Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market,
and Idiosyncratic Volatility Anomalies?
Sofiane Aboura
Y. Eser Arisoy‡
May 9, 2016
Abstract
We examine the impact of aggregate tail risk on return dynamics of size, book-to-market ratio,
and idiosyncratic volatility sorted portfolios. Using changes in VIX Tail Hedge Index (ΔVXTH)
as a proxy for aggregate tail risk, and controlling for market, size, book-to-market, and aggregate
volatility risk, we document significant portfolio return exposures to tail risk. In particular,
portfolios that contain small, value and volatile stocks exhibit consistently positive and
statistically significant tail risk betas, whereas portfolios of big, growth and non-volatile stocks
exhibit negative tail risk betas. We posit that due to their positive tail risk exposures, tail riskaverse investors demand extra compensation to hold small, value, and high idiosyncratic
volatility stocks. Our results offer a tail risk-based explanation to size, value, and idiosyncratic
volatility anomalies.
Keywords: Tail risk, Implied volatility, Idiosyncratic volatility, Size, Value, Anomalies
JEL Classification: C4, G13, G32.

Department of Economics, CEPN (UMR-CNRS 7234), Université de Paris XIII, Sorbonne Paris Cité, 99 avenue
Jean-Baptiste Clément, 93430 Villetaneuse, France. Phone: +33149403323, E-mail: sofiane.aboura@univ-paris13.fr
‡
Department of Finance, DRM-Finance, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny,
75775 Paris cedex 16, France. Phone: +33144054360, Email: eser.arisoy@dauphine.fr
Electronic copy available at: http://ssrn.com/abstract=2832893
1. Introduction
Tail risk hedging has gained considerable interest among market participants following the
aftermath of the 2008 financial crisis. It is now widely acknowledged that market returns have
much fatter tails than presumed by a Normal distribution and tail events occur much frequently
than a Normal curve would predict. Therefore, understanding the dynamics of aggregate tail risk
and its relation to portfolio returns is of crucial importance in investment decision making and
has implications for portfolio management. In this paper, we investigate the role of aggregate tail
risk in three well-documented asset pricing anomalies – size, value vs. growth, and idiosyncratic
volatility puzzle.
Keynes (1921) seems to have been the first economist to recognize that a decision maker has to
minimize the probability of obtaining an outcome below the mean.
1
In the same spirit, Roy
(1952) explains how the portfolio manager should minimize the chance of disaster based on the
“safety first” principle. Similarly, the recent revival of the rare-disasters literature in the wake of
the financial crisis is critically based on several concepts studied in the extreme value theory
literature to measure the tail risk and in particular the left tail risk (Embrechts, 1997).
On the other hand, it is well known from the option pricing literature that assets like deep out-ofthe money put contracts can become highly valuable during stress periods. For example,
Rubinstein (1994) argues that “the market's pricing of index options since the crash seems to
indicate an increasing “crash-o-phobia” among investors”. One would expect naturally a similar
sensitivity to tail risk in the stock market.2 For example, Bloom (2009) offers an uncertainty
based explanation in which economic uncertainty affects negatively firms’ investment decision
and firms’ employment decision. The author explains that firm-level tail uncertainty is a channel
through which tail risk impacts the equity premium and shows that the tail exponent, which
measures the tail heaviness, is an important determinant of asset prices and find that crashsensitive stocks bear a premium. Bollerslev and Todorov (2011) show that compensation for
rare events accounts for a large fraction of the U.S. equity risk premium. Gabaix (2012) reaches
similar findings by showing that a time-varying rare disaster risk framework can explain the
equity premium puzzle.3 Chollete and Lu (2011) suggest that tail risk should induce a monotonic
pattern in the sense that stocks that are more sensitive to tail risk should receive higher returns.
1
See Brady (1996) for a detailed discussion of "safety first" approach in decision making under risk.
For example, Yuen (2015) documents that the option-implied left tail risk of the market is priced in the crosssection of stock returns, even after controlling for risk during normal times.
3
See also Tsai and Wachter (2015) who survey recent models of disaster risk that provide explanations for the
equity premium puzzle.
2
1
Electronic copy available at: http://ssrn.com/abstract=2832893
They argue that these stocks, which tend to co-move with systemic risk, should to be unattractive
for risk-averse investors as it will be more difficult to sell them during stress periods. For that
reason, these stocks should carry a “tail risk premium”. Similarly, Chabi-Yo et al. (2015) note
that U.S. stocks that are likely to perform badly when the market crashes earn significantly
higher average returns than stocks that offer some protection against market downturns.
Bollerslev et al. (2015) confirm these results by explaining that market fear plays an important
role in understanding the return predictability since investors demand a special compensation for
bearing tail risk. In a recent work, Kelly and Jiang (2014) use monthly firm-level price crashes to
identify common fluctuations in tail risk among individual stocks. The authors find that the tail
measure is significantly correlated with tail risk measures extracted from S&P 500 index options
and negatively predicts real economic activity. Furthermore, they show that tail risk has strong
predictive power for aggregate market returns. Despite a growing body of literature, it is still not
known whether portfolios based on different stock characteristics have different exposures to
aggregate tail risk, and if yes, whether their differential exposure can help explain several stock
market anomalies documented in the literature. Our study is an attempt to fill this gap.
In particular, our paper examines the sensitivity of size, book-to-market (B/M) and idiosyncratic
volatility sorted portfolios to aggregate tail risk. There are several studies which document that
small and value stocks are prone to risk factors such as aggregate volatility risk (Barinov, 2012),
market jump risk (Arisoy, 2014; Cremers et al., 2014), financial distress risk (Avramov et al.,
2013), and liquidity risk (Asness et al., 2013). Furthermore, Herskovic, et al. (2016) document
strong comovement of individual stock return volatilities and find that idiosyncratic risk has
important implications of this behavior for asset prices. Given the difficulty in pricing smallvalue and big-growth stocks using linear factor models, and the continuing debate over why
stocks with high idiosyncratic volatility earn lower returns than low idiosyncratic volatility, tail
risk seems to be an ideal candidate as an explanatory factor as it can capture nonlinearities in the
left tail of the stock return distribution which can help improve the performance of the proposed
linear factor models. That’s why in this paper we revisit size, value and idiosyncratic volatility
anomalies, and study if and how aggregate tail risk relates to returns on small vs. big, and value
vs. growth, and high vs. low idiosyncratic volatility portfolios.
To operationalize our research framework and test our aggregate tail risk-based hypotheses, one
needs to come up with a measure of aggregate implied tail risk. We argue that VIX Tail Hedge
Index (VXTH) computed by the Chicago Board Options Exchange (CBOE) is a suitable measure
to proxy aggregate risk-neutral tail risk. In particular, VXTH deals with extreme downward
2
movements in S&P 500 stock index by tracking the performance of a hypothetical portfolio that
buys and holds the S&P 500 index and buys one-month 30-delta call options on the CBOE VIX
Index.4 Our choice of VXTH as a proxy for aggregate tail risk has several reasons. First, prices
formed in options market are forward looking, and contain valuable information about investors'
expectations about the return process of the underlying. Known as the “investor fear gauge” VIX
measures the market’s expectations of short-term volatility and extreme market events. The
power of the VXTH index comes from the exceptionally high returns earned by VIX call options
in times of extreme downward moves in the stock market. Second, VXTH is a tradable tail risk
strategy which can be implemented by market participants. Third, market completeness
assumption might also break down at times of high stress as investors are not able to associate
probabilities to states of the economy. When markets are incomplete, there should be a general
interaction between option and stock markets; hence we expect an option-implied measure of
aggregate tail risk to have implications on stock returns. Fourth, one can observe direct measures
of volatility and tail risk from options markets, which can help market participants to build up
more efficient hedging strategies against different sources of risk by disentangling volatility risk
from tail risk. Fifth, it is model-free as it is not derived from a particular setting. Hence, an
option-implied measure of aggregate tail risk has certain advantages over statistical measures,
which makes VXTH an ideal tool to summarize market sentiment about the evolution of
aggregate tail risk and study the implications of tail risk on asset returns.5 Using VXTH as a
proxy for aggregate tail risk our findings can be summarized as follows.
First, the extreme portfolios (containing smallest and biggest stocks) are more sensitive to the tail
risk factor than mid-cap stocks. Especially small stocks and the SMB strategy exhibit a positive
and statistically significant aggregate tail risk exposure both during the full sample period and
4
Most measures of tail risk proposed in the literature have been based on statistical metrics that model power laws.
Chapman and Gallmeyer (2014) mitigate the information content (at least on the short run) of the Kelly and Jiang
(2014) tail risk measure, based on the Hill (1975) estimator, concerning the average cross section of stock returns.
This estimator, as usually the case in extreme value theory, does not require knowing the whole distribution, but
only the form of behavior in the tail to draw statistical inference. Moore et al. (2013) discuss how downside tail risk
of stock returns can be differentiated cross-sectionally by including in the analysis not only the tail risk but also the
corresponding scale parameter. Andersen et al. (2016) find a clear separation between the left tail factor that is
predictive of the future equity tail risk premium and the spot variance factor that is predictive of the actual future
return variation. Chabi-Yo et al. (2013) and Weigert (2015) compute tail risk estimator on the basis of a copula to
feature the tail dependence.
5
Despite its short history beginning from 2007, it covers the biggest financial turmoil period that the markets have
witnessed for decades, i.e. the subprime crisis of 2007-2008, making it ideal to study the effects of aggregate tail
risk on stock returns and financial market anomalies. Hence the sample period that we examine, i.e. January 2007 to
February 2016, has the advantage of covering a period of extreme aggregate uncertainty, and a period with less
uncertainty about aggregate market conditions following interventions by the U.S. government and the FED to
address the issue of tail risk management.
3
the subprime and Eurozone crises period. Second, value (growth) stocks are positively
(negatively) and significantly exposed to aggregate tail risk factor and tail risk betas
monotonically increase from growth to value portfolios. This relation is in general robust during
the two sub-periods studied. Third, stocks with high idiosyncratic volatility and the strategy that
is long in high IVOL stocks and short in low IVOL stocks exhibit positive and significant
aggregate tail risk betas, with tail risk betas increasing almost monotonically from low to high
idiosyncratic volatility stocks. The positive exposure of high IVOL stocks and the High-Lo
IVOL strategy remains robust during the two subsamples. Overall, small, value and high IVOL
stocks are much riskier than their big, growth and low IVOL counterparts as they are much
heavily (positively) exposed to aggregate tail risk. Hence, tail risk-averse investors will ask for
extra compensation to hold these particular stocks in their portfolios. Our results offer an
aggregate tail risk based explanation to size, value vs. growth, and idiosyncratic volatility
anomalies.
The remainder of the paper is organized as follows. Section 2 presents data and methodology
used in our analysis. Section 3 presents the empirical results. Section 4 summarizes the main
findings and concludes.
2. Data and Methodology
In this section, we first describe the data and test assets used in our analyses. Next, we present
empirical methodology that forms the basis of our tests.
2.1. Data
Data on VIX Tail Hedge Index (VXTH) are from Chicago Board Options Exchange (CBOE). 6
CBOE has introduced this benchmark index designed to cope with extreme downward
movements in American premier stock index. VXTH index tracks the performance of a
hypothetical portfolio that buys and holds the performance of the S&P 500 index and buys onemonth 30-delta call options on the CBOE VIX Index. The power of the VXTH index comes
from the very high level of returns yielded by VIX call options in times of stock market crash
like so-called black swan events. To reduce hedging costs and monetize VIX option profits when
volatility levels peak, the weight of the VIX calls in the portfolio varies according to the forward
value of VIX to capture the likelihood of a black swan event. More precisely, the amount in
percentage allocated to VIX calls varies as follows:
6
www.cboe.com/VXTH
4

VIX futures ≤ 15%, 0% of portfolio in VIX calls,

15 < VIX ≤ 30%, 1% of portfolio in VIX calls,

30 < VIX ≤ 50%, 0.5% of portfolio in VIX calls,

VIX > 50%, 0% of portfolio in VIX calls.
This tail risk hedging strategy protects the investor from extreme market variations while
reducing the transaction costs by limiting the number of VIX calls that are purchased during
periods of expected low volatility.
The test assets are five portfolios sorted with respect to size, book-to market ratio, and
idiosyncratic volatility, as well as 6 (2x3) portfolios sorted with respect to size and book-tomarket ratio. Monthly returns of tests assets, market returns, SMB and HML factors, and
Treasury bill rates are downloaded from Ken French’s data library. 7 We further use change in
VIX index to proxy for aggregate volatility risk. The full period is from 1st January 2007 to 29th
February 2016 with a total of 110 months. The first subsample is from 1st January 2007 to 31st
July 2011 and the second subsample is from August 1st 2011 to29th February 2016, both of
which are 55 months long.
Table 1 presents the summary statistics of market returns, the VIX index, and the VXTH index
for the full sample (Panel A), the first sub-sample (Panel B), and the second sub-sample (Panel
C). Panel D documents correlations between the five factors used in our study. We use change in
VIX and VXTH rather than their levels as investors ultimately care about innovations in risk
factors rather than their levels. The correlation between ΔVXTH and ΔVIX is relatively moderate
at -0.51, which is not surprising given the aggregate tail index is built on a small fraction of VIX
options and a big fraction of stock market index, hence, the negative sign comes from the socalled leverage effect. The correlation between ΔVXTH and market returns (-0.11) is also
slightly lower than the correlation between change in ΔVIX and market returns (-0.16).
Figure 1 illustrates the level of the VIX and VXTH indices during our sample period. As can be
seen, when aggregate tail risk increases (for example during the subprime crisis period) VXTH
index goes down and when tail risk decreases (post March 2009 period) the tail risk index goes
up. One can also see an increase in tail risk after the second half of 2015.
7
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
5
2.2. Methodology
We start with the time-series analysis of excess returns on selected portfolios to examine whether
they have different exposure to aggregate tail risk. Our experimental setting builds on the Fama
and French (1993) three-factor model.8 The seminal articles by Fama and French (1992, 1993),
show that a combination of size and book-to-market ratio captures more adequately the crosssection of stock returns than the market beta set alone. Indeed, the Fama and French (1993)
model includes the market factor, the size and the book-to-market factors as they are mainly
interpreted as proxies for risk factors such as systematic risk, liquidity risk and market distress
risk. We augment the Fama and French (1993) three-factor model by adding aggregate volatility
risk factor and aggregate tail risk factor. Thus, the workhorse model that forms the basis of our
time-series regressions is the following five-factor model:
𝑟𝑖𝑡 = 𝛼𝑖 + 𝛽𝑖,𝑀𝐾𝑇 𝑀𝐾𝑇𝑡 + 𝛽𝑖,𝑆𝑀𝐵 𝑆𝑀𝐵𝑡 + 𝛽𝑖,𝐻𝑀𝐿 𝐻𝑀𝐿𝑡 + 𝛽𝑖,∆𝑉𝐼𝑋 ∆𝑉𝐼𝑋𝑡 + 𝛽𝑖,𝑉𝑋𝑇𝐻 ∆𝑉𝑋𝑇𝐻𝑡 + 𝜀𝑖𝑡 (1)
where rit is the monthly return on portfolio i in excess of the T-bill rate, 𝑀𝐾𝑇𝑡 is the market
factor, 𝑆𝑀𝐵𝑡 (Small minus Big) is the size factor that measures the return difference between the
average small cap and the average big cap portfolios, 𝐻𝑀𝐿𝑡 (High minus Low) is the book-tomarket factor that measures the return difference between the average value and the average
growth portfolios, ∆𝑉𝐼𝑋𝑡 is the proxy for aggregate volatility risk factor and ∆𝑉𝑋𝑇𝐻𝑡 is the
proxy for aggregate tail risk factor.
Section 3 presents results of time-series regressions in Equation (1), using either 5 portfolios
sorted with respect to stocks’ market capitalizations, 5 portfolios sorted with respect to book-to
market ratios, 5 portfolios sorted with respect to idiosyncratic volatility and 6 portfolios sorted
both with respect to 2 size (small and big) and 3 book-to-market (small, medium and big) as test
assets.
3. Empirical Results
This section presents results of time-series regressions in Equation (1) that form the basis of our
tests to examine the relationship between aggregate tail risk and empirically documented size
and value anomalies, and the idiosyncratic volatility puzzle.
8
We also made robustness checks using the Fama and French (2015) five-factor model and the results are
qualitatively similar although the power of the tests is slightly reduced given the over-parametrization of the model.
Results are given upon request.
6
3.1. Aggregate tail risk and size anomaly
It is well documented that stocks with small market capitalizations tend to earn higher returns on
average than stocks with higher market capitalizations, an important phenomenon that cannot be
explained by the CAPM alone (Banz, 1981; Reinganum, 1981). The literature has come up with
several explanations including rational risk-based explanations arguing that small stocks are
more prone to certain risk factors than large stocks and the return differential is a compensation
to investors who bear these risks (Fama and French, 1993, 1996). Among potential explanations
are the liquidity explanation highlighting the higher transaction costs associated with small
stocks (Amihud and Mendelson, 1986), behavioral explanations arguing that investors do not
behave optimally and make consistent pricing errors while valuing stocks, and once these errors
are corrected for the size anomaly is less significant (Lakonishok et al., 1994; La Porta, 1996; La
Porta et al., 1997), and time-varying risk and business cycle explanations arguing that small
stocks are especially more prone to business downturns with limited capacity to cope with
increased deterioration in investment opportunities (Lettau and Ludvigson, 2001; Petkova and
Zhang, 2005). Given the increase in frequency of extreme events during the subprime crisis, we
explore whether portfolios differing in their market capitalizations have different exposures to
aggregate tail risk.
Table 2 presents results of time-series regressions presented in Equation (1), using excess returns
on 5 size-sorted portfolios as test assets. Consistent with earlier studies, there is not a clear
relationship between market betas and size, and betas follow an inverse U-shaped pattern from
the smallest quintile to the highest quintile. As expected SMB factor is a strong determinant of
size-sorted portfolio returns by construction. The significance of HML factor is weaker than
SMB factor. We further document that change in the VIX index loads negatively with returns on
portfolios of small stocks and positively with returns on the portfolio of big stocks, however
none of the coefficients are significantly different from zero. Looking at tail betas, we document
that ΔVXTH betas are positive and statistically significant for small stocks and for the long-short
portfolio while they are negative and very close to being significant for big stocks. The results
imply that size-sorted portfolios are exposed to aggregate tail risk in a very distinct way than
aggregate volatility risk. The positive tail risk loadings of small stocks and the SMB portfolio
implies that small stocks and the SMB strategy are much riskier during times of extreme
downward market moves. These findings, if persistent, can offer an alternative tail-based
explanation to the well-documented size anomaly.
7
3.2. Aggregate tail risk and value vs. growth anomaly
One of the well-established features of asset returns is that firms with high book-to-market ratios
(value firms) deliver, on average, higher returns than firms with low book-to-market ratios
(growth firms). The value premium, computed as the difference in average returns between value
(high B/M) firms and growth (low B/M) firms, was first identified by Graham and Dodd (1934)
and deeply investigated by Fama and French (1992) and is viewed as a proxy for distress risk
(Fama and French, 1996).9 We investigate whether return dynamics of B/M sorted portfolios are
sensitive to aggregate tail risk.
Table 3 presents the slope coefficients of time-series regressions using excess returns on 5 B/M
sorted portfolios as test assets. We test if portfolios of stocks sorted with respect to their book-tomarket ratios (B/M) have different sensitivities with respect to the aggregate tail risk factor,
VXTH. One can see that market and HML factors have strong explanatory power on the returns
of B/M sorted portfolios. SMB factor has almost no explanatory power with the exception of the
value portfolio. Furthermore, aggregate volatility risk factor has a negative and significant
loading for the growth portfolio and a positive loading for the second lowest B/M ratio quintile.
Regarding the tail risk factor, we document significant aggregate tail risk exposures for
portfolios that contain the lowest and highest B/M stocks as well as the HML portfolio. Most
importantly, growth stocks exhibit negative tail risk betas whereas value stocks and the HML
portfolio exhibit positive tail risk betas. Furthermore, the tail index betas increase monotonically
from growth to value stocks. The results imply that value stocks and the HML strategy are risky
strategies given their positive exposure to aggregate tail risk. On the other hand, growth stocks
(with their negative exposure to aggregate tail risk) offer a potential hedge against increases in
aggregate tail risk.
However, book-to-market ratio and size are two closely related variables as the firm’s size also
displayed in the denominator of its book-to-market ratio. Because of this mechanical
relationship, it is possible to find small stocks in high B/M portfolio and likewise big stocks
might be the dominant stocks in low B/M portfolio. Therefore, it becomes crucial to disentangle
the effect of size and B/M ratios to understand the real effect of aggregate tail risk on more
refined portfolio returns.
9
Liew and Vassalou (2000) show that HML factor correlates positively with GDP growth, even after controlling for
market factor. Lettau and Ludvigson (2001) and Petkova and Zhang (2005) argue that the value premium is closely
related to business cycles, and show that the consumption and market betas of value stocks increases in bad times in
conditional CCAPM and conditional CAPM settings, respectively. Arisoy (2010, 2014) argue that value stocks are
much riskier at times of increased aggregate volatility risk.
8
3.3. Six portfolios (2x3) sorted with respect to size and book-to-market ratios
In this section, we further refine size and B/M sorted portfolios and disentangle the size and
book-to-market effects by examining returns of 6 portfolios, where stocks are first sorted with
respect to 2 size portfolios (small and big), and then within each size portfolio, stocks are sorted
with respect to their book-to-market ratios. In this manner, we can have a better understanding
about the impact of aggregate tail risk factor on the return dynamics of size and B/M sorted
portfolios, where the potential confounding effects of size and B/M are minimized as a result of a
more refined sample.
Table 4 presents the slope coefficients of time-series regressions outlined in Equation (1), using
excess returns on 6 portfolios sorted with respect to 2 size-based portfolios (small vs. big), and
then 3 B/M tertiles within each two size-based portfolios. Based on this more refined sample of
portfolios, we observe several interesting features about how aggregate tail risk impacts size and
book-to-market sorted portfolios when the effect of size on book-to-market is disentangled. First
of all, 4 out 6 portfolios document statistically significant tail risk loadings. Across small stocks,
we observe that only the small-value portfolio exhibit a positive and significant tail risk beta.
Therefore, the positive coefficient observed for small stocks documented in Table 2 is mostly
due to the presence of value stocks in this portfolio. Furthermore, there is an interesting pattern
across big stocks. It is only the portfolio of big and growth stocks which exhibit a negative and
significant tail risk beta, while the two other portfolios which contain medium and high B/M
stocks exhibit positive and significant betas. Therefore, with their negative tail risk loadings, it is
only the big and growth stocks (not small and growth stocks) which provide a hedge against
increases in tail risk. Value stocks on the other hand exhibit positive tail risk loadings regardless
of their size, hence they are viewed much riskier by tail risk averse investors. As documented
previously, the sensitivity to tail risk increases monotonically from growth to value stocks, which
implies that investors require a higher compensation to hold value stocks in their portfolios.
3.4. Aggregate tail risk and idiosyncratic volatility anomaly
Ang et al. (2006a, 2006b, 2009) document that stocks with high idiosyncratic volatility earn
lower returns than stocks with low idiosyncratic volatility in the cross-section of US and
international stock returns, respectively. This puzzling finding is at odds with the capital asset
pricing models which posit that investors should not care about idiosyncratic volatility as they
should optimally hold the market portfolio in which idiosyncratic volatility risk is already
diversified away. However Goetzmann and Kumar (2008) show that US investors hold
9
underdiversified portfolios. In the case of underdiversdification, investors could demand a
premium for bearing idiosyncratic risk. Therefore idiosyncratic risk should either not be priced
(due to diversification) or if it is priced, it should command a positive premium, not negative.
Studies attribute this puzzling negative relationship between idiosyncratic volatility and returns
to several factors ranging from illiquidity (Bali and Cakici, 2008), one-month return reversal (Fu,
2009; Huang et al. 2009), earnings surprises (Jiang, Xu, and Yao, 2009), idiosyncratic skewness
(Boyer, Mitton and Vorkink (2010), non-systematic coskewness (Chabi-Yo 2011), MAX effect
(Bali, Cakici and Whitelaw, 2011), average variance beta (Chen and Petkova, 2012), retail
trading proportion (Han and Kumar, 2013), incomplete information (Berrada and Hugonnier,
2013), and prospect theory (Bhootra and Hur, 2015).10 Given these wide range of potential
explanations, it is worth examining whether portfolios of stocks sorted with respect to
idiosyncratic volatility (IVOL) exhibit different sensitivity to aggregate tail risk.
Table 5 presents the slope coefficients of time-series regressions using excess returns on 5 IVOL
sorted portfolios to test if such portfolios of stocks sorted with respect to their idiosyncratic
volatility (IVOL) have different sensitivities with respect to innovations in the aggregate tail risk
factor, ΔVXTH. Once again, the MKT and SMB factors have significant loadings on IVOL
sorted portfolios whereas the HML factor is never significant. Aggregate volatility risk is
significant only for one portfolio. On the other hand, aggregate tail risk betas are positive and
statistically significant for the highest IVOL stocks and the long-short IVOL portfolio.
Moreover, the betas are negatively exposed to tail risk factor for low IVOL stocks and almost
monotonically increasing to positive values for high IVOL stocks. The findings imply that due to
their positive exposure to aggregate tail risk high idiosyncratic volatility stocks should be
considered riskier at times of increased tail risk. Furthermore, a strategy that is long in high
IVOL stocks and low IVOL stocks is risky as it is positively exposed to aggregate tail risk. Our
findings offer a tail risk-based alternative explanation to the idiosyncratic volatility puzzle.
3.5. Financial crisis, aggregate tail risk, size, value effects and idiosyncratic risk
This sub-section examines the impact of aggregate uncertainty on size, B/M and idiosyncratic
volatility sorted portfolios in two sub-periods, January 2007 - July 2011, and August 2011 -
10
In addition, several papers show that the idiosyncratic volatility puzzle is stronger among stocks with high
leverage (Johnson, 2004), low institutional ownership (Nagel, 2005), non-NYSE listings (Bali and Cakici, 2008),
low analyst coverage (Ang, Hodrick, Xing, and Zhang, 2009), prices of at least five dollars (George and Hwang,
2013), low credit ratings (Avramov et al. 2013), high short-sale constraints (Boehme et al. 2009; George and
Hwang, 2013; Stambaugh, Yu, and Yuan, 2015), low book-to-market ratio (Barinov, 2013), and for non-January
months (George and Hwang, 2013; Doran, Jiang, and Peterson, 2012).
10
February 2016. The subsample analysis provides us with a quasi-natural experimental setting to
test the impact of recent financial crisis, which we associate with extreme increase in aggregate
tail risk. In particular, we investigate if return dynamics of size, B/M and idiosyncratic volatility
sorted portfolios were different between a period where VXTH was more exposed to tail risk
(pre- August 2011), and a sideways market where the aggregate tail risk easing down and heat of
financial markets cooling down as the Eurozone countries, the ECB, US government and the
FED intervening and reassuring the markets, with equity markets picking up and investors
becoming relatively less tail risk-averse about macro-financial conditions (post-August 2011).
Tables 6, 7 and 8 report the slope coefficients of our 5-factor model as outlined in Equation (1),
for the 5 size, B/M, IVOL sorted portfolios during January 2007 - July 2011 for Panel A, and
during August 2011 - January 2016 for Panel B. In fact, Panel A covers both contraction and
recession period in the US and Eurozone countries, while Panel B is characterized by the
recovery and expansion period.
Looking at Panel A in Table 6, one can see that the results for the whole sample are mainly
driven by the first subsample with small stocks and the SMB portfolio being positively and
significantly exposed to aggregate tail risk. As one could expect, Panel B shows almost no
significant exposure to aggregate tail risk during the recovery phase. The findings imply that the
sensitivity of small stocks and SMB portfolio to aggregate tail risk is most prominent during the
first sub–period (when aggregate tail risk was at its highest) and it disappears during the second
sub-period.
Looking at Panel A in Table 7, one can see very similar results to those presented in Table 3.
During the recession period, growth stocks exhibit negative and statistically significant aggregate
tail risk loadings, whereas value stocks exhibit positive and significant tail risk loadings. In
addition, tail index beta is negative for growth stocks and positive for value stocks while
increasing monotonically from growth to value stocks, a finding similar to what we observe over
the whole sample period. More generally, significant aggregate tail index betas concerns
portfolios that contain lowest and highest B/M stocks as well as the HML portfolio. They are
significant in 4 out of 6 portfolios in Panel A and 3 out of 6 in Panel B.
While the sensitivity of size and B/M sorted portfolios to aggregate tail risk is generally stronger
during the first half of the sample period, IVOL sorted portfolios present a different pattern. The
positive exposure of high IVOL portfolio together with the long-short IVOL strategy persists
during both sample periods implying that the relationship between aggregate tail risk and returns
11
on high IVOL stocks is persistently positive, therefore high IVOL stocks would be deemed
riskier as a result of their positive and significant exposure to aggregate tail risk.
4. Conclusion
We examine the relation between return dynamics of size, book-to-market, and idiosyncratic
volatility sorted portfolios and aggregate tail risk. We propose a novel proxy to measure a
stock’s return sensitivity to aggregate tail risk – VIX Tail Hedge Index (VXTH). Our proposed
measure has the advantage of being forward-looking and investable, which can better summarize
a portfolio’s exposure to aggregate tail risk. Using changes in VXTH as a measure of aggregate
tail risk we document the following.
We find that small, value and high idiosyncratic volatility stocks exhibit consistently positive
and statistically significant aggregate tail risk betas during January 2007 ‒ February 2016 period.
In particular, small stocks are positively and significantly exposed to the tail risk factor and this
positive exposure is mainly driven by the recession period. Meanwhile, value (growth) stocks are
positively (negatively) and significantly exposed to aggregate tail risk with tail risk betas
monotonically increasing from growth to value stocks. A detailed analysis reveals that smallvalue portfolio is the portfolio which is exposed most positively to aggregate tail risk across
small stocks. On the other hand, big-growth portfolio is the only portfolio that offers a hedge
against aggregate tail risk with its negative tail risk exposure. We further revisit the idiosyncratic
volatility puzzle and find that stocks with high IVOL and a strategy that is long in high IVOL
stocks and short in low IVOL stocks exhibit a positive aggregate tail risk exposure.
12
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16
Table 1
Summary Statistics and Correlations
Panel A: Descriptive Statistics (Full Sample)
MKT
VIX
VXTH
Mean
0.58
21.46
140.69
Std. Dev.
4.65
9.72
34.22
Skewness
-0.63
2.12
0.28
Kurtosis
4.18
8.61
1.98
Min
-17.15
10.31
74.36
Max
11.35
68.51
204.79
Kurtosis
3.59
6.63
2.90
Min
-17.15
10.31
74.36
Max
10.20
68.51
146.37
Kurtosis
3.33
8.79
1.72
Min
-7.59
11.15
126.91
Max
11.35
45.45
204.79
Panel B: Descriptive Statistics (Jan 2007 - Jul 2011)
MKT
VIX
VXTH
Mean
0.22
25.09
112.41
Std. Dev.
5.45
11.11
15.60
Skewness
-0.67
1.80
0.14
Panel C: Descriptive Statistics (Aug 2011 - Feb 2016)
MKT
VIX
VXTH
Mean
0.94
17.82
168.98
Std. Dev.
3.69
6.37
22.16
Skewness
-0.07
2.26
0.08
Panel D: Pearson Correlation Among Factors
MKT
SMB
HML
ΔVIX
ΔVXTH
MKT
1.0000
0.4152
0.3145
-0.1632
-0.1111
SMB
HML
ΔVIX
1.0000
0.3119
-0.0813
-0.0958
1.0000
-0.0340
-0.0592
1.0000
-0.5137
ΔVXTH
1.0000
Note: Panel A presents descriptive statistics of daily levels of MKT, VIX and VXTH for the full sample
period in Panel A (January 3, 2007 to July 31, 2011), first sub-sample period in Panel B (January 3, 2007
to July 31, 2011) and second sub-sample period in Panel C (August 1, 2011 to February 29, 2016). Panel
D presents correlations between factors used in the study expressed in average daily returns (in %).
17
Table 2
Size portfolios
Portfolios
Small
Size2
Size3
Size4
Big
SMB
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
0.9794***
1.0697***
0.1148***
-0.0023
0.0305*
-0.2491***
97.95%
[45.84]
[26.48]
[3.02]
[-0.14]
[1.73]
[-2.81]
1.0148***
0.9600***
0.0013
0.0058
0.0045
-0.0019
[80.91]
[40.49]
[0.06]
[0.59]
[0.43]
[-0.04]
1.0379***
0.6677***
-0.0673*
-0.0066
-0.0094
0.1661**
[52.08]
[17.72]
[-1.90]
[-0.42]
[-0.57]
[2.01]
1.0685***
0.3433***
-0.0812**
-0.0229
0.0174
0.0091
[46.09]
[7.83]
[-1.97]
[-1.26]
[0.91]
[0.09]
0.9830***
-0.1824***
0.0024
0.0004
-0.0055
0.0075
[236.18]
[-23.18]
[0.33]
[0.11]
[-1.59]
[0.44]
-0.0007
1.2526***
0.1131***
-0.0033
0.0369**
-0.3140***
[-0.03]
[31.08]
[2.98]
[-0.20]
[2.09]
[-3.55]
99.25%
97.86%
96.78%
99.84%
92.29%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to February 29, 2016. Small is the portfolio of
stocks that are in the lowest market capitalization decile, and Big is the portfolio of stocks that are in the
largest market capitalization decile. SMB is the portfolio that is long in Small and short in Big portfolios.
The numbers in square brackets are Newey-West adjusted t-statistics and *, ** and *** denote
respectively significance at the 10%, 5% and 1% level.
18
Table 3
B/M portfolios
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
Low BM
0.9969***
-0.0140
-0.3542***
-0.0257***
-0.0222*
0.1159*
97.91%
[63.91]
[-0.47]
[-12.77]
[-2.11]
[-1.72]
[1.79]
0.9529***
-0.0523
0.0013
0.0280*
0.0026
0.1179
[51.91]
[-1.51]
[0.04]
[1.95]
[0.17]
[1.55]
1.0479***
-0.0253
0.1570***
0.0250
0.0245
-0.1399
[44.19]
[-0.56]
[3.72]
[1.34]
[1.25]
[-1.42]
0.9781***
-0.0097
0.4667***
-0.0061
0.0229
-0.1215
[47.62]
[-0.25]
[12.78]
[-0.38]
[1.35]
[-1.43]
1.0758***
0.2938***
0.5934***
0.0262
0.0517*
-0.0563
[31.34]
[4.53]
[9.72]
[0.97]
[1.82]
[-0.40]
0.0818**
[0.31]***
0.9482***
0.0513*
0.0748**
-0.2295
[2.27]
[4.53]
[14.81]
[1.82]
[2.51]
[-1.54]
BM2
BM3
BM4
High BM
HML
96.98%
96.13%
97.14%
94.44%
77.01%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to February 29, 2016. Low is the portfolio of stocks
that are in the lowest book-to-market ratio decile (growth portfolio), and High is the portfolio of stocks
that are in the highest book-to-market decile (value portfolio). HML is the portfolio that is long in High
and short in Low portfolios. The numbers in square brackets are Newey-West adjusted t-statistics and *,
** and *** denote respectively significance at the 10%, 5% and 1% level.
19
Table 4
2x3 portfolios sorted with respect to size and book-to-market
Portfolios
Size B/M
S
L
S
M
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
1.0612***
1.0495***
-0.4252***
0.0078
-0.0112
-0.1890**
98.38%
[57.01]
[29.83]
[-12.85]
[0.54]
[-0.98]
[-2.45]
0.9738***
0.8674***
0.0961***
-0.0007
-0.0116
0.0900
[72.47]
[34.15]
[4.02]
[-0.07]
[-1.04]
[1.62]
0.8817***
0.6111***
0.0030
0.0392**
0.0332
S
H
0.9842***
[71.19]
[33.74]
[24.86]
[0.28]
[2.54]
[0.58]
B
L
0.9618***
-0.1063***
-0.2700***
-0.0064
-0.0185**
0.1414***
[86.13]
[-5.03]
[-13.60]
[-0.73]
[-2.00]
[3.06]
-0.1323***
0.1592***
0.0230
0.0276*
-0.1377*
B
M
1.0456***
[58.36]
[-3.91]
[5.00]
[1.64]
[1.86]
[-1.85]
B
H
1.0387***
0.0613
0.6941***
-0.0018
0.0321*
-0.0796
[44.63]
[1.39]
[16.78]
[-0.10]
[1.66]
[-0.82]
99.08%
99.21%
98.80%
97.65%
97.12%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to February 29, 2016. The test assets are 6
portfolios sorted with respect to 2 size and 3 B/M. S and B stand for portfolio of stocks that the smallest
market capitalization and largest market capitalization, respectively. L, M and H stand for portfolio of
stocks that are in the lowest book-to-market ratio tertile, medium lowest tertile and highest book-tomarket tertile, respectively. The numbers in square brackets are Newey-West adjusted t-statistics and *,
** and *** denote respectively significance at the 10%, 5% and 1% level.
20
Table 5
5 portfolios sorted with respect to idiosyncratic volatility
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
Low IVOL
0.8029***
-0.1770***
0.0063
0.0097
-0.0128
0.1652*
93.52%
[35.64]
[-4.16]
[0.16]
[0.55]
[-0.68]
[1.77]
IVOL2
1.0560***
0.0653*
0.0476
0.0366**
0.0103
0.0482
[52.19]
[1.71]
[1.32]
[2.31]
[0.62]
[0.58]
IVOL3
1.1538***
0.1304**
-0.0068
-0.0381
-0.0125
-0.1503
[35.53]
[2.12]
[-0.12]
[-1.50]
[-0.46]
[-1.12]
IVOL4
1.3824***
0.1899**
-0.0891
-0.0236
0.0300
-0.1830
[28.54]
[2.07]
[-1.04]
[-0.62]
[0.75]
[-0.91]
High IVOL
1.4058***
0.7081***
0.1110
-0.0415
0.0994*
-0.6118**
[19.88]
[5.30]
[0.88]
[-0.75]
[1.70]
[-2.09]
Hi-Lo IVOL
0.6058***
0.8855***
0.1054
-0.0518
0.1131*
-0.8345**
[6.97]
[5.39]
[0.68]
[-0.76]
[1.77]
[-2.32]
97.19%
94.34%
91.30%
86.52%
57.90%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to February 29, 2016. The test assets are 5
portfolios sorted with respect to 5 IVOL quintiles within each size quintile. Low IVOL, IVOL 2, IVOL 3,
IVOL 4, High IVOL and Hi-Lo IVOL stand for portfolio of stocks that correspond to the lowest
idiosyncratic volatility, second smallest IVOL quintile, third smallest IVOL quintile, fourth smallest
IVOL quintile, highest IVOL quintile, respectively and Hi-Lo IVOL is the portfolio that is long in low
idiosyncratic volatility and short in high idiosyncratic volatility. The numbers in square brackets are
Newey-West adjusted t-statistics and *, ** and *** denote respectively significance at the 10%, 5% and
1% level.
21
Table 6
Subperiod analysis - 5 size portfolios
Panel A: January 2007 - July 2011
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
0.9838***
1.0092***
0.1342***
0.0112
0.0593**
-0.3608***
98.51%
[36.51]
[16.95]
[2.67]
[0.50]
[2.10]
[-2.86]
Size2
1.0027***
0.9164***
0.0414
0.0046
-0.0050
0.0460
[56.26]
[23.27]
[1.25]
[0.99]
[-0.88]
[0.55]
Size3
1.0465***
0.6276***
-0.0814
-0.0100
-0.0090
0.3389***
[37.48]
[10.17]
[-1.56]
[-0.43]
[-0.31]
[2.59]
Size4
1.0645***
0.3593***
-0.1013*
-0.0483*
0.0035
0.0636
[32.41]
[4.95]
[-1.65]
[-1.77]
[0.10]
[0.41]
Big
0.9835***
-0.1878***
0.0032
-0.0104
-0.0302
0.0034
[179.03]
[-15.48]
[0.31]
[-0.70]
[-1.62]
[0.13]
0.0014
1.2081***
0.1280**
0.0208
0.0860**
-0.4797***
[0.05]
[19.90]
[2.50]
[0.25]
[2.30]
[-3.73]
Small
SMB
99.31%
98.07%
97.13%
99.88%
92.84%
Panel B: August 2011 - February 2016
Portfolios
Small
Size2
Size3
Size4
Big
SMB
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
0.9467***
1.1717***
0.1186*
-0.0213
0.0020
-0.0562
97.10%
[24.63]
[20.11]
[1.75]
[-0.82]
[0.09]
[-0.43]
1.0399***
0.9664***
-0.0350
0.0122
0.0279**
-0.0439
[55.70]
[34.15]
[-1.06]
[0.97]
[2.45]
[-0.69]
1.0539***
0.6905***
0.0133
0.0036
-0.0057
0.0009
[32.79]
[14.17]
[0.23]
[0.17]
[-0.29]
[0.01]
1.0895***
0.3126***
-0.0254
0.0196
0.0347
-0.0810
[28.61]
[5.42]
[-0.38]
[0.77]
[1.49]
[-0.63]
0.9842***
-0.1753***
0.0043
-0.0068
-0.0062
0.0149
[132.34]
[-15.55]
[0.33]
[-1.36]
[-1.37]
[0.59]
-0.0370
1.3468***
0.1139*
-0.0144
0.0086
-0.0739
[-0.99]
[23.89]
[1.73]
[-0.58]
[0.38]
[-0.59]
99.28%
97.60%
95.96%
99.76%
92.38%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to July 31, 2011 (Panel A), and for the sample
period of August 1, 2011 to February 29, 2016 (Panel B). Small is the portfolio of stocks that are in the
lowest market capitalization quintile, and Big is the portfolio of stocks that are in the largest market
capitalization quntile. SMB is the portfolio that is long in Small and short in Big portfolios. The numbers
in square brackets are Newey-West adjusted t-statistics and *, ** and *** denote respectively significance
at the 10%, 5% and 1% level.
22
Table 7
Subperiod analysis - 5 B/M portfolios
Panel A: January 2007 - July 2011
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
Low BM
1.0136***
-0.0204
-0.3522***
-0.0582***
-0.0818***
0.2143**
98.55%
[52.33]
[-0.48]
[-9.75]
[-3.61]
[-4.04]
[2.36]
BM2
0.9341***
-0.0155
0.0287
-0.0021
0.0259
0.0809
[32.55]
[-0.24]
[0.54]
[-0.09]
[0.90]
[0.60]
BM3
1.0337***
-0.0171
0.1556***
0.0142
0.0323
-0.2258
[29.06]
[-0.22]
[2.35]
[0.34]
[0.61]
[-1.36]
BM4
1.0061***
-0.0237
0.4493***
0.0506**
0.0563*
-0.1535
[36.53]
[-0.39]
[8.75]
[2.12]
[1.88]
[-1.19]
High BM
1.0360***
0.2954***
0.6226***
0.0551*
0.0689*
-0.0245
[20.57]
[2.66]
[6.63]
[1.86]
[1.85]
[-0.10]
0.0235
0.3269***
0.9718***
0.1116*
0.1507***
-0.3543
[0.47]
[2.98]
[10.50]
[1.73]
[3.23]
[-1.53]
HML
96.70%
96.14%
97.96%
94.97%
81.24%
Panel B: August 2011 - February 2016
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
Low BM
0.9740***
-0.0519
-0.4097***
0.0031
0.0103
0.0386
97.69%
[39.92]
[-1.40]
[-9.50]
[0.19]
[0.69]
[0.47]
0.9582***
-0.0743**
-0.0549
0.0092
-0.0295**
0.1271*
[42.87]
[-2.19]
[-1.39]
[0.61]
[-2.16]
[1.68]
1.0709***
0.0006
0.1970***
-0.0061
0.0009
-0.0774
[31.24]
[0.01]
[3.25]
[-0.26]
[0.04]
[-0.67]
0.9155***
0.0289
0.4508***
-0.0128
0.0075
-0.0183
[25.15]
[0.52]
[7.00]
[-0.52]
[0.34]
[-0.15]
1.1670***
0.2531***
0.6188***
0.0384
0.0825**
-0.1782
[21.52]
[3.08]
[6.45]
[1.05]
[2.49]
[-0.97]
0.1936***
0.3049***
1.0281***
0.0354
0.0725**
-0.2196
[3.28]
[3.41]
[9.85]
[0.89]
[2.01]
[-1.10]
BM2
BM3
BM4
High BM
HML
97.92%
96.11%
94.30%
92.67%
69.23%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to July 31, 2011 (Panel A), and for the sample
period of August 1, 2011 to February 29, 2016 (Panel B). Low is the portfolio of stocks that are in the
lowest book-to-market ratio quintile (growth portfolio), and High is the portfolio of stocks that are in the
highest book-to-market quintile (value portfolio). HML is the portfolio that is long in High and short in
Low portfolios. The numbers in square brackets are Newey-West adjusted t-statistics and *, ** and ***
denote respectively significance at the 10%, 5% and 1% level.
23
Table 8
Subperiod analysis - 5 IVOL portfolios
Panel A: January 2007 - July 2011
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
Low IVOL
0.8000***
-0.1775***
0.0056
0.0103
-0.0137
0.2226**
93.45%
[35.46]
[-4.16]
[0.14]
[0.58]
[-0.73]
[2.38]
1.0531***
0.0648*
0.0470
0.0372**
0.0094
0.1056
[51.63]
[1.68]
[1.29]
[2.33]
[0.56]
[1.25]
1.1509***
0.1299**
-0.0074
-0.0374
-0.0134
-0.0929
[35.01]
[2.09]
[-0.13]
[-1.45]
[-0.49]
[-0.68]
1.3795***
0.1894**
-0.0898
-0.0230
0.0290
-0.1256
[28.45]
[2.07]
[-1.04]
[-0.60]
[0.72]
[-0.63]
1.4028***
0.7076***
0.1103
-0.0409
0.0985*
-0.5545*
[19.79]
[5.28]
[0.88]
[-0.74]
[1.68]
[-1.89]
0.6029***
0.8851***
0.1047
-0.0512
0.1122*
-0.7771**
[6,93]
[5,38]
[0,68]
[-0.75]
[1.76]
[-2.15]
IVOL2
IVOL3
IVOL4
High IVOL
Hi-Lo IVOL
97.13%
94.18%
91.25%
86.41%
57.67%
Panel B: August 2011 - February 2016
Portfolios
MKT
SMB
HML
ΔVIX
ΔVXTH
Alpha
Adj. R2
Low IVOL
0.8029***
-0.1770***
0.0063
0.0097
-0.0128
0.1652*
93.52%
[35.64]
[-4.16]
[0.16]
[0.55]
[-0.68]
[1.77]
1.0560***
0.0653*
0.0476
0.0366**
0.0103
0.0482
[52.19]
[1.71]
[1.32]
[2.31]
[0.62]
[0.58]
1.1538***
0.1304**
-0.0068
-0.0381
-0.0125
-0.1503
[35.53]
[2.12]
[-0.12]
[-1.50]
[-0.46]
[-1.12]
1.3824***
0.1899**
-0.0891
-0.0236
0.0300
-0.1830
[28.54]
[2.07]
[-1.04]
[-0.62]
[0.75]
[-0.91]
1.4058***
0.7081***
0.1110
-0.0415
0.0994*
-0.6118**
[19.88]
[5.30]
[0.88]
[-0.75]
[1.70]
[-2.09]
0.6058***
0.8855***
0.1054
-0.0518
0.1131*
-0.8345**
[6.97]
[5.39]
[0.68]
[-0.76]
[1.77]
[-2.32]
IVOL2
IVOL3
IVOL4
High IVOL
Hi-Lo IVOL
97.19%
94.34%
91.30%
86.52%
57.90%
Note: This table presents slope coefficients of the regressions of the five-factor model as outlined in
Equation (1) for the sample period of January 3, 2007 to July 31, 2011 (Panel A), and for the sample
period of August 1, 2011 to February 29, 2016 (Panel B). The test assets are 5 portfolios sorted with
respect to 5 IVOL quintiles within each size quintile. Low IVOL, IVOL 2, IVOL 3, IVOL 4, High IVOL
and Hi-Lo IVOL stand for portfolio of stocks that correspond to the lowest idiosyncratic volatility, second
smallest IVOL quintile, third smallest IVOL quintile, fourth smallest IVOL quintile, highest IVOL
quintile, respectively and Hi-Lo IVOL is the portfolio that is long in low idiosyncratic volatility and short
in high idiosyncratic volatility. The numbers in square brackets are Newey-West adjusted t-statistics and
*, ** and *** denote respectively significance at the 10%, 5% and 1% level.
24
Figure 1
This figure displays the VXTH and VIX indexes for the sample period of January 3, 2007 to February 29,
2016.
25