert and Urias (1996) reject the hypothesis that equity indices in industrial countries span the mean–variance frontier of all international equity indices and thus demonstrate the existence of diversification benefits in emerging markets. Using the international CAPM, De Santis and Gerard (1997) estimate that the expected gain from international diversification to a U.S. investor is on average 2.11% annually. Errunza et al. (1999) further show that the international diversification benefits can be obtained from investment in country funds and American Depository Receipts traded in U.S. It remains unclear whether there exist substantial benefits from diversifying over emerging equity markets after imposing short-sale constraints. In the asset management industry, where short-sale constraints are routinely imposed in optimal portfolio choice problems, practitioners believe that the diversification benefits in emerging equity markets are substantial but, to our knowledge, there has not been any formal econometric inference. Glen and Jorion (1993) empirically show the existence of the benefits in currency hedging subject to short-sale constraints. Using mean–variance spanning tests, De Roon et al. (2001) argue that the evidence of diversification benefits in emerging markets disappears after imposing short-sale constraints. However, their statistical tests show strong evidence of the diversification benefits when investing in some individual Latin American or Asian countries, but no evidence of the benefits when investing optimally in the combination of these emerging markets. It seems odd to rule out diversification benefits in emerging markets when there are clear benefits derived from particular emerging markets. De Roon et al. (2001) explain that the counterintuitive results are driven by the loss of power in the asymptotic mean–variance spanning tests when more emerging markets are included. The issue investigated in this paper is closely related to the home bias puzzle in finance. It is observed that U.S. investors tend to hold a substantially larger portion of their invested equities in domestic stocks than what is suggested by the diversified world market portfolio or an optimal portfolio that maximizes a commonly used utility function (e.g., French and Poterba, 1991)1. One explanation offered in the literature is that the diversification benefits do not exist in practice because of the difficulty of taking short positions in many non-U.S. equity markets. Thus, it is important to understand whether investing primarily at home is optimal when market frictions such as short-sale constraints are taken into account. In this paper, we use Bayesian inference to examine the impact of short-sale constraints on the international diversification benefits to U.S. investors. Unlike the asymptotic mean–variance spanning tests, our Bayesian approach incorporates the uncertainty of finite samples into the posterior distributions of the diversification benefits. Two different measures of the diversification benefits are employed. The first one follows the work of Kandel et al. (1995) and Wang (1998) on portfolio efficiency. With equal variance, the expected return on the U.S. equity index portfolio is either smaller than or equal to the expected return on the internationally efficient portfolio. We use the difference between the expected returns on the two portfolios to measure the magnitude of the international diversification benefits. The advantage of this measure is that it tells us how far the U.S. equity index portfolio is away from the efficient frontier and has an intuitive interpretation as the gain in expected returns through diversification. It is often argued that the main benefit of international diversification is the reduction in variance rather than the increase in returns. For example, a columnist in The Wall Street Journal wrote: 2 “The main reason to invest abroad isn't to replicate the global market or to boost returns. Instead, what we're trying to do by adding foreign stocks is to reduce volatility”. Elton and Gruber (1995; chapter 12) argue that, since there is no evidence to support an international CAPM, risk-averse investors with no ability to forecast expected returns might seek to minimize the variance of their portfolio. To capture this aspect of the diversification benefits, our second measure of the diversification benefits is the reduction in the standard deviation when investors switch from the U.S. equity index portfolio to the global minimum-variance portfolio. Given that expected returns are difficult to estimate, an advantage of this second measure is that it does not depend on expected returns. Hence, the estimated weights in the global minimum-variance portfolio may be more accurate and relatively stable over different sample periods. The global minimum-variance portfolio has been used by other researchers (e.g., Stambaugh, 1997). One way to think of it is that the global minimum-variance portfolio is efficient if expected returns are assumed to be equal across markets. Using either of the two measures, we find that the diversification benefits of emerging equity markets remain substantial after imposing short-sale constraints in these markets. The result holds when we limit our analysis to investable stocks, i.e., stocks that are available to nonnative investors and meet minimum size and liquidity criteria. The result is also unaffected by the fact that the U.S. equity index portfolio is not on the efficient frontier spanned by U.S. securities. The integration of world equity markets reduces, but does not eliminate, the diversification benefits of investing in emerging markets subject to short-sale constraints. The results produced by our Bayesian approach are not only robust but also sensible. Unlike the asymptotic mean–variance spanning test, our inference produces sensible results—adding more emerging markets always increases the diversification benefits. An important implication of our results is that the introduction of market frictions such as short-sale constraints does not resolve the home bias puzzle but instead reinforces it, at least for the emerging markets. The rest of the paper proceeds as follows. In Section 2, we discuss measures of the international diversification benefits and the computation of the posterior distributions. In Section 3, we describe the data used in this study. In Section 4, we present our main empirical results. In Section 5, we examine how our result is affected by the integration of global equity markets over time and by the restrictions on nonnative investors. We also study if our result is due to the fact that the U.S. equity index portfolio is not on the efficient frontier of U.S. securities. In Section 6, we discuss some related issues along with our conclusion.

We use Bayesian inference to examine the impact of short-sale constraints on the magnitude of the international diversification benefits to U.S. investors during the period of 1976–1999. Two different measures of the diversification benefits are employed. The first one captures the increase in the expected return when switching from the U.S. equity index portfolio to the efficient international portfolio with equal variance. The second one captures the reduction in the standard deviation when investors switch from the U.S. equity index portfolio to the global minimum-variance portfolio. We show that the international diversification benefits remain substantial for U.S. investors after imposing short-sale constraints on emerging markets but not after imposing short-sale constraints on G7 countries. This result is robust to investment restrictions on nonnative investors. It is also unaffected by the fact that the U.S. equity index portfolio is not on the efficient frontier spanned by U.S. securities. The integration of world equity markets reduces, but does not eliminate, the diversification benefits of investing in emerging markets subject to short-sale constraints. Our results reinforce the home bias puzzle with respect to investments in emerging markets. Our analysis of the international diversification benefits has at least three advantages. First, it is easy to implement. Once the samples of μ and Ω are drawn, the calculation of the measures of the diversification benefits is straightforward. Second, most studies focus on rejection of the null hypothesis of no diversification benefits and gauge the magnitude of the benefits by examining the strength of the rejection. In contrast, the combination of Bayesian inference and Monte Carlo simulation allows us to draw exact inference on the magnitude of the diversification benefits. Finally, our approach can be used to examine a variety of market frictions. In Section 2, we assume only that the portfolio constraints form a closed convex set. Since this assumption is rather general, it allows for other realistic constraints such as margin and collateral requirements, as well as limitations on portfolio proportions for fund managers. It also allows us to study transaction costs. For example, it is well known that proportional transaction costs can be represented by short-sale constraints. It is interesting to know if these diversification benefits can be wiped out by transaction costs. 9 There are two caveats to our analysis in this paper. First, our analysis of δ assumes that the prior belief is non-informative. Therefore, the impact of short-sale constraints on δ examined in this paper is for investors whose prior belief is non-informative. Those with a non-informative prior belief use only the sample information from historical returns to form their posterior belief. However, if one believes that the observed historical returns are too high or too low and thus will converge to some equilibria, his/her belief in equilibrium models should be incorporated into the prior distribution. Black and Litterman (1992) and Pastor and Stambaugh (2000) develop frameworks for introducing equilibrium models into prior beliefs. The diversification benefits perceived by investors with informative priors can be very different from the benefits perceived by those with non-informative priors. This issue is examined by Wang (2002). Second, the asset allocation problem we considered is static rather than conditional or dynamic. Hodrick (1981) and Harvey (1991) document the time-varying risk and expected returns for international equities. Bekaert and Hodrick (1992), Ferson and Harvey (1993), and Harvey (1995) find that international stock returns are predictable. Hodrick et al. (1999) examine the hedging demands when international asset returns are predictable. Ang and Bekaert (2002) study how the hedging demands affect the international diversification benefits in dynamic portfolio choices with regime-switching models. The point we want to make in this paper is that, with short-sale constraints, diversification benefits exist even in the static framework. However, our analysis does not necessarily predict future diversification benefits of emerging markets. To predict future diversification benefits, it is necessary to extend our study to examine the impact of short-sale constraints on the benefits of a conditionally or dynamically diversified portfolio. Out-of-sample evaluations of such conditional studies will also be required.