Aggregate volatility risk and the cross-section of stock returns: Australian evidence

    Aggregate volatility risk and the cross-section of stock returns: Australian evidence Van Anh (Vivian) Mai, Tze Chuan ‘Chewie’ Ang, Victor Fang PII: DOI: Reference:

S0927-538X(15)30028-7 doi: 10.1016/j.pacfin.2015.12.006 PACFIN 800

To appear in:

Pacific-Basin Finance Journal

Received date: Revised date: Accepted date:

10 April 2015 31 October 2015 15 December 2015

Please cite this article as: Mai, Van Anh (Vivian), Ang, Tze Chuan ‘Chewie’, Fang, Victor, Aggregate volatility risk and the cross-section of stock returns: Australian evidence, Pacific-Basin Finance Journal (2015), doi: 10.1016/j.pacfin.2015.12.006

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Aggregate Volatility Risk and the Cross-Section of Stock Returns:

SC R

IP

T

Australian Evidence

Van Anh (Vivian) Mai1

NU

Tze Chuan ‘Chewie’ Ang2*

TE

D

MA

Victor Fang3

Keywords Aggregate volatility risk; Cross-sectional return; Asset pricing test; Implied

CE P

volatility (VIX); Anomaly

AC

JEL Classification G12; G13; G14.

1

Van Anh (Vivian) Mai. E-mail: [email protected].

2

Tze Chuan ‘Chewie’ Ang. E-mail: [email protected].

3

Victor Fang. E-mail: [email protected].

Affiliation: Department of Finance, Deakin Business School, Deakin University (Australia).

* Corresponding author. Address: Department of Finance, Deakin Business School, Deakin University, 221, Burwood Highway, Burwood, Victoria 3125, AUSTRALIA. E-mail: [email protected]. Telephone: (613) 9244 6626. Fax: (613) 9244 6283.

1

ACCEPTED MANUSCRIPT Aggregate Volatility Risk and the Cross-Section of Stock Returns:

IP

T

Australian Evidence

SC R

Abstract

This study examines the relation between aggregate volatility risk and the cross-section of

NU

stock returns in Australia. We use a stock’s sensitivity to innovations in the ASX200 implied volatility (VIX) as a proxy for aggregate volatility risk. Consistent with theoretical

MA

predictions, aggregate volatility risk is negatively related to the cross-section of stock returns only when market volatility is rising. The asymmetric volatility effect is persistent throughout

D

the sample period and is robust after controlling for size, book-to-market, momentum, and

TE

liquidity issues. There is some evidence that aggregate volatility risk is a priced factor,

AC

CE P

especially in months with increasing market volatility.

2

ACCEPTED MANUSCRIPT Aggregate Volatility Risk and the Cross-Section of Stock Returns:

T

Australian Evidence

IP

1. Introduction

SC R

Understanding the relation between market volatility and stock returns is important to both academics and practitioners alike, especially in the areas of asset allocation, valuation, and risk management.1 Innovations in market volatility affect investors’ investment choices either

NU

by changing their forecast of future market performance or by changing the trade-off between

MA

risk and return. According to the multifactor models of Merton (1973) and Ross (1976), if market volatility is a systematic risk factor, it should be priced in the cross-section of stock

D

returns.

TE

Implied volatility (VIX) derived from index options often reflect investors’ expectation of future stock market volatility (see Whaley, 2000; 2009). Using changes in the VIX index as a

CE P

proxy for aggregate volatility innovations, Ang et al. (2006) find that stocks with high sensitivity to aggregate volatility earn low average future returns. Dennis et al. (2006)

AC

confirm the result and highlight the importance of the asymmetric return responses to negative shocks in aggregate volatility. Delisle et al. (2011) extend these findings by showing a negative cross-sectional relation between aggregate volatility risk and stock returns, which only exists when aggregate volatility is rising. While the knowledge about the relation between aggregate volatility risk and stock returns in the U.S. markets is advanced, there is a paucity of literature on aggregate volatility in the Australian market due to data limitations. Most Australian studies could only utilize a short sample period and focus on the information content of market volatility and/or implied volatility at the aggregate level. For example, Li and Yang (2009) and Frijns et al. (2010a)

1

We use ‘aggregate volatility’ and ‘market volatility’ interchangeably throughout the paper.

3

ACCEPTED MANUSCRIPT show that implied volatility is a better predictor of future realized aggregate volatility than other commonly used econometric models. Other Australian studies find a negative relation between aggregate volatility risk and market returns (Frijns et al., 2010b), but fail to find any

IP

findings at the aggregate and industry levels are puzzling.

T

relation at the sector or industry level (Loudon and Rai, 2007). The conflicting academic

SC R

Recently, the Australian Securities Exchange (ASX) started to post real-time S&P/ASX200 VIX index (A-VIX) on its website as an indicator of current market sentiment.

NU

The ASX also began trading futures on VIX due to increasing demand from hedgers and investors alike.2 The lack of evidence in academic research on the relation between VIX and

MA

stock returns is troubling as there seems to be a disjoint between theory and empirical evidence. These unresolved issues necessitate further studies on aggregate volatility risk in

D

the Australian market.

TE

This study fills the gap in the literature by being the first study to examine the cross-

CE P

sectional relation between aggregate volatility risk and stock returns in Australia. We are also the first to conduct asset-pricing tests on aggregate volatility risk as a priced factor in explaining the cross-sectional returns in Australia. Moreover, our study highlights the

AC

potential asymmetric relation between aggregate volatility risk and stock returns in Australia. These tests were impossible to conduct previously due to data constraints. Our study of the relation between aggregate volatility risk and stock returns in the Australian market is important. It can bridge the gap between theoretical predictions and empirical evidence on the relation between aggregate volatility risk and stock returns in Australia, which is absent in previous studies. It can also provide practical relevance of academic research to financial practitioners in light of the recent popularity of derivative products on the ASX200 VIX index. Moreover, a study of the Australian market enables us to examine whether an investment strategy based on aggregate volatility risk is practical after 2

See www.asx.com.au and www.asx.com.au/products/sp-asx200-vix-index.htm.

4

ACCEPTED MANUSCRIPT considering liquidity issues in a market populated by a large number of micro stocks, but dominated by a small number of large stocks.3 Furthermore, our study provides an out-ofsample test of the U.S. evidence on the pricing of aggregate volatility risk. It may potentially

T

rule out the data-mining concern raised by Lo and MacKinlay (1990) in typical asset-pricing

IP

studies.

SC R

Using a stock’s sensitivity to innovations in aggregate volatility as a proxy for aggregate volatility risk, we find that aggregate volatility risk is negatively related to the cross-section

NU

of stock returns in Australia when aggregate volatility is rising, but not when it is falling. The asymmetric volatility effect hinders the attempts in previous studies (e.g. Loudon and Rai

MA

(2007)) to uncover the cross-sectional link between aggregate volatility and stock returns in the Australian market. Further analyses show that this asymmetric relation is persistent

D

throughout the sample period. Size, book-to-market, momentum, and liquidity issues cannot

TE

explain the asymmetric relation. Moreover, our asset pricing tests show that aggregate

CE P

volatility risk is systematically priced, especially in months when innovations in aggregate volatility are positive. However, the incremental explanatory power of the aggregate volatility risk factor is limited in addition to the commonly used Fama and French (1993)

AC

three factor model, augmented by a momentum factor. Our findings contribute to the existing research on the cross-sectional determinants of stocks returns and asset-pricing anomalies in the Australian market.4 While previous studies show the relations between stock returns and firm size, book-to-market ratio, past returns, asset growth, amongst others, we find a robust negative relation between aggregate volatility risk and stock returns, based on a sound theoretical foundation. Furthermore, we extend the Australian asset-pricing literature (e.g. see Gray and Johnson (2011), Brailsford et al. (2012), Chai et al. (2013)) by examining the potential role of aggregate volatility risk as a factor in

3 4

See the World Federation of Exchanges website: http://www.world-exchanges.org/statistics. See O’Brien et al. (2010) and Dou et al. (2013) for a brief review on Australian asset-pricing anomalies.

5

ACCEPTED MANUSCRIPT the cross section of stock returns. In general, our study provides guidance to future assetpricing studies in Australia. The remainder of the paper proceeds as follows. Section 2 provides a brief literature

T

review and the hypotheses. Section 3 describes the sample and variables. Section 4 reports

SC R

IP

the empirical results. Section 5 concludes.

2. Background, literature review, and hypotheses

NU

The multifactor models of Merton (1973) and Ross (1976) imply that risk premiums are related to the conditional covariance between asset returns and changes in state variables that

MA

affect investors’ time-varying investment choices. In the models of Campbell (1993), (1996), investors are concerned with market returns and changes in the expectation of future market

D

returns. Chen (2002) extends the models to incorporate investors’ concern with aggregate

TE

future volatility risk. Aggregate market volatility affects investment opportunities by

CE P

changing the risk-return trade-off or investors’ expectation of future market returns. Increases in aggregate volatility limit investors’ investment choices as periods of increased volatility often coincide with adverse market movements (Whaley, 2000). Facing time-varying

AC

investment opportunities, risk-averse investors would like to hedge against a decrease in expected future market returns by purchasing stocks that are positively correlated with innovations in aggregate volatility. The demand for such stocks increases their current prices, resulting in lower expected returns in the future. This line of reasoning suggests that firm’s sensitivity to innovations in market volatility is a priced risk factor in the cross-section of stock returns.5 Implied market volatility (VIX) extracted from market index options is commonly used as an estimate of investors’ prediction of future market volatility (Whaley, 2000). Using VIX from the S&P100 index options as a proxy for aggregate volatility, Ang et al. (2006) test the 5

See Ang et al. (2006) for detailed discussions.

6

ACCEPTED MANUSCRIPT hypothesis of Campbell (1993), (1996) and Chen (2002) and find that aggregate volatility risk is priced in the cross-section of stock returns in the U.S. markets. In contrast, using portfolio formed by sectors as test assets, Loudon and Rai (2007) find no evidence that aggregate

T

volatility risk is priced in the Australian equity market.

IP

Research on the role of aggregate volatility risk on stock returns in the Australian market

SC R

is limited by data availability due to the delayed introduction of index options in Australia. In particular, the Australian Securities Exchange (ASX) only started issuing options on the

NU

ASX200 index in the early 2000s and futures on the S&P/ASX200 VIX index in October 2013 due to increasing trading and hedging demands.6 Given the data limitations, previous

MA

studies tend to focus on the risk-return relation at the aggregate market level and the information content of implied volatility about future market returns. For example, Li and

D

Yang (2009), and Frijns et al. (2010a) find that VIX has better predictive power on future

TE

realized volatility than commonly used time-series models. Frijns et al. (2010b) show an

CE P

asymmetric negative relation between aggregate volatility and ASX200 returns. In this study, we extend the Australian literature on aggregate volatility from the aggregate level to the cross-sectional (firm) level by examining the relation between aggregate volatility

AC

risk and the cross-section of stock returns in Australia. The preceding discussions suggest a negative relation between aggregate volatility risk and the cross-section of stock returns. We hypothesize that:

H1a: The sensitivity to innovations in aggregate volatility is negatively related to the cross-section of stock returns in the Australian stock market. Our hypothesis differs from Loudon and Rai (2007) as we examine the cross-sectional aggregate risk-stock return relation, rather than the pricing of aggregate risk using sectoral portfolios. Moreover, our study focuses on the cross-sectional (stock-level) returns and hence it is different from previous Australian studies, which examine the risk-return relation at the 6

See the ASX website: www.asx.com.au.

7

ACCEPTED MANUSCRIPT aggregate level. Furthermore, our sample period is longer than all previous Australian studies. Ang et al. (2006) and Loudon and Rai (2007) assume a symmetric relation between

T

innovations in market volatility and stocks returns. Nevertheless, there is a growing literature

IP

documenting the asymmetric volatility phenomenon (Schwert (1989), and Nelson (1991),

SC R

Engle and Ng (1993), Bekaert and Wu (2000), and Wu (2001) amongst others). It is a stylised fact that negative shocks in returns are associated with higher expected future volatility than

NU

positive shocks of the same magnitude. Previous studies find evidence of an asymmetric response of stock returns to innovations in volatility at the aggregate level (see Dennis et al.

MA

(2006) and Frijns et al. (2010b), for the U.S. and Australian markets, respectively.) Specifically, Delisle et al. (2011) extend the work of Ang et al. (2006) by noting that the

D

negative relation between aggregate volatility risk and the cross-section of stock returns only

TE

exists when aggregate volatility rises, but not when it falls. Based on the preceding

CE P

discussion, we hypothesize that:

H1b: The relation between aggregate volatility risk and stock returns is asymmetrical: the relation only exists when aggregate volatility rises, but not when it falls.

AC

Ang et al. (2006) find that aggregate volatility risk is negatively priced in the U.S. markets, but Loudon and Rai (2007) find no such pricing in the Australian market. We suspect that the short sample period used in Loudon and Rai (2007) substantially reduces the power of their asset-pricing tests. To reconcile the conflicting findings from these studies, we use an extensive sample period to test the following hypothesis: H2: Aggregate volatility risk is a systematically priced factor in the cross-section of stock returns in Australia. Based on the models of Campbell (1993), (1996) and Chen (2002), we expect to find a negative premium for aggregate volatility risk. For completeness, we also examine the asymmetric pricing of aggregate volatility risk. Moreover, we test whether the explanatory 8

ACCEPTED MANUSCRIPT power of a contemporary asset-pricing model (e.g. Fama and French’s (1993) three-factor model) improves with the inclusion of an aggregate volatility risk factor.

IP

T

3. Sample and variable definitions

SC R

3.1. Data

The sample contains all ordinary shares listed on the Australian Securities Exchange (ASX) from 1 January 2004 to 31 December 2014.7 We obtain all stock and accounting

NU

related data from Datastream.8 To avoid survivor bias, we include both dead and live stocks.9

MA

The number of stocks ranges from 1,240 in 2004 to 1,833 in 2014.

3.2. Measure of aggregate volatility risk

TE

D

We use the S&P/ASX200 implied market volatility (VIX) index as a proxy for aggregate volatility. The index reflects investors’ expectation of future market volatility in the

CE P

Australian market. It is sourced from www.impliedvolatility.com.au.10 Our VIX index represents the implied volatility of a synthetic, at-the-money option on the S&P/ASX200

AC

with 30 days to expiration. The VIX index is weighted with moneyness, time-to-expiry, and volume. Nearer-the-money strikes receive a higher weight than out-of-the-money strikes. Strikes more than 25% away from the underlying receive a zero weight. Options with less

7

The daily data (with at least one call and one put) on the ASX200 Index options were not consistently available up until 2004 (see Loudon and Rai (2007) and Li and Yang (2009)). We need daily data on the ASX200 Index options to construct the VIX, so we can only start our study from 2004. 8 The correlation of monthly returns between the Australian All Ordinaries Index and the value-weighted portfolio constructed from the sample is 0.985. The high correlation confirms the reliability of our data. 9 Following Ince and Porter (2006) and Griffin et al. (2010), we eliminate securities that represent cross listings, duplicates, mutual funds, trusts, certificates, notes, rights, preferred stocks, and other non-common equity. The filter rules are listed in Appendix 1. 10 Alternatively, Datastream provides data on the VIX index, but it is only available from 2008. The sample period from Datastream is too short for this study. To check for the validity of the VIX index from www.impliedvolatility.com.au, we examine its correlation with the VIX index from Datastream for the period 2008-2014. The high correlation of 0.96 confirms the reliability of our data.

9

ACCEPTED MANUSCRIPT than 7 days to expiry also receive a zero weight as near expiry options can have extreme volatility.11 Fig. 1 plots the daily level of VIX index in our sample period. It has a mean of 13.8% and

T

a standard deviation of 7.8%. These values are consistent with those reported by Frijns et al.

IP

(2010b) and Bird and Yeung (2012). The daily level of VIX is highly auto-correlated with a

SC R

first-order autocorrelation of 0.98. To achieve stationary, we measure daily innovations in aggregate volatility by using daily changes in VIX (∆VIX). Panel A of Fig. 2 plots the daily

NU

change in VIX. Its mean is effectively zero (0.001%) and its standard deviation is 1.5%. Unreported Durbin-Watson test statistic confirms that ∆VIX is not serially correlated.

MA

According to Ang et al. (2006), ∆VIX is a good proxy for changes in aggregate volatility because the VIX index is representative of traded option contracts whose prices reflect

D

volatility risk. Moreover, Frijns et al. (2010a) find that VIX is the best predictor of future

TE

stock market volatility in the Australian markets, compared to commonly used time-series

CE P

models, such as GARCH models.

[Insert Fig. 1 here] [Insert Fig. 2 here]

AC

Following Ang et al. (2006), we measure aggregate volatility risk as a stock’s sensitivity to daily innovations in VIX (∆VIX). To obtain the sensitivity measure,

, we regress daily

excess return on market excess return and innovations in VIX (∆VIX) over a two-month period: (1) where

is the excess return for firm i on day t,

is the excess market return on day t,

is the innovation in VIX from the end of day t-1 to the end of day t and

is the error

11

The methodology to construct the VIX index used in the website is similar to the one used by S&P500 and S&P/ASX200 (see Whaley (1993)), only the weighting system is different. S&P 500 and S&P/ASX200 put greater weights on at-the-money strikes than does the website. Bird and Yeung (2012) apply a similar method to construct the VIX index to measure investors’ uncertainty about future returns in Australia for the period from July 2001 to December 2007. They use the average of the implied volatilities computed from two call and two put options on the ASX200 that are closest to their respective expiry dates.

10

ACCEPTED MANUSCRIPT term. We employ a rolling regression methodology with a two-month window, re-estimated every one month.12 Each stock has a loading on the market return ( VIX (

) and innovations in

) every month.

T

Empirical studies to date have found other factors that explain the cross-section of stock

IP

returns, such as the size and value factor in Fama and French (1993) and the momentum

SC R

factor in Carhart (1997). Following Ang et al. (2006), we do not include these factors in equation (1) to avoid adding unnecessary noise in the estimation of aggregate volatility risk ). Nonetheless, we control for these factors in our cross-sectional portfolio and asset-

NU

(

pricing tests.

MA

To allow for asymmetric loadings on innovations in VIX conditional on whether VIX

if

is positive and zero otherwise,

TE

where

D

increases or decreases, we follow Delisle et al. (2011) and modify equation (1) to: (2) if

is

CE P

negative and zero otherwise. Similarly, we use a two-month estimation window, rolling forward by a month.

AC

3.3. Other variables

We also use the following variables as controls in the cross-sectional regressions. We define firm size (SIZE) as the log of market capitalization. The book-to-market ratio (BM) is the log of book equity divided by market equity. Momentum (MOM) is the cumulative returns from the end of month t-7 to the end of month t-2. We define idiosyncratic risk (IVOL) as the residual of the market model. PRET is the previous month return. TURN and VOL are monthly turnover and monthly dollar trading volume of a firm, respectively. ZEROs are the number of zero returns in the previous month, excluding zero-trading days.

12

Using a two-month estimation window with daily data is a natural trade-off between estimating coefficients with a reasonable degree of precision and incorporating the time-varying nature of the coefficients.

11

ACCEPTED MANUSCRIPT Market risk premium is the difference between market return and the risk free rate. We use the percentage change in the Australian All Ordinaries Index as a proxy for market returns. The monthly yield on 90-day bank accepted bills is the proxy for the risk free rate. The size

T

(SMB), value (HML), and momentum (WML) factors account for the return spread between

IP

small and big stocks, stocks with high and low book-to-market, and stocks with high and low

SC R

past six-month returns, respectively. The construction of the factors follow Fama and French (1993) and Carhart (1997). For our study, we modify the cut-off points according to

NU

Brailsford et al. (2012). The cut-off points for SMB and WML are the top and bottom 10th percentiles, but the cut-off points for HML is the top and bottom 30th percentiles of all ASX

MA

stocks.13

D

3.4. Descriptive statistics

,

and

CE P

of interest are

TE

Table 1 presents the descriptive statistics of the variables used in this study. The variables

respectively.14 The mean of that any impact of

. Their means are -0.065, -0.091, and -0.042,

is more than two times larger than that of

on stock returns may be stronger than

, suggesting

. Monthly return, MRET

AC

and previous-month return, PRET have similar distributions. Both of them have a mean and median of around 0.7% and 0%, respectively. The mean of SIZE and BM are comparable to those reported in Dou et al. (2013). The average firm size is around $38 million. In general, the market capitalization and liquidity measures reflect the nature of a large number of infrequently-traded micro stocks in the Australian market. Specifically, half of the market is populated by firms with market capitalization of around $25 million or less. Moreover, many firms have low turnover (TURN) and frequent zero-return trading days (ZERO). [Insert Table 1 here]

13 14

We thank Philip Gray for the Australian data on the Fama-French factors. Unreported t-statistics show that they are significant at the 1% level.

12

ACCEPTED MANUSCRIPT 4. Empirical results As a preliminary gauge of the relation between aggregate volatility risk and stock returns, we plot the daily time-series of VIX and the ASX200 Index from 31 December 2003 through

IP

T

31 December 2014 in Fig. 1. Visual inspection of the time-series suggests a negative relation between them, similar to the finding in Frijns et al. (2010a, 2010b). High (Low) levels of VIX

SC R

seem to coincide with decreases (increases) in the ASX200 Index. Furthermore, Panels A and B of Fig. 2 show that periods with large changes in VIX are contemporaneous with large

NU

changes in the ASX200 returns.

Formally, we use portfolio sorts and cross-sectional Fama-McBeth regressions to test

MA

whether stocks with different exposures to innovations in aggregate volatility have different average returns in the Australian market. Moreover, we employ asset-pricing tests to examine

CE P

4.1. Portfolio sort

TE

D

whether aggregate volatility risk is priced in the cross-section of stock returns in Australia.

To examine the relation between aggregate volatility risk and the cross-section of stock returns, we need to construct portfolios with sufficient dispersion in their sensitivity to

AC

innovations in aggregate volatility (β∆VIX). Following Ang et al. (2006), we sort stocks into quintiles based on their β∆VIX obtained from equation (1) using data over the past two months. Firms in quintile 1 have the lowest β∆VIX, while firms in quintile 5 have the highest β∆VIX. Within each quintile portfolio, we compute value-weighted mean of the variable of interest (e.g. stock returns, β∆VIX, etc.) according to their market capitalization in the previous month.15 We report the portfolio results as the time-series averages of cross-sectional valueweighted means. To examine the asymmetric effect of β∆VIX on stock returns, we follow Delisle et al. (2011) and sort stocks into quintiles based on their

and

from

15

Given that the Australian market consists of many small and illiquid stocks, empirical results based on valueweighting are more meaningful (see Gray, 2014). Nonetheless, equally-weighting stocks within a portfolio give qualitatively similar results.

13

ACCEPTED MANUSCRIPT equation (2), where

and

are the loadings on innovations in VIX conditional on

whether VIX increases or decreases.

IP

T

4.1.1. Main results

, and spread in

SC R

Panels A to C of Table 2 present the quintile portfolio characteristics sorted by

,

, respectively. The extreme portfolios in these three sorts show significant ,

, and

, respectively. Panel A shows that stocks with high

NU

are significantly larger and more liquid than those with low

as reflected by their

differences in size and liquidity measures (e.g. TURN). They have higher previous month

MA

return (PRET) and are also less volatile than their low

counterparts. However, there is

no significant difference in characteristics between the extreme quintile portfolios in terms of

D

BM or momentum.

TE

In general, the characteristics of quintiles sorted by

. In contrast, when we sort by

in Panel C, there is

CE P

are similar to those sorted by

(as shown in Panel B of Table 2)

not much difference in the characteristics between the extreme quintile portfolios, except for

AC

past returns. Previous-month and past six-month returns for stocks with high significantly larger than their low

are

counterparts. [Insert Table 2 here]

Table 3 reports the average returns and alphas from the Capital Asset Pricing Model (CAPM), Fama and French (1993) three-factor model and Carhart (1997) four-factor model for the quintile portfolios. We also show the factor loadings of the Carhart (1997) four-factor model. When we sort stocks by their

, there seems to be an inverted ‘U’ pattern in the

mean monthly portfolio returns and their alphas – increasing and then decreasing in

(as

shown in Panel A). Nonetheless, the differences in mean returns between quintile portfolios 5 and 1 (hereafter the zero-cost (hedge) returns) are all insignificant. This finding disagrees

14

ACCEPTED MANUSCRIPT with those by Ang et al. (2006), who discover the pricing of aggregate volatility risk in the U.S. markets. However, our finding is more consistent with those by Loudon and Rai (2007), who find that aggregate volatility risk is not systematically priced in Australia. Interestingly,

SC R

[Insert Table 3 here]

IP

portfolios have any significant loadings on the other factors.

T

while the portfolios show significant loadings on the market factor, almost none of the

The results in Panel A of Table 3 suggest a lack of relation between aggregate volatility

NU

risk and cross-sectional stock returns. However, under the asymmetric volatility hypothesis, we expect to find a significant difference in stock returns sorted by

, which is a stock’s sensitivity to ∆VIX when

MA

form quintile portfolios based on

. In Panel B, we

aggregate volatility is rising. Apart from portfolio 3, the mean portfolio returns and all alphas . Specifically, the zero-cost (hedge) returns are all

D

are monotonically decreasing in

portfolios have significantly negative alphas.

TE

significantly negative. Moreover, the high

CE P

Consistent with the findings in Delisle et al. (2011), the results imply that investors seem to pay a premium for stocks with high exposure to aggregate volatility risk, resulting in low average returns. If we look at the factor loadings, we see a ‘U’ shape relation between

AC

and market risk premium as we move along the

spectrum. Furthermore, high

portfolios have significantly lower exposure to the market returns than their low counterparts. However, almost none of the portfolios are significantly related to the other factors. In Panel C of Table 3, we perform a similar test as before by forming portfolios on

.

These portfolios are different from those in Panel B. There is no significant pattern in the average returns or alphas across stocks sorted on relation between

. However, there is a ‘U’ shape

and market risk premium as well as the size factor. Moreover, the

portfolio with the highest

have significant positive exposure to the momentum factor

compared to the portfolio with the lowest

. 15

ACCEPTED MANUSCRIPT Overall, the results in Table 3 suggest that the negative relation between aggregate volatility risk and the cross-section of stock returns only exists when aggregate volatility is increasing, but not when it is decreasing. Moreover, aggregate volatility risk does not covary

SC R

4.1.2. Sub-period analysis and robustness checks

IP

T

with common risk factors.

We conduct a sub-period analysis of the main results by examining the month-by-month

NU

profit from a zero-cost (hedge) investment strategy of buying the portfolio with the highest and simultaneously shorting the portfolio with the lowest

. Fig. 3 plots the profit

MA

from the strategy. Throughout of the whole sample period, the strategy generates negative returns 61% of the time and the losses are quite persistent. The analysis suggests that the

) are not a result of a one-off event, such as the Global Financial Crisis in 2008.

TE

(

D

negative average returns on stocks with high exposure to positive aggregate volatility risk

CE P

As robustness tests, we also winsorize and trim stock returns at the 0.5% and 1% levels (in turns) to avoid the influence of outliers. Moreover, we equally-weight stocks within each

AC

portfolio. Overall, the results are qualitatively similar in those tests.

4.2. Cross-sectional regressions Thus far, we have established a negative relation between aggregate volatility risk and stock returns at the portfolio level. Nonetheless, previous studies find that other characteristics, such as market capitalization and book-to-market ratio (e.g. Fama and French (1992)), and past returns (e.g. Jegadeesh and Titman (1993)) also predict future stock returns. In this section, we employ Fama-McBeth regressions to examine the role of aggregate volatility risk in explaining the cross-section of individual stock returns after controlling for

16

ACCEPTED MANUSCRIPT other stock characteristics. Specifically, we regress monthly returns on aggregate risk generated using data from the previous month and on lagged values of control variables. Panel A of Table 4 shows the average correlations between the variables used in the

T

regressions and Panel B reports the regression results. Our baseline model includes the

IP

following variables: market beta, size, book-to-market ratio, and momentum. We include

SC R

market beta for completeness and as a control for market wide movements that may be related to innovations in aggregate volatility, β∆VIX. As expected, all the models show that

NU

market beta is not related to cross-sectional stock returns. Consistent with previous Australian studies (e.g. Beedles et al. (1988) and Gaunt (2004)), Models 1 through 10 confirm the size

MA

and value effects in Australia. Small firms earn higher average stock returns than large firms and firms with high book-to-market ratios have better stock returns than their low book-to-

D

market ratios counterparts. However, the magnitude of the size (value) effect in our sample

TE

period (2004–2014) is lower (higher) than the results reported in previous studies (see Chai et

CE P

al. (2013)). Interestingly, there is a lack of momentum effect. This puzzling finding is in line with Dou et al. (2013) who find that the Australian momentum effect concentrates in large

AC

and small stocks, but is absent across the whole market. [Insert Table 4 here]

We include the sensitivity to innovations in VIX, β∆VIX in Model 2. We further decompose into

in Model 3 and

in Model 4.

is significant, but not

and

. Hence, the results from Models 2 to 4 confirm the finding in the previous section that aggregate volatility risk (as proxied by β∆VIX) explains the cross-sectional variations of stock returns only when aggregate volatility increases. Specifically, one unit increase in the sensitivity to ∆

leads to a negative 0.1% average return in the subsequent month. To

avoid any omitted variable bias, we include both

and

in Model 5. The result

remains similar.

17

ACCEPTED MANUSCRIPT We control for idiosyncratic volatility, IVOL in Model 6 since previous Australian studies find evidence of return-predictability using idiosyncratic volatility (Grant and Phung, 2010). Previous Australian studies also find a link between past-month returns and current-month

T

returns (see Gray and Gaunt, 2003), so we include past-month return, PRET to control for

becomes even more significant after controlling for PRET or IVOL.

SC R

the coefficient on

IP

short-term reversal (Jegadeesh, 1990) and bid-ask bounce in Model 7. The results show that

Moreover, the adjusted R2 in those models are the highest amongst all the models. These

NU

findings reflect the importance of idiosyncratic volatility and short-term reversal in explaining the cross-section of Australian stock returns.

MA

The asymmetric relation between aggregate volatility risk and stock returns may be driven by illiquidity issues in the Australian market (see Chan and Faff (2003) and Chai et al.

D

(2013)). Portfolios characteristics shown in Table 2 also suggest significant differences in

TE

liquidity between portfolios with extreme aggregate volatility risk. Thus, we include proxies

CE P

to control for illiquidity issues in the Australian market in Models 8 to 10. The coefficients on dollar turnover (TURN) and trading volume (VOL) are significant, but not those on the number of zero returns (ZERO). Most importantly, the main result remains unchanged.

AC

Gray (2014) raises the issues of illiquidity and non-trading in the Australian stock market and the tradability of investment strategies in Australia. Following Gray (2014), in Model 11, we limit the sample firms to the top 500 firms in Australia as they are liquid and frequently traded.16 The key result remains robust: The magnitude of

is strongly negatively related to stock returns.

is even higher compared to Models 5 to 10, but its significance

slightly diminishes. Moreover, consistent with Dou et al. (2013) and Gray (2014), we find a strong momentum and a weak value effect, but no size effect in ASX500 firms. Overall, we find a negative relation between aggregate volatility risk and future stock returns when aggregate volatility is increasing, but not when it is decreasing. The result 16

The results are qualitatively similar if we limit the sample to firms on the ASX200 or ASX300.

18

ACCEPTED MANUSCRIPT remains robust after controlling for common predictors of cross-sectional returns and illiquidity issues.

IP

T

4.3. Asset-pricing tests

In this section, we test whether aggregate volatility risk is a systematically priced factor in

SC R

the cross-section of stock returns using a two-stage cross-sectional regression approach (see Cochrane (2005)). In the first stage, we run time-series regressions to estimate factor betas on

NU

a set of test assets. In the second stage, we use a cross-sectional regression to estimate the factor risk premiums. We also examine the incremental power of the aggregate volatility risk

MA

factor in capturing common variations in stock returns.

D

4.3.1. First stage: Time-series regressions

TE

In stage one, we estimate factor betas using time-series regressions of the Carhart (1997)

CE P

four factor model, augmented with an aggregate volatility risk factor, FVIX. The model is as

where

AC

follows:

and

, are the time t excess returns on test asset

(3) and the market portfolio,

respectively; SMBt, HMLt and, WMLt are the size, value, and momentum factors; and

is

the error term. We include the size, value, and momentum factors as controls as previous studies show that they are contemporaneously related to stock returns (see Carhart (1997)). We use three sets of test assets for our assets-pricing tests. Our first set of test assets follows Ang et al. (2006). We form portfolios with sufficient cross-sectional dispersion in the factor loadings on market volatility risk to ensure that our asset-pricing tests have reasonable power. They consists of 5 x 5 portfolios independently sorted by

and

. We obtain

19

ACCEPTED MANUSCRIPT and

from equation (1). For completeness and comparability with previous

Australian asset-pricing studies, we use a second set of test assets: 5 x 5 portfolios independently sorted by market capitalization and the book-to-market ratio. Monthly average

T

returns are value-weighted within each portfolio. We also use a third set of test assets, which

IP

consist of individual stocks.17 Our choice is motivated by recent studies that advocate the

SC R

benefits of using individual test assets as opposed to portfolio-based test assets (see Ang et al. (2010), Jegadeesh and Noh (2014), and Chordia et al. (2015)).

is a poor approximation for

NU

Ang et al. (2006) note that at the monthly level,

innovations in aggregate volatility because the unanticipated change in VIX at lower

MA

frequencies is largely determined by the conditional means of VIX. To measure sensitivity to aggregate volatility risk at a monthly frequency, we follow Ang et al. (2006) and create a

D

factor, FVIX that mimics ex post aggregate volatility risk. Specifically, FVIX is a tracking

TE

portfolio of assets returns maximally correlated with realized innovations in volatility using a

CE P

set of base assets (Lamont, 2001). We start by creating daily FVIX that tracks daily changes in the VIX index. Specifically, we regress daily changes in VIX against daily excess returns on a set of base assets with a one-month rolling window. The base assets are the five quintile

AC

portfolios sorted on

where

in Table 2. Our regressions take the form of:

is the daily changes in VIX and

(4) is the daily excess returns on the

quintile portfolios. The fitted part of the regression is the aggregate volatility risk factor, FVIX: (5)

17

We thank the anonymous referee for suggesting this test. Given that the stocks are not grouped in portfolios, we exclude stocks with less than three years of data to avoid unnecessary noise created by micro stocks in the sample.

20

ACCEPTED MANUSCRIPT Finally, to proxy for aggregate volatility risk at the monthly frequency, we cumulate daily returns over the month on the underlying base assets used to construct the mimicking factor.18 FVIX allows us to examine the contemporaneous relation between factor loadings and

T

average returns.

IP

Daily FVIX depicted in Fig. 4 shows a close resemblance to the daily realized ∆VIX in

SC R

Panel A of Fig. 2. Their correlation is around 70%. Panel A of Table 5 reports the correlations between FVIX and other factors used in the asset-pricing test. Importantly, the

NU

mimicking aggregate volatility factor, FVIX is closely related to monthly realized ∆VIX. FVIX is also negatively associated with excess market return, MKT, reflecting the low market

MA

return over increasing aggregate volatility periods as depicted in Fig. 1 and Fig. 2. On the other hand, the pairwise correlations between FVIX and other pricing factors (SMB, HML and

D

WML) are low.

TE

[Insert Fig. 4 here]

CE P

[Insert Table 5 here]

Panel B of Table 5 presents the average coefficients from the first-stage time-series regressions.19 Overall, the contemporaneous relation between the factors and excess returns

AC

are consistent across all the test assets. Specifically, FVIX has a significant negative contemporaneous relation with excess returns in almost all the models (except in Models 6 and 9). However, it is important to note that the contemporaneous time-series relation does not imply that FVIX is a priced risk factor in the cross-section of returns (see Core et al. (2008)). Throughout all the models, the market, size and value factors show significant positive relation with excess returns, consistent with the results in previous Australian studies (e.g. Brailsford et al. (2012)). However, the momentum factor shows a significant negative

18

Ang et al. (2006) note the advantages of the factor mimicking aggregate volatility risk, FVIX. We can use it at any frequency and do not have to specify the conditional mean for VIX, which depends on different sampling frequency. See Barinov (2012) for an application of the methodology. 19 For parsimony, we do not tabulate all the coefficients for each regression, but the tables are available upon request.

21

ACCEPTED MANUSCRIPT relation with excess returns. This puzzling finding may be driven by the negative momentum in returns prevalent in micro stocks in Australia. It is consistent with previous studies (e.g. Dou et al., 2013) that document a lack of momentum in Australian stock returns, especially

T

when micro stocks are included in the sample.

IP

The explanatory power of the models with only the market factor and FVIX is around 50%

SC R

in the first two test portfolios and 9% in the individual test assets. However, the inclusion of size, value, and momentum factors in the models significantly improves the adjusted R2. The

NU

greatest improvement lies in the models with test portfolios sorted by size and book-tomarket ratio. Their adjusted R2s increase from 51% to almost 80%. Overall, the explanatory

MA

power of the models (adjusted R2) barely improves with the inclusion of FVIX. Thus, FVIX is an important factor in explaining the time-series variations in realized stock returns, but it

D

only marginally improves the explanatory power of a model with the size, value, and

TE

momentum factors.20

CE P

4.3.2. Second stage: Cross-section regression In stage two of the asset-pricing test, we are interested in estimating the risk premiums of

AC

the pricing factors. We run a cross-sectional regression of the time-series mean excess testasset returns on the factor betas we obtained from our time-series regressions in stage one: 21 (6) where

is the time-series mean excess return on test asset ,

and

over the sample period,

,

are the factor betas estimated from the first-stage regressions,

denote the corresponding factor risk premiums and

is the error term. Using betas from the

first-stage regressions as regressors in the second-stage regressions poses an error-invariables problem. Thus, we compute the standard errors using Shanken (1992) correction to 20

The marginal role of FVIX in terms of its explanatory power in asset-pricing models is analogous to that of a liquidity factor documented by Chai et al. (2013). 21 As a robustness check, we also run rolling Fama-MacBeth regressions. The results are qualitatively similar.

22

ACCEPTED MANUSCRIPT adjust for the overstated precision of the standard errors. If

is significant, then

aggregate volatility risk is a priced factor that explains the cross-sectional variation in stock returns. The sign of

shows whether aggregate volatility risk attracts a positive or

T

negative risk premium. We expect to find a negative aggregative volatility risk premium, but

IP

our relatively short sample period may bias against finding any significant risk premium.

SC R

Panel C of Table 5 reports the results. The aggregate volatility risk premium is insignificant in the models with test assets sorted by βMKT and β∆VIX (see part (i) of Panel C).

NU

The risk premiums for all other factors (MKT, SMB, HML, and WML) are also insignificant because they are imprecisely estimated from the test assets sorted by βMKT and β∆VIX (see Ang

MA

et al. (2006) and Core et al. (2008)).

For completeness and as a comparison with other asset-pricing studies, we present the

D

factor risk premiums of test assets sorted by size and BM in part (ii) of Panel C of Table 5.

TE

The aggregate volatility risk premium remains insignificant and has the opposite sign. This is

CE P

expected because the risk premiums are imprecisely estimated as the stocks are sorted by size and book-to-market ratio with the objective to estimate the risk premiums for the size and value factors. In all the models, the market risk premium,

is negative or insignificant.

AC

This finding is typical of asset-pricing tests that use realized returns (see Petkova (2006) and Core et al. (2008)).22 Moreover, the size and momentum factor also do not attract any risk premium in our sample period, as reflected by the insignificant

and

. The

insignificant size premium may be driven by the poor performance of small stocks in the 2000s, especially after the global financial crisis. The finding of insignificant market and size risk premium echoes the results reported in Petkova (2006) and Core et al. (2008). On the other hand, the value factor attracts a significant risk premium, which is slightly higher than that reported by Gray and Johnson (2011).

22

Fama (1996) interprets the negative market premium as a hedge against uncertainty in the states variables.

23

ACCEPTED MANUSCRIPT Part (iii) of Panel C of Table 5 presents the results for the asset-pricing test using individual test assets. We find a negative, but insignificant aggregate volatility risk premium. Moreover, our findings show a significantly positive market risk premium and a weakly

T

positive momentum premium, but an insignificant size premium. The market, size, and

IP

momentum risk premiums (in terms of signs) are somewhat consistent with those reported in

SC R

Chordia et al. (2015), but the value premium is significantly negative.23

Overall, we do not find any strong evidence that aggregate volatility risk is priced in the

NU

cross-section of stock returns in Australia.

MA

4.3.3. Asymmetric pricing of aggregate volatility risk? In this section, we repeat our asset-pricing tests by partitioning sample months into those

D

with positive and those with negative realized aggregate volatility risk to examine the

and

, where

(

) is equal to FVIX for

CE P

to partitioning FVIX into

TE

possibility of an asymmetric pricing of aggregate volatility risk. Essentially, that is equivalent

sample months with positive (negative) FVIX and zero otherwise. This exercise enable us to reconcile with our cross-sectional finding that a firm’s sensitivity to aggregate volatility risk

AC

is negatively related to stock returns when aggregate volatility increases (see Tables 3 and 4). Our asymmetric pricing tests are also motivated by the asymmetric relation between aggregate volatility risk and stock returns documented in previous studies (e.g. Delisle et al. (2011)). Panel A of Table 6 presents the summary results for the first-stage time-series regressions. Models 1 to 6 show that

is significantly negatively related to contemporaneous stock

returns. However, the contemporaneous relation between

and stock returns is

inconsistent throughout the models. The results suggest that aggregate volatility risk explains 23

We suspect that the opposite sign in the value premium is driven by the noise created in the asset-pricing test using individual test-assets with small and micro stocks in the sample. Since our focus is on the pricing of aggregate volatility risk, we leave this puzzle for future research.

24

ACCEPTED MANUSCRIPT contemporaneous stock returns very well only when aggregate volatility increases, but not when aggregate volatility decreases. Controlling for the size, value, and momentum factors does not change the results. We note that the magnitude and significance of all other factors

IP

[Insert Table 6 here]

T

in all the models are close to those presented in Panel B of Table 5.

SC R

In Panel B of Table 6, we report the results for the second-stage cross-section regressions. Parts (i) and (iii) of Panel B show that aggregate volatility risk commands a significant

NU

negative risk premium in months with increasing aggregate volatility (as reflected by the significantly negative coefficient,

), but not in months with decreasing aggregate ). Echoing Delisle et al. (2011),

MA

volatility (as shown by the insignificant coefficient,

the results highlight the need of partitioning the aggregate volatility risk factor into two

D

factors, depending on the sign of aggregate volatility. On the other hand, similar to part (ii) of

TE

Panel C of Table 5, the risk premium of aggregate volatility is not estimated precisely in test

CE P

assets sorted by size and the book-to-market ratio. Only the value factor attracts a positive risk premium. The remaining factors remain similar to their counterparts in the case without partitioning the aggregate volatility factor (see Panel C of Table 5).

AC

Overall, the evidence shows that aggregate volatility risk is priced in the cross-section of stock returns only when aggregate volatility is increasing, but not when it is decreasing. The results imply that investors pay a premium (i.e. negative premium) for stocks with high sensitivity to aggregate volatility when aggregate volatility increases. This interpretation is consistent with the view that investors wish to hedge against market downside risk (e.g. Bakshi and Kapadia (2003)) or deterioration in investment opportunities in general (e.g. Campbell (1996)), especially in the increasing aggregate volatility environment. Nonetheless, we need to interpret the aggregate volatility risk premium with caution, as noted by Ang et al. (2006). This is due to our relatively short sample period used to estimate the risk premium and the existence of positive VIX jumps in the sample period, which allow

to perform 25

ACCEPTED MANUSCRIPT well in pricing stock returns. Nonetheless, the persistency of hedge returns in Fig. 3 alleviates part of our concern and gives us more assurance that aggregate volatility risk is systematically priced. Hopefully, the availability of longer time-series of VIX and the

T

introduction of futures on VIX on the ASX may pave the path for more research on aggregate

SC R

IP

volatility risk in the near future.

5. Conclusion

NU

In the framework of multifactor models (e.g. Merton (1973)), investors would hedge aggregate volatility risk as increases in aggregate volatility erode their investment

MA

opportunities. Increased hedging demand pushes the price of assets positively correlated with aggregate volatility risk upwards, resulting in lower expected returns. This line of reasoning

D

predicts aggregate volatility risk to be negatively priced in the cross-section of stock returns.

TE

This study explores the link between aggregate volatility risk and the cross-section of

CE P

stock returns in Australia. We use a stock’s exposure to innovations in the S&P/ASX200 implied volatility (VIX) index as a proxy for aggregate volatility risk. We find a negative relation between aggregate volatility risk and the cross-section of stock returns only when

AC

aggregate volatility increases, but not when it decreases. This asymmetric relation is persistent throughout the sample period and is robust after controlling for size, book-tomarket, momentum, and liquidity. Our results highlight the importance of considering the asymmetric aggregate volatility effect on the cross-section of stock returns. We also find evidence that aggregate volatility risk is a significant priced factor in the cross-section of stock returns, especially when aggregate volatility is increasing. However, its role in explaining the time-series variation in stock returns is limited. Thus, the hunt for a better factor model to explain the cross-sectional variations in stock returns continues.

26

ACCEPTED MANUSCRIPT Acknowledgements We are grateful to an anonymous referee, Ed Lin, Daisy Doan, and seminar participants at Deakin University and the 2014 Accounting and Finance Association of Australia and New

IP

T

Zealand (AFAANZ) Conference for helpful comments. We thank Philip Gray for providing

AC

CE P

TE

D

MA

NU

SC R

data. All errors are our own.

27

ACCEPTED MANUSCRIPT References

AC

CE P

TE

D

MA

NU

SC R

IP

T

Ang, A., Hodrick, R. J., Xing, Y. & Zhang, X. 2006. The cross-section of volatility and expected returns. The Journal of Finance, 61, 259-299. Ang, A., Liu, J. & Schwarz, K. 2010. Using stocks or portfolios in tests of factor models. Unpublished working paper, Columbia University. Bakshi, G. & Kapadia, N. 2003. Delta-hedged gains and the negative market volatility risk premium. The Review of Financial Studies, 16, 527–566. Barinov, A. 2012. Aggregate volatility risk: Explaining the small growth anomaly and the new issues puzzle. Journal of Corporate Finance, 18, 763-781. Beedles, L., Dodd, P. & Officer, R. 1988. Regularities in Australian share returns. Australian Journal of Management, 13, 1-29. Bekaert, G. & Wu, G. 2000. Asymmetric volatility and risk in equity market. Review of Financial Studies, 13, 1-42. Bird, R. & Yeung, D. 2012. How do investors react under uncertainty? Pacific-Basin Finance Journal, 20, 310-327. Brailsford, T., Gaunt, C. & O'brien, M. A. 2012. Size and book-to-market factors in Australia. Australian Journal of Management, 37, 261-281. Campbell, J. Y. 1993. Intertemporal asset pricing without consumption data. American Economic Review, 83(3), 487-512. Campbell, J. Y. 1996. Understanding Risk and Return. Journal of Political Economy, 104, 298. Carhart, M. M. 1997. On Persistence in Mutual Fund Performance. The Journal of Finance, 52, 57-82. Chai, D., Faff, R. & Gharghori, P. 2013. Liquidity in asset pricing: New Australian evidence using low-frequency data. Australian Journal of Management, 38, 375-400. Chan, H. W. & Faff, R. W. 2003. An investigation into the role of liquidity in asset pricing: Australian evidence. Pacific-Basin Finance Journal, 11, 555. Chen, J. 2002. Intertemporal CAPM and the Cross-section of stock returns Intertemporal. Unpublished working paper, University of Southern California. Chordia, T., Goyal, A. & Shanken, J. 2015. Cross-sectional asset pricing with individual stocks. Unpublished working paper, Emory University. Cochrane, J. 2005. Asset Pricing. Princeton University Press, Princeton. Core, J. E., Guay, W. R. & Verdi, R. 2008. Is accruals quality a priced risk factor? Journal of Accounting & Economics, 46, 2-22. Delisle, R. J., Doran, J. S. & Peterson, D. R. 2011. Asymmetric pricing of implied systematic volatility in the cross-section of expected returns. Journal of Futures Markets, 31, 34-54. Dennis, P., Mayhew, S. & Stivers, C. 2006. Stock Returns, Implied Volatility Innovations, and the Asymmetric Volatility Phenomenon. Journal of Financial & Quantitative Analysis, 41, 381-406. Dou, P., Gallagher, D. & Schneider, D. 2013. Dissecting anomalies in the Australian stock market. Australian Journal of Management, 38, 353-373. Engle, R. F. & Ng, V. K. 1993. Measuring and Testing the Impact of News on Volatility. The Journal of Finance, 48, 1749-1778. Fama, E. F. 1996. Multifactor Portfolio Efficiency and Multifactor Asset Pricing. Journal of Financial & Quantitative Analysis, 31, 441-465. Fama, E. F. & French, K. R. 1992. The cross-section of expected stock returns. The Journal of Finance, 47, 427-465. Fama, E. F. & French, K. R. 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3-56.

28

ACCEPTED MANUSCRIPT

AC

CE P

TE

D

MA

NU

SC R

IP

T

Frijns, B., Tallau, C. & Tourani-Rad, A. 2010a. Australian implied volatility index. The Finsia Journal of Applied Finance, 31-35. Frijns, B., Tallau, C. & Tourani-Rad, A. 2010b. The Information Content of Implied Volatility: Evidence from Australia. The Journal of Futures Markets, 30, 134-155. Gaunt, C. 2004. Size and book to market effects and the Fama French three factor asset pricing model: evidence from the Australian stockmarket. Accounting and Finance, 44, 27-44. Grant, A. R. & Phung, J. 2010. Idiosyncratic Volatility, Return Reversals and Momentum: Australia Evidence. Unpublished working paper, University of Sydney. Gray, P. 2014. Stock weighting and nontrading bias in estimated portfolio returns. Accounting and Finance 54, 467-503. Gray, P. & Gaunt, C. 2003. Short-term autocorrelation in Australian equities. Australian Journal of Management, 28, 97-117. Gray, P. & Johnson, J. 2011. The relationship between asset growth and the cross-section of stock returns. Journal of Banking & Finance, 35, 670-680. Griffin, J. M., Kelly, P. J. & Nardari, F. 2010. Do Market Efficiency Measures Yield Correct Inferences? A Comparison of Developed and Emerging Markets. The Review of Financial Studies, 23, 3225-3277. Ince, O. S. & Porter, R. B. 2006. Individual Equity Return Data From Thomson Datastream: Handle with care! The Journal of Financial Research, 29, 463-479. Jegadeesh, N. 1990. Evidence of Predictable Behavior of Security Returns. The Journal of Finance, 45, 881-898. Jegedeesh, N. & Noh, J. 2013. Empirical tests of asset pricing models with individual stocks. Unpublished working paper, Emory University. Jegadeesh, N. & Titman, S. 1993. Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48, 65-91. Lamont, O. A. 2001. Economic tracking portfolios. Journal of Econometrics, 105, 161-184. Li, S. & Yang, Q. 2009. The relationship between implied and realized volatility: evidence from the Australian stock index option market. Review of Quantitative Finance and Accounting, 32(4), 405-419. Lo, A. & Mackinlay, A. C. 1990. Data-snooping biases in tests of financial asset pricing models. Review of Financial Studies, 3, 431-467. Loudon, G. F. & Rai, A. M. 2007. Is volatility risk priced after all? Some disconfirming evidence. Applied Financial Economics, 17, 357-368. Merton, R. C. 1973. An Intertemporal Capital Asset Pricing Model. Econometrica, 41, 867887. Nelson, D. B. 1991. Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, 347-370. O’brien, M. A., Brailsford, T. & Gaunt, C. 2010. Interaction of size, book-to-market and momentum effects in Australia. Accounting & Finance, 50, 197-219. Petkova, R. 2006. Do the Fama–French Factors Proxy for Innovations in Predictive Variables? Journal of Finance, 61, 581-612. Ross 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13, 341-360. Schwert, G. W. 1989. Why Does Stock Market Volatility Change Over Time? Journal of Finance, 44, 1115-1153. Shanken, J. 1992. On the estimation of beta-pricing models. Review of Financial Studies, 5. Whaley, R. E. 1993. Derivatives on Market Volatility: Hedging Tools Long Overdue. The Journal of Derivatives, 71-84. Whaley, R. E. 2000. The Investor Fear Gauge. Journal of Portfolio Management, 26, 12-17. Whaley, R. E. 2009. Understanding the VIX. Journal of Portfolio Management, 35, 98-105. 29

ACCEPTED MANUSCRIPT

AC

CE P

TE

D

MA

NU

SC R

IP

T

Wu, G. 2001. The Determinants of Asymmetric Volatility. Review of Financial Studies, 14, 837-859.

30

D

TE

CE P

AC

Fig. 1. Daily VIX and ASX200. This figure plots the daily levels of VIX and ASX200 from 31 December 2003 through 31 December 2014.

0

20

10

30

T

IP

SC R

NU

MA

Dec-2003 Feb-2004 Apr-2004 Jun-2004 Aug-2004 Oct-2004 Dec-2004 Feb-2005 Apr-2005 Jun-2005 Aug-2005 Oct-2005 Dec-2005 Feb-2006 Apr-2006 Jun-2006 Aug-2006 Oct-2006 Dec-2006 Feb-2007 Apr-2007 Jun-2007 Aug-2007 Oct-2007 Dec-2007 Feb-2008 Apr-2008 Jun-2008 Aug-2008 Oct-2008 Dec-2008 Feb-2009 Apr-2009 Jun-2009 Aug-2009 Oct-2009 Dec-2009 Feb-2010 Apr-2010 Jun-2010 Aug-2010 Oct-2010 Dec-2010 Feb-2011 Apr-2011 Jun-2011 Aug-2011 Oct-2011 Dec-2011 Feb-2012 Apr-2012 Jun-2012 Aug-2012 Oct-2012 Dec-2012 Feb-2013 Apr-2013 Jun-2013 Aug-2013 Oct-2013 Dec-2013 Feb-2014 Apr-2014 Jun-2014 Aug-2014 Oct-2014 Dec-2014

ACCEPTED MANUSCRIPT VIX ASX 200

60 8000

50 7000

40 6000

5000

4000

3000

2000

1000 0

31

-6

-10 -8 2

-2 0

6

4

D

TE

CE P

-4

Fig. 2. Daily ∆VIX and ASX200 returns. Panel A plots the daily change in VIX. Panel B plots the daily return on the ASX200 index. The sample period is from 2 January 2004 to 31 December 2014.

AC

Jan-04 Mar-04 May-04 Jul-04 Sep-04 Nov-04 Jan-05 Mar-05 May-05 Jul-05 Sep-05 Nov-05 Jan-06 Mar-06 May-06 Jul-06 Sep-06 Nov-06 Jan-07 Mar-07 May-07 Jul-07 Sep-07 Nov-07 Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09 Mar-09 May-09 Jul-09 Sep-09 Nov-09 Jan-10 Mar-10 May-10 Jul-10 Sep-10 Nov-10 Jan-11 Mar-11 May-11 Jul-11 Sep-11 Nov-11 Jan-12 Mar-12 May-12 Jul-12 Sep-12 Nov-12 Jan-13 Mar-13 May-13 Jul-13 Sep-13 Nov-13 Jan-14 Mar-14 May-14 Jul-14 Sep-14 Nov-14

B Daily ASX200 Returns

8

T

IP

25 20 15 10 5 0 -5 -10 -15 -20 -25

SC R

NU

MA

Jan-04 Mar-04 May-04 Jul-04 Sep-04 Nov-04 Jan-05 Mar-05 May-05 Jul-05 Sep-05 Nov-05 Jan-06 Mar-06 May-06 Jul-06 Sep-06 Nov-06 Jan-07 Mar-07 May-07 Jul-07 Sep-07 Nov-07 Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09 Mar-09 May-09 Jul-09 Sep-09 Nov-09 Jan-10 Mar-10 May-10 Jul-10 Sep-10 Nov-10 Jan-11 Mar-11 May-11 Jul-11 Sep-11 Nov-11 Jan-12 Mar-12 May-12 Jul-12 Sep-12 Nov-12 Jan-13 Mar-13 May-13 Jul-13 Sep-13 Nov-13 Jan-14 Mar-14 May-14 Jul-14 Sep-14 Nov-14

ACCEPTED MANUSCRIPT

A

Daily ∆VIX

32

ACCEPTED MANUSCRIPT 20 15 10 5

T

0

IP

-5

SC R

-10 -15

NU

Mar-04 Jun-04 Sep-04 Dec-04 Mar-05 Jun-05 Sep-05 Dec-05 Mar-06 Jun-06 Sep-06 Dec-06 Mar-07 Jun-07 Sep-07 Dec-07 Mar-08 Jun-08 Sep-08 Dec-08 Mar-09 Jun-09 Sep-09 Dec-09 Mar-10 Jun-10 Sep-10 Dec-10 Mar-11 Jun-11 Sep-11 Dec-11 Mar-12 Jun-12 Sep-12 Dec-12 Mar-13 Jun-13 Sep-13 Dec-13 Mar-14 Jun-14 Sep-14 Dec-14

-20

AC

CE P

TE

D

MA

Fig. 3. Monthly value-weighted mean zero-cost (hedge) returns. This figure plots the monthly value-weighted average zero-cost (hedge) returns of the quintile portfolios with the highest and lowest . is a firm’s sensitivity to innovations in market volatility when market volatility increases. It is obtained from regression (2). The sample period is from March 2004 to December 2014.

33

D

TE

CE P

AC

T

IP

12 10 8 6 4 2 0 -2 -4 -6 -8

SC R

Fig. 4. Daily FVIX. This figure plots daily FVIX, the aggregate volatility mimicking factor from 1 March 2004 to 31 December 2014.

NU

MA

1-Mar-04 1-May-04 1-Jul-04 1-Sep-04 1-Nov-04 1-Jan-05 1-Mar-05 1-May-05 1-Jul-05 1-Sep-05 1-Nov-05 1-Jan-06 1-Mar-06 1-May-06 1-Jul-06 1-Sep-06 1-Nov-06 1-Jan-07 1-Mar-07 1-May-07 1-Jul-07 1-Sep-07 1-Nov-07 1-Jan-08 1-Mar-08 1-May-08 1-Jul-08 1-Sep-08 1-Nov-08 1-Jan-09 1-Mar-09 1-May-09 1-Jul-09 1-Sep-09 1-Nov-09 1-Jan-10 1-Mar-10 1-May-10 1-Jul-10 1-Sep-10 1-Nov-10 1-Jan-11 1-Mar-11 1-May-11 1-Jul-11 1-Sep-11 1-Nov-11 1-Jan-12 1-Mar-12 1-May-12 1-Jul-12 1-Sep-12 1-Nov-12 1-Jan-13 1-Mar-13 1-May-13 1-Jul-13 1-Sep-13 1-Nov-13 1-Jan-14 1-Mar-14 1-May-14 1-Jul-14 1-Sep-14 1-Nov-14

ACCEPTED MANUSCRIPT Daily FVIX

34

ACCEPTED MANUSCRIPT Table 1 Descriptive statistics

SC R

IP

T

This table reports the descriptive statistics for all cross-sectional variables used in this study. The sample period is from March 2004 to December 2014. MRET is a firm’s monthly returns. is the sensitivity of firm’s returns to innovations in market volatility (∆VIXt). and are the sensitivities of firm’s returns to innovations in market volatility when it rises and when it falls, respectively. is the market beta. These betas are obtained from the following firm-level regressions estimated at the beginning of month to the end of month using daily data:

or

(2)

is the excess return of firm i in day t, is the excess market return in day t, is the innovation in VIX from the end of day t-1 to the end of day t, is the innovation in VIX from the end of day t-1 to the end of day t if the innovation is positive and zero otherwise, is the innovation in from the end of day t-1 to the end of day t if the innovation is negative and zero otherwise, and is the error term. Firm size (SIZE) is the natural log of a firm’s market capitalization at fiscal year-end. A firm’s book-to-market ratio (BM) is the natural log of book equity to market equity at the end of the calendar year. Momentum (MOM) is defined as the cumulative returns from the end of month to the end of month . IVOL is the standard deviation of daily residuals from the market model estimated over the past two months. PRET is the past-month return. TURN and VOL are monthly turnover and monthly dollar trading volume, respectively. ZERO is the number of zero returns in the past month for days with positive trading volume. P1 and P99 refer to the 1st and 99th percentile. Q1 and Q3 refer to the first and third quartile.

SIZE BM MOM IVOL PRET TURN VOL ZERO

Mean 0.694 -0.065 -0.091 -0.042 0.552 3.641 -0.517 1.785 4.013 0.731 0.067 25624.92 3.685

AC

MRET

CE P

TE

D

MA

NU

where

(1)

P1 -47.617 -6.196 -9.036 -10.849 -3.696 -0.151 -3.340 -73.684 0.000 -48.077 0.000 0.87 0.000

Q1 -10.170 -0.650 -0.968 -0.966 -0.081 2.019 -1.071 -22.579 2.161 -10.182 0.001 93.75 1.000

Median Q3 P99 Std. dev. 0.000 7.692 86.111 22.090 -0.027 0.507 6.109 3.165 -0.049 0.718 9.141 9.319 0.000 0.942 10.323 6.475 0.471 1.140 4.647 18.979 3.237 4.972 9.633 2.201 -0.440 0.121 1.676 0.998 -2.351 16.659 155.466 41.966 3.607 5.096 14.799 4.426 0.000 7.724 87.675 23.538 0.004 0.029 1.129 0.207 560.26 4218.18 563779.67 102767.49 3.000 6.000 14.000 3.201

35

ACCEPTED MANUSCRIPT

T

Table 2 Characteristics of portfolios sorted by their exposure to aggregate volatility shocks

TE D

MA N

US

CR

IP

Panel A of this table presents the characteristics of portfolios sorted by their exposure to aggregate volatility shocks, β∆VIX. Panel B and C presents the characteristics of portfolios sorted by their exposure to aggregate volatility shocks when aggregate volatility is increasing and decreasing, respectively. All sample firms are sorted at the end of month into quintiles based on their loadings, , or from the lowest (quintile 1) to highest (quintile 5). is the sensitivity of firm’s returns to innovations in aggregate volatility (∆VIXt). and are the sensitivities of firm’s returns to innovations in aggregate volatility when it rises and when it falls, respectively. Firm size (SIZE) is the natural log of a firm’s market capitalization at fiscal year-end. A firm’s book-to-market ratio (BM) is the natural log of book equity to market equity at the end of the calendar year. Momentum (MOM) is defined as the cumulative returns from the end of month to the end of month . IVOL is the standard deviation of daily residuals from the market model estimated over the past two months. PRET is the past-month return. TURN and VOL are monthly turnover and monthly dollar trading volume, respectively. ZERO is the number of zero returns in the past month for days with positive trading volume. Diff. refers to the mean difference in variables between portfolio 5 and portfolio 1. The sample period is from March 2004 to December 2014. ***, **, * indicate significance at the 1%, 5%, and 10% levels, respectively. Panel A: portfolios sorted by their exposure to aggregate volatility shocks, β∆VIX

-1.58 -0.48 -0.04 0.37 1.33 2.90*** (17.76)

BM

6.84 8.91 9.46 9.13 7.24 0.41** (2.27)

0.63 0.59 0.54 0.54 0.64 0.01 (0.14)

MOM

IVOL

PRET

TURN

VOL

ZERO

0.84 3.70 3.75 4.68 2.26 1.42 (0.95)

3.27 1.67 1.25 1.47 2.88 -0.39*** (-4.06)

-0.02 0.37 0.96 0.77 1.44 1.46** (2.22)

0.23 0.46 0.51 0.50 0.29 0.06*** (2.74)

128731 320540 357766 330704 144254 15522 (1.01)

2.13 0.71 0.51 0.60 1.61 -0.53*** (-4.36)

CE P

1 (Low) 2 3 4 5 (High) Diff.

SIZE

AC

Rank

36

ACCEPTED MANUSCRIPT

TE D

MA N

US

IP

CR

Panel B: portfolios sorted by their exposure to aggregate volatility shocks, Rank SIZE BM MOM IVOL 1 (Low) -2.51 6.56 0.66 9.85 3.32 2 -0.75 8.75 0.59 5.85 1.70 3 -0.07 9.43 0.55 5.12 1.26 4 0.53 9.14 0.55 6.00 1.44 5 (High) 2.02 7.15 0.63 7.53 2.86 Diff. 4.53*** 0.59*** -0.03 -2.33 -0.47*** (17.47) (3.18) (-0.67) (-1.46) (-4.82)

T

Table 2 (continued)

AC

CE P

Panel C: portfolios sorted by their exposure to aggregate volatility shocks, Rank SIZE BM MOM IVOL 1 (Low) -2.57 6.92 0.66 5.93 3.09 2 -0.70 8.94 0.59 5.23 1.58 3 0.00 9.47 0.55 5.34 1.23 4 0.70 8.94 0.55 6.51 1.55 5 (High) 2.46 6.70 0.64 10.23 3.12 Diff. 5.02*** -0.22 -0.02 4.31*** 0.03 (15.02) (-1.40) (-0.38) (3.27) (0.34)

PRET 3.17 1.39 1.14 1.25 2.66 -0.51 (-0.73)

PRET 2.57 1.10 1.05 1.59 4.70 2.14*** (3.04)

TURN 0.24 0.43 0.52 0.49 0.30 0.07*** (3.13)

TURN 0.24 0.47 0.53 0.47 0.27 0.03 (1.38)

VOL 121163.43 292032.27 364869.24 324223.03 157213.68 36050.25** (2.57)

VOL 125895.34 321052.77 369426.71 306707.41 133734.73 7839.39 (0.57)

ZERO 2.16 0.80 0.53 0.59 1.61 -0.55*** (-4.70)

ZERO 1.92 0.68 0.50 0.69 1.86 -0.06 (-0.56)

37

ACCEPTED MANUSCRIPT Table 3 Average returns, alphas, and factor loadings of portfolios sorted by exposure to aggregate volatility shocks

MA N

US

CR

IP

T

Panel A of this table presents the average returns, alphas, and factor loadings of portfolios sorted by their exposure to aggregate volatility shocks, β∆VIX. Panel B and C presents the average returns, alphas, and factor loadings of portfolios sorted by their exposure to aggregate volatility shocks when aggregate volatility is increasing and decreasing, respectively. All sample firms are sorted at the end of month into quintiles based on their loadings, , or from the lowest (quintile 1) to highest (quintile 5). Avg. Ret. is the time-series value-weighted average of post-formation monthly mean portfolio returns, expressed in percentage terms. Diff. refers to the mean difference of the variables between portfolio 5 and portfolio 1. CAPM α, FF3 α, and FF4 α are the alphas from the capital asset pricing model (CAPM), the Fama and French (1993) three-factor model, and the Carhart (1997) four-factor model, respectively. The loadings on the market, size, value, and momentum factors from the Carhart (1997) four-factor model are reported in the columns labelled , , and . The sample period is from March 2004 to December 2014. ***, **, * indicate significance at the 1%, 5%, and 10% levels, respectively.

AC

CE P

TE D

Panel A: portfolios sorted by their exposure to aggregate volatility shocks, β∆VIX Rank Avg. Ret. CAPM α FF3 α FF4 α 1 (Low) -0.21 -1.11 -0.48 -0.77 (-0.31) (-2.48) (-1.27) (-2.10) 2 0.59 -0.18 -0.13 -0.20 (1.38) (-0.91) (-0.56) (-1.01) 3 0.93 0.20 0.24 0.15 (2.73) (1.57) (1.76) (1.19) 4 0.70 -0.10 -0.17 -0.11 (1.58) (-0.56) (-0.65) (-0.57) 5 (High) -0.05 -0.95 -0.56 -0.68 (-0.08) (-2.33) (-1.62) (-1.97) Diff. 0.16 0.16 -0.08 0.10 (0.31) (0.29) (-0.13) (0.17)

1.11*** (8.16) 0.98*** (16.93) 0.90*** (22.57) 1.07*** (10.92) 1.19*** (12.74) 0.08 (0.45)

0.92*** (7.14) 0.12* (1.66) -0.04 (-1.15) -0.01 (-0.16) 0.70*** (7.12) -0.22 (-1.44)

0.14 (0.71) 0.22** (2.30) 0.06 (1.00) -0.03 (-0.32) 0.16 (1.03) 0.02 (0.07)

-0.25** (-2.13) -0.06 (-0.76) -0.01 (-0.31) -0.01 (-0.08) -0.04 (-0.39) 0.22 (1.39)

38

ACCEPTED MANUSCRIPT

Table 3 (continued)

TE D

MA N

US

CR

IP

T

Panel B: portfolios sorted by their exposure to increasing aggregate volatility shocks, Rank Avg. Ret. CAPM α FF3 α FF4 α 1 (Low) 0.74 -0.21 0.22 0.15 1.32*** (1.07) (-0.52) (0.65) (0.46) (13.27) 2 0.68 -0.06 -0.05 -0.05 0.91*** (1.77) (-0.34) (-0.21) (-0.26) (14.20) 3 0.88 0.13 0.13 0.11 0.95*** (2.50) (1.33) (1.31) (1.13) (36.11) 4 0.58 -0.18 -0.15 -0.17 0.96*** (1.52) (-1.27) (-0.89) (-1.23) (15.07) 5 (High) -0.18 -1.01 -0.58 -0.77 1.05*** (-0.32) (-2.92) (-2.09) (-2.55) (12.03) Diff. -0.92** -0.80* -0.79* -0.93** -0.28** (-2.00) (-1.79) (-1.91) (-2.09) (-2.32)

AC

CE P

Panel C: portfolios sorted by their exposure to decreasing aggregate volatility shocks, Rank Avg. Ret. CAPM α FF3 α FF4 α 1 (Low) 0.11 -0.76 -0.25 -0.52 1.07*** (0.18) (-2.09) (-0.75) (-1.60) (9.38) 2 0.59 -0.15 -0.12 -0.16 0.92*** (1.63) (-0.97) (-0.57) (-0.95) (16.60) 3 0.79 0.06 0.05 0.02 0.90*** (2.33) (0.52) (0.37) (0.21) (26.85) 4 0.98 0.19 0.15 0.21 1.03*** (2.36) (1.12) (0.67) (1.16) (13.75) 5 (High) 0.70 -0.20 0.11 0.15 1.21*** (1.05) (-0.46) (0.28) (0.41) (9.55) Diff. 0.60 0.56 0.36 0.67 0.13 (1.31) (1.11) (0.68) (1.34) (0.66)

0.84*** (5.55) 0.11* (1.85) -0.06** (-1.96) -0.02 (-0.50) 0.59*** (7.55) -0.25 (-1.54)

0.20 (1.19) 0.09 (1.22) -0.04 (-0.82) -0.07 (-1.34) 0.09 (0.62) -0.11 (-0.52)

0.02 (0.17) -0.05 (-0.75) -0.01 (-0.18) 0.03 (0.84) -0.07 (-0.64) -0.08 (-0.62)

0.65*** (8.32) 0.04 (0.88) -0.14*** (-4.95) 0.05 (1.02) 0.78*** (8.30) 0.13 (1.16)

0.08 (0.60) 0.06 (0.69) -0.09 (-1.60) 0.05 (0.75) 0.03 (0.20) -0.04 (-0.21)

-0.24 (-3.00) 0.02 (0.31) 0.02 (0.63) 0.03 (0.49) 0.02 (0.19) 0.25** (2.05) 39

ACCEPTED MANUSCRIPT Table 4 Correlation coefficients and cross-sectional Fama-Macbeth regressions

MA N

US

CR

IP

T

Panel A reports the Spearman (above diagonal) and Pearson (below diagonal) correlations of firm returns and characteristics. Panel B presents the time-series means of coefficients from monthly cross-sectional Fama-Macbeth regressions of future realized returns on past firm characteristics. The sample period is from January 2004 to December 2014. MRET is a firm’s monthly returns. is the sensitivity of firm’s returns to innovations in aggregate volatility (∆VIXt). and are the sensitivities of firm’s returns to innovations in aggregate volatility when it rises and when it falls, respectively. is the market beta, Firm size (SIZE) is the natural log of a firm’s market capitalization at fiscal year-end. A firm’s book-to-market ratio (BM) is the natural log of book equity to market equity at the end of the calendar year. Momentum (MOM) is defined as the cumulative returns from the end of month to the end of month . IVOL is the standard deviation of daily residuals from the market model estimated over the past two months. PRET is the past-month return. TURN and VOL are monthly turnover and monthly dollar trading volume over the past month, respectively. ZERO is the number of zero returns in the past month for days with positive trading volume. ***, **, * indicate significance at the 1%, 5%, and 10% levels, respectively.

Variables

MRET

SIZE

BM

MRET

1.00

0.06***

0.02***

-0.01

0.01*

SIZE

-0.02**

1.00

-0.16***

0.19***

BM

0.02***

-0.13***

1.00

-0.07***

-0.01

0.13***

-0.03***

1.00

0.00

0.01***

0.00

-0.01

-0.01*

0.02***

0.00

0.03*

0.00

0.00

0.01**

IVOL

-0.02**

-0.45***

MOM

0.01

0.07***

PRET

-0.06***

TURN

TE D

Panel A: Spearman (above diagonal) and Pearson (below diagonal) correlations of firm returns and characteristics IVOL

MOM

PRET

TURN

VOL

ZERO

0.00

-0.10***

0.04***

-0.05***

0.05

0.03***

-0.04***

0.02***

0.03***

-0.01**

-0.49***

0.15***

0.07***

0.70

0.77***

-0.31***

0.01**

0.00

0.01*

-0.01

0.07***

0.03***

-0.11***

-0.15***

0.02***

0.00

0.02***

0.00

0.08***

0.05***

0.00

0.24

0.29***

-0.06***

1.00

0.62***

0.57***

-0.05***

0.00

0.01*

0.01

0.00

-0.03***

0.57***

1.00

-0.14***

-0.06***

0.00

-0.01

0.01***

0.01

-0.03***

-0.03*

0.58***

-0.14***

1.00

0.00

0.01

0.03***

0.00

-0.01

-0.01*

-0.03***

0.06***

-0.01

-0.02**

0.01

1.00

-0.14***

-0.05**

-0.30***

-0.24***

0.35***

0.07***

0.05***

0.00

0.00

0.01

-0.03**

1.00

0.00

0.25***

0.22***

-0.12***

-0.01

0.03***

0.00

0.01

0.00

0.01

0.08***

-0.03***

1.00

0.18***

0.16***

-0.08***

0.00

0.52***

-0.10***

0.09***

0.01***

0.01***

0.01***

-0.24***

0.08***

0.05***

1.00

0.90***

-0.27***

VOL

0.00

0.54***

-0.04***

0.09***

0.01***

0.01***

0.01***

-0.23***

0.05***

0.02***

0.69***

1.00

-0.15***

ZERO

0.00

-0.32***

0.00

-0.03***

-0.01***

-0.01***

-0.01**

0.26***

-0.08***

-0.05***

-0.27***

-0.24***

1.00

AC

CE P

0.01**

40

ACCEPTED MANUSCRIPT

Table 4 (continued)

AC

CE P

TE D

MA N

US

CR

IP

T

Panel B: Cross-sectional monthly Fama-Macbeth regressions of future realized returns on firm characteristics Models 1 2 3 4 5 6 7 8 Intercept 1.68* 1.67* 1.68* 1.69* 1.69* 3.23*** 1.59 2.12** (1.71) (1.70) (1.70) (1.70) (1.70) (3.75) (1.53) (2.20) -0.19 -0.19 -0.19 -0.20 -0.20 -0.13 -0.21 -0.19 (-1.42) (-1.47) (-1.46) (-1.43) (-1.41) (-1.35) (-1.42) (-1.42) SIZE -0.20** -0.20** -0.20** -0.20** -0.20** -0.34*** -0.19* -0.35*** (-2.03) (-2.01) (-2.02) (-2.02) (-2.00) (-3.97) (-1.83) (-3.50) BM 0.38*** 0.38*** 0.38*** 0.38*** 0.38*** 0.32*** 0.40*** 0.39*** (5.66) (5.73) (5.72) (5.80) (5.86) (5.14) (5.74) (6.15) MOM 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 (1.00) (0.98) (0.92) (0.91) (0.86) (1.24) (0.83) (1.20) -0.04 (-0.69) -0.09** -0.09* -0.09** -0.10** -0.08* (-2.04) (-1.91) (-2.59) (-2.37) (-1.95) 0.05 0.04 0.04 0.02 0.03 (1.25) (0.96) (1.02) (0.33) (0.45) IVOL -0.33*** (-4.64) PRET -0.07*** (-6.82) TURN 2.04*** (7.58) VOL

9 2.12** (2.17) -0.19 (-1.40) -0.34*** (-3.31) 0.37*** (5.74) 0.01 (1.34)

10 1.91** (2.15) -0.19 (-1.47) -0.22** (-2.41) 0.37*** (5.82) 0.01 (1.25)

11 1.74** (2.03) -0.07 (-0.42) -0.04 (-0.49) 0.15 (1.33) 0.03*** (5.54)

-0.08* (-1.95) 0.03 (0.56)

-0.08** (-2.00) 0.02 (0.37)

-0.31* (-1.92) 0.09 (0.69) -0.44*** (-3.07)

0.01*** (6.66)

ZERO Adj. R2

0.018

0.019

0.020

0.020

0.021

0.027

0.028

0.019

0.020

-0.03 (-0.93) 0.021

0.063 41

ACCEPTED MANUSCRIPT

Table 5

T

Estimating the price of volatility risk: overall results

MA N

US

CR

IP

Panel A presents the Spearman (above diagonal) and Pearson (below diagonal) correlations between the factors. Panel B reports the average coefficients across the test assets from the stage 1 monthly time-series regressions of portfolio or stock excess returns ( on the Carhart (1997) four factors: market (MKT), size (SMB), value (HML), and momentum (WML) factors; and the aggregate volatility risk mimicking factor (FVIX). Panel C shows the estimates (i.e. risk premiums) from the stage 2 cross-sectional regression of mean excess portfolio or stock return ( on the factor betas estimated in stage 1. We report the robust t-statistics according to Shanken (1992) that account for the errors-in-variables for the stage 1estimation of the coefficients. We use three sets of test assets: (i) 5 x 5 portfolios independently sorted by and , (ii) 5 x 5 portfolios independently sorted by size and the book-to-market ratio, and (iii) individual stocks. The sample period is from March 2004 to December 2014. ***, **, * indicate significance at the 1%, 5%, and 10% levels, respectively.

AC

CE P

TE D

Panel A: The Spearman (above diagonal) and Pearson (below diagonal) correlations between the factors MKT SMB HML WML FVIX FVIX+ FVIXMKT 1.00 0.13 -0.14 -0.10 -0.57 -0.54 -0.56 SMB 0.19 1.00 -0.15 -0.06 -0.11 -0.11 -0.10 HML -0.13 -0.16 1.00 -0.29 0.12 0.09 0.11 WML -0.18 -0.07 -0.38 1.00 0.09 0.14 0.07 FVIX -0.42 -0.17 0.08 0.08 1.00 0.85 0.98 FVIX+ -0.52 -0.24 0.12 0.15 0.82 1.00 0.82 FVIX-0.11 -0.02 0.00 -0.03 0.76 0.25 1.00 -0.57 -0.24 0.13 0.18 0.41 0.50 0.13 -0.59 -0.25 0.25 0.04 0.37 0.58 -0.03 -0.34 -0.14 -0.04 0.27 0.30 0.23 0.26

-0.46 -0.18 0.12 0.10 0.40 0.45 0.36 1.00 0.84 0.80

-0.43 -0.17 0.15 0.06 0.39 0.46 0.34 0.95 1.00 0.35

-0.43 -0.15 0.09 0.14 0.37 0.38 0.35 0.91 0.85 1.00

42

ACCEPTED MANUSCRIPT

T

Table 5 (continued)

43%

50%

AC

Adj. R2

CE P

TE D

MA N

US

CR

IP

Panel B: Stage 1 time-series regressions of excess portfolio or stock returns on risk factors (i) 5x5 βMKT and βVIX portfolios (ii) 5x5 size and BM portfolios Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Intercept -0.280** 0.073 0.065 0.057 0.719*** 0.721*** (-2.44) (0.81) (0.72) (0.23) (2.67) (2.67) βFVIX -0.098*** -0.062** -0.063*** 0.019 (-3.43) (-2.38) (-4.14) (1.23) βMKT 1.009*** 0.973*** 0.942*** 1.283*** 1.138*** 1.147*** (16.90) (17.56) (16.86) (42.41) (54.68) (47.89) βSMB 0.503*** 0.495*** 1.120*** 1.112*** (5.39) (5.36) (9.37) (9.34) βHML 0.108*** 0.110*** 0.200*** 0.200*** (2.63) (2.67) (4.30) (4.31) βWML -0.070*** -0.070*** -0.068*** -0.068*** (-2.97) (-2.95) (-3.51) (-3.53) 51%

51%

77%

77%

(iii) Individual stocks Model 7 Model 8 -0.071* 0.608*** (-1.73) (13.15) -0.069*** (-5.64) 1.318*** 1.143*** (72.45) (71.20) 1.222*** (53.40) 0.185*** (7.77) -0.085*** (-5.76) 9%

14%

Model 9 0.610*** (13.25) 0.015 (1.28) 1.151*** (65.24) 1.222*** (53.23) 0.181*** (7.66) -0.085*** (-5.78) 14%

43

ACCEPTED MANUSCRIPT

T

Table 5 (continued)

(iii) Individual test assets Model 7 Model 8 -2.327 7.014 (-0.25) (0.76) -0.587 (-0.60) 0.216* 0.322** (1.69) (2.07) -0.085 (-0.96) -0.257** (-2.30) 0.258 (1.55)

Model 9 7.059 (0.77) -1.204 (-1.09) 0.322** (2.08) -0.085 (-0.96) -0.259** (-2.30) 0.261 (1.57)

AC

CE P

TE D

MA N

US

CR

IP

Panel C: Stage 2 cross-sectional regression of average returns on factor betas (i) 5x5 βMKT and βVIX portfolios (ii) 5x5 size and BM portfolios Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Intercept 0.882** 0.868** 0.858** 0.148 4.987 5.056 (2.47) (2.38) (2.31) (0.05) (1.03) (1.03) 0.621 -0.562 3.854 3.917 (0.89) (-0.71) (0.81) (0.51) -0.667 -0.452 -0.454 0.594 -4.978 -5.000 (-1.54) (-1.27) (-1.29) (0.25) (-1.16) (-1.15) -0.360 -0.391 0.450 0.414 (-1.40) (-1.56) (1.03) (0.82) -0.456 -0.528 3.813* 3.606* (-0.77) (-0.88) (1.83) (1.79) 0.695 0.918 -1.223 -1.416 (0.78) (0.98) (-0.25) (-0.29)

44

ACCEPTED MANUSCRIPT

Table 6

T

Estimating the price of volatility risk: increasing versus decreasing market volatility

MA N

US

CR

IP

Panel A reports the average coefficients across the test assets from the stage 1 monthly time-series regressions of portfolio or stock excess returns ( on the Carhart (1997) four factors: market (MKT), size (SMB), value (HML), and momentum (WML) factors; and the upward volatility risk factor ( ) and the downward volatility risk factor (FVIX-). is equal to FVIX for months with positive FVIX and zero otherwise. is equal to FVIX for months with negative FVIX and zero otherwise. FVIX refers to the aggregate volatility risk mimicking factor. Panel B shows the estimates (i.e. risk premiums) from the stage 2 cross-sectional regression of mean excess portfolio or stock return ( on the factor betas estimated in stage 1. We report the robust t-statistics according to Shanken (1992) that account for the errors-in-variables for the stage 1estimation of the coefficients. We use three sets of test assets: (i) 5 x 5 portfolios independently sorted by and , (ii) 5 x 5 portfolios independently sorted by size and the book-to-market ratio, and (iii) individual stocks. The sample period is from March 2004 to December 2014. ***, **, * indicate significance at the 1%, 5%, and 10% levels, respectively.

AC

CE P

TE D

Panel A: Stage 1 Time series regression of portfolio or stock returns on risk factors (i) 5x5 βMKT and βVIX portfolios (ii) 5x5 size and BM portfolios (iii) Individual test assets Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Intercept -0.241 -0.097 0.232 0.464 0.198*** 0.423*** (-1.45) (-0.97) (0.92) (1.81) (3.14) (6.71) βFVIX+ -0.120*** -0.097** -0.117*** -0.056* -0.150*** -0.077*** (-3.93) (-2.21) (-5.74) (-1.82) (-8.49) (-4.24) βFVIX-0.086* -0.071 -0.009 -0.049* 0.009 0.046** (-1.99) (-1.59) (-0.44) (-1.70) (0.41) (2.27) βMKT 1.001*** 0.960*** 1.264*** 1.174*** 1.284*** 1.169*** (15.91) (16.17) (41.36) (44.86) (65.89) (62.59) βSMB 0.502*** 1.123*** 1.228*** (5.31) (9.30) (52.26) βHML 0.103** 0.188*** 0.177*** (2.56) (4.11) (7.41) βWML -0.076*** -0.078*** -0.088*** (-2.92) (-3.98) (-6.04) Adj. R2

43%

51%

51%

77%

9%

14% 45

ACCEPTED MANUSCRIPT

T

Table 6 (continued)

AC

CE P

TE D

MA N

US

CR

IP

Panel B: Stage 2 cross-sectional regression of average returns on factor betas (i) 5x5 βMKT and βVIX portfolios (ii) 5x5 Size and BM portfolios Model 1 Model 2 Model 3 Model 4 Intercept 0.544 0.549 0.241 5.455** (1.51) (1.36) (0.07) (2.31) -0.828* -1.432* 2.917 4.657 (-1.71) (-1.94) (0.77) (1.65) 0.831 0.336 0.970 0.175 (1.41) (0.57) (0.26) (0.08) -0.413 -0.226 0.616 -4.237 (-1.29) (-0.57) (0.25) (-1.49) -0.213 0.100 (-0.72) (0.19) -0.448 3.511*** (-0.75) (3.06) 0.011 -1.531 (0.01) (-0.65)

(iii) Individual test assets Model 5 Model 6 -7.168 3.471 (-0.75) (-0.38) -1.140* -1.689** (-1.73) (-2.25) 0.591 0.462 (1.01) (0.79) 0.248** 0.346** (1.97) (2.14) -0.072 (-0.82) -0.270** (-2.32) 0.240 (1.44)

46

ACCEPTED MANUSCRIPT Appendix 1 Filter rules for excluding non-common equity in Datastream

SC R

Non-common equity security codes RTS DEF DFD DEFF

TE

D

MA

NU

PAID PRF DUPLICATE DUPL DUP DUPE DULP DUPLI PREFERRED PF PFD PREF 'PF' WARRANT WARRANTS WTS WTS2 WARRT DEB DB DCB DEBT DEBENTURES DEBENTURE RLST IT, TST, TRUST INVESTMENT, INV EXPIRED EXPD EXPIRY EXPY 500 BOND DEFER DEP DEPY ELKS ETF FUND FD IDX INDEX LP MIPS MITS MITT MPS NIKKEI NOTE PERQS PINES PRTF PTNS PTSHP QUIBS QUIDS RATE RCPTS RECEIPTS REIT RETUR SCORE SPDR STRYPES TOPRS UNIT UNT UTS WTS XXXXX YIELD YLD

AC

CE P

Non-common equity Rights Deferred Fully and Partially Paid Duplicates Preferred Stock Warrants Debt Trusts Investment Expired securities Recommended by Ince and Porter (2006)

IP

T

This table lists non-common equity security codes used in a screen to identify Datastream securities for which the underlying asset is not common equity. The left column lists securities excluded from this study and the right column lists words in the security name that indicate it is of the type in the left column. If part of a security name is matched to a word in the right column, it is excluded from this study.

47

ACCEPTED MANUSCRIPT Highlights Aggregate volatility risk is negatively related to the cross-section of stock returns.



The relation only exists when market volatility is increasing.



The asymmetric effect is persistent and robust to other characteristics.



Aggregate volatility risk is negatively priced in months with increasing market

IP

T



AC

CE P

TE

D

MA

NU

SC R

volatility.

48