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An Ignored Risk Factor in International Markets: Tail Risk

Yanchu Wang

Sep 13th

, 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 2014. 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.

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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 2014. 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;

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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.

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Therefore, using global market makes it possible to investigate such cross-country or cross-

regional 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 2014. I also examine in details about the role of tail risk during the global financial

crisis happened in 2007 and 2009. 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)).

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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

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investors are tail risk averse and market is subject to its tail risk. In addition, I found that time-

varying 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,

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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 2007-2009 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

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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 2009. 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.

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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 well-

studied 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

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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

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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.

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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

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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)

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, 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). is the dummy variable for

country i.

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,

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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)

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, (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.

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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 2014. US stock market daily and monthly data are obtained from

CRSP and Compustat during the sample period. According to the MSCI, there are 23 developed-

market and 23 emerging-market countries. The initial sample covers 62552 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

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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 1980-2014. 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

64799 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

19

each country. In total there are 10428828 firm-month observations and 218459208 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 64799 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 cross-

sectional 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 301.09 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.

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

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,

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

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 0.34.

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.

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 value-

weighted portfolio returns of this long-short strategy in a twelve-month or one-month post-

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 post-

formation 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 6.64. 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 3.84. 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

26

tail risk is the combination of global tail risk and local specific tail risk, results could be

insignificant as stocks with the lowest loadings of country tail risk could be those have high

loadings on global tail risk yet very low loadings on local specific tail risk.

In addition, return difference between stocks in highest and lowest country tail risk loading

portfolios is positive and 5% significant in regions such as developed Europe. It is also

significant in United States, 7.04% if post-formation is one year, or 4.85% if post-formation is

one month.

In summary, results are broadly consistent with expectations and priced tail risk hypothesis, that

tail risk helps explain differences in expected returns across stocks.

3.3 Tail risk and its risk price

Previous results, that tail risk correlates with market aggregate return, tail risk can predict future

market return if persistent and tail risk helps explain cross-sectional differences in expected

returns, are consistent with priced tail risk hypothesis. In the tests, country’s tail risk measure is

not as clean as using global and local specific tail risks, as country’s tail risk captures the mixture

of both global and local specific tail risks. Therefore, in this section, I investigate the pricing of

global and local specific tail risks using cross-sectional regressions.

I employ individual stocks as test assets because an analysis at the level of individual stocks

provides the following benefits. First, the use of individual stocks as test assets helps to avoid

potentially spurious results that could arise when characteristic-based portfolios are used as test

assets (Brennan, Chordia, and Subrahmanyam (1998), Berk (2000)). Second, potential loss of

information contained in each stock can be minimized by performing empirical tests at the level

of individual stock. Third, a stock-level analysis could increase the power of the test by

providing ample observations for empirical tests. It is also suitable for controlling for individual

stock characteristics, such as market capitalization and book-to market ratio. On the cost side, the

loading estimated at the level of individual stock generally have a higher level of noise than

27

those estimated at the portfolio level and possibly decrease the significance of the coefficients

estimates.

The individual stock global and local specific tail risk betas, and , are estimated from

previously mentioned equation (9). To avoid look-ahead bias, I use rolling window of 60 months

to obtain a time series of betas for each stocks. This 5-year rolling window starts at either

January 1980 or the first month in which stocks are present in the sample. The window rolls

forward at monthly interval. A stock should have at least 36 monthly returns within the 5 year

window in order to estimate its betas. Similarly, I obtained stock’s market, SMB, HML, and

MOM betas.

The sample period is relatively short. In addition, unlike the case of US, the quality of data from

other countries is not guaranteed (Ince, and Porter (2006), Bekaert, Harvey, and Lundblad

(2007)). Given these potential problems, I preform the cross-sectional regressions not only

within each country, but also across countries, developed or emerging markets, or different

regions. When the regression is performed within more than one country, I run regression at each

month with country dummy variables to provide an interpretation of the coefficient estimates in

terms of within-country effects and to control for unknown country-specific effects (McLean,

Pontiff, and Watanabe (2009)).

3.3.1 Pricing for tail risks by country

I present the results of the cross-sectional regression by each country in this sub-section. Table 6

reports the summary of time series average of risk price estimated for global and local specific

risk from equation (10),

∑ , (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

28

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.

The first two rows in table 6 reports the averages of tail risks price across all countries. No

matter what control variable is included in the regression, global tail risk is consistently

positively and significantly priced on average across all countries, while local specific tail risk is

not even marginally significant. When average across developed or emerging markets, global

and local specific tail risk are both positively significantly priced in developed markets, while

only global tail risk is significantly priced among emerging markets.

I then average across five different geographic regions: Developed Asia, Developed Europe,

Emerging Asia, Emerging Europe/Middle East/Africa, and Latin America. Countries included in

each group are specified in Table 1. Among Developed countries, only across developed Europe

both global and local specific tail risks are significantly priced. In developed Asia only local

specific tail risk is significantly price. In addition, among emerging markets, global tail risk is

only significant priced in emerging Asia, but not in emerging Europe/Middle East/Africa, which

is conceivable as countries included in this group are very different from each other in terms of

economic, political, and geographic conditions.

I also check whether tail risk can be priced predictively. Table 7 reports the summary of time

series average of predictive risk price estimated for global and local specific risk from equation

(12),

∑ . (12)

in which and are predictive loadings on global and local specific tail risks for stock j in

country i at time t estimated from rolling window regression (11). is control

variable for stock j in country i at time t. Similar to (1), the control variables used are size,

market to book ratio, and market/SMB/HML/MOM betas.

29

The first two rows in table 7 reports the averages of tail risks price across all countries. No

matter what control variable is included in the regression, global tail risk is positively priced, but

only with marginal significance on average across all countries, while local specific tail risk is

not significant and sometime has negative sign. When average across developed or emerging

markets, global and local specific tail risk has similar predictive risk price as across all countries.

The averages across five different geographic regions are also reported. Among Developed

countries, global tail risk has marginally significant risk price in developed Asia. And among

emerging markets, global tail risk only has marginally significant risk price as well.

In summary, the results are consistent with hypothesis that tail risk has positive risk price. And in

some countries, the predictive risk price for tail risk is also positive and significant.

3.3.2 Pricing for tail risks across countries, markets, and regions

For robustness checks, I also perform cross-sectional regression (13) across countries, developed

or emerging markets, or different regions, and I present the results in this sub-section. Table 8

reports the summary of time series average of risk price estimated for global and local specific

risk, from equation (13),

∑ ∑ (13)

, 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). is the dummy variable for

country i.

No matter what control variable is included in the regression, across all countries,

developed/emerging markets, as well as three different regions, global tail risk is always

positively and significantly priced at 5%, except Developed Asia and Emerging Europe/Middle

East/Africa where countries differ significantly from each other. In most cases, global tail risk

price is always more significant than local specific risk price, except in Developed Europe. In

30

addition, local specific tail risk appears to be significantly priced in Developed Europe and Latin

America, indicating that investors in those countries require compensation to hold local tail risky

portfolios.

Table 9 reports the summary of time series average of predictive risk price estimated for global

and local specific risk from equation (14),

∑ ∑ . (14)

The results are mixed. In most cases, both tail risks don’t have significant predictive risk price,

regardless the cross-sectional regression is performed across all countries, or in different regions.

However, when pooling all countries together, local tail risk price appear to be slightly more

significant than global tail risk price, but is just marginally significant. When comparing between

developed or emerging markets, results are a bit stronger in developed markets than emerging

markets.

In summary, the results are consistent with hypothesis that tail risk is a globally priced risk factor.

It has positive risk price and investors require higher return to hold tail riskier assets/portfolios.

IV. Tail risk as contagion channel during financial crisis

In previous section, I show that tail risk is a globally priced risk factor. In this section, I will

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)

31

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, investors might shy away from tail risky assets and flee to safe assets, and

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.

Table 10 reports results of (15)-(20). Overall, consistent with expectations, estimated from (15)

– (20) are positive and significant. Not only tail risk is relatively higher during the crisis period,

but also the risk price of tail risk is higher during the time.

Following Bakaert, Ehrmann, Fratzscher, and Mehl (2014), during crisis time, investors shun

risky assets and flee into safer assets when their risk aversions substantially increase. Therefore,

investors’ risk aversion may be influenced by level of global risks, as during crisis time tail risk

is high and extreme events tend to happen more frequently, As a result, as tail risk is a globally

32

priced risk factor, it is important to examine the role of tail risk affecting investors’ investment

decisions. In this section, I investigate whether tail risk serves as a possible contagion channel

during the financial crisis.

First I construct 2 types of factors – global factors, and local specific factors. The global factor is

the value-weighted country factors across all countries in the sample, and the local specific factor

is the orthogonal component in a country’s factor with respect to global factor. Similar to

Bakaert, Ehrmann, Fratzscher, Mehl (2014), I formulate the 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 described in section 1 equation (15) - (18).

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 Bakaert, Ehrmann, Fratzsher, Mehl (2014), 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

33

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.

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 that helps to explain the co-movements among stocks during financial crisis.

Mounting evidence suggests that international asset prices are quite sensitive to global measures

of risk aversion, and risk aversion of investors may substantially increase during the crisis,

making them shun risky assets and flee into safer assets. It is shown from the previous results

that investors are averse to global tail risk across all countries, and in some countries, local

specific tail risk is also priced. Therefore, here I test whether risk aversion to tail risk can help to

explain the contagion during financial crisis.

Table 10 reports the model estimation results for base model, interdependence model, and

contagion model (full model). Consistent with expectation, is negative for global tail risk and

significant at 1% level, suggesting that global tail risk serves a potential channel of contagion

during crisis. In addition, factor exposures to global and local financial factors varies with tail

risks, also suggesting tail risks could be a potential channel of contagion during crisis. The

substantial positive correlation between the interdependence and contagion coefficient indicates

that portfolios that were exposed to the factors before the crisis experienced the strongest

contagion during the crisis. This is true both for international and domestic exposure. Note that

global tail risk contributes more to the change in exposure to global financial factor, while local

specific tail risk contribute more to the change in exposure to local financial factor. This is

34

expected as investors who invest in global market care more about global tail risk, while

investors focus on local market are more averse to local specific tail risk. Adjusted r square is

higher in contagion model (12.62%) by 1 basis point, suggesting that contagion model can fit the

co-movement of stock returns the better.

What would the model predict for the crisis? If the model correctly specified, the factor

exposures are sufficient to predict the relative vulnerability across the different stocks across

different countries during the financial crisis. Table 11 reports the how well the base model,

interdependence model, and contagion model can predict stock return performance during

financial crisis across countries. The first column in Table 11 reports the real value-weighted

average excess return during financial crisis for each country. The second to fourth columns

report the deviation between the real excess returns and base model prediction, interdependence

model prediction, and contagion model prediction during financial crisis across different

countries. The computation is straightforward as we obtain estimated return stock each stock i in

country j at time t, and then obtain from these the total predicted return and compare this to the

total actual return during the crisis period.

On average across all countries, stocks monthly returns are negative, -2.88%, during financial

crisis. The countries that affected the most are in Europe and US, as well as most emerging

countries such as South Africa, Taiwan, and Thailand, where countries were affected not only in

terms of equity market performance, but also in terms of economic growth and activity. The

contagion model would predict some of the European countries to be moderately affected or not

affected, while the interdependence model predicts some of the emerging countries to be

moderately affected. The average deviation of base model from actual returns is -0.44%, and the

average deviation of interdependence model from actual returns is -0.44%. Contagion model can

predict stock performance during the crisis period better than the base model and contagion

model, with the average deviation equal to 0.12%. Note that both base model and

interdependence model over-predict the severity of the crisis on average across all countries, but

contagion model under-predicts the severity of the crisis.

35

In summary, the contagion model using global and local tail risks as a possible channel of

contagion during crisis can fit stock returns internationally the best, and also predict stock return

performance better than base model and interdependence model during the financial crisis.

Therefore, the evidence is consistent with the expectation that investors tail risk aversion

increases during the crisis, making them shun risky assets and flee into safer assets such as US

government bond.

V. Conclusion

This paper empirically investigate an equilibrium asset pricing relation with tail risks, using a

large sample of assets covering 64799 stocks from 40 countries around the world during the

period of Jan 1980 to Dec 2014.

The empirical evidence presented in the paper is supportive that tail risks are priced in

international financial markets, even after controlling for size, book-to-market, and other risks

such as market, SMB, HML, and MOM. Specifically, when tail risk is high, the

contemporaneous market return is high as investors require higher return to hold tail risky

portfolios. In the countries where tail risks are persistent, tail risk can predict future market

return as investors only adjust their discounting factors in response to the shocks in tail risks. In

addition, tail risk help to explain cross-sectional return difference as investors require higher

return to hold stocks that are not a good hedge to tail risk when tail risk is high. Results from

cross-sectional regression show that tail risk is positively and significantly priced, especially

global tail risk in more developed markets.

These findings imply that tail risk is an important concern when investors rebalance their

portfolios in the face of down markets or markets with high risk of extreme events. Therefore,

the findings have implications for international portfolio diversification, because tail risk is

another dimension to consider in addition to traditional risks.

36

In this paper, I also try to understand whether tail risk acts as a possible global transmission

channel of the crisis in equity markets. From the perspective of a factor model with global and

domestic factors, I find evidence of tail risk as a source of contagion. In addition to providing

evidence that tail risk is a potential channel of contagion during financial crisis, I also found

evidence that global tail risk is more important when global investors are present – specifically,

their exposure to global financial factor is more correlated with global tail risk than local specific

tail risk. This finding sheds some lights on the importance of possible mechanism where tail risk

is served as source of contagion during financial crisis.

37

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40

Table 1.Summary statistics.

Table 1 provide summary statistics of data coverage of 40 countries in the sample from 1980 Jan 1st to 2014 Dec 31

st. Column

"Start" reports the start of coverage for each country. Column "Type" reports whether the country is classified by MSCI as

developed (D) or emerging (E). Column " Region Group" reports the region group of the country classified by MSCI. Column

"N(firm-month)“ reports the number of firm-month observations included in the sample for each country. Column "N(firm-

day)“ reports the number of firm-day observations included in the sample for each country. Column "N(firm)" reports the number

of firms included in the sample for each country. Column "Return", "Size", and "BM" report the time series mean of cross-

sectional median monthly return, size, and book to market ratio for each country, respectively. The returns are all calculated using

total return index denominated in US dollar.

Country Type Region Group Start N(firm-

month)

N(firm-

day) N(firm) Return Size BM

Australia D Developed Asia 1980 521372 11327564 3260 0.04% 29.87 0.74

Austria D Developed Europe 1992 37819 821453 233 -0.01% 82.76 0.76

Belgium D Developed Europe 1986 74352 1615629 358 0.18% 47.86 0.79

Canada D Latin America 1980 595953 12946375 3003 -0.09% 27.51 0.70

Denmark D Developed Europe 1988 74290 1613583 381 0.01% 46.48 0.87

Finland D Developed Europe 1994 37364 811627 236 0.11% 100.98 0.66

France D Developed Europe 1980 392158 8518247 2213 0.28% 89.56 0.75

Germany D Developed Europe 1980 242095 5258541 1506 -0.01% 118.99 0.60

Hong Kong D Developed Asia 1985 258901 5627539 1661 -0.31% 84.82 1.01

Israel D Developed Europe 1986 187262 4070227 878 -0.15% 21.62 0.77

Italy D Developed Europe 1986 102272 2220648 624 -0.28% 168.94 0.76

Japan D Developed Asia 1980 868398 18872066 3610 0.08% 268.09 0.78

Netherlands D Developed Europe 1980 106726 2318560 405 0.16% 44.24 0.84

New Zealand D Developed Asia 1988 59551 1294051 335 0.18% 24.89 0.74

Norway D Developed Europe 1985 84084 1825851 579 0.00% 55.48 0.78

Portugal D Developed Europe 1990 43895 953728 221 -0.05% 18.06 0.95

Singapore D Developed Asia 1984 127372 2767475 796 0.15% 83.60 0.90

Spain D Developed Europe 1989 60451 1313214 351 -0.04% 301.78 0.70

Sweden D Developed Europe 1984 176301 3830048 1041 0.15% 42.08 0.60

41

Switzerland D Developed Europe 1983 94518 2053886 428 0.32% 199.09 0.70

UK D Developed Europe 1980 1294505 28118395 6082 -0.08% 24.92 0.67

US D US 1980 2300019 41843439 18967 0.10% 174.30 0.58

Brazil E Latin America 1997 33128 719703 295 -0.32% 326.85 0.58

Chile E Latin America 1989 63443 1378717 316 0.20% 85.87 0.79

China E Emerging Asia 1993 332295 7225248 2626 0.37% 324.67 0.34

Czech Republic E Emerging Europe/Middle

East/Africa 1994 55173 1198880 277 -0.12% 2.49 1.16

Egypt E Emerging Europe/Middle

East/Africa 1999 42510 924345 470 -0.56% 15.91 0.79

Greece E Emerging Europe/Middle

East/Africa 1991 73494 1596567 414 -0.45% 48.82 0.91

India E Emerging Asia 1990 612174 13312736 3493 -0.60% 2.13 1.20

Korea E Emerging Asia 1984 406905 8828573 2723 -0.25% 42.10 1.10

Malaysia E Emerging Asia 1986 211080 4587078 1081 0.09% 63.60 0.94

Mexico E Latin America 1992 48509 1053979 273 -0.45% 131.03 0.82

Peru E Latin America 1994 54734 1189449 301 -0.12% 9.50 0.98

Philippines E Emerging Asia 1993 53036 1152655 301 -0.58% 46.73 0.98

Poland E Emerging Europe/Middle

East/Africa 1998 78567 1707883 1007 -0.45% 23.41 0.84

Russia E Emerging Europe/Middle

East/Africa 1998 72903 1584067 742 -0.07% 48.39 1.62

South Africa E Emerging Europe/Middle

East/Africa 1990 148401 3222309 962 -0.40% 43.50 0.69

Taiwan E Emerging Asia 1989 178940 3889467 1017 -0.51% 198.38 0.69

Thailand E Emerging Asia 1988 147479 3205201 857 -0.16% 41.44 0.86

Turkey E Emerging Europe/Middle

East/Africa 1991 76399 1660205 476 -0.26% 55.23 0.77

42

Table 2.Summary statistics of country tail risk estimates

This table provides summary statistics of tail estimates for 40 countries in the sample from 1980 Jan 1st to 2014 Dec 31

st. Column

"Start" reports the start of coverage for each country. Column "N(firm-month)“ reports the number of firm-month observations

included in the sample for each country. Column "N(firm-day)“ reports the number of firm-day observations included in the

sample for each country. Column "N(firm)" reports the number of firms included in the sample for each country. Column "Mean

Tail" reports the time series average of tail estimates for each country. Column ”STD Tail" reports the standard deviation of tail

estimates for each country. Column "Median Tail" reports the time series median of tail estimates for each country.

Corr(Country Tail, Global Tail) Corr(Country Tail, US Tail)

Country AR(1) Mean

Tail

STD

Tail

Median

Tail Global Tail P Value US Tail P Value

AUSTRALIA 0.81 0.58 0.12 0.55 0.21 <.0001 0.50 <.0001

AUSTRIA 0.73 0.62 0.14 0.60 0.60 <.0001 0.06 0.2872

BELGIUM 0.53 0.55 0.10 0.55 0.62 <.0001 0.09 0.0802

CANADA 0.80 0.54 0.08 0.54 0.63 <.0001 0.47 <.0001

DENMARK 0.56 0.58 0.09 0.58 0.23 <.0001 0.51 <.0001

FINLAND 0.58 0.47 0.08 0.46 0.56 <.0001 0.67 <.0001

FRANCE 0.90 0.51 0.15 0.55 0.75 <.0001 -0.12 0.0118

GERMANY 0.87 0.46 0.13 0.44 0.51 <.0001 -0.22 <.0001

HONG KONG 0.70 0.43 0.08 0.42 0.52 <.0001 -0.04 0.3991

ISRAEL 0.70 0.50 0.13 0.48 0.69 <.0001 -0.06 0.2493

ITALY 0.86 0.48 0.14 0.43 -0.27 <.0001 0.57 <.0001

JAPAN 0.78 0.37 0.06 0.36 0.63 <.0001 -0.24 <.0001

NETHERLANDS 0.53 0.51 0.08 0.50 0.63 <.0001 0.33 <.0001

NEW ZEALAND 0.50 0.67 0.13 0.66 0.23 <.0001 0.35 <.0001

NORWAY 0.66 0.53 0.10 0.52 0.26 <.0001 0.48 <.0001

PORTUGAL 0.48 0.69 0.11 0.68 0.40 <.0001 0.14 0.0161

SINGAPORE 0.79 0.45 0.12 0.41 0.47 <.0001 -0.22 <.0001

SPAIN 0.45 0.42 0.07 0.41 0.38 <.0001 0.27 <.0001

SWEDEN 0.75 0.55 0.11 0.53 0.54 <.0001 0.16 0.0027

SWITZERLAND 0.59 0.46 0.08 0.46 0.45 <.0001 0.39 <.0001

43

UNITED

KINGDOM 0.47 0.66 0.15 0.66 0.75 <.0001 0.15 0.0016

United States 0.73 0.44 0.05 0.44 0.21 <.0001 1.00

Brazil 0.59 0.55 0.18 0.52 0.39 <.0001 0.47 <.0001

Chile 0.59 0.66 0.17 0.64 0.50 <.0001 0.05 0.3745

China 0.20 0.29 0.11 0.28 0.18 0.0042 0.11 0.0899

Czech Republic 0.71 0.48 0.19 0.47 0.36 <.0001 -0.08 0.2016

Egypt 0.63 0.43 0.21 0.44 0.22 0.0021 -0.02 0.7460

Greece 0.76 0.35 0.13 0.34 0.39 <.0001 0.09 0.1394

India 0.90 0.45 0.18 0.42 0.14 0.0185 0.30 <.0001

Korea 0.87 0.52 0.20 0.48 0.65 <.0001 -0.27 <.0001

Malaysia 0.72 0.40 0.10 0.39 0.34 <.0001 -0.33 <.0001

Mexico 0.42 0.56 0.13 0.55 0.47 <.0001 0.28 <.0001

Peru 0.55 1.17 0.47 1.06 0.33 <.0001 -0.07 0.2750

Philippines 0.69 0.59 0.15 0.55 0.46 <.0001 0.11 0.0571

Poland 0.78 0.46 0.12 0.45 0.58 <.0001 0.40 <.0001

Russia 0.72 1.16 0.64 0.90 0.30 <.0001 0.36 <.0001

South Africa 0.57 0.68 0.13 0.68 0.42 <.0001 0.33 <.0001

Taiwan 0.46 0.30 0.11 0.32 0.34 <.0001 0.07 0.2579

Thailand 0.77 0.45 0.13 0.47 0.34 <.0001 -0.34 <.0001

Turkey 0.38 0.34 0.07 0.33 0.22 0.0002 0.22 0.0002

44

45

Table 3. Contemporaneous Regression Results

This table reports the result of contemporaneous regression of market return on tail estimates (regression

results for equation (2), (4), and (6)). Panel A reports the number of countries with coefficients having

positive sign and significance at 5%. Panel B reports the average of coefficient estimates for countries in

each region groups. The dependent variable is the monthly market return. In the first two columns of

panel A, the independent variable used in regression is either country tail risk estimates, or global tails. In

the last two columns of panel A, the independent variable used in regression is global tails and

orthogonalized local specific tails. The sample period is from 1980 Jan 1st to 2014 Dec 31st.

Panel A. Estimated coefficients count

Global+Local Specific Tail

Country

Tail

Global

Tail Global Tail Local Tail

# coefficients having correct

sign 40 40 40 34

# coefficients having correct

sign and significant at 5% 37 39 39 24

# coefficients having wrong sign

and significant at 5% 0 0 0 1

46

Panel B. EW and VW average of coefficient estimates

Global+Local Specific Tail

Country Tail Global Tail Global Tail Local Tail

EW Coef T Coef T Coef T Coef T

World 0.17 9.35 0.53 15.46 0.53 15.70 0.10 5.58

Developed 0.18 9.00 0.45 14.55 0.45 14.84 0.10 4.56

Emerging 0.17 4.93 0.63 10.55 0.63 10.81 0.11 3.40

Developed Asia 0.11 6.60 0.36 7.47 0.36 8.52 0.04 1.04

Developed Europe 0.18 8.34 0.50 13.40 0.50 13.57 0.10 4.65

Emerging Asia 0.14 3.71 0.45 7.86 0.46 8.57 0.10 2.79

Emerging Europe/Middle

East/Africa 0.21 2.74 0.85 21.20 0.85 19.12 0.12 1.60

Latin America 0.16 3.53 0.52 4.14 0.52 4.08 0.10 2.69

US 0.40 9.13 0.28 6.54 0.29 7.26 0.36 8.24

Global+Local Specific Tail

Country Tail Global Tail Global Tail Local Tail

VW Coef T Coef T Coef T Coef T

World 0.23 10.09 0.36 13.41 0.37 14.02 0.17 6.46

Developed 0.25 8.01 0.32 14.78 0.33 15.95 0.18 4.86

Emerging 0.15 5.59 0.52 7.93 0.53 8.29 0.11 4.45

Developed Asia 0.11 11.34 0.25 6.04 0.27 7.58 0.01 0.25

Developed Europe 0.14 6.48 0.42 14.94 0.42 14.46 0.06 2.25

Emerging Asia 0.16 5.27 0.36 6.04 0.38 6.31 0.13 4.32

Emerging Europe/Middle

East/Africa 0.17 2.27 0.86 23.48 0.85 22.69 0.10 1.57

Latin America 0.15 3.62 0.50 3.94 0.50 3.85 0.09 2.64

US 0.40 9.13 0.28 6.54 0.29 7.26 0.36 8.24

47

Table 4. Predictive Regression Results.

This table reports the result of predictive regression of future market return on tail estimates (regression

results for equation (3), (5), and (7)). Panel A reports the number of countries with coefficients having

positive sign and significance at 5%. Panel B reports the average of coefficient estimates for countries in

each region groups, with next one month market return used as dependent variable. Panel C reports the

average of coefficient estimates for countries in each region groups, with next one year market return

used as dependent variable. In the first 4 columns of panel A, summary of regression results reported

with the dependent variable used as next one month market return, and in the last four columns regression

results reported with next one year market return used as dependent variable. Under each set of results

with different dependent variables, the first two columns having independent variable used in regression

to be either country tail risk estimates, or global tails. In the last two columns, the independent variable

used in regression is global tails and orthogonalized local specific tails. The sample period is from 1980

Jan 1st to 2014 Dec 31st.

Panel A. Estimated coefficients count

Next one month Next one year

Global+Local

Specific Tail

Global+Local

Specific Tail

Country

Tail

Global

Tail

Global

Tail

Local

Tail

Country

Tail

Global

Tail

Global

Tail

Local

Tail

# coefficients having

correct sign 30 37 37 28 29 38 38 25

# coefficients having

correct sign and significant

at 5%

7 8 8 2 8 12 12 5

# coefficients having

wrong sign and significant

at 5%

0 0 0 1 0 0 0 3

48

Panel B. EW and VW average of coefficient estimates – Next one month return

Global+Local Specific Tail

Country Tail Global Tail Global Tail Local Tail

EW Coef T Coef T Coef T Coef T

World 0.03 4.05 0.12 6.86 0.12 6.86 0.02 1.88

Developed 0.03 2.82 0.08 3.88 0.08 3.88 0.01 0.96

Emerging 0.04 2.90 0.17 6.56 0.17 6.56 0.02 1.64

Developed Asia 0.02 0.95 0.05 1.42 0.05 1.42 0.01 0.41

Developed Europe 0.02 2.13 0.09 3.35 0.09 3.35 0.00 0.45

Emerging Asia 0.05 1.86 0.12 4.13 0.12 4.13 0.04 1.64

Emerging Europe/Middle East/Africa 0.04 2.07 0.26 7.12 0.26 7.12 0.02 0.67

Latin America 0.01 1.25 0.08 6.09 0.08 6.09 0.00 -0.01

US 0.11 2.06 0.02 0.46 0.02 0.47 0.11 2.10

Global+Local Specific Tail

Country Tail Global Tail Global Tail Local Tail

VW Coef T Coef T Coef T Coef T

World 0.04 3.53 0.05 4.84 0.05 4.84 0.02 1.99

Developed 0.04 3.27 0.03 3.69 0.03 3.69 0.03 1.86

Emerging 0.00 0.28 0.13 6.47 0.13 6.47 0.00 -0.25

Developed Asia -0.02 -0.65 0.02 1.51 0.02 1.51 -0.04 -1.02

Developed Europe 0.00 -0.03 0.04 2.81 0.04 2.81 -0.02 -2.01

Emerging Asia -0.01 -0.24 0.10 6.35 0.10 6.35 -0.01 -0.38

Emerging Europe/Middle East/Africa 0.03 1.85 0.25 7.29 0.25 7.29 0.02 0.73

Latin America 0.01 1.19 0.08 7.02 0.08 7.02 -0.01 -0.56

US 0.11 2.06 0.02 0.46 0.02 0.47 0.11 2.10

49

Panel C. EW and VW average of coefficient estimates – Next one year return

Global+Local Specific Tail

Country Tail Global Tail Global Tail Local Tail

EW Coef T Coef T Coef T Coef T

World 0.29 4.94 1.09 7.04 0.13 1.67 1.09 7.03

Developed 0.25 2.88 0.86 7.23 0.06 0.47 0.85 7.25

Emerging 0.33 4.47 1.37 4.53 0.22 2.39 1.37 4.51

Developed Asia 0.29 1.33 0.66 2.67 0.21 0.59 0.67 2.72

Developed Europe 0.18 1.92 0.95 6.40 -0.05 -0.44 0.94 6.37

Emerging Asia 0.43 4.10 0.67 2.82 0.46 3.47 0.66 2.83

Emerging Europe/Middle East/Africa 0.41 3.34 2.50 7.50 0.16 1.03 2.49 7.44

Latin America 0.07 0.97 0.72 1.23 -0.09 -1.22 0.72 1.22

US 1.08 2.48 0.30 0.87 0.30 0.94 1.06 2.34

Global+Local Specific Tail

Country Tail Global Tail Global Tail Local Tail

VW Coef T Coef T Coef T Coef T

World 0.45 5.23 0.60 6.89 0.28 2.40 0.60 6.87

Developed 0.50 4.04 0.50 7.25 0.31 1.79 0.49 7.25

Emerging 0.21 4.03 1.04 4.50 0.15 2.08 1.03 4.51

Developed Asia 0.10 0.47 0.55 4.60 -0.25 -0.63 0.54 4.55

Developed Europe -0.02 -0.22 0.69 6.54 -0.33 -3.06 0.69 6.55

Emerging Asia 0.26 2.93 0.59 3.32 0.26 2.22 0.59 3.35

Emerging Europe/Middle East/Africa 0.29 3.34 2.16 9.49 0.13 1.21 2.15 9.45

Latin America 0.14 1.67 0.98 2.04 -0.10 -1.48 0.98 2.02

US 1.08 2.48 0.30 0.87 0.30 0.94 1.06 2.34

50

Table 5.Long-short Portfolio Performance.

This table reports performance of long-short value weighted portfolios over time. The portfolios are

created by sorting stocks' sensitivity to tail risks in the market, in which the sensitivity is estimated using

past 60 month rolling window from equation (9). Panel A reports the summary of portfolio spreads across

countries. Panel B reports the spread of portfolios formed based on firms' sensitivity to tail estimates in

the country. The reported return spread is annualized. The sample period is from 1980 Jan 1st to 2014

Dec 31st.

Panel A. Summary of portfolio performance

Global Tail -

by year

Country Tail - by

year

Global Tail -

by month

Country Tail - by

month

# positive spread 36 31 33 31

# positive spread and

significant at 5% 28 25 21 25

# negative spread and

significant at 5% 3 5 4 6

Panel B. Portfolio performance

Global Tail - by

year

Country Tail -

by year

Global Tail - by

month

Country Tail -

by month

EW Return T Return T Return T Return T

World 6.35% 6.64 3.60% 3.35 5.06% 3.84 3.11% 2.21

Developed 5.24% 4.84 4.85% 4.62 3.30% 2.78 5.48% 4.64

Emerging 7.69% 4.69 2.07% 1.04 7.21% 2.89 0.22% 0.08

Developed Asia 6.31% 3.51 5.27% 1.47 3.78% 2.48 7.00% 2.55

Developed Europe 5.08% 3.49 4.75% 4.48 3.01% 1.79 5.26% 3.53

Emerging Asia 2.88% 1.96 1.28% 0.44 0.28% 0.16 -2.33% -0.53

Emerging Europe/Middle

East/Africa 10.71% 3.57 4.76% 1.66 12.12% 2.32 3.71% 0.78

Latin America 10.09% 4.49 -0.59% -0.13 9.77% 4.41 -0.81% -0.23

VW Return T Return T Return T Return T

World 4.20% 5.37 5.30% 7.26 3.99% 5.43 3.83% 5.45

Developed 3.26% 4.37 5.55% 8.26 3.30% 5.74 4.49% 7.97

Emerging 8.15% 4.51 4.25% 2.14 6.90% 3.40 1.09% 0.56

Developed Asia 5.08% 9.60 3.35% 1.72 2.84% 2.20 2.42% 1.95

Developed Europe 5.58% 5.15 5.25% 5.62 4.18% 3.98 5.62% 6.10

51

Emerging Asia 3.31% 2.33 5.28% 3.04 1.55% 1.71 2.06% 0.74

Emerging Europe/Middle

East/Africa 15.32% 4.51 9.29% 3.43 15.60% 3.65 4.04% 1.16

Latin America 10.62% 5.14 -1.60% -0.35 9.15% 4.15 -2.23% -0.68

52

Table 6.FM Regression Results.

This table reports summary of FM regression results with global and local specific tails used in the

regression (10). On each month in each country, I conduct cross-secitonal regression of stock return on its

sensitivity to tail risks in the market, with control variables such as size, market to book ratio,

MKT/SMB/HML/MOM betas included in the regression. The stock’s tail risk sensitivity is estimated

using past 60 month rolling window. The sample period is from 1980 Jan 1st to 2014 Dec 31st.

g_ltail and

l_ltail

g_ltail and

l_ltail, size, mb

g_ltail and

l_ltail &

CAPM, size,

mb

g_ltail and

l_ltail & FF3,

size, mb

g_ltail and

l_ltail & FF4,

size, mb

Tails Coef T Coef T Coef T Coef T Coef T

World g_tail 0.0055 6.87 0.0040 5.13 0.0028 3.02 0.0059 6.29 0.0056 2.29

l_tail 0.0026 0.75 0.0023 0.75 0.0021 0.60 0.0010 0.25 -0.0070 -0.82

Developed g_tail 0.0053 5.08 0.0043 4.27 0.0036 3.03 0.0076 7.30 0.0103 10.05

l_tail 0.0069 3.10 0.0053 2.22 0.0058 2.11 0.0061 2.32 0.0069 2.63

Emerging g_tail 0.0058 4.51 0.0035 2.90 0.0018 1.24 0.0039 2.50 -0.0001 -0.03

l_tail -0.0027 -0.37 -0.0013 -0.21 -0.0024 -0.34 -0.0052 -0.65 -0.0240 -1.32

Developed Asia g_tail 0.0038 14.26 0.0035 4.92 0.0024 3.88 0.0064 3.67 0.0095 4.38

l_tail 0.0065 1.94 0.0026 1.18 0.0021 1.20 0.0010 0.24 0.0011 0.21

Developed

Europe g_tail 0.0059 3.85 0.0046 3.11 0.0039 2.25 0.0082 5.87 0.0108 8.23

l_tail 0.0074 2.49 0.0064 1.93 0.0074 1.90 0.0085 2.48 0.0096 2.96

Emerging Asia g_tail 0.0042 2.47 0.0034 2.11 0.0017 1.49 0.0036 2.68 0.0046 2.74

l_tail 0.0032 0.69 0.0026 0.47 0.0020 0.35 0.0019 0.33 0.0011 0.21

Emerging

Europe/Middle

East/Africa

g_tail 0.0048 2.10 0.0015 0.65 0.0008 0.21 0.0038 0.97 -0.0084 -0.66

l_tail -0.0017 -0.10 -0.0035 -0.31 -0.0098 -1.30 -0.0160 -1.22 -0.0569 -1.31

Latin America g_tail 0.0095 4.97 0.0067 5.08 0.0039 3.11 0.0052 5.19 0.0071 3.89

l_tail -0.0090 -0.89 -0.0009 -0.06 0.0044 0.19 0.0022 0.10 -0.0071 -0.35

53

Table 7.FM Predictive Regression Results.

This table reports summary of FM regression results with global and local specific tails used in the

regression (12). On each month in each country, I conduct cross-secitonal regression of stock return on its

past sensitivity to tail risks in the market with control variables such as size, market to book ratio,

MKT/SMB/HML/MOM betas included in the regression. The stock’s tail risk sensitivity is estimated

using past 60 month rolling window. The sample period is from 1980 Jan 1st to 2014 Dec 31st.

g_ltail and

l_ltail

g_ltail and

l_ltail, size, mb

g_ltail and

l_ltail &

CAPM, size,

mb

g_ltail and

l_ltail & FF3,

size, mb

g_ltail and

l_ltail & FF4,

size, mb

Tails Coef T Coef T Coef T Coef T Coef T

World g_tail 0.0033 10.77 0.0020 4.80 0.0015 3.49 0.0028 0.97 0.0022 0.78

l_tail 0.0020 2.97 0.0018 1.19 0.0014 0.93 -0.0048 -0.25 -0.0060 -0.32

Developed g_tail 0.0034 11.35 0.0020 3.85 0.0017 2.93 0.0032 0.76 0.0027 0.62

l_tail 0.0013 1.91 0.0018 1.18 0.0016 0.86 -0.0073 -0.26 -0.0077 -0.27

Emerging g_tail 0.0031 3.74 0.0020 2.88 0.0006 1.03 0.0007 0.78 0.0004 0.47

l_tail 0.0047 3.14 0.0018 0.62 0.0005 0.18 0.0059 1.99 0.0012 0.25

Developed

Asia

g_tail 0.0030 14.22 0.0022 2.96 0.0022 3.73 0.0022 3.12 0.0020 2.51

l_tail -0.0004 -0.38 -0.0014 -1.11 -0.0010 -0.76 -0.0015 -1.25 -0.0008 -0.60

Developed

Europe

g_tail 0.0025 5.15 0.0018 2.47 0.0004 0.38 0.0049 0.53 0.0048 0.52

l_tail -0.0005 -0.49 0.0026 1.22 0.0015 0.39 -0.0273 -0.44 -0.0268 -0.43

Emerging Asia g_tail 0.0007 0.85 0.0006 1.42 -0.0005 -0.94 -0.0009 -1.26 -0.0011 -1.66

l_tail 0.0058 4.48 0.0058 2.75 0.0044 1.77 0.0073 3.01 0.0075 2.86

Emerging

Europe/Middle

East/Africa

g_tail 0.0059 4.69 0.0024 1.50 0.0026 1.88 0.0037 2.41 0.0039 2.99

l_tail 0.0037 1.85 -0.0017 -0.26 -0.0025 -0.61 -0.0075 -1.51 -0.0229 -2.26

Latin America g_tail 0.0063 13.96 0.0033 6.00 0.0016 1.55 0.0016 0.71 0.0007 0.36

l_tail 0.0032 0.74 0.0015 0.54 -0.0024 -0.29 0.0116 2.13 0.0076 1.69

54

Table 8.World FM Regression Results

This table reports pooled FM regression (13) across countries, markets, or regions. On each month in all

countries/markets/region, I conduct cross-secitonal regression of stock return on its sensitivity to tail risks,

with country fixed effect included in the regression, as well as other control variables such as size, market

to book ratio, MKT/SMB/HML/MOM betas. The stock’s tail risk sensitivity is estimated using past 60

month rolling window. The sample period is from 1980 Jan 1st to 2014 Dec 31st.

g_ltail and

l_ltail

g_ltail and

l_ltail, size, mb

g_ltail and

l_ltail & CAPM,

size, mb

g_ltail and

l_ltail & FF3,

size, mb

g_ltail and

l_ltail & FF4,

size, mb

Tails Coef T Coef T Coef T Coef T Coef T

World g_tail 0.0054 2.98 0.0058 3.00 0.0051 2.57 0.0055 2.80 0.0049 2.63

l_tail 0.0018 1.59 -0.0002 -0.19 0.0000 -0.02 0.0011 0.93 0.0010 0.91

Developed g_tail 0.0056 2.95 0.0061 3.05 0.0056 2.70 0.0058 2.84 0.0051 2.67

l_tail 0.0015 1.21 -0.0004 -0.33 -0.0002 -0.16 0.0011 0.90 0.0010 0.82

Emerging g_tail 0.0053 2.48 0.0041 1.97 0.0040 1.87 0.0046 2.20 0.0045 2.18

l_tail 0.0046 1.23 0.0039 1.14 0.0024 0.69 0.0037 1.04 0.0039 1.15

Developed

Asia

g_tail 0.0034 1.42 0.0036 1.55 0.0017 0.71 0.0018 0.72 0.0014 0.58

l_tail 0.0057 2.75 0.0056 2.60 0.0051 2.18 0.0059 2.67 0.0057 2.73

Developed

Europe

g_tail 0.0050 2.53 0.0060 2.92 0.0047 2.21 0.0058 2.81 0.0062 2.97

l_tail 0.0087 3.13 0.0062 2.23 0.0064 2.31 0.0072 2.71 0.0071 2.74

Emerging Asia g_tail 0.0060 2.62 0.0051 2.31 0.0039 1.68 0.0051 2.24 0.0056 2.40

l_tail 0.0062 1.32 0.0058 1.31 0.0047 0.97 0.0060 1.28 0.0057 1.32

Emerging

Europe/Middle

East/Africa

g_tail 0.0007 0.32 -0.0017 -0.67 -0.0030 -1.27 -0.0023 -0.94 -0.0029 -1.19

l_tail -0.0003 -

0.08

-0.0029 -0.61 -0.0054 -1.01 -0.0031 -0.60 -0.0019 -0.41

Latin America g_tail 0.0059 2.57 0.0062 2.60 0.0075 2.77 0.0080 3.10 0.0099 3.85

l_tail 0.0124 3.39 0.0100 2.81 0.0089 2.42 0.0047 1.37 0.0036 1.05

55

Table 9.World Predictive FM Regression Results.

This table reports pooled predictive FM regression (14) across countries, markets, or regions. On each

month in all countries/markets/region, I conduct cross-secitonal regression of stock return on its past

sensitivity to tail risks, with country fixed effect included in the regression, as well as other control

variables such as size, market to book ratio, MKT/SMB/HML/MOM betas. The stock’s tail risk

sensitivity is estimated using past 60 month rolling window. The sample period is from 1980 Jan 1st to

2014 Dec 31st.

g_ltail and

l_ltail

g_ltail and

l_ltail, size, mb

g_ltail and

l_ltail &

CAPM, size,

mb

g_ltail and

l_ltail & FF3,

size, mb

g_ltail and

l_ltail & FF4,

size, mb

Tails Coef T Coef T Coef T Coef T Coef T

World g_tail 0.0024 3.06 0.0014 1.98 0.0013 1.98 0.0012 1.83 0.0012 1.77

l_tail 0.0014 2.44 0.0009 1.39 0.0010 1.61 0.0011 2.06 0.0012 2.20

Developed g_tail 0.0023 2.67 0.0015 2.00 0.0014 2.07 0.0013 1.90 0.0013 1.85

l_tail 0.0011 1.74 0.0007 1.14 0.0009 1.39 0.0010 1.74 0.0010 1.83

Emerging g_tail 0.0021 1.69 0.0005 0.38 0.0006 0.53 0.0007 0.65 0.0007 0.62

l_tail 0.0043 2.24 0.0031 1.55 0.0043 2.03 0.0039 2.04 0.0040 1.81

Developed

Asia

g_tail 0.0025 2.83 0.0027 3.07 0.0025 2.94 0.0022 2.68 0.0021 2.49

l_tail 0.0001 0.13 -0.0009 -0.94 -0.0009 -0.98 -0.0011 -1.24 -0.0006 -0.80

Developed

Europe

g_tail 0.0025 2.34 0.0013 1.56 0.0013 1.54 0.0010 1.25 0.0012 1.42

l_tail -0.0007 -0.61 -0.0008 -0.65 -0.0006 -0.51 0.0004 0.33 0.0002 0.18

Emerging Asia g_tail 0.0019 1.44 0.0006 0.43 0.0007 0.57 0.0007 0.59 0.0007 0.57

l_tail 0.0051 2.36 0.0035 1.48 0.0044 1.84 0.0041 1.80 0.0045 1.81

Emerging

Europe/Middle

East/Africa

g_tail 0.0027 2.28 0.0004 0.35 0.0005 0.45 0.0003 0.26 0.0006 0.51

l_tail 0.0005 0.26 0.0023 0.97 0.0030 1.29 0.0030 1.22 0.0014 0.55

Latin America g_tail 0.0062 4.61 0.0023 1.69 0.0019 1.46 0.0016 1.15 0.0013 0.87

l_tail 0.0037 2.14 0.0045 2.35 0.0041 2.26 0.0032 1.85 0.0022 1.18

56

Table 10. Tail Risk during Financial Crisis

This table provides regression results (15)-(20) of level of tail risk, its risk exposure, as well as its risk

price during 2008 financial crisis. The first columns reports results about level of tail risk, estimated from

(15) and (16). The second columns reports results about exposure to tail risk, estimated from (17) and

(18). And the last four columns reports results about price of tail risk, estimated from (19) and (20). The

sample period is from 1980 Jan 1st to 2014 Dec 31st.

g_ltail and

l_ltail

g_ltail and

l_ltail,

size, mb

g_ltail and

l_ltail &

CAPM,

size, mb

g_ltail and

l_ltail &

FF3, size,

mb

g_ltail and

l_ltail &

FF4, size,

mb

Level Exposure Price

GTail 0.05 0.09 0.06 0.06 0.05 0.05 0.04

T 4.63 2.13 24.97 23.25 15.11 13.19 2.24

LTail 0.01 0.07 0.01 0.01 0.02 0.01 -0.01

T 3.36 3.14 1.35 1.82 2.09 1.79 -0.21

57

Table 11.Contagion Estimation Results

This table reports pooled regression results (equation (21)-(24) using all countries observations) results

Following BEFM2014 model. The dependent variable is stock return. The control variables are past

month excess return, past dividend yield, past size, and past market to book ratio. The factors used are

global and local specific factors constructed following Bekeart, Hodrick and Zhang (2009). The tail risks

used are past one month global and local specific tails. Panel A reports results using model based on

CAPM. Panel B reports results using model based on Fama-French 3 factors. Panel C reports results

suing model with risk factors of Fama-French 3 factors and the momentum factor. The sample period is

from 1980 Jan 1st to 2014 Dec 31st.

Panel A. CAPM

Base Model Interdependence

Model Contagion Model

PARMS T PARMS T PARMS T

Intercept 2.90E-03 41.54 2.85E-03 40.37 3.51E-03 46.97

l1exmret -7.48E-03 -19.03 -7.47E-03 -19.00 -9.00E-03 -22.75

l1dy 8.83E-09 2.44 8.92E-09 2.47 9.01E-09 2.49

l1size -2.50E-09 -1.46 -2.53E-09 -1.48 -2.40E-09 -1.40

l1mb 1.76E-08 1.22 1.77E-08 1.22 1.80E-08 1.24

g_mkt 9.69E-01 616.07 7.99E-01 53.03 5.69E-01 33.89

l_mkt 9.61E-01 637.09 9.36E-01 55.28 7.42E-01 40.59

Global Mkt * Tails g_mkt_g_ltail . . 3.66E-01 11.19 8.15E-01 22.69

g_mkt_l_ltail . . 1.43E-01 9.52 1.89E-01 11.06

Local Mkt * Tails l_mkt_g_ltail . . 4.80E-02 1.34 4.43E-01 11.56

l_mkt_l_ltail . . -2.53E-01 -23.17 -2.37E-01 -20.95

Crisis * Mkts g_mkt_crisis . . . . 1.12E+00 23.94

l_mkt_crisis . . . . 1.73E+00 25.97

Crisis * Tails crisis_g_ltail . . . . -1.51E-02 -24.45

crisis_l_ltail . . . . 1.57E-03 0.67

Crisis * Mkts * Tails g_mkt_crisis_g_ltail . . . . -2.45E+00 -23.04

g_mkt_crisis_l_ltail . . . . -1.07E-01 -2.80

l_mkt_crisis_g_ltail . . . . -3.78E+00 -25.14

l_mkt_crisis_l_ltail . . . . -1.82E-01 -4.36

R-squared 16.08% . 16.10% . 16.12% .

58

Panel B. Fama-French 3 Factors

Base Model Interdependence

Model Contagion Model

PARMS T PARMS T PARMS T

Intercept 1.56E-03 22.27 1.54E-03 21.32 1.55E-03 20.12

l1exmret -2.64E-02 -68.05 -2.64E-02 -68.04 -2.64E-02 -67.62

l1dy 7.92E-09 2.24 7.85E-09 2.22 7.82E-09 2.21

l1size -2.58E-09 -1.53 -2.56E-09 -1.52 -2.52E-09 -1.50

l1mb 1.40E-08 0.99 1.38E-08 0.97 1.38E-08 0.97

g_mkt 9.94E-01 627.80 9.32E-01 57.09 8.80E-01 49.50

l_mkt 9.78E-01 658.84 1.09E+00 65.47 1.04E+00 57.27

g_smb -5.08E-01 -160.94 -4.03E-01 -12.69 -4.17E-01 -12.61

l_smb -6.41E-01 -379.85 -5.72E-01 -31.55 -4.35E-01 -21.95

g_hml 7.03E-02 27.53 3.31E-01 11.08 2.98E-01 9.59

l_hml 1.07E-01 67.53 2.49E-01 14.35 2.41E-01 12.40

Global Mkt * Tails g_mkt_g_ltail . . 1.37E-01 3.84 2.32E-01 6.04

g_mkt_l_ltail . . 2.45E-01 15.48 1.88E-01 10.45

Local Mkt * Tails l_mkt_g_ltail . . -2.38E-01 -6.77 -1.23E-01 -3.23

l_mkt_l_ltail . . -4.96E-02 -4.53 -8.06E-02 -7.07

Global SMB * Tails g_smb_g_ltail . . -2.37E-01 -3.53 -1.87E-01 -2.68

g_smb_l_ltail . . -5.07E-01 -16.10 -4.81E-01 -14.41

Local SMB * Tails l_smb_g_ltail . . -1.53E-01 -4.05 -4.33E-01 -10.59

l_smb_l_ltail . . -2.63E-01 -20.35 -1.64E-01 -12.01

Global HML * Tails g_hml_g_ltail . . -5.66E-01 -8.75 -4.81E-01 -7.21

g_hml_l_ltail . . -2.20E-01 -8.70 -2.22E-01 -8.04

Local HML * Tails l_hml_g_ltail . . -2.99E-01 -8.28 -2.90E-01 -7.22

l_hml_l_ltail . . -2.25E-02 -2.02 5.19E-02 4.47

Crisis * Tails crisis_g_ltail . . . . 3.66E-03 5.61

crisis_l_ltail . . . . 7.77E-05 0.03

Crisis * Mkts g_mkt_crisis . . . . -8.80E-02 -1.23

l_mkt_crisis . . . . 2.40E-01 3.56

Crisis * Mkts * Tails g_mkt_crisis_g_ltail . . . . 3.54E-01 2.17

g_mkt_crisis_l_ltail . . . . 2.05E-01 4.75

l_mkt_crisis_g_ltail . . . . -5.66E-01 -3.72

l_mkt_crisis_l_ltail . . . . 4.17E-01 9.82

Crisis * SMB g_smb_crisis . . . . 1.26E+00 7.92

l_smb_crisis . . . . -1.66E+00 -21.56

59

Crisis * SMB * Tails g_smb_crisis_g_ltail . . . . -3.05E+00 -8.63

g_smb_crisis_l_ltail . . . . 9.89E-02 0.90

l_smb_crisis_g_ltail . . . . 3.60E+00 20.95

l_smb_crisis_l_ltail . . . . -1.03E+00 -22.36

Crisis * HML g_hml_crisis . . . . 9.52E-01 6.27

l_hml_crisis . . . . -4.23E-01 -6.83

Crisis * HML * Tails g_hml_crisis_g_ltail . . . . -2.22E+00 -6.62

g_hml_crisis_l_ltail . . . . 1.80E-01 2.48

l_hml_crisis_g_ltail . . . . 9.69E-01 6.97

l_hml_crisis_l_ltail . . . . -6.83E-01 -15.61

R-squared 16.08% . 16.10% . 16.12% .

60

Panel C. Fama-French 3 Factors and Momentum Factor

Base Model Interdependence

Model Contagion Model

PARMS T PARMS T PARMS T

Intercept 1.58E-03 20.53 1.48E-03 18.75 1.36E-03 16.02

l1exmret -2.63E-02 -67.64 -2.66E-02 -68.42 -2.65E-02 -67.63

l1dy 7.87E-09 2.22 8.35E-09 2.36 8.29E-09 2.34

l1size -2.62E-09 -1.56 -2.64E-09 -1.57 -2.59E-09 -1.54

l1mb 1.43E-08 1.01 1.41E-08 0.99 1.41E-08 0.99

g_mkt 9.93E-01 597.13 8.53E-01 50.07 8.23E-01 44.96

l_mkt 9.75E-01 648.71 1.09E+00 64.42 1.04E+00 56.40

g_smb -5.10E-01 -160.80 -4.84E-01 -15.00 -5.26E-01 -15.56

l_smb -6.37E-01 -374.31 -5.73E-01 -31.12 -4.29E-01 -21.25

g_hml 6.94E-02 20.97 -5.28E-02 -1.31 -6.10E-02 -1.47

l_hml 8.95E-02 53.05 1.69E-01 9.10 1.43E-01 6.90

g_mom 3.81E-03 1.57 -4.10E-01 -15.09 -4.24E-01 -14.18

l_mom -4.68E-02 -31.26 -1.21E-01 -7.41 -1.49E-01 -8.40

Global Mkt * Tails g_mkt_g_ltail . . 3.08E-01 8.23 3.65E-01 9.18

g_mkt_l_ltail . . 2.21E-01 13.52 1.72E-01 9.34

Local Mkt * Tails l_mkt_g_ltail . . -2.33E-01 -6.54 -1.23E-01 -3.20

l_mkt_l_ltail . . -1.80E-02 -1.50 -5.06E-02 -4.01

Global SMB * Tails g_smb_g_ltail . . -5.52E-02 -0.81 4.69E-02 0.66

g_smb_l_ltail . . -4.77E-01 -15.02 -4.61E-01 -13.69

Local SMB * Tails l_smb_g_ltail . . -1.47E-01 -3.84 -4.41E-01 -10.59

l_smb_l_ltail . . -2.84E-01 -21.76 -1.88E-01 -13.60

Global HML * Tails g_hml_g_ltail . . 2.36E-01 2.78 2.80E-01 3.20

g_hml_l_ltail . . -2.96E-01 -9.71 -2.79E-01 -8.55

Local HML * Tails l_hml_g_ltail . . -1.73E-01 -4.48 -1.28E-01 -2.99

l_hml_l_ltail . . 2.59E-02 2.24 9.87E-02 8.22

Global MOM * Tails g_mom_g_ltail . . 8.67E-01 15.46 9.05E-01 14.74

g_mom_l_ltail . . -1.29E-01 -5.92 -9.01E-02 -3.98

Local MOM * Tails l_mom_g_ltail . . 1.54E-01 4.55 2.09E-01 5.70

l_mom_l_ltail . . 1.54E-01 15.99 1.41E-01 14.16

Crisis * Tails crisis_g_ltail . . . . 4.06E-03 5.30

crisis_l_ltail . . . . 1.90E-03 0.77

Crisis * Mkts g_mkt_crisis . . . . -1.44E-02 -0.17

l_mkt_crisis . . . . 2.10E-01 3.04

61

Crisis * Mkts * Tails g_mkt_crisis_g_ltail . . . . 1.37E-01 0.73

g_mkt_crisis_l_ltail . . . . 1.14E-01 2.36

l_mkt_crisis_g_ltail . . . . -4.97E-01 -3.20

l_mkt_crisis_l_ltail . . . . 4.04E-01 9.30

Crisis * SMB g_smb_crisis . . . . 9.88E-01 5.89

l_smb_crisis . . . . -1.62E+00 -20.97

Crisis * SMB * Tails g_smb_crisis_g_ltail . . . . -2.32E+00 -6.09

g_smb_crisis_l_ltail . . . . 3.17E-01 2.61

l_smb_crisis_g_ltail . . . . 3.51E+00 20.35

l_smb_crisis_l_ltail . . . . -9.93E-01 -21.42

Crisis * HML g_hml_crisis . . . . 1.28E+00 4.19

l_hml_crisis . . . . -4.56E-01 -6.37

Crisis * HML * Tails g_hml_crisis_g_ltail . . . . -3.09E+00 -4.64

g_hml_crisis_l_ltail . . . . -8.38E-02 -0.74

l_hml_crisis_g_ltail . . . . 1.07E+00 6.62

l_hml_crisis_l_ltail . . . . -7.57E-01 -15.14

Crisis * MOM g_mom_crisis . . . . 6.38E-01 3.58

l_mom_crisis . . . . -1.33E-01 -2.01

Crisis * MOM * Tails g_mom_crisis_g_ltail . . . . -1.58E+00 -3.99

g_mom_crisis_l_ltail . . . . -3.53E-01 -3.43

l_mom_crisis_g_ltail . . . . 3.67E-01 2.46

l_mom_crisis_l_ltail . . . . -9.32E-02 -1.94

R-squared 16.07% . 16.09% . 16.12% .

62

Table 12.Contagion by country during crisis

This table reports countries' performance estimated from the pooled regression (for each country)

Following BEFM2014 model during the crisis period. The dependent variable is stock return. The control

variables are past month excess return, past dividend yield, past size, and past market to book ratio. The

factors used are global and local specific factors constructed following Bekeart, Hodrick and Zhang

(2009). The tail risks used are past one month global and local specific tails. The sample period is from

1980 Jan 1st to 2014 Dec 31st.

Country Excess Monthly

Return

Base Model

Deviation

Interdependence

Model Deviation

Contagion Model

Deviation

Australia -2.43% 0.01% -0.03% 0.52%

Austria -1.84% 0.93% 0.91% 1.51%

Belgium -3.06% 0.77% 0.75% 1.41%

Canada -1.77% 0.56% 0.54% 1.10%

Denmark -5.63% -2.30% -2.33% -1.72%

Finland -1.77% 0.15% 0.14% 0.69%

France -4.70% -2.05% -2.02% -1.46%

Germany -0.66% 1.53% 1.59% 2.14%

Hong Kong -4.90% -2.64% -2.64% -2.09%

Israel -3.39% -2.92% -2.93% -2.49%

Italy -2.11% 0.69% 0.65% 1.22%

Japan -1.74% 0.84% 0.85% 1.38%

Netherlands -3.29% -1.05% -1.06% -0.50%

New Zealand -2.31% 1.09% 1.07% 1.70%

Norway -4.27% -1.65% -1.69% -1.12%

Portugal -3.27% -0.50% -0.53% 0.07%

Singapore -6.53% -4.58% -4.55% -4.00%

Spain -2.58% -0.28% -0.30% 0.25%

Sweden -2.24% 0.55% 0.54% 1.15%

Switzerland -4.89% -1.98% -2.01% -1.43%

UK -2.08% 1.41% 1.41% 1.99%

US -6.98% -4.56% -4.58% -4.02%

Brazil -2.64% 0.19% 0.11% 0.66%

63

Chile 2.05% 4.76% 4.82% 5.41%

China -2.11% 2.75% 2.73% 3.42%

Czech Republic -0.65% 0.33% 0.40% 0.87%

Egypt -1.41% 0.32% 0.40% 0.94%

Greece -2.74% -0.64% -0.65% -0.09%

India -0.08% 3.70% 3.69% 4.33%

Korea -2.22% 0.74% 0.77% 1.38%

Malaysia -3.11% -1.00% -0.96% -0.39%

Mexico -2.58% -0.63% -0.62% -0.08%

Peru 2.65% 2.79% 2.76% 3.23%

Philippines -4.96% -2.66% -2.65% -2.08%

Poland -7.39% -4.91% -4.92% -4.35%

Russia -2.06% -0.18% -0.37% 0.13%

South Africa -4.27% -2.23% -2.27% -1.72%

Taiwan -4.33% -2.58% -2.63% -2.10%

Thailand -4.42% -2.25% -2.21% -1.64%

Turkey -2.42% 0.04% 0.03% 0.61%

All -2.88% -0.44% -0.44% 0.12%

64

Figure 1. Time series plot of US and global tail risks.

This figure provides time series plot for US and Global Tails during the sample period from 1980 Jan 1st

to 2014 Dec 31st. Solid line is the plot for global tail risk estimates and dashed line is the plot for US tail

estimates over time.

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013

US Tail Global Tail