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We investigate tail risk in emerging stock markets at the country, regional and world levels, by comparing the investable and non-investable segments in terms of the expected shortfall of standardized returns and tail dependence on the world market. Employing the skewed Student-t GJR-GARCH model and the SJC copula, we show that most investable portfolios have lower tail risk but higher tail dependence than non-investable ones; emerging markets are likely more dependent on the world market during large joint losses than large joint gains; and tail dependence of the aggregate and investable markets on the world market varies across countries and regions.

Tail risk is the additional risk which fat-tailed return distributions, widely reported in the literature, have in relation to normal distributions. The foremost motivation of our study on the tail risk of emerging stock markets stems from the consequences of ignoring tail risk and the inability of volatility to capture tail risk. To illustrate, consider the Peruvian stock market from our sample. The (conditional) standard deviation and (conditional) mean of the Peruvian stock market returns for August 16, 2007 are estimated as 1.618% and − 1.081% respectively. Use of the normal distribution indicates a stock market typically will not fluctuate beyond three standard deviations, as 99.73% of the probability lies within three standard deviations. So, on August 16, 2007 there was only a 0.135% chance the Peruvian stock market would fall by more than 5.935%. Yet, the market fell by 8.457%. Further, it fell by more than three (conditional) standard deviations for 22 out of 3211 days (0.69%), which is 5.11 times the probability implied by the normal distribution (0.135%). In other words, the chance for a mutual fund holding the Peruvian stock index to suffer a given loss would be 5.11 times as great as a normal distribution estimate of volatility predicts. The consequence of using volatility to predict extreme market movements could be the misforecast of the October 1987 stock market crash as well as other financial events like the demise of Long Term Capital Management. This explains why the BIS Committee on the Global Financial System (2000) points out variance disregards the risk of extreme loss, and why “financial firms and regulators are in fact very concerned with the possibility that their risk models do not adequately account for fat tails” (Berkowitz, 2001). Thus, as an attempt to fill the gap in the literature, we probe into the neglected issue of tail risk for emerging stock markets. In the literature on emerging capital markets, studies have so far investigated the effects of market integration, increased foreign investment activity and liberalization on three variables: volatility, correlations and the world beta. With respect to volatility, earlier studies, such as Holmes and Wong, 2001, Froot et al., 2001, Bekaert and Harvey, 2000, Choe et al., 1999 and Levine and Zervos, 1998, provide mixed evidence that emerging stock markets have a higher or lower or unchanged return volatility after they become more integrated with the world market. More recently, Bae et al. (2004) find that in emerging economies, investable stocks have a higher volatility than non-investable stocks, and Cunado et al. (2006) document that financial liberalization has generally reduced the levels of six emerging market volatilities and their sensitivities to news. Concerning correlations, Bailey and Lim, 1992 and Bekaert and Urias, 1996 pioneer the research and suggest correlations may increase after emerging markets open up and become more integrated with the world market. This finding is confirmed in Bekaert and Harvey (2000) who also report an increase in beta with the world market. In a recent paper, De Jong and De Roon (2005) model the world beta of emerging stock markets as a function of market segmentation. They show the segmentation variable has a significant, negative effect on the world beta of investable stocks from emerging markets of all but the Mideast/Africa region; and an increase in beta due to a decrease in segmentation in turn implies higher expected returns. The above brief review of some selected studies and the importance of tail risk as illustrated by the example of the Peruvian market suggest several further questions worth exploring for emerging economies. Our main focus is the following two: Do the more integrated stock markets have (i) higher or lower tail risk (analogous to volatility) and (ii) higher or lower tail dependence on the world market (analogous to correlations or world beta) than the more segmented markets? As noticed in Bae et al., 2004 and De Jong and De Roon, 2005, a typical characteristic of emerging stock markets is that some stocks are eligible for purchase by foreigners (i.e., investable) while others are not (i.e., non-investable). Like the two studies, we treat the investable submarket as integrated, and the non-investable submarket as segmented. This existent division provides an ideal laboratory for examining the two questions posed above. Many previous studies have compared emerging stock market volatilities before and after liberalization, controlling for other variables than liberalization. We compare tail risks between concurrent, opened and unopened segments of an emerging stock market during its liberalization process. This way, we too are able to attribute the difference in tail risk, if any, to the difference in market integration. We believe Question (i) is largely an empirical one, just as whether market opening would lead to increased, decreased or unchanged volatility. Investable markets can, while non-investable markets cannot, access foreign investors. The increasing presence of foreign investors should induce a greater flow of information shocks to the former than the latter; and the 1997 Asian crisis witnessed that shocks were transmitted through investable rather than non-investable stocks (Boyer et al., 2006). These would suggest higher tail risk of investable relative to non-investable markets. On the other hand, however, some researchers believe that increased foreign participation can improve liquidity, and reduce sensitivity of prices to large, temporary surges in the volume of buy and sell orders (Hargis and Ramanlal, 1998). Foreign investors are mostly institutional investors from already developed markets, and base their decisions and investment strategies more on rational investment analyses and fundamental valuation factors (Jayasuriya, 2005). These considerations would lead one to expect lower tail risk of investable than non-investable markets. In addition, Jayasuriya (2005) argues that a fully integrated market is influenced by world factors rather than local factors such as political risk and unstable macroeconomic policies that are prevalent in countries with poorly developed stock markets. A logical inference from this argument is that investable markets, being integrated, should again possess less tail risk than non-investable markets which are segmented and so influenced mainly by adverse local factors. All the above-proposed conflicting economic stories/rationales imply the answer to Question (i) depends on the net outcome of offsetting effects. An important policy implication of our findings on this net outcome concerns stock market liberalization. If the investable submarket is found to have lower tail risk than the non-investable, this should serve as an argument in favor of further opening up stock markets to foreign investors. Question (ii) relates to, and extends, Question (i) with respect to the issue raised above: the relative influences of the world factors on the segmented and integrated segments of an emerging stock market. According to the capital asset pricing model (CAPM), market returns play a role as a risky factor in explaining the movements of individual stock returns. Roll (2001) argues during extreme episodes, such as the stock market crash of October 1987, the world market is the only factor driving the extreme movements of countries' stock markets. This suggests tail dependence may be present between a nation's and the world stock market. Note, tail dependence offers to gauge extreme co-movements, while the CAPM's beta can only quantify moderate co-movements. Despite so, the idea of the CAPM about the link between a stock and the market is still valid in guiding us to pose and investigate Question (ii). The results of this investigation will presumably provide some evidence regarding whether the tail risk of non-investable portfolios should be accounted for by local factors only; and whether the tail risk of investable portfolios is attributable to the world portfolio. In addition, our findings should also be relevant to a foreign portfolio manager striving to diversify between portfolios consisting of emerging markets' indices (investable and aggregate) and the world market index. For example, in periods of large downside movements of the world market, a prudent portfolio manager should remove (add) an emerging market's indices whose tail dependence coefficients are large (small). To investigate Question (i), we use the expected shortfall (ES) of volatility-filtered returns to measure tail risk. ES is defined as the expected value of the loss of a $1 portfolio for a given small probability over a given time horizon. Its use is proposed by Artzner et al., 1999 and Basak and Shapiro, 2001. There are two main advantages of ES over Value-at-Risk (VaR) for asset allocation (Jondeau et al., 2007): first, ES satisfies the sub-additivity property and so can be reduced by diversification; and second, ES directly controls the risk in the left tail of the distribution, while VaR (and volatility), as argued in the BIS Committee on the Global Financial System (2000), disregards the risk of extreme loss. The expected shortfall of asset returns contains two elements: volatility (conditional variance) and the expected shortfall of volatility-filtered (or standardized) returns. We take this to imply total risk is caused by volatility and tail risk. This is consistent with our notion that tail risk is the risk beyond volatility, and so requires volatility be removed. We estimate the Skew-t GJR-GARCH model for a demeaned return series to obtain the estimates of tail-fatness and skewness of volatility-filtered returns. This way, we are able to obtain the tail risk estimates attributed only to tail-fatness and skewness uncontaminated by volatility. Question (ii), also an empirical one, concerns the risk of extreme co-movements which may be understood as multivariate tail risk. This is because tail dependence measures the probability that one variable takes on an extremely large positive (negative) value given the other variable also has an extremely large positive (negative) realization. 1 There has been growing interest in examining tail dependence for emerging stock markets. For instance, Mendes et al. (2007) consider pairwise tail dependence of return series for identifying the most important emerging markets clusters. They select the Clayton, Gumbel and Tawn copulas in the test for the best bivariate fits. In this paper, we employ the symmetrized Joe–Clayton (SJC) copula proposed by Patton (2006), as the model has the advantage of accommodating all the five different circumstances as follows: (a) no tail dependence exists in both the upper and the lower tail; (b) tail dependence exists in, and is equal across, the upper and the lower tail; (c) tail dependence exists in the lower but not the upper tail; (d) tail dependence exists in the upper but not the lower tail; and (e) tail dependence exists in, and may be unequal across, the upper and the lower tail. The rest of the paper proceeds as follows. Section 2 outlines econometric methodology, Section 3 presents and discusses empirical results, and Section 4 offers a summary and conclusion.

We have conducted an empirical investigation of the tail risk of emerging stock markets by comparing their investable and non-investable segments in terms of the expected shortfall of volatility-filtered returns and tail dependence on the world market. The technologies used include the skewed Student-t GJR-GARCH model for the marginal distributions, and the symmetrized Joe–Clayton copula for the bivariate distribution. We employ data on emerging stock markets at the country, regional and world levels. We show, for p = 0.135% (say), that at the local level 80%, and at the regional and world levels 83%, of investable markets are characterized by lower tail risk relative to non-investable ones, and the difference can be as great as $1.387 for a 0.135% probability for $1 invested. We also demonstrate that at the local level 67%, and at the regional and world levels 100%, of the estimated left tail dependence parameters for the investable-vs-world pairs are greater than those for the non-investable-vs-world pairs. Another finding is that emerging markets are likely more dependent on the world market during large joint losses than large joint gains. Finally, we provide evidence on how tail dependence of the aggregate and the investable market on the world market varies across countries and across regions. Our results have implications for both policymaking and asset allocation. Regarding policymaking, we argue the benefits of further stock market opening up would actually include reducing market tail risk, in addition to stimulating economic growth as conventional wisdom. As far as asset allocation is concerned, foreign portfolio managers who care about tail risk would be able to reap diversification benefits from adding (removing), in their portfolios, those Global or Investable Indices whose λAL or λIL is found to be very small (large). As a first attempt, our study has adopted a static framework. An obvious extension is to make the tail risk of emerging stock markets evolve as a function of time-varying market integration and other controlling variables. We leave this for future research.