An Ignored Risk Factor in International Markets: Tail Risk. Yanchu Wang. Sep 13 th, Abstract

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1 An Ignored Risk Factor in International Markets: Tail Risk Yanchu Wang Sep 13 th, 2015 Abstract Tail risk is a risk factor that investors consider when making investment decisions. This paper empirically tests the role of tail risk in international market. I find evidence that tail risks are priced using sample of 40 countries from 1980 to Across all countries, investors require lower rate of return to hold asset which are a better hedge to the tail risk. Pricing of tail risk varies across different countries with different level of integrations into the global financial market. In addition, I show that tail risk act as a global transmission channel of contagion during crisis. The findings provide implications for international portfolio diversification as well as understanding the role of tail risk in asset prices on international financial markets and during the financial crisis. Keywords: Tail Risk; Asset Pricing; International Financial Markets; JEL Classification: G11; G12; G15; Wang, yanchu-wang@purdue.edu is from Krannert School of Management, Purdue University. I acknowledge research support from the Purdue University. I benefit from discussion with Xiaoyan Zhang and I thank my dissertation committee for their comments and support throughout the project. Any remaining errors are my own. 1

2 A Previously Ignored Risk Factor in International Markets: Tail Risk Abstract Tail risk is a risk factor that investors consider when making investment decisions. This paper empirically tests the role of tail risk in international market. I find evidence that tail risks are priced using sample of 40 countries from 1980 to Across all countries, investors require lower rate of return to hold asset which are a better hedge to the tail risk. Pricing of tail risk varies across different countries with different level of integrations into the global financial market. In addition, I show that tail risk act as a global transmission channel of contagion during crisis. The findings provide implications for international portfolio diversification as well as understanding the role of tail risk in asset prices on international financial markets and during the financial crisis. Keywords: Tail Risk; Asset Pricing; International Financial Markets; JEL Classification: G11; G12; G15; 2

3 Tail risk, defined as extreme event risk in asset markets, is an important aspect for investor to consider when making investment decisions. Recently, various theoretical models have incorporated the tail risk and shown that heavy-tailed shocks to economic fundamentals help explain asset pricing behavior (Rietz 1988; Barro 2006; Gabaix 2012; Gourio 2012; Wachter 2013; Bansal and Yaron 2004; Eraker and Shaliastovich 2008; Bansal and Shaliastovich 2010; Bansal and Shaliastovich 2011; Drechsler and Yaron 2011). Empirically, Bollerslev and Todorov (2011) find that the compensation for extreme events accounts for a large fraction of US equity risk premium. Jiang and Kelly (2014) show that tail risk has strong predictive power for aggregate market returns and also has significant predictive power for cross-section of average asset returns in the US markets. Overall, the existing literature provides some supporting evidence in US market that investors are tail risk averse and require higher return to hold tail risky assets. However, while it is important to investigate tail risk in international financial markets, there is little empirical evidence showing tail risk is a globally priced risk factor. Using global markets for the investigation in tail risk is crucial as the importance of tail risk could be more pronounced in markets other than US, where tail risk is allegedly high, while the importance of tail risk could be less pronounced in some markets where tail risk is low. On the other hand, it would also be possible that tail risk is not important in some markets, unlike the results found in US market. Hence, extending the study of tail risk to world markets could provide a good opportunity to evaluate and understand the role of tail risk as a possible source of global systematic risk. In addition, different countries have different level of integration into the global financial market, thus the importance of global and local specific tail risk could be different across countries. For investors in countries with high integration into the global financial market, they might concern more about global tail risk instead of local specific tail risk. As a result, global tail risk could have bigger impact on investment decisions than local specific tail risk. On the other hand, investors from countries with low integration into the global financial market might care more about local specific tail risk instead of global tail risk when they make investment decisions. 3

4 Therefore, using global market makes it possible to investigate such cross-country or crossregional variations in the pricing of tail risk, and provide excellent out-of-sample test outside of US. Most importantly, extreme events are not restricted to US market, developed markets, or emerging markets, but they can occur worldwide, making it necessary to investigate all financial markets together. In addition, during financial crisis, extreme events are more likely to occur in multiple countries, making it especially important to use international markets to study and understand the role of tail risk during the period. In this paper, I examine the role of tail risk, as being a global risk factor, in international financial markets by using around 60 thousand stocks from 40 countries from January 1980 to December I also examine in details about the role of tail risk during the global financial crisis happened in 2007 and The crisis started initially in a relatively small segment of the lending market, the subprime mortgage market, in the United States, then it spreads rapidly and violently across all economies in the world, both developed and developing, as well as across economic sectors. During the crisis, equity markets worldwide are affected and the extreme events happen more frequently than normal period. Many countries experiencing even sharper equity market crashes than the United States. After the crisis, researchers try to understand how and why the crisis in a small sector in US has spread so violently and transformed into a global financial crisis. There are various papers suggesting the possible sources of contagion such as transmission through banking exposure channel (Kaminsky and Reinhart (2000), Van Rijckeghem and Weder (2001), Caramazza, Ricci, and Salgano (2004), and Tong and Wei (2010, 2011)), banking policy channel (King (2009)), external exposure/segmentation channel (Mendoza and Quadrini (2010), Briere, Chapelle, and Szafarz (2012), Fratzscher (2012)), information asymmetries channel (Albuquerque, Bauer, and Schneider (2009), and Dumas, Lewis, and Osambela (2011)), domestic macroeconomic fundamentals channel (Ahnert and Bertsch (2013)), and global/common risk and liquidity channel (Bekaert et al. (2011) and Baker, Wurgler, and Yuan (2012)). 4

5 Although many studies have been done to understand the 2008 financial crisis, little studies ever investigate the role of tail risk during the time, while it is the perfect time to check how tail risk impacts asset prices. During the crisis, investors might care more about tail risk as extreme events can occur more frequently as firms tend to fail together. As a result, examining tail risk s role during financial crisis becomes crucial to deepen our understanding about the 2008 global financial crisis. I contribute to the literature as the first paper that empirically analyzing the role of tail risk in asset prices during the financial crisis on international financial markets. Previously the chief obstacle to investigate the effects of time-varying extreme event risk in asset markets was a viable measure of tail risk over time. There are three current approaches to measuring tail risk dynamics for stock returns: one based on option price data, one on high frequency return data, and the other on panel return data. Examples of the option-based approach include Bakshi, Kapadia, and Madan (2003), who study risk-neutral skewness and kurtosis; Bollerslev, Tauchen, and Zhou (2009), who examine how the variance risk premium relates to the equity premium; and Backus, Chernov, and Martin (2011) and Gao and Song (2013), who infer disaster risk premium from options. Tail estimate from high-frequency data is exemplified by Bollerslev and Todorov (2011). Panel estimation approach using daily return data is proposed by Jiang and Kelly (2014), who investigate the effects of time-varying extreme event risk in US market. All three approaches are powerful but the first two are subject to data limitations. The third approach can provide a time series of tail risk estimates as long as a large cross-section data is available, which allows me to construct tail risk estimates for most of the important stock markets around the world. In this paper, I examine tail risk as a globally priced risk factor in international asset pricing and provide empirical evidence that tail risk is a risk that investors are averse to, and it is priced internationally. In details, I first construct tail risk estimates for each country using stocks daily return data, and examine the characteristics of tail risks. If tail risk is a risk factor, then investors shall be averse to it and require high return to hold tail risky assets and portfolios. As a result, contemporaneously, tail risk should be positively correlated with aggregate market return as 5

6 investors are tail risk averse and market is subject to its tail risk. In addition, I found that timevarying tail exponent is highly persistent in some countries such as US, with AR(1) above 0.7. Therefore, I expect that in these countries, tail risk estimates should have strong predictive power for future extreme returns of individual stocks as investors might use it to predict future level of tail risk. To better distinguish the impact of tail risk from global part and local specific part in each country, I construct global tail risk as the value weighted countries tail risk, and local specific tail risk as the orthogonalized part of country tail risk with respect to global tail risk. I test weather tail risk is correlated or can forecast aggregate stock market returns using different types of tail risks constructed. Consistent with expectations that investors are averse to tail risk and require high return to hold tail risky assets and portfolios, contemporaneous regressions show that all tail risk measures are positively and significantly correlated with market aggregate return. Nevertheless, predictive regressions also show that all tail risk measures used can significantly and positively predict future market return in most of the countries, consistent with expectations, at the one month and one year horizons. Next, I test whether assets that better hedge tail risk command a relatively high price and earn low expected returns. In each country, I estimate individual stock s sensitivity to tail risk using past 60 month rolling window, and then form portfolios based stocks sensitivities. Among around 20 countries which account for more than 70% of total market weight, portfolios with high sensitivity earn significantly higher returns than portfolios with low sensitivity. Then I empirically examine whether tail risks are significantly priced in international financial markets, controlling for other risks. I also investigate which type of tail risks is significant in pricing (global/local tail risk), and in which type of countries that tail risk has significant price. I employ a cross-sectional regression framework and factor model regressions to investigate this issue. Overall, in most of the countries (around 30), global tail risk has significant and positive price, while corresponding local tail risk are only significant in 11 countries, most of which are classified by MSCI as emerging markets. In addition, global tail risk is shown to be more important than local tail risk in countries with high integration into the global financial market, 6

7 which are more open, and more developed countries. On the other hand, local tail risk is more important in countries with low integration into the global financial markets, which are less open, and less developed countries. After showing that global tail risk is a globally price risk factor, I then empirically examine the role of tail risk during a special time period 2007 to 2009 financial crisis. I show that tail risk affects investors risk aversion, thus during crisis time, when tail risk is high, investors shun away risky assets and fly to safety. Following the setting in Bakaert, Ehrmann, Fratzscher, and Mehl (2014), I found evidence suggesting that tail risk plays an important part in the spread of financial crisis by testing whether and how the dependence of factor exposures on tail risk changed during the crisis. The results suggest that tail risk is a possible source of contagion during financial crisis though the global/common risk channel. My findings contribute to several strands of literatures. Researchers have hypothesized that heavy-tailed shocks to economic fundamentals help explain certain asset pricing behavior that has proved otherwise difficult to reconcile with traditional macro-finance theory. Examples include the Rietz (1988) and Barro (2006) rare disaster hypothesis and its extensions to dynamic setting by Gabaix (2012), Gourio (2012), and Wachter (2013), as well as extensions of Bansal and Yaron s (2004) long-run risks model that incorporate fat-tailed endowment shocks (Eraker and Shaliastovich 2008; Bansal and Shaliastovich 2010, 2011; Drechsler and Yaron 2011). Using tail risk constructed using method from Jiang and Kelly (2014), mine is the first paper to directly document time-varying tail risks worldwide, show tail risk is significantly priced internationally, and provide evidence consistent with two key equity premium implications from above models. In addition, using international sample helps better investigate tail risk as a globally priced risk factor and provide more comprehensive out-of-sample test than just examining US markets alone. It also helps to better understand the cross-country variation of tail risk s impact on investors investment decisions, which depends on the level of integration of local market into the global financial market. Overall, I show that investors are tail risk averse, increases in tail risk raise the return required by investors to hold the tail risky assets, such as aggregate market returns. I also 7

8 show that tail risk affect cross-section of expected returns. High tail risk is associated with bad states of the world and high marginal utility. Hence, assets that hedge tail risk are more valuable and have lower expected returns than those that are exposed to tail risk. Consistent with expectations, the price of tail risk is positive and significant in most of the countries in my sample. There is the vast literature on international market integration, shock transmission, and contagion (Bekaert, Harvey, and Ng (2005), and Bakaert, Ehrmann, Fratzscher, and Mehl (2014)). I add to the literature by examining role of tail risk during financial crisis and show that tail risk acts as one of the sources of contagion during the period. In addition, my work also relates the growing literature on the global financial crisis of 2007 to This includes articles focusing on the drivers of the transmission of the crisis across firms and markets within the United States, such as Tong and Wei (2010), Almeida et al. (2012), and Diebold and Yilmax (2010), or articles taking a more macroeconomic perspective such as Eichengreen et al. (2012). The findings of this paper also have important implications for international investment and portfolio diversification. In the traditional capital asset pricing model, any systematic fluctuation of asset prices is captured solely by market risk. Therefore, the covariance of stocks returns with global market returns is the key to the success of international portfolio diversification. However, the findings in this paper show that the tail risk also systematically affects asset prices, and is a globally priced risk factor. Hence, investors should take tail risk into consideration when they seek to diversify away risks in global financial markets. The significant pricing of global tail risk in developed and open countries implies the importance of global investors and the relatively high degree of financial market integration in such countries. Supporting this view, Chan, Covrig, and Ng (2005) show that countries with these properties attract more global investors. The finding indicates that stocks that perform well when tail risk is high are appreciated by global investors as tail risk is an important concern, especially when investors rebalance their portfolios globally in the face of high likelihood of market wide extremes. 8

9 The rest of the paper is organized as the following. Section 1 presents the empirical framework and hypotheses. Section 2 briefly introduces the tail risk measure used in the paper, describes the data and the sample construction procedure. Section 3 provides empirical evidence on the pricing of country, and global tail risk in the international financial markets. Section 4 tests whether tail risk acts as a possible source of contagion during financial crisis. Section 5 concludes. I. Empirical Methodology This section describes the main assumption in the paper and empirical approach used to test the hypothesis. In this paper, the risk factors other than tail risk considered are well-known and wellstudied risk factors such as market factor in CAPM, small-minus-big (SMB) and high-minus-low (HML) factors in Fama-French factors model (Fama and French 1993), and momentum (MOM) factor. Tail risk, constructed each month using daily returns in each country following Jiang and Kelly s (2014) method, captures the common time-varying component of return tails based on assumption that an asset s return obeys the power law probability distribution. Applied to the pooled cross-section each month, it takes the form, (1), where is the kth daily return that falls below an extreme value threshold during month t in country i, and is the total number of such exceedances within month t in country i. The threshold is chosen by the econometrician and defines where the center of the distribution ends and the tail begins. It represents a suitably extreme quantile such that any returns below this cutoff are assumed to obey the specified tail distribution. Following Jiang and Kelly (2014), here I define as the fifith percentile of the cross-section each month in each country. After constructing tail risk for each country at each month, I construct global and local specific tail risks following Bekeart, Hodrick and Zhang (2009) in order to better distinguish the effect of 9

10 tail risk between global part and local specific part. The global tail risk at each month t,, is calculated as the value weighted average of country tail risks:, in which is country i s size at time t. Correspondingly, the local specific tail risk for each country i at time t,, is estimated from the following regression using whole sample observations:. As a result, captures the orthogonal/residual component in country tail risk estimate with respect to global tail risk at each time t. Similarly, I construct country market factors, and SMB/HML/MOM factors following method described on French s website, and then decompose the factors into 2 components, the part correlated with global factor (which is the value weighted average of factors at each time) and the local specific part for each country. 1.1 Tail Risk in International Financial Markets The main assumption I have is that investors marginal utility is increasing in tail risk. As a result, the stochastic discount factor is also increasing in tail risk. This assumption has three testable implications. The first implication is related to time series equity premium time series. As investors are tail risk averse, an increase in tail risk will increase the return required by investors to hold any tail risky assets. To test this, I estimate a simple regression of market return on tail risk, as stock market as a whole is subject to its tail risk, like any other assets:, (2), (3) in which is tail risk estimated from (1) for country i at time t, and is market return for country i at time t. In contemporaneous regression (2) I use monthly market returns as dependent variable, and in predictive regressions (3) I use next one month or one year market return. All the observations used in the regression are at monthly frequency. To address the overlapping estimation window problem in the predictive regression, I adjusted statistical 10

11 inferences using Newey-West standard error correction with lag equal to 1 or 12, respectively. To be consistent with my assumption, coefficient estimate on tail risk,, in (2) and (3) should be positive and significant. As different countries have different level of integration into the global market, investors can be sensitive to global tail risks in some countries, while investors in other countries can be more sensitive to local specific tail risks rather than the global tail risks. For example, in a small and open market like Singapore, which is highly integrated into global market, investors might invest mainly in global portfolios, thus are more sensitive to global tail risk. On the other hand, in closed market which lowly integrates with global market, investors might hold portfolios mainly contain local assets, thus are more sensitive to local specific tail risk. Overall, investors would demand different returns to hold portfolios with different exposure to global or local specific tail risk. In order to test this hypothesis, I construct global tail risk,, and local specific tail risk,, based on g country tail risk,,and estimate the following regression:, (4), (5) and,, (6), (7) in which is global tail risk at time t, and is local specific tail risk for country i at time t. Global tail risk is constructed as the value weighted average of countries tail risks at time t. And local specific tail risk is the orthogonal component in country tail risk estimate with respect to global tail risk. Similarly, as investors are averse to tail risk, I expect coefficient estimate on tail risks, and, in (4), (5), (6), and (7) should be positive and significant. 11

12 The second implication is related to cross-sectional stock returns. As investors are averse to tail risk, they will price assets with better hedge to tail risk higher and require lower expected returns. To test this, I sort stocks based on their sensitivity to tail risk and compare returns between high and low sensitivity groups. In line with the aggregate analysis above, I estimate country tail risk sensitivities and global tail risk sensitivities of individual stocks with regression of the form:, (8), (9) where is the monthly return for stock j in country i at time t, is tail risk estimated from (1) for country i at time t, is global tail risk at time t, and is local specific tail risk for country i at time t. The regression is conducted each month using past 60 months observations. In line with the intuition behind aggregate tail risk regressions, I expect that stocks with high values of are those that most sensitive to tail risk in country j, and are deeply discounted when tail risk is high and have high expected returns going forward. On the other hand, stocks with low or negative are good tail risk hedges because, when tail risk rises, their prices rise contemporaneously, and their expected future returns fall. Overall, I expect that stocks in the high sensitivity group should on average earn higher returns than stocks in low sensitivity group. The third implication, closely related to the second, is that tail risk should be priced across time, even after controlling for other risks. To test this, I conduct Fama-Macbeth regression and I expect that tail risk should be positively and significantly priced:, (10) in which and are loadings on global and local specific tail risks for stock j in country i at time t estimated from rolling window regression (9). is control variable for stock 12

13 j in country i at time t. In the regression, the control variables used are size, market to book ratio, and market/smb/hml/mom betas. I expect to be positive and significant in countries that are highly integrated with world financial market, and to be positive and significant in countries that are lowly integrated with world financial market. In order to check whether tail risk can be priced predictively, I also estimate rolling regressions and obtain predictive loadings on global and local tail risks, at each month t:. (11) And then using the predictive loadings obtained from (11), I perform cross-sectional regression at each month in each country:. (12) To be consistent with my expectation, the coefficient estimates should be positive and significant in countries that are highly integrated with world financial market, and should be positive and significant in countries that are lowly integrated with world financial market, with persistent local specific tail risk. For robustness checks, I also perform cross-sectional regression across countries, developed or emerging markets, or different regions. When the regression is performed within more than one country, country dummies are added to control for unknown country-specific effects. I estimate the following model each month to obtain contemporaneous tail risk price estimates across all countries, developed/emerging markets, or five different regions: (13) 13

14 , where and are loadings on global and local specific tail risks for stock j in country i at time t estimated from rolling window regression (9). country i. is the dummy variable for To examine whether tail risk can be priced predictively, similar to (12), I use the predictive loadings obtained from (11) to perform cross-sectional regression at each month across all countries, developed/emerging markets, or five different regions:. (14) Overall, I expect results from (13) and (14) are consistent with results from (10) and (12), that is positive and significant in countries that are relatively highly integrated with world financial market, and is positive and significant in countries that are lowly integrated with world financial market. 1.2 Tail Risk during Financial Crisis After investigating whether tail risk is a globally priced risk factor, I then proceed to empirically examine the role of tail risk during a special time period 2007 to 2009 financial crisis, during which tail risk is high and extreme events tend to happen more frequently. First, I examine whether tail risk, as I expected, is higher during this crisis period:, (15), (16) in which is a dummy variable which equals to 1 if month t is during the crisis period. is the dummy variable for country i. If extreme events are more likely to occur during financial crisis, I expect that estimated from (15) and (16) should be positive and significant. During the crisis, it is also possible that investors change their risk exposure towards tail risk accordingly, as investors might shy away from tail risky assets and flee to safe assets. Also, 14

15 investors might be more averse to tail risk by requiring a higher risk premium during the crisis. Therefore, I examine whether stocks risk exposures are different during the financial crisis, and whether investors are more averse to tail risk by estimating following regressions:, (17), (18), (19), (20) in which and are loadings on global and local specific tail risks for stock j in country i at time t estimated from rolling window regression (9). is a dummy variable which equals to 1 if month t is during the crisis period. is the dummy variable for country I firm j. If investors shy away from risky assets during the financial crisis, I expect that estimated in (17)-(20) should be positive and significant. Following the setting in Bakaert, Ehrmann, Fratzscher, and Mehl (2014), investors risk aversion may be influenced by level of global risks, during crisis time. As a result, investors shun risky assets and flee into safer assets when their risk aversions substantially increase during the crisis. As tail risk is a globally priced risk factor, it is important to examine the role of tail risk affecting investors investment decisions during the crisis time. In order to test this, I formulate an international factor model with 4 kinds of factors: global & local market factor, global & local SMB, global & local HML, and global & local MOM. The full model is the following:, (21), (22), (23) 15

16 , (24), where is monthly excess return for stock j in country i at time t (i.e. the return minus the three-month US T-bill rate in monthly unit). is the dividend yield of the stock j (so that the expected excess return is a linear function of the lagged excess return and dividend yield). is a vector of the factors (i.e. global and local market factors, etc). is a crisis dummy at time t. It equals 1 if time t is in the crisis. and are global and local specific tail risk variables that is designed to capture time and cross-sectional variation in factor exposure. When only including global and local market factors, the model potentially embeds 2 CAPMS as special cases: a domestic CAPM when on the global market factor is set to zero; and a world CAPM when on the local market factor is set to zero. When including global and local market factors, as well as global and local SMB and HML factors, the model embeds 2 Fama-French three factors model as special cases: a domestic Fama-French three factors model when on the global factors are set to zero; and a world Fama-French three factors model when on the local factors are set to zero. Similarly, when including global and local market, SMB, HML and MOM factors, the model embed 2 four factors model as special cases as well: a domestic four factors (Fama-French three factors plus momentum) model, and a world four factors model. Following naming convention in Bakaert, Ehrmann, Fratzsher, Mehl (2014), the contagion model is the full model where everything is included. When is excluded from the model for all time, I refer to it as the interdependence model. And when both and tail risks ( and ) are excluded, I refer to it as the base model in which factor exposure are the same no matter in the crisis or not. Under the null hypothesis, the co-movement between various stocks is determined by the factor exposures and the variance-covariance matrix of the factors. As the factors are orthogonal, interdependence model can potentially fit the observed increase in correlations during the crisis through an increase in factor volatilities. The model works because the correlation between a stock return and a factor is the beta with respect to the factor, times the ratio of factor to stock return volatility, which can be shown to be increasing in factor s volatility. 16

17 As volatilities tend to dramatically increase during crises, increased correlations are thus not necessarily indicative of contagion (Forbes and Rigobon (2002)). In the contagion model, in equation (15) captures contagion unrelated to the observable factors of the model. If is substantially negative for a set of stocks, then these stocks show excess co-movement during the crisis. In this paper, I used global and local specific tail risk as a potential channel and test whether risk aversion to tail risk can help to explain the contagion during financial crisis. If tail risk is a potential channel of contagion during crisis, then we should observe the following: first, is significantly negative in contagion model; second, adjusted R- square from contagion model should be highest among three models; third, contagion model should be able to predict stock returns during crisis time better than other two models. II. Data Daily returns are calculated using a daily total return index, which is adjusted for stock splits and dividend payments, from Datastream for all available stocks from 45 countries for the period of January 1980 to December US stock market daily and monthly data are obtained from CRSP and Compustat during the sample period. According to the MSCI, there are 23 developedmarket and 23 emerging-market countries. The initial sample covers stocks from 46 countries. To build a reliable sample, I applied the following screening procedures following to those in Lee (2011) and Hou, Karoyli, and Kho (2011). For a stock to be included in the sample, it should have positive market capitalization data, as well as positive shares outstanding and stock price, in US dollars at the end of previous month. I select only stocks from major exchanges, which are defined as those in which the majority of stocks for a given country are traded. Most countries in the sample have a single major exchange except for China (Shenzhen and Shanghai stock exchanges), Germany (Frankfurt stock exchange and Xetra), Japan (Osaka and Tokyo stock exchanges), and the US (Amex, NYSE, and Nasdaq). I include only common stocks by excluding stocks with special features. First I exclude stocks with Datastream defined type as 17

18 American Depositary Receipt, Closed-End Fund, Exchange-Traded Fund, Genussschein (Profit Participation Certificate), Global Depositary Receipt, Non-voting Depository Receipt, Preference Share, Warrant. In addition, I exclude stocks with special features by examining the names of the securities. Examples of such name filters are as follows. I extracted stocks with names including REIT, REAL EST, GDR, PF, PERF, or PRF because these terms could represent real estate investment trusts, global depository receipts, or preferred stocks. In Belgium, stocks with names including AFV and VVPR are dropped as they have preferential dividend or tax incentives. In Canada, income trusts excluded by removing stocks with names including INC.FD. In Mexico, shares of the types ACP and BCP are removed because they are convertible into series A and B shares, respectively, after one year. In France, ADP and CIP type of stocks are dropped because they carry no voting rights but carry prefenrential dividend rights. In Germany, GSH type of shares is excluded because they offer fixed dividends and no voting rights. In Italy, RSP shares are dropped due to their nonvoting provisions. For US stocks, I only include stock with share code 10 or 11. To avoid survivorship bias, I retain all data for dead stocks in the sample and exclude stock observations after the dead date provided by Datastream. The monthly sample is constructed based on daily data after implementation of all these screens described above. The proxy for tail risk is calculated following method in Jiang and Kelly (2014), which calculated using lower 5% daily return data in each month for each country. To make sure that a country has sufficient cross-sectional distribution of daily data to construct tail risk estimates, I require that a country should have at least 100 stocks with daily returns available in a month to be included in the sample from In addition, a country has to have more than 60 month of tail risk estimates to be included in the sample. As a result, my final sample contains firms from 40 countries. I use the 30-day US Treasury bill as a risk-free asset, which is obtained through K. French s data library. Table 1 reports countries summary statistics. The first 3 columns report countries name, market development, and countries region. Next 4 columns report the beginning year of coverage, number of firms, number of firm-month and firm-day observations included in the sample for 18

19 each country. In total there are firm-month observations and firm-day observations included in the sample. Country US contains the most number of firms, as well as firm-month/firm-day observations across all countries, while country Austria contains the least. The total number of stocks in the sample is and varies across countries and years. During the sample period, the country with largest number of stocks in the sample is the US (7406 firms in 1998), and the country with smallest number of stocks is Mexico (101 firms in 1992). The starting year of sample coverage also varies across countries. Egypt, which has the shortest sample period, has data beginning with 1999, while the starting year is 1980 for most of the developed countries. The last four columns of Table 1 show the time series average of crosssectional monthly median return, size, and book to market ratio in each country, as well as the time series average of market total size of each country. The returns are all calculated using total return index denominated in US dollar. The time series average of cross-sectional median varies a lot across different countries, with monthly return ranging from -0.60% in India to 0.37% in China, firm size ranging from 2.13 Million in India to Million in Spain, and book to market ratio ranging from 0.34 in China to 1.62 in Russia. Across all countries, US have the largest market size over time, and Czech Republic is the smallest market in the sample. Table 2 reports summary statistics of countries tail risk estimates. Tail risk is constructed each month using daily returns in each country using equation (1), following Jiang and Kelly s (2014) method, and it captures the common time-varying component of return tails. The global tail risk, GTail, is calculated as the value weighted average of country tail risks. The local specific tail risk, LTail, is the orthogonal component in country tail risk estimate with respect to global tail risk. Figure 1 plot the time series of global tail risk and tail risk estimated for United States. In the graph, global and US tail risks appear to fluctuate together. During the technology boom, both globally and US tail risks retreat sharply but briefly, then rising to the highest post-2000 level. And bother are high during the recent financial crisis and recessions. 19

20 Table 2 reports the summary statistics of countries tail risk estimates. Across all countries, tail risk estimates appear to be persistent over time. 33 out of 40 countries have AR(1) coefficient bigger than 0.5, and can be as high as 0.90 in France and India. Countries time series mean, standard deviation, and median of tail risks are reported in Table 2. Russia and Peru, with mean of tail risk equal to 1.16 and 1.17, appear to have largest tail risk on average across time in all countries. These two also have highest standard deviation, and median of tail risks across countries. The last 6 columns in Table 2 report the correlation coefficient between country tail risk and global/us tail risks and corresponding p value. All countries tail risk estimates significantly correlate with global tails at 5%. Most developed countries tail risk significantly correlate with US tails at 5% level, except Austria, Israel, and Italy. Among 18 emerging markets, only 10 have tail risks significantly correlate with US tails. III. Pricing of Tail Risks Investors in the market are risk averse and their marginal utility is increasing in risks. I assume that investors are also averse to tail risk as tail risk is a type of risk in the market. A high tail risk increases the return required by investors to hold any tail risky portfolios, such as market portfolio. In addition, as tail risk is quite persistent in most of the countries, investors might only dynamically adjust their discount rates in response to shocks that are informative about future level of tail risks. Empirical I test whether tail risk positively correlates with contemporaneous market return and positively predicts future market return. In addition, assets that better hedge tail risk will command a relatively high price and earn low expected returns as investors require higher returns to hold tail riskier portfolios. I tested this implication by comparing average returns of assets to their estimated tail risk sensitivities cross-sectionally. Last, tail risk should be positively priced in the market and I test this using Fama-Macbeth approach. 3.1 Tail risk and stock market returns If investors are tail risk averse, a high tail risk increases the return required by investors to hold any tail risky portfolios, even market portfolio. As a result, I expect tail risk to be positively 20

21 correlates with contemporaneous market return. In addition, as tail risk is quite persistent in some countries, investors might only dynamically adjust their discount rates in response to shocks that are informative about future level of tail risks, thus tail risk should be able to positively predict future market return in countries with highly persistent tail risks. I test above hypothesis whether tail risk positively correlates contemporaneous market return and positively predicts future market return by estimating contemporaneous regression (2) and predictive regression (3),, (2), (3) in which is tail risk estimated from (1) for country i at time t, and is market return for country i at time t. In contemporaneous regression (2) I use monthly market returns as dependent variable, and in predictive regressions (3) I use next one month or one year market return. As different countries have different level of integration into the global market, as well as development, market quality, and macro conditions, investors can be sensitive to global tail risks in some countries, while investors in other countries can be more sensitive to local specific tail risks rather than the global tail risks. As a result, investors would demand different returns to hold portfolios with different exposure to global or local specific tail risk. In order to test this hypothesis, I decompose country tail risk,, into global tail risk,, and local specific tail risk,, and estimate contemporaneous regressions (4) and (6), and predictive regressions (5) and (7):, (4), (5) and, 21

22 , (6), (7) in which is global tail risk at time t, and is local specific tail risk for country i at time t. Global tail risk is constructed as the value weighted average of countries tail risks at time t. And local specific tail risk is the orthogonal component in country tail risk estimate with respect to global tail risk. I adjust statistical inferences using Newey-West standard error correction for the overlapping data in predictive regression (3), (5), and (7). Table 3 reports the contemporaneous regression results for (2), (4), and (6). Panel A reports the summary of estimated coefficients across 40 countries in the sample. Panel B results the value weighted or equally weighted coefficient estimates,, for countries in different regions. In all countries, country tail risk,, is positively correlated with market return, among which 37 countries have positive and 5% significant coefficients, except Hong Kong, Malaysia, and India. Global tail risk,, correlated with market returns positively in all countries, and significant in 39, except China. It is conceivable that investors in China are not so averse to global tail risk as the stock market in China is highly regulated and protected by the government from the rare disasters. When controlling for local specific tail risk, global tail risk still correlated with market returns positively in all countries, and significant in 39. On the other hand, Local tail risk,, positively correlates with market return in 34 countries, and significant in 24 countries (9 out of 18 emerging countries, and 15 out of 32 developed countries). In markets like Austria, Hong Kong, Singapore where market is open and country tail risk is highly correlated with global tail risk, investors might only averse to global tail risk that significantly correlates with stock market returns. Table 4 reports the predictive regression results for (3), (5), and (7). Similarly to Table 3, panel A reports the summary of estimated coefficients and panel B reports the value or equally weighted coefficient estimates,, across different country. Overall in 30 countries, country tail 22

23 risk,, can positively predicts future next one month market return, among which 7 countries (Austria, Portugal, Unite States, Cezech Republic, Peru, Philippines, and Thailand) have positive and 5% significant coefficients. These 7 countries all have highly persistent country tail risks, which is the key assumption that we have in order to observe the predictive power of country s tail risk. As if tail risk is persistent in a country, investors might only dynamically adjust their discount rates in response to shocks that are informative about future level of tail risks. In addition, global tail risk,, predicts next one month market returns positively in 37 countries, and 5% significant in 8 (Austria, New Zealand, Portugal, Czech Republic, Egypt, Greece, India, and Philippines). When controlling for local specific tail risk, global tail risk still predict next one month market return positively in 37 countries, and 5% significant in 8. On the other hand, Local tail risk,, positively predicts next one month market return in 28 countries, and 5% significant in 2 countries (United States, and Thailand). United States has the largest financial market in the world and its investors not only averse to global tail risk, but also require a compensation to hold local specific tail risky market portfolios. In Thailand, future one month return can be predicted by local tail risk instead of global tail risk, probably because its country tail risk lowly correlate with global tails at When predicting next one year market return, loadings on country tail risk is positive in 29 countries, among which 8 are 5% significant (Austria, Hong Kong, Israel, United States, Czech Republic, Peru, Philippines, and Russia). Global tail risk,, predicts next one year market returns positively in 38 countries, 10% significant in 17 countries, and 5% significant in 12 (Austria, Canada, New Zealand, Portugal, Spain, Brazil, Czech Republic, Egypt, Greece, Poland, Russia, and South Africa), When controlling for local specific tail risk, global tail risk still predict next year month market return positively in 38 countries, and 5% significant in 12. On the other hand, Local tail risk,, positively predicts next one year market return in 25 countries, and 5% significant in 5 countries. 23

24 In summary, regression results of (2) (7) presented in Table 3 and Table 4 are consistent with my expectations that tail risk is positively correlated with contemporaneous market return as investors are tail risk averse and require a higher return to hold a portfolio with higher tail risk. In addition, consistent with expectation, tail risk can predict future market returns in some countries, most of which have quite persistent tail risk time series, indicating that in these countries investors might only dynamically adjust their discount rates in response to shocks that are informative about future level of tail risks. 3.2 Tail risk and cross-section of expected stock returns I next test whether tail risk helps explain differences in expected returns across stocks, consistent with the priced tail risk hypothesis. If investors are averse to tail risk, stocks with high loadings on tail risk will be discounted more steeply and thus have higher expected returns going forward. On the other hand, stocks with low or negative tail risk loadings serve as effective hedges and therefore will have comparatively higher prices and lower expected returns. I estimate country tail risk sensitivities and global tail risk sensitivities of individual stocks with regression (8) and (9) each month, using the most recent 60 months of data:, (8), (9) where is the monthly return for stock j in country i at time t, is tail risk estimated from (1) for country i at time t, is global tail risk at time t, and is local specific tail risk for country i at time t. Stocks are then sorted into 10 portfolios in each country based on their estimated country tail risk loadings or global tail risk loadings. For each month I long portfolios with highest tail risk loadings and short portfolios with lowest tail risk loadings and track average monthly valueweighted portfolio returns of this long-short strategy in a twelve-month or one-month post- 24

25 formation window. Portfolio returns are out-of sample, as there is no overlap between data used for estimating loadings and data used in the post-formation performance period. To address the overlapping estimation window problem, I adjust standard error with lag equal to 12 (if postformation window is one year) or 1 (if post-formation window is one month) using Newey-West method. Table 5 reports the annualized long-short portfolio returns. Panel A reports the summary of portfolio spreads across countries. Panel B reports detailed value or equally weighted spreads of portfolios returns across all countries, or in different markets, or in different regions. On average across all countries, if post-formation window is one year, stocks in the highest global tail risk loading portfolios earn value-weighted average annual returns 6.35% higher than stocks in the lowest portfolio, with a t-statistics of When post-formation window is one month, stocks in the highest global tail risk loading portfolios earn value-weighted average annual returns 5.06% higher than stocks in the lowest portfolio, with a t-statistics of Comparing developed markets and emerging markets, return difference between stocks in the highest and lowest global tail risk loading portfolios is significant, but always higher in emerging markets. As emerging markets are in general less developed, vulnerable to global disaster event, and has weaker enforcement of investor protections, investors might require a higher return to hold stocks with higher exposure to global tail risk. Among the emerging countries, return difference in emerging Europe/Middle East/Africa are particular high as investor in these market probably exposed more to global markets than investors in emerging Asia. The return difference between stocks in the highest and lowest global tail risk loading portfolios is positive, but not significant in US, consistent with results from the aggregate analysis. When sorting stocks based on loadings on country tail risk, on average across all countries, stocks in highest loading portfolios on average earn 3.60% higher value-weighted annual returns if post-formation window is one year, or 3.11% is post-formation window is one month, than stocks in lowest loading portfolios. Comparing developed and emerging markets, the return difference in both markets are positive but only significant in developed markets. As the country 25