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The Graduate School
2008
Essays on the Forecasting Power of Implied
Volatility
Prithviraj Shyamal Banerjee
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FLORIDA STATE UNIVERSITY
COLLEGE OF BUSINESS
ESSAYS ON THE FORECASTING POWER OF IMPLIED VOLATILITY
By
PRITHVIRAJ SHYAMAL BANERJEE
A Dissertation submitted to the
Department of finance
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Degree Awarded:
Spring Semester, 2008
The members of the Committee approve the Dissertation of Prithviraj Shyamal Banerjee
defended on March 18, 2008.
Dr. David R. Peterson
Professor Directing Dissertation
Dr. Thomas Zuehlke
Outside Committee Member
Dr. William Christiansen
Committee Member
Dr. James S. Doran
Committee Member
Dr. Danling Jiang
Committee Member
Approved:
Caryn Beck-Dudley, Dean, College of Business
The Office of Graduate Studies has verified and approved the above named committee
members.
ii
I dedicate this work to my parents
iii
ACKNOWLEDGEMENTS
I gratefully acknowledge the immense help and guidance of my Chair, Dr. David R.
Peterson, from whom I have learnt to do research. I also gratefully acknowledge the help
of my other committee members, especially Dr. James Doran and Dr. Danling Jiang, and
my uncle Dr. Tarun K Mukherjee, who has helped me more times than I can thank him
for.
iv
TABLE OF CONTENTS
List of Tables
............................................................................................vii
List of Figures
............................................................................................xi
Abstract
.................................................................................................xii
1. Introduction
............................................................................................1
2. Implied Volatility and Future Portfolio Returns ...........................................11
3. The Forecasting Power of the Risk and Sentiment
Components of Implied Volatility ....................................................................47
4. Forecasting Future Portfolio Volatility: The Role of Risk and Sentiment
Components of Implied Volatility and other Forecast ......................................112
v
REFERENCES
............................................................................................
164
BIOGRAPHICAL SKETCH ...........................................................................
170
vi
LIST OF TABLES
Table 1: Estimates from 22-Day and 44-Day Future Market
Returns Regressed on VIX ...............................................................................35
Table 2: Regression Estimates for the Fama-French
25 Portfolios Sorted on Book-to-Market Equity and Size .................................35
Table 3: Regression Estimates for the Fama-French 25 Portfolios
Sorted on Book-to-Market Equityand Size, Including
Four Factors as Independent Variables .............................................................37
Table 4: Descriptive Statistics ..........................................................................38
Table 5: Return Regression Estimates for the Twelve Portfolios
Sorted on Book-to-Market Equity, Size, and Beta ............................................39
Table 6: 22-Day Regression Estimates for the Twelve Portfolios
Sorted on Book-to-Market Equity, Size, and Beta ............................................41
Table 7: 44-Day Regression Estimates for the Twelve Portfolios
Sorted on Book-to-Market Equity, Size, and Beta ...........................................42
Table 8: Return Regression Estimates using High VIX
Level Observations ..........................................................................................44
Table 9: 22-Day and 44-Day Regression Estimates
of the Four Factors on VIX ..............................................................................45
Table 10: Descriptive Statistics .......................................................................66
Table 11: Regression Estimates of the Raw Sentiment
Proxies on Risk Factors ................................................................................70
Table 12: Regression Estimates of VIX on the Orthogonal
Sentiment Proxies ............................................................................................73
Table 13: Regression Estimates of 22-day and 44-day Future
Returns of Portfolios on VIX............................................................................73
vii
Table 14: Regression Estimates of 22-day Future Returns of
Portfolios on VIXRISK....................................................................................79
Table 15: Regression Estimates of VIX on the Risk Measures..........................86
Table 16: Regression Estimates of 22-day Future Returns of Portfolios
on VIXSENT
............................................................................................87
Table 17: Regression Estimates of 22-day Future Returns of Portfolios
on VIXRISK and VIXSENT ............................................................................93
Table 18: Regression Estimates of 22-day and 44-day Future Returns
of Portfolios on VIXRISK and the Orthogonal Sentiment Measures.................100
Table 19: Tabulation of Significant Variables with Signs in Table 9.................111
Table 20: Regression Estimates of 22-day Realized Standard Deviation
of Portfolios on VIX.........................................................................................127
Table 21: Regression Estimates of 22-day Realized Standard Deviation
of Portfolios on Lagged Market Standard Deviation .........................................130
Table 22: Regression Estimates of 22-day Realized Standard Deviation
of Portfolios on VIX and Lagged Market Standard Deviation...........................133
Table 23: Regression Estimates of 22-day Realized Standard Deviation
of Portfolios on VIXRISK, Lagged Portfolio Standard Deviation,
and Lagged Market Standard Deviation............................................................136
Table 24: Regression Estimates of 22-day Realized Standard
Deviation of Portfolios on VIXRISK, GARCH Forecast,
and Lagged Market Standard Deviation............................................................140
Table 25: Regression Estimates of 22-day Realized Standard
Deviation of Portfolios on VIXSENT, Lagged Portfolio
Standard Deviation, and Lagged Market Standard Deviation............................145
Table 26: Regression Estimates of 22-day Realized
Standard Deviation of Portfolios on VIXSENT,
GARCH Forecast, and Lagged Market Standard Deviation ..............................148
viii
Table 27: Regression Estimates of 22-day Realized
Standard Deviation of Portfolios on VIXRISK, VIXSENT, Lagged
Portfolio Standard Deviation, and Lagged Market Standard Deviation .............153
Table 28: Regression Estimates of 22-day Realized Standard
Deviation of Portfolios on VIXRISK, VIXSENT, GARCH
Forecast, and Lagged Market Standard Deviation ............................................158
ix
LIST OF FIGURES
Figure 1: Mean Returns for the 12 B/M, Size and Beta Portfolios.....................34
x
ABSTRACT
In this dissertation, I look at the forecasting power of implied volatility. I decompose implied
volatility into a risk component and a sentiment component, and examine the forecasting power
of these components for future returns and volatilities of portfolios sorted by important firm
characteristics. I find that the forecasting power of implied volatility for returns is higher for
higher beta portfolios and for longer horizon holding periods. I also find that the sentiment
component of implied volatility has more (less) forecasting power for future returns (volatility)
than the risk component.
xi
CHAPTER 1
INTRODUCTION
The Black and Scholes (1973) model implies a one-to-one correspondence between the
price of the option and the volatility of the underlying asset. By inverting the option price
and using an algorithmic procedure we can back out the volatility, which is called the
implied volatility for the asset1. If markets are efficient, the implied volatility of the asset
is the market’s best guess of the underlying asset’s volatility over the remaining life of
the option. Past studies involving implied volatility have focused on things like its
properties and its reaction to events. Especially important is that prior studies analyze
implied volatility’s forecasting power for future realized volatility and to a lesser extent,
for future realized returns.
Poterba and Summers (1986) and Diz and Finucane (1993) find that implied volatility has
a mean reverting component. Stein (1989) finds that long-term options “overreact” to
changes in the implied volatility of short-term options. Poteshman (2001) finds evidence
of under reaction to changes in contemporaneous instantaneous variance and overreaction
to increasing or decreasing variance over the prior few days.
Event studies of implied volatility examine the reaction of implied volatility to corporate
events. Patell and Wolfson (1981) find that implied volatility falls after earnings
announcements. French and Dubofsky (1986) find that implied volatility increases with
stock splits, whereas Klein and Peterson (1988) find no response of implied volatility to
stock splits2. Implied volatility functions have also been used to obtain the risk neutral
densities of the underlying asset (Campa, Chang and Reider (1998), Bliss and
Panigirtzoglou (2004)).
1
2
The notion of implied volatility was introduced by Schmalensee and Trippi (1978).
See Mayhew (1995) for a discussion of these studies.
1
In theory, if Black-Scholes is the correct option-pricing model, we should observe the
same volatility for all European options with the same exercise price and time to
maturity. But in reality, due to either Black-Scholes not being the correct model or to the
existence of market frictions and measurement problems, we observe different implied
volatilities for options on the same underlying asset with different strike prices. One such
pattern is called a volatility smile. A “smile” is when at-the-money options have lower
implied volatilities than other options. Smiles were apparent for the S&P 500 index
options before the 1987 October crash, and these have since turned into a “smirk”. A
“smirk” is when implied volatility decreases as strike prices increase. Stein (1989) finds
different implied volatilities for options on the same underlying asset with the same strike
price and different maturities; this is called the term structure of volatility. To correct for
the smile phenomenon, early authors have employed different weighting schemes for
different options. Schmalensee and Trippi (1978) use equal weightings. Latane and
Rendleman (1976) use the vegas3 of the options as weights. Whaley (1982) minimizes the
squared pricing error. 4
Even when the mismeasurement and microstructure issues in option pricing are addressed
by increasing the weighting of near-the-money options, we still see differences in implied
volatility across different strike prices. To further explain these patterns, stochastic
volatility (SV) models have been developed. SV models specify processes for the
underlying asset and the volatility, the correlation between them, and the various risk
premiums for price and volatility risk. These models can produce the observed smirks in
index options if returns and volatility are negatively correlated. The earlier SV models by
Hull and White (1987) and others assume that the market price of volatility risk is zero.
Later models, like that of Heston (1993), allow for a non-zero price of volatility risk and
generate closed form solutions for option prices5. However, Bakshi, Cao and Chen (1997)
and Bates (2000) show that SV models cannot provide the entire solution to the
smile/smirk phenomenon. Other causes of the smile pattern may be related to economic
3
Vega is the derivative of the option price with respect to volatility.
See Mayhew (1995) for a discussion of these studies.
5
Some further modifications of the SV models include the addition of jump components (Bates (1996))
and stochastic short-term interest rates (Bakshi, Cao and Chen (1997)).
4
2
fundamentals and differences in beliefs. Bollen and Whaley (2004) find that the changes
in demand and supply for different options can explain volatility patterns in index and
individual stock options. Bursachi and Jiltsov (2006) find that the steepness of the
volatility smile is related to heterogeneity in beliefs.
A more practical way to capture the differences in volatility across strike prices is to use
different options with different exercise prices in calculating the implied volatility.
According to Blair, Poon and Taylor (2001), the CBOE implied volatility index (VIX) is
a better measure of implied volatility of the market since it is calculated in such a way
that eliminates smile effects and measurement errors due to the bid-ask bounce. Prior to
2003, VIX is constructed as a weighted index of implied volatilities calculated from eight
near-the-money, near-to-expiry S&P 100 index options.6 It uses the binomial valuation
model that is adjusted to reflect anticipated dividends.
From its inception, VIX has become popular with academic and practitioners alike,
though for different reasons. Academic literature, such as studies by Fleming, Ostidiek
and Whaley (1995) and Blair, Poon and Taylor (2001), focus on the ability of the VIX
index to forecast future realized volatilities, consistent with market efficiency. Whaley
(2000) calls VIX the “investor fear gauge” since it peaks at times when the market is
falling.
A few studies such as Copeland and Copeland (1999) and Giot (2005) also focus on the
forecasting power of VIX of future returns for broad stock market indices. On the other
hand, many traders in financial markets use VIX as a market-timing tool, since they look
upon VIX as mainly a sentiment measure. In my essays, I tie together the academic and
the practitioner points of view about VIX by looking at the forecasting ability of VIX for
future realized returns and volatilities. Below I outline my three essays.
Essay One: Implied Volatility and Future Realized Returns
6
The CBOE uses the S&P 500 index options and a different methodology for calculation of the volatility
index beginning in September 2003.
3
Not surprisingly, very few studies deal with the forecasting properties of implied
volatility for future realized returns. This is presumably because in an efficient market,
returns are, by definition, unforecastable. This may not be completely true, however, if
we start with the assumption that implied volatility is a risk factor separate from or
adding to realized volatility. Indeed, studies that examine the forecasting power of VIX
for future returns generally conclude that VIX has the ability to forecast future realized
returns.
Copeland and Copeland (1999) examine if the deviation of VIX from its mean has
forecasting power for indices based on the market value of equity or a measure of value
versus growth. They find that when VIX is high, large firm and value firm based indices
do well. They attribute this result to investors seeking “safe” portfolios after VIX is high.
Giot (2005) examines the forecasting ability of the VIX for the S&P 100 index by
dividing the history of the value of VIX into twenty percentiles. He finds that when VIX
is very high, future returns are always positive, and when VIX is very low, future returns
are always negative. The reason why VIX has forecasting power for future realized
returns might be related to risk.
Modern asset pricing literature has tried to address the issue of whether there is a
volatility risk premium in addition to the traditional price risk premium. In the traditional
asset pricing literature, the relation between expected returns and volatility is put forth by
Merton (1973). If investment opportunities are not constant, he suggests a positive
relation between expected returns on the market and the expected volatility of the market.
However, empirical studies of the relationship between returns and volatility are mostly
inconclusive7.
7
Campbell (1987) and Glosten, Jagannathan,and Runkle (1993) document a negative relationship between
conditional volatility and the risk premium, contrary to economic theory, while Harvey (1989) and Turner,
Startz and Nelson (1989) find a positive relationship. Scruggs (1998) decomposes the CAPM into a partial
relation in a two-stage estimation, and is thus able to explain away the negative relationship of Campbell
(1987) and Glosten et al. (1993). Brandt and Kang (2004) resolve these contemporaneous correlation
differences by implementing a VAR technique. By incorporating time-varying volatility, their conclusions
suggest that these differences can be explained by the conditional and unconditional correlations.
4
In addition to the price risk premium, an array of option pricing literature shows the
apparent existence of a separate volatility risk premium. Buraschi and Jackeworth (2001)
find that the underlying asset and the risk free interest rate cannot span the option-pricing
kernel, implying the existence of other risk premiums. Coval and Shumway (2001) find
that zero-beta, at-the-money straddle positions produce average losses of approximately
three percent per week. This suggests that some additional factor, such as systematic
stochastic volatility, is priced in option returns. Bakshi and Kapadia (2003), using optiontrading strategies, show that the market price of volatility risk is actually negative. Ang,
Hodrick, Xing and Zhang (2006) show that stocks with high sensitivity to changes in
VIX have low cross-sectional returns, and they attribute the negative price of volatility
risk as one of the causes of this phenomenon. However, Branger and Schlag (2004) show
that with discrete time hedging errors, the sign of the volatility risk premium may be
indeterminate.
In a time series context, implied volatility may be a price risk factor in the sense of
Merton’s (1973) intertemporal relation between expected returns and expected volatility.
If implied volatility is an efficient forecast of future realized volatility, Bali and Peng
(2006) show that implied volatility can be used in place of expected volatility in the
Merton relation. However, this does not account for the possibility that implied volatility
could also be related to the volatility risk premium. Implied volatility is a biased predictor
of future realized volatility. Doran and Ronn (2005) show that the negative price of
volatility risk gives rise to the bias in implied volatility. Also, the mean reversion of VIX
may also be part of the risk of VIX; if VIX is unduly low, it is likely to be higher in the
future. In essence, the risk in VIX seems to be of a multi-dimensional nature and there
may be several risk factors associated with VIX.
The objective of my first essay is to examine this multi-dimensional nature of risk in VIX
by examining the forecasting ability of VIX in terms of both levels and mean deviations
for portfolio returns based on different firm characteristics. The forecasting ability is
investigated after appropriate risk adjustment that controls for the traditional market,
small firm, value, and momentum premiums. My main contribution in this essay is that I
isolate the differential responses of different portfolios to both the level of VIX and the
5
deviations from the mean of VIX, and this gives us insight into both market efficiency
and the risks in implied volatility.
Essay Two: The Forecasting Power of the Risk and Sentiment Components of
Implied Volatility
Noise traders are traders who trade on “pseudo-signals” from various market gurus or
brokers that are not based on fundamental information (Shleifer and Summers (1990)).
The collective trading on these pseudo-signals leads to periods of bullish or bearish
sentiment. Bullish and bearish sentiments are defined as positive and negative deviations,
respectively, from a value determined by risk-based asset pricing models. Delong,
Shleifer, Summers and Waldman (1990) show that such bullish and bearish sentiment
may affect prices if rational investors are risk-averse. Fisher and Statman (2000) find that
there is a negative relation between future stock returns and the bullishness and
bearishness of individual and institutional investors about future market prices. Baker and
Wurgler (2006) examine the effects of irrational investor sentiment on the future returns
of stocks that are hard to value such as small, volatile, and growth stocks. They find that
these stocks earn low returns after the beginning-of-period sentiment is high. Brown and
Cliff (2005) find that the sentiment of institutional investors about future market
prospects negatively affects future returns for large and growth firm portfolios, especially
in the long run. Lemmon and Portniaguina (2006) find that the sentiment portion of
consumer confidence indices has forecasting power for the future returns of small stocks
and stocks which are mostly held by individual investors.
Since option prices and option implied volatilities are positively related, implied volatility
as proxied by VIX is determined by the trading of put and call options. VIX reflects a
compensation for risk that put sellers have to bear to insure investors against a market
fall. However, VIX may also reflect the irrational behavior of investors. Investors may be
bullish, or more optimistic in their valuations than what a rational risk based asset pricing
model would suggest, and lower their demand for put insurance. When this happens, the
level of VIX may go down. Similarly, investors may be bearish, or more pessimistic in
6
their valuations than what a rational risk based asset pricing model would suggest, and
increase their demand for put insurance. When this happens, the level of VIX may go up.
Traders in the marketplace often refer to VIX as a contrary sentiment indicator, with
some traders having books on elaborate trading strategies based on VIX (Connors, 2002).
The widely held belief is that when VIX is high, there is fear in the market, and so it is a
good time to buy stocks. As the market recovers from the fear, stocks rise. Empirically,
studies have documented that implied volatility is influenced by sentiment. Vlad (2004)
shows that the implied volatility of the 50 most actively traded options on the S&P100 is
impacted by sentiment. Deuskar (2006) finds that a measure of risk misperception, as
measured by the difference of VIX and realized volatility, is correlated with sentiment
measures.
So, VIX may contain both risk and sentiment components. As I show in my first essay,
VIX also has power to forecast future returns. The pressing issue then is how much this
forecasting power of VIX for future returns is due to the risk component of VIX and how
much of it is due to the sentiment component of VIX. This second essay uses two
approaches to address the issue. The first approach isolates the risk component of VIX
and focuses on it’s forecasting power for future returns, and the second approach isolates
the sentiment component of VIX and looks at it’s forecasting power for future returns.
Two previous studies have used the VIX as a sentiment indicator. Simon and Wiggins
(2001) examine the forecasting ability of technical sentiment indicators, including the
VIX index, for future returns of the S&P 500 futures contract. They show that these
indicators, including VIX, have significant forecasting power. Brown and Cliff (2004)
study the forecasting power of several sentiment variables for future returns, and use the
ratio of VIX to realized volatility as one of the proxies for sentiment. However, these two
studies do not decompose VIX into risk and sentiment components. Without proper
decomposition of VIX into risk and sentiment components, it is impossible to isolate and
compare the forecasting powers of both components. My essay improves upon these two
studies to show and contrast the forecasting power of both risk and sentiment
components of VIX for future returns of portfolios sorted multivariately by book-to7
market equity, market equity and beta, and univariately by the number of analysts
following the firm, age of the firm, dividend payout ratio of the firm, and profitability of
the firm, respectively.
Essay Three: Implied Volatility versus ARCH Models as Predictors of Future
Volatility
Most studies of implied volatility address the issue whether implied volatility is an
unbiased and efficient forecast of future realized volatility. The underlying belief is that if
option markets are informationally efficient, then implied volatility should contain all
relevant information about future realized volatility, and no other additional information
matters. Lamoureux and Lastrapes (1993) examine stock options and find that implied
volatility is an inefficient predictor of future realized volatility, since there is information
in past volatility, in addition to that contained in implied volatility, that is useful in
forecasting future realized volatility. On the other hand, Christensen and Prabhala (1998),
using longer sample periods and non-overlapping data, find that implied volatility
subsumes the information content of past volatility. Fleming, Ostidiek and Whaley
(1995) find that VIX has forecasting ability for the future realized volatility of the S&P
100. Blair, Poon and Taylor (2001) find that VIX subsumes information in high-powered
low frequency data in forecasting future realized volatility. Consistent with Doran and
Ronn (2005), the general finding in the literature is that implied volatility has some
forecasting power for future realized volatility beyond that found in other forecasts of
future volatility, but also that it is a biased predictor of future realized volatility.
Most of the previous literature that deals with implied volatility as a forecast of future
realized volatility does so by examining the incremental forecasting power of implied
volatility versus some forecast of future volatility (like past volatility or a GARCH8 type
8
ARCH stands for autoregressive conditional heterskedasticity and GARCH stands for generalized
autoregressive conditional heterskedasticity. These processes model both the mean process and volatility
process simultaneously, and account for the empirically observed persistence and clustering in volatility.
8
forecast). For example, Christensen and Prabhala (1998) regress future realized volatility
on past implied volatility and past realized volatility. Lamoureux and Lastrapes (1993)
use a GARCH model for forecasting volatility and include implied volatility in the
volatility regression as an exogenous variable. However, this literature deals mainly with
the volatility of broad market indices, and not with portfolios formed on the basis of
important firm characteristics.
Previous literature also examines if bullish and bearish sentiment has power in
forecasting future volatility. Lee, Jiang and Indro (2002) find that an institutional survey
measure of sentiment about future stock market conditions has an impact on the
conditional volatility of stock returns. On the other hand, Wang, Keswani and Taylor
(2005) find that the ARMS index9, which is a contrary sentiment indicator, has limited
forecasting ability for future realized volatility after controlling for volatility as proxied
by VIX and the leverage effect.
So, previous literature has established two results: one, that VIX has power to forecast
future realized volatility and, two, that a good proxy for bullish and bearish investor
sentiment may have power to forecast future realized volatility. However, as I point out
in my second essay, VIX may have both risk and sentiment components. The literature
has not examined how much of the forecasting power of VIX for future realized volatility
comes from the risk component of VIX and how much of it comes from the sentiment
component of VIX. I extend the Lee, Jiang and Indro (2002) and Wang, Keswani and
Taylor studies by examining the relative forecasting powers for future volatility of the
risk component and the sentiment component of VIX, respectively, when compared to a
multivariate GARCH forecast of volatility. The risk component sentiment components of
VIX are isolated using the same two approaches as I use in my second essay.
There are two contributions in this essay. First, I clearly outline and contrast the
forecasting power of the risk portion of VIX and the sentiment portion of VIX for future
9
The ARMS index is defined as the number of advancing stocks on the NYSE scaled by the volume of
advancing stocks divided by the number of declining stocks on the NYSE scaled by the volume of
declining stocks.
9
realized volatility when compared to a multivariate GARCH forecast of volatility. This is
useful since although we know that implied volatility has forecasting power for future
realized volatility, we do not know how much of the forecasting ability comes from the
risk and sentiment components separately. Knowing the forecasting ability of the risk and
sentiment components separately gives us a deeper insight into the degree of market
efficiency.
Second, unlike previous studies that look at the forecasting power of VIX versus GARCH
forecasts for broad indices, I examine the forecasting power of the risk and sentiment
components of VIX for various portfolios sorted multivariately by the firm characteristics
book-to-market equity, market equity and beta, and univariately by the number of
analysts following the firm, age of the firm, dividend payout ratio of the firm, and
profitability of the firm, respectively. It may be more useful for practitioners like actively
managed mutual funds to forecast the volatility of portfolios sorted by firm characteristics
rather than broad indices since they may be invested in portfolios that are tilted towards
stocks with some specific characteristic.
Dissertation Preview
The rest of the dissertation is as follows. Chapter 2 is essay one. Chapter 3 is essay two.
Chapter 4 is essay three. Chapter 5 concludes the dissertation.
10
CHAPTER 2
IMPLIED VOLATILITY AND FUTURE PORTFOLIO RETURNS
I. Introduction
The CBOE Volatility Index (VIX) is a measure of market expectations of stock
return volatility over the next 30 calendar days and is calculated from S&P 100 (OEX)
stock index options. It was introduced in 1993 and originally computed on a minute-byminute basis from the implied volatility of eight option series that are near-the-money,
nearby, and second- nearby OEX option series, and was weighted to reflect the implied
volatility of a 30 calendar-day at-the-money OEX option.10 The option valuation model
used in the calculation is a cash dividend adjusted binomial method based on Black and
Scholes (1973). VIX has been referred to as the ‘investor fear gauge’ (Whaley, 2000),
since high levels of VIX coincided with high degrees of market turmoil. In addition to
VIX being used to gauge market volatility, some traders (Connors, 2002) advocate the
use of VIX as a stock market timing tool. This is based on the observation that high
levels of VIX often coincide with market bottoms, and seem to indicate “oversold”
markets. Traders can take long positions in the market in anticipation of an increase after
VIX is high.
Giot (2005) tests if high levels of VIX indicate oversold stock markets by dividing the
VIX price history into 21 equally spaced rolling percentiles and examining the returns on
the S&P 100 for various future holding periods up to 60 days for each of these 21
percentiles. He finds that for very high levels of VIX, future returns are always positive
10
In the new methodology introduced in 2003, VIX is calculated from the S&P500 (SPX) index option
prices, rather than from the S&P100. The calculation also involves a wide range of strike prices. This
calculation is independent of any option-pricing model. The CBOE calculates and distributes the original
OEX VIX under the new ticker “VXO”. The old and new VIX series are highly correlated (Carr and Wu,
2004).
11
and for very low levels of VIX, future returns are always negative. His findings suggest
that extremely high levels of VIX may signal attractive buying opportunities. This is
surprising, since VIX information is readily available and should not allow for timing
profits if market participants are rational. Another explanation of this effect could be that
extreme levels of VIX act as a time-series risk factor for returns, and there would be no
abnormal returns after adjusting for this factor. This coincides with the notion of a
negative market price of volatility risk, documented by Bakshi and Kapadia (2003) and
Coval and Shumway (2000). If investors have aversion to volatility, high levels of
volatility will translate to high price risk premiums since prices and volatility are
negatively correlated.
In conjunction with the notion of a negative volatility risk premium, Doran and Ronn
(2005) document that implied volatility is a biased predictor of future realized volatility
due to volatility risk aversion. Since realized volatility will be lower in the future, prices
will rise. This is consistent with the notion formulated by Merton (1973, 1980) that there
is a positive relationship between contemporaneous market volatility and returns.
Copeland and Copeland (1999) also advocate the use of VIX as a size and style rotation
tool. They find that large and value stocks earn high returns after VIX is high. They
attribute this effect to investors seeking safer portfolios after the increase in implied
volatility.
Giot’s (2005) findings are based on the entire index (S&P 100), and not on segments of
the market grouped by characteristics of stocks. Copeland and Copeland (1999) also
focus on indices rather than portfolios; they examine BARRA’s indices (value and
growth stocks), S&P 500 futures (large stocks), and Value Line futures (small stocks). I
expand the analysis to portfolios grouped by characteristics. By doing so I can learn if
implied volatility has predictive power for future returns of all types of portfolios as it
does for the indices and, if so, the sign and magnitude of such predictive power. This has
not been explicitly considered in previous studies. In addition, I control for the Fama and
French (1993) factors consisting of the excess market return, the size premium, and the
value premium. I also control for the Carhart (1997) momentum factor. These factors are
12
known to affect security returns and characteristic-sorted portfolios are known to have
different sensitivities to these factors. No other study adjusts for these risk factors and
explores portfolios grouped by firm characteristics. Guo and Whitelaw (2006) find that
implied volatilities are positively related to market returns, even after controlling for
macroeconomic variables. However, they do not examine characteristic-sorted portfolios
or the role of the four Fama and French and Carhart factors. If implied volatility is a risk
factor in the time series of returns, then it should have predictive ability for the future
returns of all portfolios, even after appropriate adjustment for other risk factors. On the
other hand, if markets are inefficient, then alternative portfolios may have sporadic or
random patterns of responses.
I expand the analysis of Copeland and Copeland (1999) and Giot (2005) in another way
as well. Since investors may have non-symmetric responses to high and low volatility
periods, I introduce a model that incorporates short-term and long-term deviations from
volatility means that can result in different portfolio returns based upon not only the level
of volatility, but also these volatility deviations. Specifically, I explore whether the level
of VIX relative to recent values provides information beyond just the level of VIX. This
idea is consistent with option pricing studies that show a mean reverting parameter
improves the fit of implied volatilities (Gatheral, 2003).
My model shows that,
conditional on VIX being above a given threshold value, volatility deviations from the
short-term mean will affect future portfolio returns beyond that due to the level of VIX
alone. To capture this effect I incorporate binary variables into the analysis.11
When
VIX is below the threshold, deviations from the mean do not matter.
I examine future 22 trading-day and 44 trading-day return portfolios sorted by beta, size,
and book-to-market equity. Beta is chosen as a grouping characteristic because of the
positive relationship shown in prior studies between levels of VIX and future market
returns. As such, I sort on beta to determine if high beta firms have a stronger return
relationship with VIX and if low beta firms have a weaker return relationship with VIX.
11
While Copeland and Copeland (1999) include a variable that partially incorporates mean-reversion in
VIX, it is the only specification that they include. There is no control for mean-reversion with levels, or
separate binary variables for high and low levels.
13
Size and book-to-market equity are chosen as grouping characteristics since this
methodology is commonly followed to analyze the risk and returns of stocks. In addition,
Fama and French (1992, 1993) and others find that size and book-to-market equity are
related to stock returns. Copeland and Copeland (1999) use size and value indices in
their study.
It is necessary to adjust the future returns of the portfolios for other risk factors. I use the
Fama and French (1993) three-factor model, which includes as variables the market
return minus the risk free rate (MKT), the firm size factor (SMB), and the book-to-market
equity factor (HML). SMB is the return on a zero investment portfolio of buying smallsize stocks and selling large-size stocks. HML is the return on a zero investment portfolio
of buying value stocks and selling growth stocks. I also include as a fourth variable the
Carhart (1997) momentum factor of past winners minus past losers (UMD).
I further examine if VIX has forecasting power for the market, small firm, value, and
momentum premiums. These four factors are portfolios that may be predictable by VIX.
Higher implied volatility today implies a higher risk premium today, but in the future
volatility will be lower and, thus, prices will rise. This implies a direct relation between
VIX and MKT. Since small stocks are more risky than large stocks, the same relation
should hold for VIX and SMB. If growth stocks are more risky than value stocks, then
there should be a negative relation between VIX and HML. The relation for UMD is less
obvious, but stocks that have had high past appreciation may have lower risk premiums
today. Since high implied volatility suggests that high risk-premium stocks will perform
well in the future, losers should beat winners, and thus there should be a negative relation
between VIX and UMD.
My objective is to learn if the implied volatility of the market has predictive power for
future returns on portfolios sorted by the security characteristics beta, size, and book-tomarket equity. Thus, it allows me to uncover the relation between implied volatility as a
factor in the time series of portfolio returns in a detailed fashion. This has implications
for asset pricing and market efficiency. This is distinct from the results in Ang, Hodrick,
14
Xing, and Zhang (2006), where firms are sorted into portfolios based upon VIX exposure,
and where the authors find a contemporaneous negative relationship between crosssectional returns and their measure of VIX exposure. They claim this result is consistent
with a negative market price of volatility risk, since holding high beta VIX exposure
firms is tantamount to hedging high levels of volatility. My conclusion of a positive
relationship between VIX and future returns is also consistent with a negative volatility
risk premium.
I develop the study as follows. Section II provides a theoretical foundation. Section III
gives details of the data and methodology. Section IV reports the numerical results.
Section V concludes the paper.
II. Theoretical Foundation
A. Implied Volatility and Future Returns
Substantial work has tested the relationship between volatility and returns, with
mixed results. Most studies focus on the contemporaneous relationship between realized
volatility and the risk premium, testing the theoretical implication of the CAPM that there
is a positive relationship between the level of volatility and the size of the premium.12
However, these studies make limited to no statements on the relationship between
implied volatility and future returns. Guo and Whitelaw (2006) use implied variances to
help find reasonable parameter estimates for relative risk aversion to explain the positive
relationship between stock market risk and return. The power of implied variances to
explain returns is retained even in the presence of macroeconomic variables. This finding
is consistent with my hypothesis, developed below, that contends implied volatilities
possess information for forecasting future market returns.
12
Campbell (1987) and Glosten, Jagannathan,and Runkle (1993) document a negative relationship
between the conditional volatility and the risk premium, contrary to economic theory, while Harvey (1989),
and Nelson, Startz, and Turner (1989) find a positive relationship. Scruggs (1998) decomposes the CAPM
into a partial relation in a two-stage estimation, and is thus able to explain away the negative relationship of
Campbell (1987) and Glosten et al. (1993). Brandt and Kang (2004) resolve these differences regarding
contemporaneous correlation by implementing a VAR technique. By incorporating time-varying volatility,
their conclusions suggest that these differences can be explained by the conditional and unconditional
correlations.
15
The ability of implied variances to predict future returns emanates from two
widely known empirical findings, the existence of a negative volatility risk premium and
the equity premium puzzle. It is well documented that implied volatility is an efficient
predictor of future realized volatility.13 While the literature debates the biased nature of
implied volatility’s predictive power, the general framework used in testing the
relationship does not vary. As such, this framework is a good starting point to extend the
analysis to future returns. From Christensen and Prabhala (1998) and Doran and Ronn
(2005), I have:14
σ tr→t +τ = α + βσti + εt
(1)
where σ tr→t +τ is an asset’s realized volatility, calculated using returns from day t through
t+ τ, and σ ti is the asset’s implied volatility inferred from VIX on day t. As mentioned
before, prior studies present two findings for α and β. First, as Christensen and Prabhala
(1998) claim, implied volatility is an efficient and unbiased estimator of realized
volatility, with β=1 and α=0. The second scenario is similar to the findings in Doran and
Ronn (2005), where implied volatility is upward biased, with either β<1 or α<0. Doran
and Ronn claim that this is a result of a negative market price of volatility risk. The
theoretical underpinnings of a negative volatility risk premium may help explain why the
realized Sharpe ratio is higher than the expected Sharpe ratio.
Based on the findings of Mehra and Prescott (1985) and the numerous studies that
followed, it is well documented that the returns on equities over the past century cannot
be quantitatively rectified with current theoretical models for expected returns.
In
particular, the realized market price of risk, or Sharpe ratio, λ, is higher than the expected
13
For specific evidence, see Christensen and Prabhala (1998), Canina and Figlweski (1993), and Doran
Ronn (2005).
14
This is a simplification of both the Christensen and Prabhala (1998) and Doran and Ronn (2005)
argument. Their specific empirical tests employ instrumental variables, and use the log of volatilities.
16
value for the price risk premium, E[λ], given reasonable parameter estimates for the riskfree rate and levels of risk-aversion. Noting that the realized Sharpe ratio is calculated as
the realized mean return of an asset, µ, minus the risk free rate, rf, divided by realized
volatility, the Mehra and Prescott (1985) findings imply:
E[λ] <
µ − rf
σr
(2)
Many studies, such as Fama and French (2002), focus on exploring the discrepancy
between the realized and expected excess returns. However, this ignores the implications
that a negative volatility risk premium has on realized Sharpe ratios. From equation (2) it
is clear that realized Sharpe ratios are higher than expected Sharpe ratios because either
realized returns are higher than expected returns, or because realized volatility is less than
expected volatility. Higher realized Sharpe ratios are then synonymous with a negative
market price of volatility, and is shown by substituting equation (1) into equation (2):
E[λ] <
µ − rf
α + βσi
(3)
Using the relationship between realized and implied volatility, as given in equation (1),
and noting that a negative market price of volatility risk translates to the empirical finding
of α < 0 or β < 1 , then realized risk premiums will be higher than expected risk
premiums.
Explicitly, I argue that a higher realized than expected risk premium can be the result of
lower realized volatility due to a negative market price of volatility risk. This is not to
say that it is a sufficient explanation, but ignoring this relationship would be in contrast to
prior findings. If implied volatility is an unbiased predictor of future realized volatility,
and inconsistent with a negative volatility risk premium, then implied volatility should
not contain information about future returns, once risk is controlled for. With no aversion
to volatility risk, prices are only affected by price risk, and future realized volatility does
17
not impact returns. If there is negative volatility risk aversion, today’s risk-adjusted price
will be lower if volatility is higher, consistent with findings by Ang et al (2006). Since
implied volatility is an upward biased predictor of future realized volatility, prices will be
higher in the future since realized volatility is lower than predicted. This pattern is
contingent upon a contemporaneous negative relation between prices and volatility and
suggests that implied volatility should have a positive relation to future returns.
B. Incorporating Mean-Reversion
To this point, the specification ignores the mean-reverting component to implied
volatility. To enhance the specification I include a mean-reverting process, similar to the
two-factor Schwartz (1997) and Schwartz and Smith (2000) process. Like their process,
mine has both short-term and long-term mean-reverting factors, and is given as:
∆σ
2
(4)
= (κ l (θ l − σ 2 ) + F (θ s ,t |σ 2 )) ∆ t + ξσ e
σ t2 = (κ l (θ l − σ t2−1 ) + F (θ s ,t |σ t2−1 )) ∆ t + σ t2−1 + ξσ t −1 e t
where
F (θ s ,t |σ t2−1 ) = κ s (θ s ,t − σ t2−1 )
if
σ >Θ
F (θ s ,t | σ t2−1 ) = 0
if
σ ≤Θ
(5)
(6)
where κl and κs are the speed of mean-reversion in the long-term and short-term,
respectively, θl and θs,t are the mean long-term and short-term volatilities, respectively, ξ
is the variance of the volatility process, Θ is a threshold value for volatility, and e is the
discrete-time version of the geometric Brownian motion innovation. The mean long-term
volatility is constant while the mean short-term volatility varies through time.
For
brevity, I remove the i superscript from σ. The difference between this model and the
Schwartz and Smith (2000) model is that I assume that the short-term mean is non-
18
stochastic but it is a function of volatility above a certain threshold.15 The threshold level
for volatility is the level at which investors become sensitive to volatility changes.
Substituting the square-root of equation (5) into equation (3) and removing, for brevity,
the t subscripts results in:
E[λ] <
R − rf
α + β κ l (θ l − σ 2 ) + F(θ s,t | σ 2 ))∆t + σ 2
(7)
Equation (7) suggests that not only is the level of volatility related to future prices, but
the deviation of volatility from its long-term and short-term means is related to future
prices, too. The variance of the volatility process will not matter since the error term, e,
has a mean of zero. Four potential scenarios result from equation (7) given current level
of volatility σ:
1)
σ 2 > θ l and σ 2 > θ s,t with σ > Θ
2)
σ 2 > θ l and σ 2 < θ s,t with σ > Θ
3)
σ 2 > θ l with σ < Θ , and
4)
σ 2 < θ l with σ < Θ .
The implication of this framework is the capturing of three specific effects. First, higher
levels of volatility can result in greater realized risk premiums, but the relationship is not
necessarily continuous. Second, volatility deviations above the short-term or long-term
means result in higher realized risk premiums. Finally, volatility deviations below the
short-term or long-term means result in lower realized risk premiums.
For example, compare the first and third scenarios. The major distinction is that in the
first scenario, where current implied volatility is above the threshold value, short-term
and long-term deviations above the mean result in a lower value for the denominator in
equation (7), and consequently a higher realized risk premium. If the speed of mean15
Schwartz and Smith (2000) discuss their model in terms of commodity prices versus volatilities.
19
reversion in the short-term is faster than in the long-term, which is likely, then the
resulting impact is magnified when volatility is above this threshold value. For the third
scenario, only long-term deviations matter. Thus, I expect to observe greater future
returns with higher levels of current implied volatility under both the first and third
scenarios, but the relationship should be stronger under the first scenario.
The opposite holds true for the second scenario, where current implied volatility is below
it short-term mean, but above the long-run mean and the threshold level. Volatility levels
below the short-term mean result in a positive value for κ (θ s − σ 2 ) , causing higher
values in the denominator in equation (7) and lower realized risk premiums.
My
conjecture is that at high levels of volatility, investors respond to quick volatility declines
with stronger positive reactions versus volatility declines at lower volatility levels. Thus,
when volatility is high, but below its short-term mean, I expect a negative incremental
relationship between future returns and current levels of implied volatility.
When volatility is below the threshold, as in scenarios 3 and 4, the impact on the risk
premium is small. This is because of the proportional bias in implied and realized
volatility and because there is no additional impact from short-term volatility deviations
in either direction. This captures the non-continuous aspect to investors’ reaction to
volatility.
While this framework has been modeled in terms of risk premiums, it can be tested using
returns. If risk can be controlled for, such as by using the Fama and French (1993) and
Carhart (1997) factors, and implied volatility is an empirical proxy for the volatility risk
premium, then there should be a relationship between implied volatility and future market
returns. This can then be extended to test returns on characteristic portfolios. If implied
volatility variables have a significant relationship with future returns across all portfolios,
then this may suggest that these variables are a good proxy for a risk-pricing factor.
However, if implied volatility variables can only price some portfolios, then this may be
evidence for some degree of market inefficiency in certain portfolios.
20
III. Data and Methodology
A. Dependent Variables
I employ daily data from June, 1996, through June, 2005. I use excess returns (return
minus the risk-free rate) on twelve portfolios formed on size, book-to-market equity, and
beta as dependent variables in the time-series regressions. The twelve portfolios are
formed in the Fama and French (1993) style. Specifically, at the end of June of each year
t from 1986 to 2005, I independently sort NYSE stocks on CRSP by beta, size (market
value of equity), and book-to-market equity.16 Book value of equity is for fiscal year end
t-1 and is defined as the COMPUSTAT book value of shareholders’ equity, plus balance
sheet deferred-taxes and investment tax credits, if available, minus the book value of
preferred stock. Market value of equity (ME) is measured at the end of June of year t.
Book-to-market equity is the ratio of the book value of equity divided by the market
value of equity. Beta is measured at the end of June of year t by estimating the market
model over the prior 200 trading days. The CRSP value-weighted index is the market
proxy.
I use the NYSE breakpoints for ME, book-to-market equity, and beta to allocate NYSE,
AMEX and Nasdaq stocks to two size, two book-to-market, and three beta categories.17
The size and BE/ME breakpoint is the 50th percentile and beta breakpoints are the 30th and
70th NYSE percentiles. I construct twelve portfolios from the intersection of the size,
book-to-market equity, and beta categories and calculate the daily value-weighted returns
on these portfolios from July of year t through June of year t+1.18 The 22-trading-days
and 44-trading-days excess holding period returns on these twelve portfolios, from July
1986 through June 2005, are the dependent variables in the time-series regressions. I
obtain the daily risk-free rates from Kenneth French’s website.19
16
Similar to Fama and French (1993), I delete negative book equity firms, financial firms, and utilities.
Only firms with ordinary common equity (as classified by CRSP) are used. Thus, ADRs, REITS, and
units of beneficial interest are excluded.
18
I also formed equally-weighted portfolios. The results are even stronger than the value weighted returns,
and are available upon request.
19
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
17
21
B. Independent Variables
The independent variables are the daily returns for the three Fama and French (1993)
factors (MKT, SMB, HML), the Carhart (1997) momentum factor (UMD), the daily
levels of the VIX index, and two binary variables capturing extreme levels of VIX
relative to recent values.
The Fama and French and momentum factor returns are
obtained from the webpage of Kenneth French.
The data on implied volatility are
obtained from the CBOE website (www.cboe.com/vix) (Ticker:VIX). The binary variable
HD takes the value 1 on any day that VIX is more than one standard deviation above its
200-day moving average, and is zero otherwise. The binary variable LD takes the value
1 on any day that VIX is more than one standard deviation below its 200-day moving
average, and is zero otherwise.
C. Motivating Regressions
As a preliminary check to examine if VIX levels have forecasting power for the future
returns of the portfolios, I regress the 22-trading-day and 44-trading-day future holdingperiod excess returns for each of the twelve portfolios on the levels of daily VIX. An
augmented Dickey-Fuller test for the stationarity of the VIX index reveals a test statistic
of 7.49, rejecting the null hypothesis of a unit root. Stambaugh (1999) points out that
coefficients from a predictive regression of this type are subject to small sample bias
when an independent variable, such as VIX, follows an AR(1) process. However, Bali
and Peng (2006) show that the magnitude of this bias decreases as the sample size
increases. They find no significant bias in their sample of sixteen years of daily data.
Since I am using daily data over nineteen years, the effect of this bias on my estimates
should be very small.
I choose the 22-trading-day (approximately one calendar month) holding period since this
corresponds with the forecast horizon of VIX and the 44-trading-day (approximately two
months) holding period as this is the longest horizon used by Giot (2005), and it is the
22
horizon with the greatest forecasting power for VIX for future returns.
Given the
findings for speed of mean reversion in Pan (2000) and Doran and Ronn (2005), using 44
trading days is a close approximation to the number of days it takes for VIX to revert
back to its mean long-term volatility.20
I employ Newey and West (1987) standard errors in the two equations below, and all
regressions that follow, to account for residual correlation due to overlapping portfolio
returns. This procedure is used by Giot (2005). The regression equations are given as:
(8a)
Rpt22 = α p +υ pVIXt + ε pt
Rpt44 = α p +υ pVIXt + ε pt
(8b)
where R pt22 is the 22-day compounded future holding period excess returns at time t for
portfolio p, and R pt44 is the 44-day compounded future holding period excess returns at
time t for portfolio p. VIXt is the level of VIX on day t and εpt is the error term. I expect
the υ coefficients to be positive and significant, consistent with my proposition that
returns are positively related to implied volatility.
D. Volatility and Future Portfolio Returns
My analysis in Section II suggests that risk should be controlled for in the regressions of
return on VIX. It is also important to know if VIX has an effect on returns independent
of known explanatory factors. To check whether the ability of VIX to forecast returns
holds in the presence of risk factors, I estimate for each of my twelve portfolios the
following regressions:
(9a)
R pt22 = α p + υ pVIX t + β p MKTt 22 + γ p HML22
t
+ ς p SMBt22 + µ pUMDt22 + ε pt
R pt44 = α p + υ pVIX t + β p MKTt 44 + γ p HML44
t
(9b)
44
t
44
t
+ ς p SMB + µ pUMD + ε pt
20
These works make no distinction between short-term and long-term mean, and are used simply as a
proxy for the potential speed to which volatility reverts. In particular, Pan (2000) finds a value for speed of
mean-reversion of 6.7 while Doran and Ronn (2005) report 14.5.
23
HML22
and HML44
are the 22-day and 44-day geometric future returns, respectively, on
t
t
the Fama and French (1993) HML factor formed by compounding the daily HML values.
SMB t22 and SMB t44 are the 22-day and 44-day geometric future returns, respectively, on
the Fama and French SMB factor formed by compounding the daily SMB values.
MKTt 22 and MKTt 44 are the 22-day and 44-day geometric future returns, respectively, on
the Fama and French market factor formed by compounding the daily MKT values.
UMDt22 and UMDt44 are the 22-day and 44-day geometric future returns, respectively, on
the Carhart (1997) momentum factor formed by compounding the daily UMD values.21
If VIX is a predictor of the time series of portfolio returns, then the υ coefficients on VIX
levels should be positive and significant in equations 9a and 9b, even in the presence of
the Fama and French and Carhart factors.
The next pair of regressions expands equations (9a) and (9b) to incorporate binary
variables for extreme levels of VIX relative to past values. These are included to capture
the importance of deviations from the mean exclusive of the effects of VIX levels. The
regression equations are:
R pt22 = α p + υ pVIXt + hp HDt + l p LDt + β p MKTt 22 + γ p HML22
t
+ ς p SMBt22 + µ pUMDt22 + ε pt
(10a)
R pt44 = α p + υ pVIXt + hp HDt + l p LDt + β p MKTt 44 + γ p HML44
t
+ ς p SMBt44 + µ pUMDt44 + ε pt
(10b)
where the binary variable HD equals 1 on any day t that VIX is more than one standard
deviation above its 200-trading-day moving average, and is zero otherwise, and the
21
22
44
The HML, SMB, MKT, and UMD variables are measured over the same time period as R pt and R pt .
24
binary variable LD equals 1 on any day t that VIX is more than one standard deviation
below its 200-trading-day moving average, and is zero otherwise. Two hundred tradingdays represents the length of time over which I measure short-term means.22 I expect the
coefficient on HD to be positive if high VIX values relative to recent levels (short-term
means) lead to mean reversion in VIX and higher stock returns. This prediction is
consistent with equation (7) if and only if the short-term volatility deviations from the
mean volatility dominate long-term deviations, which I expect, and volatility is above the
given level to which investors are sensitive, the threshold value. Otherwise, under
alternative conditions there is no expectation for the sign on the coefficient for HD.
The coefficient on LD should be negative when VIX levels are high in terms of being
above the threshold and low in relation to recent prior levels (short-term mean).
However, if volatility is below the threshold level, the coefficient on LD should be
insignificant due to low volatility risk aversion. With low levels of VIX, individuals are
less averse to deviations from the short-term volatility mean. When volatility is low, a
deviation below the short-term mean results in a negligible change in investors’ risk
aversion since it is very difficult to drive risk aversion any lower and, thus, will not have
an effect on future returns.
To summarize the above discussion, my conclusions suggest that LD and HD will have
negative and positive coefficients, respectively, when volatility is above its threshold
value. There is no expected relation between LD and HD and portfolio excess returns
when volatility is below its threshold value. Thus, I estimate equations (10a) and (10b)
only when volatility is considered to be “high”, or above its threshold value. As a proxy
for the threshold value I use one standard deviation above the long-term mean value of
VIX (implied volatility) over my sample period.
I do not proxy directly for the long-term volatility deviations from the mean because of
the high correlation of these deviations with the level of VIX. In essence, the level of
22
Alternative specifications were examined, using 100-day and 300-day moving averages, as well as using
two standard deviations as the breakpoint. Results did not qualitatively change.
25
VIX is a proxy for deviations from the long-term mean. Demeaning VIX and using that
demeaned variable in the regressions would essentially represent deviations from the
long-term mean and result in perfect multicollinearity.
E. Volatility and Risk Premiums
Next, I examine if VIX has predictive power for the three Fama and French (1993)
factors and the Carhart (1997) momentum factor.
These four portfolios represent
investment opportunities that may be forecasted by VIX. I examine these issues by
estimating the following eight regressions:
MKT
22
pt
=α
MKT
44
pt
=α
p
+ υ p VIX t + ε pt
(11)
p
+ υ p VIX t + ε pt
(12)
SMB
22
pt
= α p + υ p VIX t + ε pt
(13)
SMB
44
pt
= α p + υ p VIX t + ε pt
(14)
HML
22
pt
=α
HML
44
pt
=α
UMD
22
pt
UMD
44
pt
p
+ υ p VIX t + ε pt
(15)
p
+ υ p VIX t + ε pt
(16)
=α
p
+ υ p VIX t + ε pt
(17)
=α
p
+ υ p VIX t + ε pt
(18)
I expect the υ coefficients on VIX to be positive in equations (11, 12, 13, and 14). This is
because the higher the implied volatility, the higher the risk premium today, and the
higher market returns tomorrow. The same rational holds for SMB since small stocks are
riskier (more volatile) than big stocks. The sign for υ should be negative in equations
(15, 16, 17, and 18) using the same rationale. Growth stocks are more risky than value
stocks, implying a negative relationship between future HML and VIX. Future UMD and
VIX will have a negative relationship since winners today should have a lower risk
premium than losers, and thus lower returns when VIX is high.
IV. Empirical Results
A. VIX and the S&P 500
26
Before testing the characteristic portfolios, I determine if there is a significant positive
relationship between future market excess returns and VIX. To test this hypothesis, and
confirm the results in Giot (2005), the 22-day and 44-day excess returns on the S&P 500
are regressed on the level of VIX using Newey and West (1987) adjusted standard errors.
The regressions are identical to those in equations (8a) and (8b), except the dependent
variable is the return on the S&P 500 instead of a characteristic-based portfolio. The
results are reported in table 1 and show significantly positive coefficients on VIX at the
5% level. They are not surprising and consistent with prior findings related to VIX and
future returns, and the notion of a significant negative volatility risk premium.
B. Fama-French Portfolios
Prior to estimating regressions for my twelve portfolios, I first estimate equations (8a, 8b,
9a, and 9b) for the Fama and French (1993) 25 portfolios formed by sorting on size and
book-to-market equity. I obtain returns for these 25 portfolios from July, 1986, through
June, 2005, from Ken French’s website. This provides an opportunity to see if VIX is
able to predict returns for portfolios sorted on size and book-to-market, but not beta.
In table 2 I present estimation results when VIX is the sole explanatory variable and in
table 3 I provide results when VIX is joined by the three Fama and French (1993) factors
and the Carhart (1997) factor. In table 2 I show results for all 25 Fama and French
portfolios and there are only two instances where the coefficient on VIX is negative and
both are statistically insignificant at the 5% level. Of the 48 positive coefficients on VIX,
21 are significant at the 5% level or higher. Nineteen of these significant coefficients are
for the 44-day returns. Thus, in table 2 there is virtually no evidence that VIX predicts
22-day returns, but there is considerable evidence that it predicts 44-day returns. In table
3 I provide, for brevity, results for only the ten extreme size and book-to-market equity
Fama and French portfolios.23 Conclusions from results for the larger model are the same
as from the simple model in table 2. I find virtually no evidence that VIX predicts 22-day
23
Results for the other 40 portfolios are available on request.
27
returns, but substantial evidence that it predicts 44-day returns. However, some of the
coefficients on VIX have negative signs.
C. Book-to-Market Equity, Size, and Beta Sorted Portfolios
My attention now turns to the impact VIX has on my twelve cross-sectional portfolios.
Before conducting my statistical analyses, I present in table 4 the mean returns and
standard deviations of returns for the twelve portfolios formed on book-to-market, size,
and beta sorting. High book-to-market firms tend to have larger returns than low bookto-market firms, while small firms beat large firms. The relationship between returns and
betas varies depending on the size and book-to-market equity ratio. This pattern is
demonstrated in figure 1 and is consistent across 22-day and 44-day returns.
I next estimate equations (8a and 8b) for each of the twelve portfolios and present results
in table 5. All 24 coefficients on VIX are positive. For the 22-day (44-day) returns, six
(eleven) of twelve VIX coefficients are significant at the 5% level or higher. Also note
that there is a monotonic increase in the VIX coefficient from low beta to high beta
portfolios in all book-to-market equity and size groups. Sorting on beta reveals that high
beta firms are more response to VIX than low beta firms. The results for the three-way
sort in table 5 are stronger than in table three for the Fama and French (1993) portfolios,
suggesting that VIX predicts 22-day and 44-day returns, and that this power may be
linked to the additional sort on beta that I perform.
My next estimation for the twelve portfolios is for the full model expressed in equations
(9a and 9b). Results for the 22-day returns are presented in table 6 and results for the 44day returns are in table 7. For the 22-day returns, the coefficient on VIX is positive
eleven of twelve times. The negative coefficient is insignificant and seven of the eleven
positive coefficients are significant at the 5% level or higher. Again, there is a monotonic
increase in the VIX coefficient from low beta to high beta portfolios in all book-tomarket and size groups. Even in the presence of the four factors, there is considerable
evidence that VIX is able to predict 22-day returns. Findings are similar for the 44-day
28
returns in table 7. Eleven of twelve VIX coefficients are positive, the negative coefficient
is insignificant, and six of the eleven positive coefficients are significant at the 5% level
or higher. The monotonic ordering of beta remains except in the bottom right, where for
large size and high book-to-market equity firms the middle beta portfolio has the lowest
VIX coefficient. Even in the presence of the four factors, there is strong evidence that
VIX is able to predict both 22-day and 44-day returns.
The final estimations for each of the twelve portfolios incorporate the binary variables
HD and LD into the model, and equations (10a and 10b) are estimated when VIX is more
than one standard deviation above its sample mean. The coefficients on HD are expected
to be positive and the coefficients on LD are expected to be negative. The results are
provided in table 8. Panel A shows results for the 22-day returns and panel B shows
results for the 44-day returns.
For the 22-day returns the coefficient on VIX is positive eleven out of twelve times and
positively significant at the 5% level or better twice. The coefficient on HD is positive
eleven times, the negative coefficient is insignificant, and seven of the coefficients are
positively significant at the 5% level or better. The coefficient on LD is negative ten
times, both of the positive coefficients are insignificant, and seven of the coefficients are
negatively significant at the 5% level or better. The coefficients on VIX, HD, and LD are
generally consistent with my expectations. There is a monotonic increase in coefficients
on VIX levels and HD as a function of beta for the small size groups. For the large size
groups there is a monotonic increase in the coefficient on HD as the beta categories move
from low to high. All portfolios except one (low book-to-market, large size, and low
beta) have at least one VIX-related variable significant at the 5% level or better and these
results suggest a strong and unique predictive link for VIX-related variables for 22-day
returns.
Results for the 44-day returns in panel B are slightly stronger than for the 22-day returns
in panel A, especially with respect to VIX and HD. The coefficient on VIX is positive
eleven times, the one negative coefficient is insignificant, and nine of the eleven positive
29
coefficients are significant at the 5% level or better. In addition, the coefficient on HD
has the expected positive sign ten times, and eight of these coefficients are significant at
the 5% level or better. Neither of the two negative coefficients is significant. Nine of the
coefficients on LD have the expected negative sign and five are significant at the 5%
level or better. None of the negative coefficients are significant. However, two of the
positive coefficients are significant at the five percent level or better. Every one of the
portfolios has at least one VIX-related variable significant with the hypothesized sign,
indicating an important influence for VIX-related variables on 44-day returns. There is a
near-monotonic ordering of VIX levels as related to beta for small size groupings, and a
monotonic ordering of HD coefficients with respect to beta for all size and book-tomarket equity categories.
What do my results mean for whether implied volatility is a risk factor in returns or an
indicator of market inefficiency? The results in tables 6, 7, and 8 indicate that implied
volatility has a pervasive effect on portfolio returns. Thus, the possibility must remain
open that implied volatility represents a priced risk factor. However, the effect of implied
volatility on future returns may be more complex than previously thought. Results in
table 8 show that for high levels of implied volatility, not just the level of volatility
matters; volatility deviations from short-term means are also important. These measures
have different impacts on different portfolios. Thus, until the role of implied volatility is
better understood, market inefficiency is still a possibility.
D. VIX and the Fama-French and Carhart Factors
Finally, I examine the ability of VIX to predict returns for the four factors MKT, SMB,
HML, and UMD. I estimate equations (11) through (18) for the 22-day and 44-day factor
returns and provide the results in table 9. As I expected, there is a positive relation
between VIX and MKT, and a negative relation between VIX and HML and UMD, for
both the 22-day and 44-day returns. The relations are significant at the five percent level
or higher.
For SMB the 22-day and 44-day coefficients are close to zero and
insignificant. Copeland and Copeland (1999) find that large stocks do well when VIX is
30
high, and this may explain my insignificant results for SMB. Thus, VIX has a strong
ability to predict returns for three of the four factor portfolios. Higher levels of VIX
increases the MKT risk premium, and decreases the HML and UMD risk premiums.
While I am not suggesting that VIX itself is a risk premium, the effect of VIX on
commonly associated risk factors cannot be ignored.
V. Conclusion
I examine the forecasting power of implied volatility for future returns of portfolios
grouped by the characteristics book-to-market equity, size, and beta. Empirically, I
examine daily VIX levels and control for the three Fama and French (1993) factors MKT,
SMB, and HML, and the Carhart (1997) momentum factor UMD. I also develop a model
that shows the effects of implied volatility on security prices is complex, including
consideration of volatility deviations from short-term and long-term volatility means and
whether volatility is sufficiently high enough to be above a “threshold” value. This leads
to a model including binary variables capturing significant deviations of VIX from recent
levels and which is estimated when implied volatilities are high.
My findings add to the literature in three important ways. First, VIX can help explain returns,
through either levels or mean-reversion. The effect is pervasive across portfolios. When
volatility is high and the binary variables incorporating volatility deviations from short-term
means are included, returns are affected in different ways depending on the type of
characteristic-based portfolio. The evidence suggests that VIX may be a priced risk factor,
although the possibility exists that this is an example of market inefficiency. Regardless, it
appears to be necessary to address whether volatility is high or low and to decompose volatility
into various parts to fully understand its relationship with returns across different portfolios.
While the literature on the market price of volatility of risk suggests a negative risk premium,
there has been no statement about whether volatility risk itself has multiple parts. In other
words, should there be a separate premium for volatility and deviations from mean values?
The results here suggest that our notion of volatility needs to be expanded.
31
Second, the relationship between VIX and future returns is strong when beta is included as a
sorting characteristic. In the Fama and French (1993) portfolios, the positive relationship was
somewhat weaker. Thus, sorting on beta appears useful to discern valuable information. Third,
and related to the second point, there is monotonic or near-monotonic increase in the degree of
the relationship between returns and VIX from low beta firms to high beta firms. This
relationship remains, even in the presence of other priced factors. The inclusion of the binary
variables results in a near-monotonic ordering of coefficients on volatility levels solely for
small firms. Overall, my results support the findings by Harvey (1989) and Nelson, Starz, and
Turner (1989) of a positive relationship between conditional volatility and the risk premium.
The ability of VIX and VIX related variables to predict portfolio returns provides a challenge
to asset pricing. Is VIX related to some unknown risk measure that prices risky securities? Or,
is the predictive ability of VIX an example of market inefficiency? Future research can
hopefully provide a more thorough understanding of why VIX can forecast returns.
32
Figure 1
This figure shows the mean geometric returns for the 12 portfolios sorted on book-to-market (B/M), size, and beta. The mean
returns are calculated for the 22-day (Panel A) and 44-day (Panel B) holding periods.
Panel A
5.00%
Low Beta
44 Day Return
Mid Beta
4.50%
High Beta
4.00%
3.50%
3.00%
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
Low B/M, Small Size
Low B/M, Big Size
High B/M, Small Size
Mean Returns for the 12 B/M, Size and Beta Portfolios
33
High B/M, Big Size
Figure 1-Continued
Panel B
5.00%
Low Beta
44 Day Return
Mid Beta
4.50%
High Beta
4.00%
3.50%
3.00%
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
Low B/M, Small Size
Low B/M, Big Size
High B/M, Small Size
High B/M, Big Size
Mean Returns for the 12 B/M, Size and Beta Portfolios
34
Table 1
Estimates from 22-Day and 44-Day Future Market Returns Regressed on VIX
The table below shows the results of the Newey-West regression of the future S&P 500 returns on VIX. Newey-West regressions use
up to five (ten) lags to correct the standard errors for the 22-day (44-day) regression. The observations are over the period from July,
1986, through June, 2005. Absolute values of the t-statistics are shown in parentheses.
VIX
Constant
Observations
22-Day
44-Day
Returns
Returns
0.031
0.056
(2.12)**
(3.11)**
0.001
0.003
(0.17)
(0.53)
4765
4744
*significant at 5% level; **significant at 1% level
Table 2
Regression Estimates for the Fama-French 25 Portfolios Sorted on Book-to-Market Equity and Size
The table below shows the results of regressions of the 25 Fama-French portfolio returns, sorted on book-to-market equity (B/M)
and size, on VIX. The returns to the portfolios are the 22-day and 44-day geometric returns, beginning the day after the observation
of VIX, over the period from July, 1986, through June, 2005. Newey-West regressions are estimated, using up to five (ten) lags to
correct the standard errors for the 22-day (44-day) regressions. Portfolio r11 represents low B/M and low size, portfolio r51 is high
B/M and low size, and portfolio r55 is high B/M and high size. Absolute values of the t-statistics are shown in parentheses.
35
Table 2-Continued
22-Day Returns
Portfolio
VIX
Constant
Observations
Portfolio
VIX
Constant
Observations
Portfolio
VIX
Constant
Observations
Portfolio
VIX
Constant
Observations
Portfolio
VIX
r11
r21
r31
r41
0.032
0.014
0.011
0.006
-0.021
(0.88)
(0.51)
(0.47)
(0.27)
(0.98)
-0.008
0.004
0.006
0.009
0.015
-0.033
-0.006
-0.002
0.004
(1.14)
(0.75)
(1.26)
(1.95)
(3.47)**
(2.84)**
(0.72)
(0.26)
(0.57)
4765
4765
4765
4765
4765
4744
4744
4744
4744
r52
r12
r22
r32
r42
0.055
0.035
0.016
0.006
(1.60)
(1.22)
(0.73)
-0.009
-0.002
(1.26)
4765
Observations
r51
r11
r21
r31
r41
r51
0.145
0.101
0.089
0.081
0.034
(2.54)*
(2.35)*
(2.57)*
(2.23)*
(1.00)
0.015
(2.11)*
4744
r12
r22
r32
r42
r52
-0.010
0.156
0.127
0.082
0.062
0.053
(0.27)
(0.05)
(3.50)**
(3.41)**
(2.85)**
0.005
0.008
0.009
-0.027
-0.015
0.000
0.004
0.006
(0.29)
(1.21)
(1.83)
(0.07)
(0.76)
(1.01)
4765
4765
4765
4765
4744
4744
4744
r53
r13
r23
r33
r43
r53
0.060
0.080
(2.09)*
(2.97)**
4744
(2.04)*
4744
(2.14)*
(1.67)
r13
r23
r33
r43
0.056
0.043
0.021
0.016
0.022
0.131
0.114
0.073
(1.78)
(1.73)
(1.00)
(0.80)
(1.03)
(3.43)**
(3.63)**
(2.77)**
-0.007
-0.002
0.002
0.005
0.006
-0.019
-0.010
-0.003
0.003
0.004
(1.21)
(0.47)
(0.45)
(1.26)
(1.47)
(1.66)
(0.53)
(0.68)
(0.75)
4765
4765
4765
4765
4765
4744
4744
4744
4744
r54
r14
r24
r34
r44
r54
(2.47)*
4744
(2.35)*
(2.69)**
r14
r24
r34
r44
0.068
0.044
0.026
0.028
0.019
0.140
0.109
0.071
0.064
0.048
(2.64)**
(1.88)
(1.25)
(1.64)
(0.93)
(4.41)**
(3.91)**
(2.76)**
(2.72)**
(1.80)
-0.007
-0.002
0.002
0.003
0.004
-0.016
-0.009
0.000
0.004
0.006
(1.46)
(0.46)
(0.56)
(0.87)
(1.12)
(1.60)
(0.05)
(0.80)
(1.19)
4765
4765
4765
4765
4765
4744
4744
4744
4744
r55
r15
r25
r35
r45
r55
(2.50)*
4744
r15
r25
r35
r45
0.047
0.019
0.026
0.013
0.001
0.077
0.033
0.055
0.022
0.012
(1.05)
(1.55)
(0.83)
(0.03)
(3.31)**
(1.68)
(2.73)**
(1.18)
(0.54)
-0.003
0.003
0.001
0.004
0.007
-0.003
0.007
0.002
0.008
0.011
(0.80)
(0.95)
(0.38)
(1.12)
(1.76)
(0.61)
(1.73)
(0.42)
(1.94)
4765
4765
4765
4765
4765
4744
4744
4744
4744
(2.38)*
Constant
44-Day Returns
36
(2.20)*
4744
•
significant at 5% level; ** significant at 1% level
Table 3
Regression Estimates for the Fama-French 25 Portfolios Sorted on Book-to-Market Equity and Size,
Including Four Factors as Independent Variables
The table below shows the results of regressions of the 25 Fama-French portfolio returns, sorted on book-to-market equity (B/M)
and size, on VIX and the four factors MKT, SMB, HML, and UMD. The returns to the portfolios are the 22-day and 44-day geometric
returns, beginning the day after the observation of VIX, over the period from July, 1986, through June, 2005.
Newey-West
regressions are estimated, using up to five (ten) lags to correct the standard errors for the 22-day (44-day) regressions. Portfolio r11
represents low B/M and low size, portfolio r51 is high B/M and low size, and portfolio r55 is high B/M and high size. Absolute
values of the t-statistics are shown in parentheses.
Panel A: 22-Day Returns
VIX
MKT
SMB
HML
UMD
Constant
Observations
r11
r21
r31
r41
r51
r15
r25
r35
r45
r55
-0.005
0.001
0.006
0.009
-0.016
-0.003
-0.007
0.009
0.001
-0.012
(0.44)
(0.15)
(1.12)
(1.27)
(3.31)**
(0.81)
(1.30)
(1.69)
(0.23)
(1.46)
1.013
0.925
0.836
0.837
0.916
0.953
1.055
1.006
0.956
1.105
(38.04)**
(50.17)**
(79.42)**
(76.71)**
(77.90)**
(91.45)**
(74.23)**
(55.47)**
(80.56)**
(55.95)**
1.407
1.299
0.992
0.988
1.063
-0.355
-0.180
-0.155
-0.253
-0.131
(38.99)**
(47.11)**
(66.20)**
(63.65)**
(54.83)**
(20.72)**
(10.22)**
(7.61)**
(14.53)**
(4.55)**
-0.331
0.116
0.271
0.448
0.658
-0.393
0.281
0.481
0.655
0.794
(8.76)**
(4.74)**
(12.69)**
(25.10)**
(32.47)**
(21.54)**
(10.73)**
(18.14)**
(26.23)**
(21.54)**
-0.093
-0.015
0.029
0.050
-0.025
0.022
-0.006
-0.015
-0.074
-0.112
(3.18)**
(0.82)
(2.23)*
(4.43)**
(1.81)
(1.83)
(0.39)
(0.86)
(4.97)**
(4.93)**
-0.004
0.002
0.001
0.002
0.007
0.003
0.001
-0.003
-0.002
0.001
(1.85)
(1.22)
(0.93)
(1.11)
(6.28)**
(2.82)**
(0.99)
(2.65)**
(1.22)
(0.27)
4765
4765
4765
4765
4765
4765
4765
4765
4765
4765
37
Table 3-Continued
Panel B: 44-Day Returns
VIX
MKT
SMB
HML
UMD
Constant
Observations
r11
r21
r31
r41
r51
r15
r25
r35
r45
r55
0.002
0.003
0.021
0.029
-0.020
0.001
-0.015
0.019
-0.006
-0.024
(0.10)
(0.26)
(2.24)*
(2.03)*
(2.32)*
(0.10)
(1.47)
(2.12)*
(0.61)
(1.39)
1.003
0.905
0.828
0.831
0.954
0.981
1.050
0.984
0.929
1.108
(27.79)**
(35.46)**
(67.37)**
(55.74)**
(60.83)**
(71.33)**
(54.55)**
(45.87)**
(58.66)**
(43.85)**
1.451
1.371
1.058
1.044
1.111
-0.359
-0.141
-0.142
-0.233
-0.144
(23.82)**
(34.54)**
(51.61)**
(50.91)**
(44.13)**
(18.51)**
(6.06)**
(5.38)**
(11.28)**
(3.74)**
-0.414
0.077
0.276
0.451
0.696
-0.362
0.319
0.469
0.619
0.745
(8.51)**
(2.23)*
(11.22)**
(19.75)**
(24.67)**
(15.05)**
(10.18)**
(14.95)**
(22.05)**
(15.32)**
-0.041
-0.006
0.025
0.058
-0.010
0.033
-0.018
-0.025
-0.118
-0.127
(1.10)
(0.25)
(1.56)
(3.78)**
(0.63)
(2.10)*
(0.96)
(1.20)
(6.37)**
(4.45)**
-0.010
0.004
0.001
0.001
0.010
0.003
0.003
-0.006
0.000
0.002
(1.92)
(1.66)
(0.34)
(0.47)
(5.34)**
(1.78)
(1.07)
(2.82)**
(0.01)
(0.40)
4744
4744
4744
4744
4744
4744
4744
4744
4744
4744
* significant at 5% level; ** significant at 1% level
Table 4
Descriptive Statistics
The table shows the mean returns and standard deviations for the twelve 22-day and 44-day book-to-market equity (B/M), size, and
beta portfolios. All returns are calculated over the sample period July, 1986, through June, 2005.
38
Table 4-Continued
22-Day Returns
Low B/M, Small Size
Low Beta
44-Day Returns
High Beta
Low Beta
High Beta
Mean Return
1.48%
1.46%
1.33%
3.00%
2.98%
2.68%
Standard Deviation
4.90%
5.94%
9.28%
7.41%
8.88%
13.47%
Mean Return
1.87%
1.75%
2.05%
3.83%
3.57%
4.21%
Standard Deviation
4.76%
5.78%
8.42%
7.51%
8.76%
12.69%
Mean Return
0.99%
1.11%
1.05%
2.00%
2.21%
2.05%
Standard Deviation
4.22%
4.39%
6.20%
5.98%
6.06%
8.59%
Mean Return
1.29%
1.39%
1.25%
2.57%
2.76%
2.47%
Standard Deviation
4.94%
4.77%
6.09%
7.18%
6.71%
8.63%
High B/M, Small Size
Low B/M, Big Size
High B/M, Big Size
Table 5
Return Regression Estimates for the Twelve Portfolios Sorted on Book-to-Market Equity, Size, and
Beta
The table below shows the results of regressions of the 12 portfolio returns, sorted on book-to-market equity (B/M), size, and beta,
on VIX. The returns to the portfolios are the 22-day and 44-day geometric returns, beginning the day after the observation of VIX,
over the period from July, 1986, through June, 2005. Newey-West regressions are estimated, using up to five (ten) lags to correct the
standard errors for the 22-day (44-day) regressions. Portfolio r111 represents low B/M, low size, and low beta, portfolio r113 is low
39
B/M, low size, and high beta, and portfolio r223 is high B/M, high size, and high beta. Absolute values of the t-statistics are shown
in parentheses.
Table 5-Continued
r111
VIX
Constant
Observations
VIX
Constant
Observations
VIX
Constant
Observations
VIX
Constant
Observations
22-Day
44-Day
Returns
Returns
r112
r113
r111
r112
r113
0.011
0.047
0.128
0.081
0.148
0.292
(0.45)
(1.58)
(2.69)**
(2.51)*
(4.00)**
(4.66)**
0.009
0.001
-0.018
0.005
-0.009
-0.043
(1.85)
(0.17)
(1.93)
(0.81)
(1.24)
(3.45)**
4765
4765
4765
4744
4744
4744
r121
r122
r123
r121
r122
r123
0.009
0.035
0.080
0.036
0.058
0.138
(0.46)
(2.01)*
(3.06)**
(1.51)
(3.28)**
(4.15)**
0.004
0.001
-0.010
0.005
0.002
-0.016
(1.17)
(0.02)
(2.05)*
(0.98)
(0.57)
(2.53)*
4765
4765
4765
4744
4744
4744
r211
r212
r213
r211
r212
r213
0.003
0.029
0.099
0.078
0.119
0.275
(0.12)
(1.10)
(2.28)*
(2.33)*
(3.18)**
(4.63)**
0.014
0.008
-0.004
0.014
0.003
-0.024
(3.30)**
(1.45)
(0.51)
(2.13)*
(0.35)
(2.04)*
4765
4765
4765
4744
4744
4744
r221
r222
r223
r221
r222
r223
0.010
0.035
0.061
0.053
0.078
0.133
(0.52)
(2.05)*
(2.34)*
(2.21)*
(3.77)**
(3.87)**
0.007
0.003
-0.004
0.007
0.004
-0.011
(1.92)
(0.77)
(0.83)
(1.40)
(0.84)
(1.57)
4765
4765
4765
4744
4744
4744
* significant at 5% level; ** significant at 1% level
40
Table 6
22-Day Regression Estimates for the Twelve Portfolios Sorted on Book-to-Market
Equity, Size, and Beta
The table below shows the results of regressions of the 12 portfolio returns, sorted on book-to-market equity (B/M), size, and beta,
on VIX and the four factors MKT, SMB, HML, and UMD. The returns to the portfolios are the 22-day geometric returns, beginning
the day after the observation of VIX, over the period from July, 1986, through June, 2005. Newey-West regressions are estimated,
using up to five lags to correct the standard errors. Portfolio r111 represents low B/M, low size, and low beta, portfolio r113 is low
B/M, low size, and high beta, and portfolio r223 is high B/M, high size, and high beta. Absolute values of the t-statistics are shown
in parentheses.
VIX
MKT
SMB
HML
UMD
Constant
Observations
r111
r112
R113
r121
r122
r123
0.002
0.027
0.059
-0.005
0.008
0.013
(0.26)
(2.89)**
(6.08)**
(0.32)
(1.12)
(1.96)*
0.880
1.042
1.311
0.786
0.909
1.080
(48.87)**
(55.36)**
(56.83)**
(21.51)**
(34.83)**
(70.60)**
0.745
0.829
1.162
0.028
-0.241
-0.160
(25.33)**
(25.95)**
(39.30)**
(0.68)
(8.16)**
(6.47)**
0.424
0.328
-0.377
0.367
0.263
-0.468
(16.37)**
(10.55)**
(10.39)**
(8.86)**
(7.17)**
(20.07)**
-0.084
-0.136
-0.443
-0.041
-0.087
-0.229
(4.05)**
(5.48)**
(14.40)**
(1.22)
(3.32)**
(12.17)**
0.005
-0.001
-0.005
0.001
0.000
0.001
(3.23)**
(0.49)
(2.76)**
(0.44)
(0.25)
(0.68)
4765
4765
4765
4765
4765
4765
r211
VIX
MKT
SMB
HML
UMD
r212
r213
r221
r222
r223
0.002
0.022
0.064
0.008
0.017
0.031
(0.26)
(3.16)**
(5.65)**
(0.55)
(2.14)*
(3.09)**
0.862
1.095
1.372
0.887
0.985
1.202
(51.63)**
(61.02)**
(59.94)**
(20.89)**
(44.27)**
(55.63)**
0.809
0.855
1.267
0.052
-0.010
0.281
(29.60)**
(24.95)**
(34.87)**
(1.14)
(0.35)
(9.15)**
0.651
0.708
0.400
0.788
0.652
0.444
(27.21)**
(23.90)**
(10.47)**
(16.28)**
(18.13)**
(11.52)**
-0.129
-0.161
-0.365
-0.085
-0.219
-0.225
41
Table 6-Continued
Constant
Observations
r111
r112
R113
r121
r122
r123
(6.30)**
(7.07)**
(12.15)**
(2.41)*
(8.79)**
(9.38)**
0.008
0.002
-0.003
0.000
0.000
-0.005
(6.48)**
(1.06)
(1.30)
(0.04)
(0.08)
(2.24)*
4765
4765
4765
4765
4765
4765
* significant at 5% level; ** significant at 1% level
Table 7
44-Day Regression Estimates for the Twelve Portfolios Sorted on Book-to-Market
Equity, Size, and Beta
The table below shows the results of regressions of the 12 portfolio returns, sorted on book-to-market equity (B/M), size, and beta,
on VIX and the four factors MKT, SMB, HML, and UMD. The returns to the portfolios are the 44-day geometric returns, beginning
the day after the observation of VIX, over the period from July, 1986, through June, 2005. Newey-West regressions are estimated,
using up to five lags to correct the standard errors. Portfolio r111 represents low B/M, low size, and low beta, portfolio r113 is low
B/M, low size, and high beta, and portfolio r223 is high B/M, high size, and high beta. Absolute values of the t-statistics are shown
in parentheses.
r111
VIX
MKT
r112
R113
r121
r122
r123
0.018
0.060
0.103
-0.003
0.007
0.020
(1.47)
(4.15)**
(6.40)**
(0.10)
(0.55)
(1.68)
0.879
1.003
1.233
0.762
0.880
1.086
(40.15)**
(39.34)**
(44.49)**
(19.92)**
(26.78)**
(67.64)**
42
Table 7-Continued
SMB
HML
UMD
Constant
Observations
r111
r112
R113
r121
r122
r123
0.757
0.874
1.190
0.041
-0.223
-0.173
(19.00)**
(21.08)**
(30.52)**
(0.87)
(6.67)**
(6.20)**
0.439
0.344
-0.415
0.353
0.251
-0.444
(14.23)**
(8.96)**
(9.14)**
(8.25)**
(5.41)**
(16.92)**
-0.081
-0.155
-0.415
-0.084
-0.137
-0.196
(3.05)**
(5.13)**
(12.38)**
(2.16)*
(4.39)**
(9.26)**
0.007
-0.002
-0.007
0.003
0.003
0.002
(2.61)**
(0.62)
(1.95)
(0.44)
(0.89)
(0.75)
4744
4744
4744
4744
4744
4744
r211
VIX
MKT
SMB
HML
UMD
Constant
Observations
r212
R213
r221
r222
r223
0.024
0.048
0.133
0.033
0.028
0.050
(1.99)*
(4.01)**
(7.42)**
(1.15)
(1.83)
(2.89)**
0.874
1.065
1.316
0.854
0.913
1.153
(38.99)**
(45.72)**
(46.29)**
(17.38)**
(29.39)**
(40.26)**
0.846
0.878
1.324
0.023
0.002
0.278
(23.61)**
(19.61)**
(27.10)**
(0.45)
(0.05)
(6.15)**
0.700
0.708
0.379
0.833
0.628
0.413
(23.76)**
(20.27)**
(7.95)**
(14.91)**
(15.11)**
(8.04)**
-0.140
-0.174
-0.363
-0.145
-0.275
-0.225
(6.06)**
(6.30)**
(10.42)**
(3.55)**
(8.87)**
(7.11)**
0.013
0.003
-0.005
-0.003
0.003
-0.006
(5.19)**
(1.23)
(1.34)
(0.44)
(0.96)
(1.57)
4744
4744
4744
4744
4744
4744
* significant at 5% level; ** significant at 1% level
43
Table 8
Return Regression Estimates using High VIX Level Observations
The table below shows the results of regressions of the 12 portfolio returns, sorted on book-to-market equity (B/M), size, and beta,
on VIX, the binary variables HD and LD, and the four factors MKT, SMB, HML, and UMD. HD (LD) equals 1 on any day that VIX
is more than one standard deviation above (below) its 200-day moving average. The returns to the portfolios are the 22-day and 44day geometric returns, beginning the day after the observation of VIX, over the period from July, 1986, through June, 2005. The
regressions are estimated using only the days that VIX is above its sample mean plus one standard deviation (VIX>29.4%). NeweyWest regressions are estimated, using up to five (ten) lags to correct the standard errors for the 22-day (44-day) return regressions.
Portfolio r111 represents low B/M, low size, and low beta, portfolio r113 is low B/M, low size, and high beta, and portfolio r223 is
high B/M, high size, and high beta. Absolute values of the t-statistics are shown in parentheses.
Panel A: High VIX for 22-Day Returns
VIX
HD
LD
MKT
R111
r112
r113
r121
r122
r123
r211
r212
r213
r221
r222
r223
0.006
0.012
0.062
0.054
0.020
0.016
0.004
0.015
0.038
0.051
0.010
-0.002
(0.50)
(0.81)
(2.83)**
(1.83)
(1.73)
(1.19)
(0.56)
(1.34)
(1.90)
(2.12)*
(0.48)
(0.12)
0.009
0.011
0.015
0.008
0.012
0.005
-0.004
0.005
0.011
0.013
0.009
0.007
(2.90)**
(2.78)**
(3.51)**
(1.64)
(3.59)**
(1.53)
(1.36)
(1.45)
(2.10)*
(2.35)*
(2.30)*
(1.45)
0.002
-0.018
-0.009
0.007
-0.002
-0.019
-0.020
-0.020
-0.008
-0.010
-0.016
-0.012
(0.50)
(4.49)**
(1.63)
(1.54)
(0.60)
(5.63)**
(5.80)**
(6.52)**
(1.60)
(2.26)*
(4.52)**
(2.17)*
0.950
1.104
1.275
0.870
0.969
0.930
0.838
1.164
1.386
0.979
0.940
1.125
(25.74)**
(21.73)**
(23.58)*
(14.47)**
(24.34)**
(27.84)**
(25.72)**
(26.43)**
(22.67)**
(16.38)**
(23.09)**
(19.94)
*
SMB
**
1.005
1.103
1.243
0.495
-0.111
-0.185
1.015
1.078
1.376
0.630
0.196
0.098
(17.81)**
(18.42)**
(16.17)*
(5.58)**
(2.20)*
(3.51)**
(24.33)**
(20.82)**
(16.89)**
(6.79)**
(3.25)**
(1.44)
*
HML
0.362
0.256
-0.405
0.119
0.189
-0.545
0.541
0.714
0.328
0.557
0.573
0.479
(6.67)**
(4.34)**
(4.99)**
(1.25)
(2.75)**
(8.72)**
(13.12)**
(14.07)**
(3.61)**
(6.19)**
(8.29)**
(4.74)*
*
UMD
0.102
0.088
-0.626
0.404
0.140
-0.406
-0.051
-0.018
-0.429
0.326
-0.036
-0.342
(2.24)*
(1.48)
(9.24)**
(5.74)**
(2.75)**
(12.01)**
(1.14)
(0.40)
(5.76)**
(4.28)**
(0.69)
(6.06)*
*
Cons
Obs
0.001
0.004
-0.014
-0.018
-0.008
0.000
0.013
0.002
0.000
-0.016
0.003
0.006
(0.27)
(0.79)
(1.82)
(1.79)
(1.99)*
(0.07)
(4.37)**
(0.57)
(0.06)
(1.85)
(0.44)
(0.95)
574
574
574
574
574
574
574
574
574
574
574
574
44
Table 8-Continued
Panel B: High VIX for 44-Day Returns
VIX
HD
LD
MKT
SMB
HML
UMD
Cons
Obs
R111
r112
r113
r121
r122
r123
r211
r212
r213
r221
r222
r223
0.034
0.080
0.095
0.153
0.036
0.010
0.053
0.048
0.113
0.183
0.045
-0.012
(1.37)
(2.91)**
(3.52)**
(2.99)**
(2.64)**
(0.40)
(2.79)**
(3.13)**
(4.12)**
(4.40)**
(2.95)**
(0.38)
0.010
0.019
0.033
-0.002
0.015
0.021
-0.001
0.010
0.034
0.000
0.014
0.023
(2.00)*
(2.98)**
(5.34)**
(0.30)
(3.50)**
(4.82)**
(0.18)
(1.92)
(4.14)**
(0.02)
(2.47)*
(3.24)**
0.010
-0.035
0.027
0.021
-0.008
-0.029
-0.026
-0.038
-0.012
-0.016
-0.025
-0.012
(1.59)
(5.22)**
(3.93)**
(2.48)*
(1.77)
(4.31)**
(3.74)**
(7.03)**
(1.35)
(1.84)
(4.19)**
(1.52)
0.931
0.958
1.309
0.752
0.806
1.052
0.877
1.202
1.363
0.749
0.781
1.181
(19.72)**
(15.67)**
(22.40)**
(12.41)**
(19.28)**
(24.09)**
(18.81)**
(22.54)**
(17.34)**
(13.82)**
(15.77)**
(17.62)**
0.835
0.969
1.265
0.304
-0.201
-0.084
0.999
0.936
1.387
0.365
0.171
0.248
(10.23)**
(12.27)**
(15.09)**
(2.68)**
(3.66)**
(1.61)
(14.47)**
(12.49)**
(15.20)**
(3.24)**
(2.43)*
(2.99)**
0.599
0.507
-0.252
0.272
0.272
-0.460
0.900
0.977
0.512
0.879
0.784
0.558
(9.18)**
(5.98)**
(2.39)*
(3.13)**
(3.40)**
(8.08)**
(12.50)**
(12.96)**
(5.19)**
(10.86)**
(11.46)**
(6.30)**
0.032
-0.046
-0.568
0.226
-0.023
-0.278
-0.097
-0.066
-0.471
-0.018
-0.142
-0.189
(0.65)
(0.88)
(8.71)**
(3.02)**
(0.61)
(7.47)**
(1.96)
(1.35)
(8.40)**
(0.25)
(3.22)**
(3.67)**
0.000
-0.009
-0.021
-0.047
-0.008
-0.003
0.009
-0.002
-0.019
-0.050
0.002
0.014
(0.00)
(0.99)
(2.08)*
(2.60)**
(1.46)
(0.34)
(1.23)
(0.38)
(1.97)*
(3.36)**
(0.41)
(1.11)
574
574
574
574
574
574
574
574
574
574
574
574
Table 9
22-Day and 44-Day Regression Estimates of the Four Factors on VIX
The table below shows the results of the regression of the Fama-French and Carhart four factors on VIX. The regression is estimated
on both the 22-day and 44-day geometric returns, beginning the day after the observation of VIX over the period from July, 1986,
through June, 2005. Newey-West regressions are estimated, using up to five (ten) lags to correct the standard errors for the 22-day
(44-day) regressions. Absolute values of the t-statistics are shown in parentheses.
45
Table 9-Continued
22-Day Returns
MKT
VIX
Constant
Observations
SMB
HML
44-Day Returns
UMD
MKT
SMB
HML
UMD
0.033
-0.010
-0.039
-0.051
0.068
0.030
-0.064
-0.101
(2.03)*
(0.72)
(3.17)**
(2.34)*
(2.23)*
(1.25)
(3.52)**
(2.31)*
-0.001
0.002
0.012
0.019
-0.002
-0.010
0.021
0.047
(0.21)
(0.62)
(4.74)**
(4.79)**
(0.50)
(1.51)
(4.97)**
(4.59)**
4765
4765
4765
4765
4744
4744
4744
4744
* significant at 5% level; ** significant at 1% level
46
CHAPTER 3
THE FORECASTING POWER OF THE RISK AND SENTIMENT COMPONENTS OF
IMPLIED VOLATILITY
Introduction
There is a positive relation between the price of an option and the implied volatility of the option.
The buying and selling of put and call options by investors determines their prices or,
equivalently, their implied volatilities. The implied volatility of options reflects a compensation
for risk. For example, when investors think that the market may decline in the future they may
buy puts to protect themselves. Put sellers will demand a premium to protect themselves for
insuring investors and this premium, called the volatility risk premium, will be reflected in the
put prices and implied volatilities.
However, investors are not always rational, and the implied volatility of options may reflect
irrational behavior or sentiment. Sentiment is defined as the degree of bullishness or bearishness
of investors. When market prices are above or below values suggested as equilibrium prices by
risk-based asset pricing models, investors are considered bullish or bearish, respectively.
For
example, as pointed out by Low (2004), investors may be bearish and overreact to a fear of
future declining markets, and buy puts when, in fact, rational asset pricing models based on risk
factors suggest little possibility of this occurring. So, when investors are bearish or more
pessimistic than would be suggested by rational asset pricing models, then implied volatility, as
proxied by VIX, may rise. Similarly, investors may to too complacent and reduce their demand
for put insurance when they feel that markets will substantially increase, even though rational
47
asset pricing models suggest a small likelihood of this occurring. So, when investors are bullish
or more optimistic than warranted by a risk based asset-pricing model, then VIX may fall.
Thus, VIX may contain a component that reflects compensation for risk and a component that
reflects investor sentiment.24 The risk portion may be associated with price, volatility and/or
jump risk. The sentiment portion may be associated with the bullishness and bearishness of
markets.
The constructor of the VIX index, the CBOE, claims that VIX is a measure of sentiment in
addition to a proxy for risk, as indicated by the following quote on its website. “Since its
introduction in 1993, VIX has been considered by many to be the world's premier barometer of
investor sentiment and market volatility.”25 In addition, many technical analysts treat the VIX
index as a contrary sentiment indicator and recommend market timing strategies based on the
level of VIX. Their position on VIX can be summarized by the following quote from
Moneycentral, “A good working hypothesis is that when the VIX is high, sentiment is unusually
pessimistic and it's a good time to buy stocks”26.
Prior Research and Development of Hypotheses
Theoretically, implied volatility may be influenced by sentiment, as shown by Shefrin (2000),
who proposes a model with heterogeneous beliefs where the pricing kernel is impacted by both
fundamentals and sentiment. In his model, sentiment’s impact on the pricing kernel helps explain
the smile effect in options prices. Several empirical studies also show that sentiment impacts
implied volatility. Vlad (2004) shows that the implied volatility of the 50 most actively traded
options on the S&P100 is impacted by sentiment. Deuskar (2006) finds that a measure of risk
24
This has also been suggested by Kumar and Persaud (2002) and Bandyopadhyay and Jones (2005), who take a
different approach.
25
http://www.cboe.com/micro/vix/introduction.aspx
26
http://www.moneycentral.msn.com/content/ Investing/Powertools/P38977.asp
48
misperception, as measured by the difference of VIX and realized volatility, is correlated with
sentiment measures.
Sentiment may have power to forecast future returns. Theoretically, Delong, Shleifer, Summers
and Waldmann (1990) examine the impact of bullish and bearish sentiment of noise traders in an
overlapping generations model and find that noise traders may affect prices. In their model,
noise traders “create their own space”. In other words, the trading by noise traders by itself
increases risk. Since rational investors are risk averse, their arbitrage capacities are limited and,
hence, they are unwilling to bear the excess risk. Thus, noise traders may earn high returns for
bearing the high risk they themselves create and thus affect returns.
There should be a negative relation between the level of current sentiment and future returns.
This is because if sentiment is bullish, prices are above equilibrium values and so returns would
be lower in the future as prices correct towards equilibrium. The opposite would be true if
sentiment is bearish. Baker and Wurgler (2006) study the effects of irrational investor sentiment
on the cross section of stocks by using a principal component of various sentiment measures.
They find that future returns on small, volatile, distressed and growth stock returns are low when
beginning of period sentiment is high. Brown and Cliff (2005) find that long-term returns on
large and growth stocks are low when institutional measure of sentiment about future market
prices is bullish. They also find that this sentiment is positively related to deviations of prices
from fundamental values. Kumar and Lee (2006) also find that returns are influenced by
sentiment, even at the monthly level.
So, prior studies show that both risk and sentiment have negative forecasting properties for
future returns. As I show in my first essay, implied volatilities, as proxied by VIX, have
forecasting power for future returns. If VIX contains risk and sentiment components, its
forecasting power for future returns may come from either the risk or the sentiment component,
or both. However, an aspect of the relationship between implied volatility and stock returns
remains unexplored. This issue is how much of the forecasting power of VIX for future returns
comes from the risk component of VIX and how much of it comes from the sentiment
component of VIX. Further, I show in my first essay that portfolios sorted by beta have a
49
monotonic relationship to VIX when VIX is high. This relation is especially strong for small
firms. Small firms may be more vulnerable to sentiment, so, it is important to find out whether
this effect comes from the risk or the sentiment component of VIX, or both.
I address this issue by two separate approaches, the first focusing on the forecasting power of the
risk component of VIX and the second on the forecasting power of the sentiment component of
VIX. The process of looking at the forecasting power of risk and sentiment separately gives us a
deeper insight into the degree of market efficiency. If markets are fully efficient, then only the
risk portion should have forecasting power for future returns. In relatively efficient markets, we
should see that the forecasting power of risk is much greater than that of sentiment. If most of the
forecasting power comes from the sentiment component, it would suggest that markets are
inefficient, and abnormal returns can be made. It would also suggest that the role of VIX as a
sentiment indicator is dominant over its role as a proxy for risk.
Two prior studies use VIX as a sentiment proxy for forecasting future returns. Simon and
Wiggins (2001) examine the forecasting ability of the following technical sentiment indicators
for future returns of the S&P 500 futures contract; the S&P 100 put-call ratio, TRIN, and the
VIX index27. They show that these indicators, including VIX, have significant forecasting power.
Simon and Wiggins do not decompose VIX into risk and sentiment components. Thus, the
forecasting power that they find for VIX may be from either the risk or the sentiment component
of VIX, or both.
Brown and Cliff (2004) study the forecasting power of several sentiment proxies for future
returns, and use the ratio of VIX to realized volatility as one of the proxies for sentiment. It is not
possible to isolate the effects of the risk and sentiment components of VIX in the Brown and
Cliff study for two reasons. First, since they focus on a transformed VIX measure (ratio of VIX
to realized volatility) rather than VIX, the forecasting power of VIX alone is not obvious.
27
The put–call ratio, as defined by Simon and Wiggins (2001) is the total trading volume of puts divided by the total
trading volume of calls of S&P 100 index options. The TRIN, also called the ARMS ratio, is defined to be the
number of advancing stocks on the NYSE scaled by the volume of advancing stocks divided by the number of
declining stocks on the NYSE scaled by the volume of declining stocks.
50
Second, since they base their main conclusion on results from principal components or Kalman
filters of their sentiment proxies, and both these methodologies extract combinations of all the
proxies, it is impossible to isolate the forecasting power of any single sentiment proxy.
Also, in the above studies, the true magnitude of the explanatory power of the sentiment proxies
may be inaccurate since they may reflect rational and irrational aspects of sentiment. As Baker
and Wurgler (2006) point out, sentiment can originate from and move partially with fundamental
risk factors. The sentiment proxies in the above studies may be correlated with rational risk
proxies that have been demonstrated in prior research to have forecasting power for returns.
Since the above studies do not separate the sentiment proxies from risk, the forecasting power of
the sentiment proxies may be related to the forecasting power of risk along with the forecasting
power of pure sentiment.
I improve upon prior studies by examining the forecasting power of both the risk component of
VIX and the sentiment component of VIX. Through various techniques I attempt to separate and
isolate the risk and sentiment components of VIX. My first hypothesis relates to the risk
component of VIX.
Hypothesis one: Consistent with a negative volatility risk premium, the risk component of VIX
should have positive forecasting power for the returns of all portfolios sorted by firm
characteristics.
My second hypothesis relates to the sentiment component of VIX.
Hypothesis two: Consistent with investor sentiment affecting future returns, the sentiment
component of VIX has forecasting power for future returns. Since VIX is high when sentiment is
low, the inverse relationship between the level of sentiment and future return should translate
into a positive relation between the sentiment component of VIX and future returns.
51
Data and Methodology
Data
Sentiment proxies
I use five sentiment proxies that have been used in previous literature. These are the University
of Michigan Index of Consumer Sentiment, the American Association of Individual Investors
survey of sentiment, the Investors’ Intelligence survey of sentiment, the number of IPOs, and the
average first day return of IPOs. Lemmon and Portniagina (2006) find that the University of
Michigan Index of Consumer Sentiment has a sentiment component that has power to forecast
returns on small stocks. Brown and Cliff (2004) use the American Association of Individual
Investors survey and the Investors’ Intelligence survey to forecast future returns. Vlad (2004)
uses the Investors’ Intelligence survey to examine the impact of sentiment on implied volatilities
of individual options. Han (2006) use the American Association of Individual Investors survey of
sentiment and the Investors’ Intelligence survey to examine the relation between sentiment and
the option smile, option skeweness, and index misvaluation. Baker and Wurgler (2006) use the
number of IPOs and average first day return of IPOs as proxies of sentiment for studying the
effects of sentiment on the cross-section of returns. Deuskar (2006) uses the number of IPOs and
average first day return of IPOs for explaining misperceptions of risk.
The University of Michigan index of consumer sentiment is derived by computing the relative
scores on the following five questions:
1] We are interested in how people are getting along financially these days. Would you say that
you (and your family living there) are better off or worse off financially than you were a year
ago?"
2] Now looking ahead--do you think that a year from now you (and your family living there) will
be better off financially, or worse off, or just about the same as now?"
52
3]Now turning to business conditions in the country as a whole--do you think that during the
next twelve months we'll have good times financially, or bad times, or what?"
4] Looking ahead, which would you say is more likely--that in the country as a whole we'll have
continuous good times during the next five years or so, or that we will have periods of
widespread unemployment or depression, or what?"
5]About the big things people buy for their homes--such as furniture, a refrigerator, stove,
television, and things like that. Generally speaking, do you think now is a good or bad time for
people to buy major household items?"
The index is calculated by rounding and summing the five relative scores, then dividing by the
1966 base period total of 6.7558, and adding two to this result. The monthly data for the index is
obtained from the University of Michigan website28.
The American Association of Individual Investors (AAII) takes a random poll of its members
every week, and based on their responses, calculates the number of members that are bullish,
bearish, or neutral, respectively, about where the market will be in the next six months. This
survey is more representative of the sentiment of individual investors. I use the percentage of
bullish investors minus the percentage of bearish investors as my proxy for sentiment. This is the
same measure used by Brown and Cliff (2004). The data is obtained from the American
Association of Individual Investors.
The Investors Intelligence (II) survey classifies more than 150 independent investment advisory
newsletters every week into the percentage of bullish newsletters, the percentage of bearish
newsletters, and the percentage of newsletters that are not clearly bullish or bearish. I use the
percentage of bullish newsletters minus the percentage of bearish newsletters as my proxy of
sentiment. This measure is also used by Brown and Cliff (2004). The data is obtained from
Investors Intelligence.
28
http://www.sca.isr.umich.edu/
53
Baker and Wurgler (2006) point out that IPO activity is generally high when investor sentiment
is high, and use the average first day return of IPOs as proxy of the sentiment level. This is
obtained from the website of Jay Ritter29. VIX data is obtained from the CBOE website30.
The University of Michigan consumer sentiment index and the average first day return on IPOs
are available on a monthly basis. The American Association of Individual Investor’s survey and
the Investor Intelligence survey are available on a weekly basis. I use all data at weekly
frequencies. Thus, the monthly measures are the same for each week of the month.
Control Variables used to Orthogonalize Sentiment Proxies for Risk
Since sentiment should be independent of risk, the raw sentiment proxies must be orthogonal to
traditional risk measures. The set of traditional risk measures used to orthogonalize the sentiment
proxies from risk are the term spread, the default spread, and the returns on the Fama and French
(1993) market, size, and value factors. The term spread is the difference between the yield on
Treasury bonds that have maturity of over ten years and the yield on a Treasury bill with
maturity of three months. The default spread is the difference between the yield on Moody’s
BAA rated bonds and the yield on Moody’s AAA rated bonds. The term spread and the default
spread are calculated from the data obtained from the Federal Reserve website31. Returns on the
Fama and French (1993) factors are obtained from the website of Kenneth French.32 I use these
proxies following Fama and French (1993), who use these risk proxies to explain the returns on
stocks and bonds.
Portfolio Returns
Univariate sorting
29
http://bear.cba.ufl.edu/ritter/publ_papers/IPOALL.xls
http://www.cboe.com/micro/vix/introduction.aspx
31
https://www.federalreserve.gov/releases
32
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
30
54
To better understand the relation between VIX as a sentiment proxy and future portfolio returns,
I sort all firms into quintiles by the number of analysts following the firm, age of the firm,
dividend payout ratio of the firm, and profitability of the firm, respectively33. The 22-trading-day
and 44-trading-day excess holding period returns on these portfolios, from July 1996 through
June 2005, are the dependent variables in the time-series regressions34. I obtain the daily riskfree rates from Kenneth French’s website.
The number of analysts following the firm is obtained from IBES. Sorting firms by age, dividend
payout and profitability are done in the manner followed by Baker and Wurgler (2006). The age
of the firm is measured by the number of years (to the nearest month) the firm has been on
CRSP. Dividend payout is calculated as dividends (D) divided by book value of equity (BE).
Dividends (D) is dividends per share at the ex date (Item 26 of Compustat) times shares
outstanding (Item 25 of Compustat). BE is shareholders equity (Item 60 of Compustat) plus
balance sheet deferred taxes (Item 35 of Compustat).
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book
value of equity (BE). Earnings (E) are calculated as income before extraordinary items (Item 18
of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus preferred
dividends (Item 19 of Compustat).
At the end of June of every year t from 1996 to 2004, I sort the stocks into the univariate
portfolios based on data from year t-1. The equally-weighted returns for these portfolios are
measured from July of year t to June of year t+1. I use excess returns (return minus the risk-free
rate) on these portfolios as dependent variables in the time-series regressions.
Multivariate Sorting
33
Similar to Fama and French (1993), I delete negative book equity firms, financial firms, and utilities. Only firms
with ordinary common equity (as classified by CRSP) are used. Thus, ADRs, REITS, and units of beneficial
interest are excluded.
34
I use 22-day returns as this corresponds to the one month horizon. However, I also use the 44-day returns to
account for the possibility that returns may be impacted by VIX over a longer period than it’s forecasting horizon.
55
I use excess returns (return minus the risk-free rate) on twelve portfolios formed on size, bookto-market equity, and beta as dependent variables in the time-series regressions. The twelve
portfolios are formed in the Fama and French (1993) style. Specifically, at the end of June of
each year t from 1996 to 2004, I independently sort NYSE stocks on CRSP by beta, size (market
value of equity), and book-to-market equity.35 Book value of equity is for fiscal year end t-1 and
is defined as the COMPUSTAT book value of shareholders’ equity, plus balance sheet deferredtaxes and investment tax credits, if available, minus the book value of preferred stock.
Depending on availability, the redemption, liquidation, or par value (in that order) is used to
estimate the value of preferred stock. Market value of equity (ME) is measured at the end of
June of year t. Book-to-market equity is the ratio of the book value of equity divided by the
market value of equity. Beta is measured at the end of June of year t by estimating the market
model over the prior 200 trading days. The CRSP value-weighted index is the market proxy.
I use the NYSE breakpoints for ME, book-to-market equity, and beta to allocate NYSE, AMEX
and Nasdaq stocks to two size, two book-to-market, and three beta categories.36 The size and
BE/ME breakpoint is the 50th percentile and beta breakpoints are the 30th and 70th NYSE
percentiles. I construct twelve portfolios from the intersection of the size, book-to-market
equity, and beta categories and calculate the daily value-weighted returns on these portfolios
from July of year t through June of year t+1. The 22-trading-day and 44-trading-day excess
holding period returns on these twelve portfolios, from July 1996 through June 2005, are the
dependent variables in the time-series regressions.
Methodology
Orthogonalization of the Sentiment Proxies
Risk and sentiment should be orthogonal to each other. Since the sentiment proxies may contain
a risk component, it is first necessary to remove the risk component from the sentiment proxies
to get proxies that represent pure sentiment. In their analyses, Baker and Wurgler (2006) and
Lemmon and Portniaguina (2006) orthogonalize their raw sentiment proxies by regressing them
35
Similar to Fama and French (1993), I delete negative book equity firms, financial firms, and utilities.
Only firms with ordinary common equity (as classified by CRSP) are used. Thus, ADRs, REITS, and units of
beneficial interest are excluded.
36
56
on macro variables, and using the residuals as pure sentiment proxies. Similar in spirit to their
analysis, I orthogonalize each sentiment proxy to the Fama and French (1993) market, size and
value factors, the term spread and the default spread. I estimate the following equation with
weekly data for each sentiment proxy separately:
SENTt=α+ β(Rm-Rf) t + sSMBt + hHMLt+ tTERM t+ dDEFt+iIPt+pPCEt+ et
(1)
SENT is, alternatively, the University of Michigan Consumer Sentiment Index, the percentage of
bullish members minus the percentage of bearish members as measured by American
Association of individual investor’s survey, the percentage of bullish newsletters minus the
percentage of bearish newsletters as measured by the Investors’ Intelligence survey, and the
average first day return on IPOs, respectively. Rm-Rf, SMB and HML are the Fama and French
(1993) market, size and value factors, respectively. The term spread (TERM) is the difference
between the yield on T-Bonds that have maturity of over ten years, and the yield on T-Bills with
maturity of three months. The default spread (DEF) is the difference between the yield on
Moody’s BAA rated bonds and the yield on Moody’s AAA rated bonds. IPt is the monthly
industrial production index. PCEt is the monthly personal consumption expenditure. All the
variables are measured every week. Since the University of Michigan Consumer Sentiment
Index, the average first day return on IPOs, the term spread, the default spread, the industrial
production index, and personal consumption expenditure are available on a monthly basis, I use
the monthly value for these variables for all the Fridays in the corresponding month. If Friday is
a holiday, I use the observation on the prior trading day. The intercept plus the residual in each
regression is the respective orthogonalized sentiment proxy.
Isolating the risk component of VIX from VIX
VIX may consist of both risk and sentiment components. To isolate the risk component of VIX
from VIX, I regress VIX on the orthogonalized sentiment proxies. I estimate the following
regression, with weekly observations:
VIXt = α + cCCORt+aAAIIORt+ iIIORt+rRIPOORt+et
57
(2)
VIX(t) is the Friday’s VIX observation. CCOR is the orthogonalized University of Michigan
Consumer Sentiment Index, AAIIOR is the orthogonalized percentage of bullish members minus
the percentage of bearish members as measured by American Association of Individual Investors
survey, IIOR is the orthogonalized percentage of bullish newsletters minus the percentage of
bearish newsletters as measured by the Investors’ Intelligence survey, and RIPOOR is the
orthogonalized first day return on IPOs. All of the orthogonalized measures are obtained from
the estimation of equation (1) and are measured weekly. I expect the sign on the all of the
orthogonalized sentiment proxies to be negative, since all the sentiment proxies are positively
correlated with the current level of sentiment, whereas VIX is negatively correlated with the
current level of sentiment. The intercept plus the residual in this regression is the component of
VIX related to risk only. I call this component VIXRISK, and it is observed weekly.
Testing hypotheses one and two
Hypothesis one says that the risk component of VIX should have positive forecasting power for
the returns of all portfolios sorted by portfolio characteristics. To test hypothesis one, I first
establish that VIX in its entirety has significant forecasting power for the 22-day and 44-day
future returns of the twelve portfolios. I estimate the following regression with weekly
observations:
R 22
pt = α p + vp VIXt+ ept
(3)
R pt44 = α p + vp VIXt+ept
(4)
R pt22 is the 22-day compounded future holding period excess returns for portfolio p and R pt44 is
the 44-day compounded future holding period excess returns for portfolio p. The future holding
period returns are measured every Friday. I expect the coefficients on VIX to be positive. I
employ Newey and West (1987) standard errors in the two equations above, and the equations
that follow, to account for residual correlation due to overlapping portfolio returns.
58
Then, to estimate the forecasting power of only the risk component of VIX, I estimate the
following regression:
R 22
pt = α p + sp VIXRISKt+ ept
(5)
R pt44 = α p + sp VIXRISKt+ept
(6)
If my hypothesis one is correct, the coefficients on VIXRISK should be positive.
Hypothesis two says that, consistent with investor sentiment affecting future returns, the
sentiment component of VIX has forecasting power for future returns. Since VIX is high when
sentiment is low, the inverse relationship between the level of sentiment and future return should
translate into a positive relation between the sentiment component of VIX and future returns.
To test hypothesis two, first I need to isolate the sentiment component of VIX. Since the risk in
VIX should be associated with the volatility risk premium, the portion of VIX not associated
with the volatility risk premium would give the component of VIX that should be associated with
sentiment. I estimate the following regression with weekly observations:
VIXt = α + β(Rm-Rf) t + sSMBt + hHMLt+ tTERM t+ dDEFt+ iIPt+pPCEt+ et
(7)
where Rm-Rf, SMB and HML are the Fama and French (1993) market, size and value factors,
respectively. The term spread (TERM) is the difference between the yield on T-Bonds that have
maturity of over ten years, and the yield on T-Bills with maturity of three months. The default
spread (DEF) is the difference between the yield on Moody’s BAA rated bonds and the yield on
Moody’s AAA rated bonds. The intercept plus the residual in this regression is the part of VIX
not correlated with the volatility risk premium. I call this portion VIXSENT, since this is the
portion of VIX that should reflect sentiment.
59
For testing hypothesis two, I estimate the following two equations:
R 22
pt = α p + sp VIXSENTt+ ept
(8)
R pt44 = α p + sp VIXSENTt+ept
(9)
VIXSENTt is the Friday’s VIXSENT observation estimated by equation (7). If my second
hypothesis is correct, the coefficients on VIXSENT should be positive.
Comparing the forecasting power of VIXRISK and VIXSENT
I next compare the forecasting power for future realized returns of the risk component and
sentiment component of VIX. I estimate the following equations:
R 22
pt = α p + rpVIXRISKt+ sp VIXSENTt+ept
(10)
R pt44 = α p + rpVIXRISKt + sp VIXSENTt+ept
(11)
I expect the coefficient of both VIXRISK and VIXSENT to be positive. However, if markets are
efficient, the forecasting power of VIXRISK should be much higher than the forecasting power
of VIXSENT.
The forecasting power of the risk component of VIX and sentiment can also be tested using two
other types of estimations. I estimate the following equations:
R 22
pt = α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt+ rp RIPOORt+ cpCCOR+ept
(12)
R pt44 = α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt+ rp RIPOORt+ cpCCOR +ept
(13)
If the risk component of VIX is the only part related to future returns, the coefficients of the
orthogonalized sentiment proxies in equations (12) and (13) should not be significant.
60
Results
Table 10 shows the means and the standard deviations of the dependent and independent
variables. Returns for the high book-to market equity portfolios are higher than the low book-tomarket equity portfolios. Small size portfolios show higher returns than large size portfolios.
There is a pattern of diminishing returns as we move from the highest to the lowest quintile for
portfolios sorted by number of analysts and profitability.
Table 11 shows the output from the regression of the four raw sentiment proxies, alternatively,
the University of Michigan Consumer Sentiment Index (CC), the percentage of bullish members
minus the percentage of bearish members as measured by American Association of Individual
Investors survey (AAII), the percentage of bullish newsletters minus the percentage of bearish
newsletters as measured by the Investors’ Intelligence survey(II), and the average first day return
on IPOs (RIPO), respectively, on the Fama and French risk factors Rm-Rf, SMB and HML, and
the macroeconomic factors Industrial production (IP), personal consumption expenditure (PCE),
term spread (TERM) and default spread (DEF).
The raw sentiment proxies are associated more with the macroeconomic risk factors than the
Fama and French risk factors. Industrial production (IP) and term spread (TERM) are positively
related to all the four raw sentiment measures. This is consistent with sentiment increasing as
industrial production increases and economic stability (as proxied by the term spread) increases.
Default spread (DEF) is negatively related to all the raw measures, and this is expected given
that default spread is a proxy for economic instability. A counterintuitive finding is that personal
consumption expenditure (PCE) is positively related to all the measures except II. In the case of
the Fama and French risk factors, HML is positively related to the survey measures of sentiment.
This may be caused by the value factor being connected more with investor trading behavior
than with economic variables.
61
The explanatory power of the Fama and French risk and macroeconomic factors combined is
highest for the consumer sentiment index (CC), followed by the first day return on IPOs (RIPO).
The lowest explanatory power is for the survey measures of sentiment AAII and II, consistent
with the idea that these survey measures proxy more for sentiment than risk.
Table 12 shows the output from the regression of VIX on the orthogonalized sentiment proxies:
the orthogonalized University of Michigan Consumer Sentiment Index (CCOR), the
orthogonalized percentage of bullish members minus the percentage of bearish members as
measured by American Association of Individual Investors survey (AAIIOR), the orthogonalized
percentage of bullish newsletters minus the percentage of bearish newsletters as measured by the
Investors’ Intelligence survey (IIOR), and the orthogonalized first day return on IPOs
(RIPOOR). The signs on all of the coefficients on the orthogonalized sentiment proxies (except
AAIIOR) are negative, consistent with the notion that VIX is inversely related to sentiment. The
institutional investor sentiment index (IIOR) and the consumer confidence index (CCOR) are
significantly related to VIX. The former association may imply that the behavior of VIX is
influenced by institutional investor sentiment, as expected. The latter association may imply be
that the consumer confidence index (CCOR) is a better proxy of individual investor sentiment
that the AAIIOR, and hence VIX is associated with both institutional and individual investor
sentiment.
Table 13 shows the output from the regression of 22-day and 44-day future returns of the
portfolios on VIX. For the 22-day returns, the signs of all the coefficients are positive, consistent
with VIX being both a proxy for risk and sentiment. For the univariately sorted portfolios, none
of the coefficients are significant. For the portfolios sorted by book-to-market equity, size, and
beta, four out of the twelve coefficients are significant.
For the 44-day returns, five of the coefficients on the portfolios sorted by number of analysts and
four of the coefficients on the portfolios sorted by age are positive and significant. However, we
see no specific pattern in the magnitudes of the coefficient among the quintiles. For the portfolios
sorted by book-to-market equity, size, and beta, six out of the twelve coefficients are positive and
significant and all of the coefficients are in the medium and high beta portfolios. This table
62
shows that VIX has significant explanatory power for returns, and this power is higher for longer
horizons and high beta portfolios.
Table 14 shows the output from the regressions of 22-day and 44-day future returns of portfolios
on the risk component of VIX, or VIXRISK. Some of the coefficients have negative signs, but
none of them are significant. For both the univariately sorted portfolios and the portfolios sorted
by book-to-market equity, size, and beta, none of the coefficients are significant. For the 44-day
returns and in case of the univariately sorted portfolios, all of the coefficients on VIXRISK have
positive signs. Two coefficients are significant. For the portfolios sorted by book-to-market
equity, size, and beta, all coefficients on VIXRISK have positive signs, two coefficients are
significant and both are high beta portfolios. From these results, it appears that the risk
component of VIX has little explanatory power for future returns, even though VIX as a whole
has explanatory power. This is in opposition to the efficient market hypothesis which would
predict that the explanatory power of VIX should come from the risk component of VIX.
Table 15 shows the output from the regressions of VIX on the various risk measures, namely, the
Fama and French factors Rm-Rf, SMB, and HML, and the macroeconomic factors term spread
(TERM), default spread (DEF), industrial production (IP) and personal consumption expenditure
(PCE). Consistent with previous literature, VIX is negatively associated with the market factor
(Rm-Rf). VIX is negatively related to HML, which implies that VIX is high when growth stocks
beat value stocks.
For the macroeconomic factors, VIX is negatively related to the term spread (TERM), which is a
proxy for economic stability, and positively related to the default spread (DEF), which is a proxy
for economic instability. However, two counterintuitive results are that VIX is positively related
to industrial production (IP) and negatively related to personal consumption expenditure (PCE).
Table 16 shows the output from the regressions of 22-day and 44-day future returns of portfolios
on the sentiment component of VIX, or VIXSENT. The signs on the VIXSENT coefficients are
positive as expected. For the 22-day returns and in case of the univariately sorted portfolios, five
63
coefficients are significant. For the portfolios sorted by book-to-market equity, size, and beta, six
coefficients on the medium and high beta portfolios are significant.
For the 44-day returns, the results are stronger for the univariately sorted portfolios. The
coefficients for all these portfolios are significant. However we don’t see a pattern in the
magnitude of the coefficients. For the portfolios sorted by book-to-market equity, size, and beta,
eight out of the twelve coefficients are significant and seven of them are in the high to medium
beta portfolios. There is also a pattern of increasing magnitudes of the coefficients from lowest to
highest beta portfolios. This may imply that beta also acts as a proxy for misvaluation (Jiang
(2006)) and higher the beta, higher the market misvaluation.
Table 17 shows the output from the regressions of 22-day and 44-day future returns of portfolios
on both the risk and sentiment components of VIX. The coefficients on VIXSENT are positive.
For the 22-day returns and for the univariately sorted portfolios, six coefficients on VIXSENT
are significant. For the portfolios sorted by book-to-market equity, size, and beta, five
coefficients on VIXSENT are significant and all of them are in the medium and high beta
portfolios.
For the 44-day returns and for the univariately sorted portfolios, all of the coefficients on
VIXSENT are positive and fourteen coefficients are significant. For the portfolios sorted by
book-to-market equity, size, and beta, all coeffcients on VIXSENT are positive. Eight
coefficients on VIXSENT are significant and all of them are in the medium and high beta
portfolios. For the 22-day returns, twenty-four coefficients on VIXRISK have negative signs. For
the 44-day returns fifteen of the coefficients on VIXRISK have negative signs. However, none of
the coefficients on VIXRISK are significant.
The results in this table confirm that VIXSENT has more forecasting power for returns than
VIXRISK, and this power increases with the forecasting horizon and high beta portfolios.
Table 18 shows the output from the regressions of 22-day and 44-day future returns of portfolios
on the risk component of VIX, and the orthogonalized sentiment measures. Five coefficients on
VIXRISK are negative for the 22-day and 44-day returns, but none of them are significant. For
64
the 22-day returns, none of the coefficients on VIXRISK are significant. Eleven coefficients on
CCOR and one coefficient on IIOR are significant with the expected negative sign. Seven
coefficients on RIPOOR and one coefficient on AAIIOR are significant with the opposite sign.
For the portfolios sorted on book-to-market equity, size, and beta, none of the coefficients on
VIXRISK are significant. Four coefficients on CCOR, two coefficients on IIOR, and one
coefficient on AAIIOR are significant with the expected negative sign. Four coefficients on
RIPOOR are significant with the opposite sign.
For the 44-day returns and in case of the univariately sorted portfolios the coefficients on
VIXRISK are positive and one coefficient is significant. Two coefficients on IIOR are significant
with the expected negative sign. Thirteen coefficients on RIPOOR and nine coefficients on
AAIIOR are significant with the opposite sign.
For the portfolios sorted book-to-market equity, size, and beta, two coefficients on VIXRISK
are significant. Three coefficients on IIOR and one coefficient on CCOR are significant with the
expected negative sign. Three coefficients on IIOR are significant with the expected negative
sign. Six coefficients on RIPOOR and four coefficients on AAIIOR are significant with the
opposite sign.
Table 19 shows the variables, the number of times the coefficients on the variables are
significant and their respective signs. From this table, we observe that the coefficients on the
sentiment variables RIPOOR and AAIIOR have the wrong signs when predicting short horizon
returns. This could imply that these variables are good for explaining returns only at longer
horizons. The coefficients on CCOR and IIOR generally have the correct signs over the horizons
used in this study.
Conclusion
In this essay, I decompose VIX into a risk component, VIXRISK, and a sentiment component
VIXSENT, and examine the forecasting power of these two components for future returns on
portfolio sorted by various characteristics. VIX is associated with both institutional and
individual sentiment and with macroeconomic measures of risk including term and default
65
spreads. The sentiment component of VIX, VIXSENT, has more explanatory power for future
returns than VIXRISK. This evidence is contradictory to the efficient markets hypothesis. Also,
the explanatory power for VIXSENT is higher for longer horizon returns and high beta
portfolios. The power observed for VIXSENT in forecasting high beta portfolios may imply that
beta also acts as a proxy for market misvaluation. However, for VIXSENT, we don’t see the
expected pattern of coefficient magnitudes for portfolio quintiles sorted by the number of
analysts, age, dividend payout, or profitability of the firm. This failure may be due to the short
horizons over which these returns are calculated. One interesting extension would be to examine
forecasting powers of VIXSENT over longer horizons.
Table 10
Descriptive Statistics
The table below shows the mean and the standard deviation of the dependent and independent variables calculated using weekly
data from July 1996 to June 2005. Portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low
size, and high beta, and portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data
for the fiscal year t-1. The returns on the portfolios are measure from July of year t to June of year t+1.
Panel A shows the means and standard deviations of the 22-day-returns. Analystfiveret22 is the top quintile portfolio formed by
the number of analysts following the firm (obtained from IBES). Analystoneret22 is the bottom quintile portfolio.
Analystfourret22, analystthreeret22, and analysttworet22 are the fourth, third and second quintile portfolios, respectively.
Agefiveret22 is the 22-day return on the top quintile portfolio formed by the age of the firm. Ageoneret22 is the bottom quintile
portfolio. Agefourret22, agethreeret22, and agetworet22 are the fourth, third and second quintile portfolios, respectively. The age
of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP. Divfiveret22 is the 22-day
return on the top quintile portfolio formed by the dividend payout ratio of the firm. Divoneret22 is the bottom quintile portfolio.
Divfourret22, divthreeret22 and divtworet22 are the fourth, third and second quintile portfolios, respectively. Dividend payout is
calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends per share at the ex date (Item 26 of
Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is shareholders equity (Item 60 of
Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefiveret22 is the 22-day return on the top quintile
portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio. Roefourret22, Roethreeret22 and
Roetworet22 are the fourth, third and second quintile portfolios, respectively. Profitability is measured by the ratio of return on
equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated as income before extraordinary
items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus preferred dividends (Item 19
66
of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1. The equally-weighted returns on
the portfolios are measured from July of year t to June of year t+1.
Panel B shows the means and standard deviations of the 44-day-returns Analystfiveret44 is the top quintile portfolio formed by
the number of analysts following the firm (obtained from IBES). Analystoneret44 is the bottom quintile portfolio.
Analystfourret44,
analystthreeret44,
and
analysttworet44
are
the
fourth,
third
and
second
quintile
portfolios,
respectively.Agefiveret44 are the 44-day return on the top quintile portfolio formed by the age of the firm. Ageoneret44 is the
bottom quintile portfolio. Agefourret44, agethreeret44, and agetworet44 are the fourth, third and second quintile portfolios,
respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP.
Divfiveret44 is the 44-day return on the top quintile portfolio formed by the dividend payout ratio of the firm. Divoneret44 is the
bottom quintile portfolio. Divfourret44, divthreeret44 and divtworet44 are the fourth, third and second quintile portfolios,
respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends
per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is
shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefiveret44 is the 44-day
return on the top quintile portfolio formed by the profitability of the firm. Roeoneret44 is the bottom quintile portfolio.
Roefourret44, Roethreeret44 and Roetworet44 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1.
Panel C shows the means and standard deviations of the other variables. VXO is the daily VIX level. Rm-Rf, SMB and HML are
the Friday’s value each week of the Fama and French (1993) market, size and value factors, respectively. The term spread
(TERM) is the difference between the yield on T-Bonds that have maturity of over ten years, and the yield on T-Bills with
maturity of three months. The default spread (DEF) is the difference between the yield on Moody’s BAA rated bonds and the
yield on Moody’s AAA rated bonds. IP is the monthly industrial production index. PCE is the monthly personal consumption
expenditure. All the variables are measured every week. Since the University of Michigan Consumer Sentiment Index, the
average first day return on IPOs, the term spread, the default spread, the industrial production index, and personal consumption
expenditure are available on a monthly basis, I use the monthly value for these variables for all the Fridays in the corresponding
month. If Friday is a holiday, I use the observation on the prior trading day. AAII is the percentage of bullish members minus the
percentage of bearish members as measured by American Association of Individual Investors survey, II is the percentage of
bullish newsletters minus the percentage of bearish newsletters as measured by the Investors’ Intelligence survey. VIXSENT is
the sentiment component of VIX estimated with equation (7) and VIXRISK is the risk component of VIX estimated with
equation (2).
67
Table 10-Continued
Panel A: 22-Day Return
Analystfiveret22
Mean
Analystfourret22
Analystthreeret22
Analysttworet22
Analystoneret22
0.010
0.010
0.012
0.016
0.022
0.063
0.073
0.076
0.076
0.070
Standard
Deviation
Agefiveret22
Mean
Agefourret22
Agethreeret22
Agetworet22
Ageoneret22
0.015
0.022
0.022
0.023
0.012
0.045
0.059
0.070
0.079
0.095
Standard
Deviation
Roefiveret22
Mean
Roefourret22
Roethreeret22
Roetworet22
Roeoneret22
0.012
0.013
0.015
0.018
0.020
0.057
0.058
0.058
0.063
0.072
Standard
Deviation
Divfiveret22
Mean
Divfourret22
Divthreeret22
Divtworet22
Divoneret22
0.012
0.011
0.012
0.015
0.012
0.044
0.045
0.047
0.050
0.059
Standard
Deviation
R111
Mean
R112
R113
R121
R122
R123
0.012
0.012
0.008
0.006
0.008
0.004
0.052
0.060
0.109
0.046
0.046
0.074
Standard
Deviation
R211
Mean
R212
R213
R221
R222
R223
0.017
0.015
0.016
0.007
0.011
0.009
0.051
0.059
0.093
0.053
0.054
0.069
Standard
Deviation
68
Table 10-Continued
Panel B: 44-Day Return
Analystfiveret44
Mean
Analystfourret44
Analystthreeret44
Analysttworet44
Analystoneret44
0.021
0.020
0.025
0.033
0.048
0.093
0.109
0.116
0.115
0.109
Standard
Deviation
Agefiveret44
Mean
Agefourret44
Agethreeret44
Agetworet44
Ageoneret44
0.033
0.048
0.049
0.050
0.028
0.067
0.090
0.107
0.122
0.145
Standard
Deviation
Roefiveret44
Mean
Roefourret44
Roethreeret44
Roetworet44
Roeoneret44
0.026
0.028
0.032
0.039
0.043
0.083
0.085
0.088
0.094
0.109
Standard
Deviation
Divfiveret44
Mean
Divfourret44
Divthreeret44
Divtworet44
Divoneret44
0.023
0.023
0.024
0.031
0.025
0.064
0.068
0.069
0.073
0.086
Standard
Deviation
R111
Mean
R112
R113
R121
R122
R123
0.027
0.026
0.016
0.014
0.016
0.004
0.077
0.087
0.162
0.067
0.064
0.111
Standard
Deviation
R211
Mean
R212
R213
R221
R222
R223
0.037
0.033
0.034
0.016
0.023
0.017
0.079
0.089
0.140
0.078
0.078
0.098
Standard
Deviation
69
Table 10-Continued
Panel C: Other Variables
VXO
SMB
HML
Mean
0.238
Rm-Rf
0.00045
0.00052
0.00041
Standard Deviation
0.071
0.01148
0.00585
0.00648
II
DEF
TERM
RIPO
Mean
0.200
0.008
0.017
0.243
Standard Deviation
0.114
0.002
0.011
0.265
AAII
IP
PCE
CC
Mean
0.159
27.147
1.011
0.975
Standard Deviation
0.181
1.359
0.050
0.082
VIXSENT
VIXRISK
Mean
0.586
0.993
Standard Deviation
0.055
0.060
Table 11
Regression Estimates of the Raw Sentiment Proxies on Risk Factors
The table below shows the estimation results of equation (1) with weekly data from July 1996 to June 2005:
SENTt=α+ β(Rm-Rf) t + sSMBt + hHMLt+ tTERM t+ dDEFt+iIPt+pPCEt+ et
(1)
The dependent variable, SENT, is alternatively, the University of Michigan Consumer Sentiment Index (CC), the percentage of
bullish members minus the percentage of bearish members as measured by American Association of individual investors survey
(AAII), the percentage of bullish newsletters minus the percentage of bearish newsletters as measured by the Investors’
70
Intelligence survey (II), the average first day return on IPOs (RIPO), respectively. The independent variables Rm-Rf, SMB and
HML are the Friday’s value each week of the Fama and French (1993) market, size and value factors, respectively. The term
spread (TERM) is the difference between the yield on T-Bonds that have maturity of over ten years, and the yield on T-Bills with
maturity of three months. The default spread (DEF) is the difference between the yield on Moody’s BAA rated bonds and the
yield on Moody’s AAA rated bonds. IP is the monthly industrial production index. PCE is the monthly personal consumption
expenditure. All the variables are measured every week. Since the University of Michigan Consumer Sentiment Index, the
average first day return on IPOs, the term spread, the default spread, the industrial production index, and personal consumption
expenditure are available on a monthly basis, I use the monthly value for these variables for all the Fridays in the corresponding
month. If Friday is a holiday, I use the observation on the prior trading day. OBS is the number of observations. ADJR is the
adjusted R-Squared from the regression. The intercept plus the residual in each regression is the respective orthogonalized
sentiment proxy.
Dependent Variable: University of Michigan Consumer Sentiment Index (CC)
INTERCEPT
COEFFICIENT
T-STAT
1.732
34.140**
Rm-Rf
0.283
1.080
SMB
0.465
1.240
HML
0.627
1.340
IP
0.058
15.540**
PCE
-2.200
-18.190**
TERM
1.804
4.970**
DEF
-17.364
-14.550**
OBS
454
ADJR
0.71
Dependent Variable: Percentage of bullish members minus the percentage of bearish members as measured by American
Association of Individual Investors survey (AAII)
INTERCEPT
COEFFICIENT
T-STAT
0.310
1.520
Rm-Rf
2.020
1.920
SMB
0.585
0.390
HML
6.212
3.310**
IP
0.056
3.760**
PCE
-1.602
-3.30**
TERM
4.96
3.410**
DEF
-18.438
-3.850**
OBS
454
ADJR
0.05
71
Table 11- Continued
Dependent Variable: Percentage of bearish newsletters as measured by the Investors’ Intelligence survey(II)
COEFFICIENT
T-STAT
INTERCEPT
-0.753
-6.510**
Rm-Rf
0.883
1.480
SMB
0.776
0.910
HML
2.946
2.760**
IP
0.026
3.110**
PCE
0.266
0.970
TERM
1.911
2.310*
DEF
-8.646
-3.180**
OBS
454
ADJR
0.22
Dependent Variable: The average first day return on IPOs (RIPO)
COEFFICIENT
T-STAT
INTERCEPT
1.453
6.700**
Rm-Rf
1.513
1.350
SMB
1.363
0.850
HML
-0.644
-0.320
IP
0.266
16.620**
PCE
-8.338
-16.120**
TERM
9.501
6.120**
DEF
-21.454
-4.200**
OBS
454
ADJR
0.49
•
significant at 5% level; ** significant at 1% level
72
Table 12
Regression Estimates of VIX on the Orthogonal Sentiment Proxies
The table below shows the estimation results of equation (2) with weekly data from July 1996 to June 2005:
VIXt = α + cCCORt+aAAIIORt+ iIIORt+rRIPOORt+et
(2)
The dependent variable VIX is the Friday’s VIX observation. CCOR is the orthogonalized University of Michigan Consumer
Sentiment Index, AAIIOR is the orthogonalized percentage of bullish members minus the percentage of bearish members as
measured by American Association of Individual Investors survey, IIOR is the orthogonalized percentage of bullish newsletters
minus the percentage of bearish newsletters as measured by the Investors’ Intelligence survey, and RIPOOR is the orthogonalized
first day return on IPOs. All of the orthogonalized measures are obtained from the estimation of equation (1) and are measured
weekly. The intercept plus the residual in this regression is the component of VIX related to risk only. I call this component
VIXRISK, and it is observed weekly. OBS is the number of observations. ADJR is the adjusted R-Squared from the regression.
Dependent Variable: VIX
COEFFICIENT
T-STAT
INTERCEPT
0.993
7.320**
AAIIOR
0.003
0.180
IIOR
-0.205
-5.970**
CCOR
-0.502
-6.990**
RIPOOR
-0.028
-1.790
OBS
454
ADJR
0.27
* significant at 5% level; ** significant at 1% level
Table 13
Regression Estimates of 22-day and 44-day Future Returns of Portfolios on VIX
The table below shows the estimation results of equation (3) with weekly data from July 1996 to June 2005:
73
R 22
pt = α p + vp VIXt+ ept
R pt22
(3)
is the 22-day compounded future holding period excess returns for portfolio p. VIX is the Friday’s VIX observation.In
panel A, Analystfiveret22 is the top quintile portfolio formed by the number of analysts following the firm (obtained from IBES).
Analystoneret22 is the bottom quintile portfolio. Analystfourret22, analystthreeret22, and analysttworet22 are the fourth, third
and second quintile portfolios, respectively. Agefiveret22 is the 22-day return on the top quintile portfolio formed by the age of
the firm. Ageoneret22 is the bottom quintile portfolio. Agefourret22, agethreeret22, and agetworet22 are the fourth, third and
second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the firm
has been on CRSP. Divfiveret22 is the 22-day return on the top quintile portfolio formed by the dividend payout ratio of the firm.
Divoneret22 is the bottom quintile portfolio. Divfourret22, divthreeret22 and divtworet22 are the fourth, third and second quintile
portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is
dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity
(BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefiveret22 is the
22-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio.
Roefourret22, Roethreeret22 and Roetworet22 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1.
In panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
74
Table 13-Continued
PanelA: Regression Estimates of 22-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIX
PORTFOLIO
ANALYSTFIVERET22
ANALYSTFOURRET22
ANALYSTTHREERET22
COEFFICIENT
T-STAT
PORTFOLIO
AGEFIVERET22
INTERCEPT
-0.024
-1.490
VXO
0.145
1.950
INTERCEPT
-0.023
-1.270
VXO
0.138
1.650
AGEFOURRET22
INTERCEPT
-0.014
-0.740
VXO
0.108
1.250
ANALYSTTWORET22
INTERCEPT
-0.011
-0.620
VXO
0.112
1.380
ANALYSTONERET22
INTERCEPT
0.002
0.140
VXO
0.081
1.120
COEFFICIENT
T-STAT
PORTFOLIO
DIVFIVERET22
PORTFOLIO
ROEFIVERET22
INTERCEPT
-0.002
-0.110
VXO
0.059
0.900
ROEFOURRET22
INTERCEPT
-0.003
-0.200
VXO
0.068
1.030
INTERCEPT
0.000
-0.010
VXO
0.063
0.970
INTERCEPT
0.001
0.040
VXO
0.075
1.080
INTERCEPT
-0.002
-0.090
VXO
0.090
1.170
ROETHREERET22
ROETWORET22
ROEONERET22
AGETHREERET22
AGETWORET22
AGEONERET22
DIVFOURRET22
DIVTHREERET22
DIVTWORET22
DIVONERET22
* significant at 5% level; ** significant at 1% level
75
COEFFICIENT
T-STAT
INTERCEPT
0.004
0.360
VXO
0.048
0.970
INTERCEPT
0.001
0.050
VXO
0.089
1.410
INTERCEPT
-0.004
-0.250
VXO
0.111
1.490
INTERCEPT
-0.010
-0.530
VXO
0.136
1.630
INTERCEPT
-0.024
-1.140
VXO
0.151
1.530
COEFFICIENT
T-STAT
INTERCEPT
0.000
0.011
VXO
0.050
0.047
INTERCEPT
-0.002
0.011
VXO
0.054
0.048
INTERCEPT
0.002
0.012
VXO
0.043
0.053
INTERCEPT
0.009
0.012
VXO
0.023
0.054
INTERCEPT
-0.004
0.014
VXO
0.065
0.064
Table 13-Continued
Panel B: Regression Estimates of 22-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIX
COEFFICIENT
T-STAT
INTERCEPT
0.006
0.450
VXO
0.026
0.430
INTERCEPT
-0.008
-0.590
VXO
0.086
1.360
INTERCEPT
-0.050
-1.930
VXO
0.244
2.020*
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
-0.005
-0.450
VXO
0.047
0.980
INTERCEPT
-0.014
-1.420
VXO
0.091
2.120*
INTERCEPT
-0.037
-2.250*
VXO
0.174
2.370*
INTERCEPT
0.017
1.360
VXO
-0.001
-0.010
INTERCEPT
0.010
0.670
VXO
0.024
0.350
INTERCEPT
-0.028
-1.180
VXO
0.185
1.690
INTERCEPT
0.013
1.110
VXO
-0.023
-0.450
INTERCEPT
-0.003
-0.320
VXO
0.060
1.380
INTERCEPT
-0.029
-1.810
VXO
0.159
2.280*
* significant at 5% level; ** significant at 1% level
76
Table 13-Continued
Regression Estimates 44-day Future Returns of Portfolios on VIX
The table below shows the estimation results of equation (4) with weekly data from July 1996 to June 2005:
R pt44
=
R pt44
is the 44-day compounded future holding period excess returns for portfolio p. VIX is the Friday’s VIX observation. In
α p + vp VIXt+ept
(4)
Panel C, Analystfiveret44 is the top quintile portfolio formed by the number of analysts following the firm (obtained from
IBES). Analystoneret44 is the bottom quintile portfolio. Analystfourret44, analystthreeret44, and analysttworet44 are the fourth,
third and second quintile portfolios, respectively.Agefiveret44 are the 44-day return on the top quintile portfolio formed by the
age of the firm. Ageoneret44 is the bottom quintile portfolio. Agefourret44, agethreeret44, and agetworet44 are the fourth, third
and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the
firm has been on CRSP. Divfiveret44 is the 44-day return on the top quintile portfolio formed by the dividend payout ratio of the
firm. Divoneret44 is the bottom quintile portfolio. Divfourret44, divthreeret44 and divtworet44 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefiveret44 is the 44-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret44 is the bottom
quintile portfolio. Roefourret44, Roethreeret44 and Roetworet44 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1.
In Panel D, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to
account for residual correlation due to overlapping portfolio returns.
77
Table 13-Continued
Panel C: Regression Estimates of 44-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIX
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.058
-1.820
AGEFIVERET44
VXO
0.322
2.400*
INTERCEPT
-0.066
-1.900
VXO
0.355
2.400*
ANALYSTTHREERET44
INTERCEPT
-0.055
-1.540
VXO
0.328
2.180*
ANALYSTTWORET44
INTERCEPT
-0.049
-1.370
VXO
0.336
2.270*
INTERCEPT
-0.015
-0.450
VXO
0.256
1.970*
PORTFOLIO
ANALYSTFIVERET44
ANALYSTFOURRET44
ANALYSTONERET44
PORTFOLIO
ROEFIVERET44
ROEFOURRET44
ROETHREERET44
ROETWORET44
ROEONERET44
AGEFOURRET44
AGETHREERET44
AGETWORET44
AGEONERET44
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.019
-0.680
DIVFIVERET44
VXO
0.183
1.560
INTERCEPT
-0.021
-0.790
VXO
0.201
1.830
INTERCEPT
-0.016
-0.560
VXO
0.195
1.640
INTERCEPT
-0.013
-0.430
VXO
0.212
1.710
INTERCEPT
-0.021
-0.620
VXO
0.259
1.930
DIVFOURRET44
DIVTHREERET44
DIVTWORET44
DIVONERET44
* significant at 5% level; ** significant at 1% level
78
COEFFICIENT
T-STAT
INTERCEPT
0.003
0.120
VXO
0.122
1.380
INTERCEPT
-0.007
-0.250
VXO
0.223
2.000*
INTERCEPT
-0.023
-0.720
VXO
0.294
2.280*
INTERCEPT
-0.038
-1.090
VXO
0.363
2.510*
INTERCEPT
-0.068
-1.670
VXO
0.395
2.260*
COEFFICIENT
T-STAT
INTERCEPT
-0.012
-0.570
VXO
0.141
1.670
INTERCEPT
-0.017
-0.790
VXO
0.166
1.870
INTERCEPT
-0.009
-0.370
VXO
0.136
1.460
INTERCEPT
0.004
0.180
VXO
0.107
1.090
INTERCEPT
-0.024
-0.870
VXO
0.199
1.810
Table 13-Continued
Panel D: Regression Estimates of 44-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIX
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.004
-0.150
VXO
0.124
1.190
INTERCEPT
-0.031
-1.150
VXO
0.232
2.150*
INTERCEPT
-0.119
-2.450*
VXO
0.553
2.680**
INTERCEPT
-0.007
-0.380
VXO
0.084
1.080
INTERCEPT
-0.023
-1.230
VXO
0.155
2.220*
INTERCEPT
-0.068
-1.990*
VXO
0.302
2.090*
R211
INTERCEPT
0.015
0.540
VXO
0.089
0.800
R212
INTERCEPT
-0.005
-0.180
VXO
0.154
1.250
INTERCEPT
-0.087
-1.940
VXO
0.499
2.570**
INTERCEPT
0.019
0.920
VXO
-0.017
-0.210
INTERCEPT
-0.011
-0.520
VXO
0.142
1.720
INTERCEPT
-0.064
-1.990*
VXO
0.333
2.56*
R111
R112
R113
R121
R122
R123
R213
R221
R222
R223
* significant at 5% level; ** significant at 1% level
79
Table 14
Regression Estimates of 22-day Future Returns of Portfolios on VIXRISK
The table below shows the estimation results of equation (5) with weekly data from July 1996 to June 2005:
R 22
pt = α p + sp VIXRISKt+ ept
R pt22
(5)
is the 22-day compounded future holding period excess returns for portfolio p.
In panel A, Analystfiveret22 is the top quintile portfolio formed by the number of analysts following the firm (obtained from
IBES). Analystoneret22 is the bottom quintile portfolio. Analystfourret22, analystthreeret22, and analysttworet22 are the fourth,
third and second quintile portfolios, respectively. Agefiveret22 is the 22-day return on the top quintile portfolio formed by the
age of the firm. Ageoneret22 is the bottom quintile portfolio. Agefourret22, agethreeret22, and agetworet22 are the fourth, third
and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the
firm has been on CRSP. Divfiveret22 is the 22-day return on the top quintile portfolio formed by the dividend payout ratio of the
firm. Divoneret22 is the bottom quintile portfolio. Divfourret22, divthreeret22 and divtworet22 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefiveret22 is the 22-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom
quintile portfolio. Roefourret22, Roethreeret22 and Roetworet22 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. VIXRISK is
the risk component of VIX estimated with equation (2).
In panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1. The future holding period returns are measured
every Friday. I employ Newey and West (1987) standard errors to account for residual correlation due to overlapping portfolio
returns.
80
Table 14-Continued
Panel A: Regression Estimates of 22-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIXRISK
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
ANALYSTFIVERET22
INTERCEPT
-0.091
-1.250
AGEFIVERET22
INTERCEPT
-0.016
-0.340
VIXRISK
0.102
1.370
VIXRISK
0.032
0.640
ANALYSTFOURRET22
INTERCEPT
-0.056
-0.680
AGEFOURRET22
INTERCEPT
-0.047
-0.750
VIXRISK
0.066
0.780
VIXRISK
0.070
1.070
INTERCEPT
-0.044
-0.520
INTERCEPT
-0.057
-0.770
VIXRISK
0.056
0.640
VIXRISK
0.080
1.040
INTERCEPT
-0.045
-0.550
INTERCEPT
-0.084
-1.000
VIXRISK
0.061
0.720
VIXRISK
0.107
1.230
INTERCEPT
-0.040
-0.530
INTERCEPT
-0.055
-0.580
VIXRISK
0.063
0.790
VIXRISK
0.068
0.680
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.006
-0.100
DIVFIVERET22
INTERCEPT
-0.013
-0.270
VIXRISK
0.019
0.290
VIXRISK
0.024
0.510
INTERCEPT
-0.023
-0.360
INTERCEPT
-0.023
-0.460
VIXRISK
0.036
0.550
VIXRISK
0.035
0.680
INTERCEPT
-0.013
-0.200
INTERCEPT
-0.019
-0.340
VIXRISK
0.028
0.420
VIXRISK
0.031
0.560
INTERCEPT
-0.030
-0.430
INTERCEPT
0.026
0.480
VIXRISK
0.049
0.680
VIXRISK
-0.011
-0.210
INTERCEPT
-0.029
-0.370
INTERCEPT
-0.022
-0.330
VIXRISK
0.049
0.600
VIXRISK
0.034
0.500
PORTFOLIO
ANALYSTTHREERET22
ANALYSTTWORET22
ANALYSTONERET22
PORTFOLIO
ROEFIVERET22
ROEFOURRET22
ROETHREERET22
ROETWORET22
ROEONERET22
AGETHREERET22
AGETWORET22
AGEONERET22
DIVFOURRET22
DIVTHREERET22
DIVTWORET22
DIVONERET22
* significant at 5% level; ** significant at 1% level
81
Table 14-Continued
Panel B: Regression Estimates of 22-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXRISK
COEFFICIENT
T-STAT
INTERCEPT
0.021
0.350
VIXRISK
-0.009
-0.140
INTERCEPT
-0.013
-0.200
VIXRISK
0.026
0.380
INTERCEPT
-0.124
-1.020
VIXRISK
0.133
1.050
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
-0.021
-0.450
VIXRISK
0.028
0.570
INTERCEPT
-0.067
-1.500
VIXRISK
0.075
1.650
INTERCEPT
-0.103
-1.370
VIXRISK
0.108
1.410
INTERCEPT
0.037
0.650
VIXRISK
-0.020
-0.350
INTERCEPT
0.019
0.290
VIXRISK
-0.003
-0.050
INTERCEPT
-0.127
-1.170
VIXRISK
0.144
1.280
INTERCEPT
0.059
1.060
VIXRISK
-0.052
-0.910
INTERCEPT
-0.049
-1.010
VIXRISK
0.060
1.220
INTERCEPT
-0.126
-1.750
VIXRISK
0.136
1.850
* significant at 5% level; ** significant at 1% level
82
Table 14-Continued
Regression Estimates of 44-day Future Returns of Portfolios on VIXRISK
The table below shows the estimation results of equation (6) with weekly data from July 1996 to June 2005:
R pt44
=
R pt44
is the 44-day compounded future holding period excess returns for portfolio p.
α p + sp VIXRISKt+ept
(6)
In Panel C, Analystfiveret44 is the top quintile portfolio formed by the number of analysts following the firm (obtained from
IBES). Analystoneret44 is the bottom quintile portfolio. Analystfourret44, analystthreeret44, and analysttworet44 are the fourth,
third and second quintile portfolios, respectively.Agefiveret44 are the 44-day return on the top quintile portfolio formed by the
age of the firm. Ageoneret44 is the bottom quintile portfolio. Agefourret44, agethreeret44, and agetworet44 are the fourth, third
and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the
firm has been on CRSP. Divfiveret44 is the 44-day return on the top quintile portfolio formed by the dividend payout ratio of the
firm. Divoneret44 is the bottom quintile portfolio. Divfourret44, divthreeret44 and divtworet44 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefiveret44 is the 44-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret44 is the bottom
quintile portfolio. Roefourret44, Roethreeret44 and Roetworet44 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. VIXRISK is
the risk component of VIX estimated with equation (2).
In Panel D, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
83
Table 14-Continued
Panel C: Regression Estimates of 44-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIXRISK
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.248
-1.840
AGEFIVERET44
VIXRISK
0.269
1.970**
INTERCEPT
-0.239
-1.590
VIXRISK
0.259
1.690
INTERCEPT
-0.248
-1.620
VIXRISK
0.273
1.750
INTERCEPT
-0.253
-1.630
VIXRISK
0.286
1.810
INTERCEPT
-0.195
-1.340
VIXRISK
0.242
1.650
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.107
-0.870
DIVFIVERET44
VIXRISK
0.132
1.060
INTERCEPT
-0.142
-1.220
VIXRISK
0.170
1.440
INTERCEPT
-0.125
-0.980
VIXRISK
0.156
1.200
INTERCEPT
-0.155
-1.150
VIXRISK
0.194
1.430
INTERCEPT
-0.177
-1.210
VIXRISK
0.220
1.490
PORTFOLIO
ANALYSTFIVERET44
ANALYSTFOURRET44
ANALYSTTHREERET44
ANALYSTTWORET44
ANALYSTONERET44
PORTFOLIO
ROEFIVERET44
ROEFOURRET44
ROETHREERET44
ROETWORET44
ROEONERET44
AGEFOURRET44
AGETHREERET44
AGETWORET44
AGEONERET44
DIVFOURRET44
DIVTHREERET44
DIVTWORET44
DIVONERET44
* significant at 5% level; ** significant at 1% level
84
COEFFICIENT
T-STAT
INTERCEPT
-0.072
-0.760
VIXRISK
0.104
1.090
INTERCEPT
-0.157
-1.340
VIXRISK
0.205
1.710
INTERCEPT
-0.205
-1.510
VIXRISK
0.254
1.840
INTERCEPT
-0.276
-1.800
VIXRISK
0.326
2.090*
INTERCEPT
-0.241
-1.440
VIXRISK
0.269
1.570
COEFICIENT
T-STAT
INTERCEPT
-0.083
-0.940
VIXRISK
0.106
1.180
INTERCEPT
-0.124
-1.270
VIXRISK
0.147
1.490
INTERCEPT
-0.109
-1.050
VIXRISK
0.134
1.270
INTERCEPT
-0.049
-0.480
VIXRISK
0.079
0.760
INTERCEPT
-0.151
-1.170
VIXRISK
0.175
1.360
Table 14-Continued
Panel D: Regression Estimates of 44-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXRISK
COEFFICIENT
T-STAT
INTERCEPT
-0.046
-0.390
VIXRISK
0.072
0.600
INTERCEPT
-0.130
-1.050
VIXRISK
0.156
1.240
INTERCEPT
-0.405
-1.890
VIXRISK
0.421
1.930
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
-0.034
-0.430
VIXRISK
0.048
0.580
INTERCEPT
-0.099
-1.230
VIXRISK
0.115
1.420
INTERCEPT
-0.200
-1.360
VIXRISK
0.205
1.390
INTERCEPT
-0.026
-0.220
VIXRISK
0.063
0.510
INTERCEPT
-0.097
-0.770
VIXRISK
0.130
1.000
INTERCEPT
-0.424
-2.100*
VIXRISK
0.459
2.220*
INTERCEPT
0.080
0.830
VIXRISK
-0.064
-0.660
INTERCEPT
-0.126
-1.220
VIXRISK
0.149
1.450
INTERCEPT
-0.301
-2.170*
VIXRISK
0.319
2.280*
* significant at 5% level; ** significant at 1% leve
85
Table 15
Regression Estimates of VIX on the Risk Measures
The table below shows the estimation results of equation (7) with weekly data from July 1996 to June 2005 :
VIXt = α + β(Rm-Rf) t + sSMBt + hHMLt+ tTERM t+ dDEFt+ iIPt+pPCEt+ et
(7)
where Rm-Rf, SMB and HML are the Friday’s value each week Fama and French (1993) market, size and value factors,
respectively. The term spread (TERM) is the difference between the yield on T-Bonds that have maturity of over ten years, and
the yield on T-Bills with maturity of three months. The default spread (DEF) is the difference between the yield on Moody’s
BAA rated bonds and the yield on Moody’s AAA rated bonds. IP is the monthly industrial production index. PCE is the monthly
personal consumption expenditure. The intercept plus the residual in this regression is called VIXSENT. OBS is the number of
observations. ADJR is the adjusted R-Squared from the regression.
Dependent Variable: VIX
COEFFICIENT
T-STAT
INTERCEPT
0.58559
9.23**
Rm-Rf
-1.40135
-4.27**
SMB
-0.43401
-0.92
HML
-1.53966
-2.63**
TERM
-1.06305
-2.34*
DEF
18.28594
12.26**
IP
0.0179
3.81**
PCE
-0.95808
-6.34**
OBS
454
ADJR
0.39
* significant at 5% level; ** significant at 1% level
86
Table 16
Regression Estimates of 22-day Future Returns of Portfolios on VIXSENT
The table below shows the estimation results of equation (8) with weekly data from July 1996 to June 2005:
R 22
pt = α p + sp VIXSENTt + ept
R pt22
(8)
is the 22-day compounded future holding period excess returns for portfolio p. In panel A, Analystfiveret22 is the top
quintile portfolio formed by the number of analysts following the firm (obtained from IBES). Analystoneret22 is the bottom
quintile portfolio. Analystfourret22, analystthreeret22, and analysttworet22 are the fourth, third and second quintile portfolios,
respectively. Agefiveret22 is the 22-day return on the top quintile portfolio formed by the age of the firm. Ageoneret22 is the
bottom quintile portfolio. Agefourret22, agethreeret22, and agetworet22 are the fourth, third and second quintile portfolios,
respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP.
Divfiveret22 is the 22-day return on the top quintile portfolio formed by the dividend payout ratio of the firm. Divoneret22 is the
bottom quintile portfolio. Divfourret22, divthreeret22 and divtworet22 are the fourth, third and second quintile portfolios,
respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends
per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is
shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefiveret22 is the 22-day
return on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio.
Roefourret22, Roethreeret22 and Roetworet22 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. VIXSENT is the sentiment
component of VIX estimated with equation (7).
In Panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
87
Table 16-Continued
Panel A: Regression Estimates of 22-day Future Returns of Portfolios Sorted Univariately by the Number of Analysts, Age
of the Firm, Profitability and Dividend Payout on VIXSENT
PORTFOLIO
COEFFICIENT
T-STAT
PORTFOLIO
AGEFIVERET22
ANALYSTFIVERET22
INTERCEPT
-0.144
-2.670**
VIXSENT
0.264
2.800**
ANALYSTfourRET22
INTERCEPT
-0.150
-2.390*
VIXSENT
0.273
2.480*
ANALYSTTHREERET22
INTERCEPT
-0.105
-1.630
VIXSENT
0.200
1.770
ANALYSTTWORET22
INTERCEPT
-0.098
-1.590
VIXSENT
0.193
1.810
ANALYSTONERET22
INTERCEPT
-0.050
-0.940
VIXSENT
0.123
1.320
PORTFOLIO
AGEFOURRET22
AGETHREERET22
AGETWORET22
AGEONERET22
COEFFICIENT
T-STAT
INTERCEPT
-0.060
-1.640
VIXSENT
0.129
2.020*
INTERCEPT
-0.061
-1.260
VIXSENT
0.141
1.670
INTERCEPT
-0.074
-1.290
VIXSENT
0.164
1.640
INTERCEPT
-0.076
-1.200
VIXSENT
0.169
1.520
INTERCEPT
-0.143
-1.850
VIXSENT
0.265
1.960*
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
ROEFIVERET22
INTERCEPT
-0.068
-1.380
DIVFIVERET22
INTERCEPT
-0.057
-1.590
VIXSENT
0.138
1.600
VIXSENT
0.117
1.880
ROEFOURRET22
INTERCEPT
-0.076
-1.510
DIVFOURRET22
INTERCEPT
-0.063
-1.780
VIXSENT
0.153
1.740
VIXSENT
0.127
2.070*
ROETHREERET22
ROETWORET22
ROEONERET22
INTERCEPT
-0.071
-1.450
VIXSENT
0.146
1.720
INTERCEPT
-0.061
-1.190
VIXSENT
0.136
1.510
INTERCEPT
-0.075
-1.300
VIXSENT
0.162
1.610
DIVTHREERET22
DIVTWORET22
DIVONERET22
* significant at 5% level; ** significant at 1% level
88
INTERCEPT
-0.054
-1.380
VIXSENT
0.112
1.650
INTERCEPT
-0.044
-1.100
VIXSENT
0.100
1.430
INTERCEPT
-0.073
-1.570
VIXSENT
0.145
1.790
Table 16-Continued
Panel B: Regression Estimates of 22-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXSENT
COEFFICIENT
T-STAT
INTERCEPT
-0.042
-0.930
VIXSENT
0.093
1.190
INTERCEPT
-0.097
-2.040*
VIXSENT
0.187
2.260*
INTERCEPT
-0.229
-2.540*
VIXSENT
0.404
2.570**
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
-0.051
-1.500
VIXSENT
0.099
1.650
INTERCEPT
-0.085
-2.820**
VIXSENT
0.158
3.030**
INTERCEPT
-0.176
-3.210**
VIXSENT
0.308
3.240**
INTERCEPT
-0.015
-0.360
VIXSENT
0.055
0.750
INTERCEPT
-0.033
-0.650
VIXSENT
0.082
0.940
INTERCEPT
-0.142
-1.780
VIXSENT
0.270
1.930
INTERCEPT
-0.033
-0.850
VIXSENT
0.068
1.040
INTERCEPT
-0.067
-1.980*
VIXSENT
0.134
2.290*
INTERCEPT
-0.147
-2.710**
VIXSENT
0.268
2.860**
* significant at 5% level; ** significant at 1% level
89
Table 16-Continued
Regression Estimates of 44-day Future Returns of Portfolios on VIXSENT
The table below shows the estimation results of equation (11) with weekly data from July 1996 to June 2005:
R pt44
=
R pt44
is the 44-day compounded future holding period excess returns for portfolio p.
α p + sp VIXSENTt+ept
(9)
In Panel C, Analystfiveret44 is the top quintile portfolio formed by the number of analysts following the firm (obtained from
IBES). Analystoneret44 is the bottom quintile portfolio. Analystfourret44, analystthreeret44, and analysttworet44 are the fourth,
third and second quintile portfolios, respectively.Agefiveret44 are the 44-day return on the top quintile portfolio formed by the
age of the firm. Ageoneret44 is the bottom quintile portfolio. Agefourret44, agethreeret44, and agetworet44 are the fourth, third
and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the
firm has been on CRSP. Divfiveret44 is the 44-day return on the top quintile portfolio formed by the dividend payout ratio of the
firm. Divoneret44 is the bottom quintile portfolio. Divfourret44, divthreeret44 and divtworet44 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefiveret44 is the 44-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret44 is the bottom
quintile portfolio. Roefourret44, Roethreeret44 and Roetworet44 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. VIXSENT is
the sentiment component of VIX estimated with equation (7).
In Panel D, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
90
Table 16-Continued
Panel C: Regression Estimates of 44-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIXSENT
PORTFOLIO
ANALYSTFIVERET44
ANALYSTFOURRET44
ANALYSTTHREERET44
ANALYSTTWORET44
ANALYSTONERET44
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.309
-3.320**
AGEFIVERET44
VIXSENT
0.560
3.540**
INTERCEPT
-0.354
-3.330**
VIXSENT
0.636
3.520**
INTERCEPT
-0.294
-2.740**
VIXSENT
0.542
2.960**
INTERCEPT
-0.269
-2.460*
VIXSENT
0.514
2.770**
INTERCEPT
-0.167
-1.730
VIXSENT
0.363
2.250*
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.182
-2.140*
DIVFIVERET44
VIXSENT
0.352
2.460*
INTERCEPT
-0.195
-2.330*
VIXSENT
0.379
2.700**
INTERCEPT
-0.191
-2.210*
VIXSENT
0.377
2.590*
INTERCEPT
-0.162
-1.780
VIXSENT
0.341
2.220*
INTERCEPT
-0.197
-1.930
VIXSENT
0.407
2.370*
PORTFOLIO
ROEFIVERET44
ROEFOURRET44
ROETHREERET44
ROETWORET44
ROEONERET44
* significant at 5% level; ** significant at 1% level
91
AGEFOURRET44
AGETHREERET44
AGETWORET44
AGEONERET44
DIVFOURRET44
DIVTHREERET44
DIVTWORET44
DIVONERET44
COEFFICIENT
T-STAT
INTERCEPT
-0.141
-2.150*
VIXSENT
0.295
2.690**
INTERCEPT
-0.151
-1.790
VIXSENT
0.337
2.370*
INTERCEPT
-0.198
-1.980*
VIXSENT
0.420
2.480*
INTERCEPT
-0.223
-1.960*
VIXSENT
0.464
2.420*
INTERCEPT
-0.366
-2.640**
VIXSENT
0.669
2.850**
COEFFICIENT
T-STAT
INTERCEPT
-0.139
-2.110*
VIXSENT
0.275
2.490*
INTERCEPT
-0.157
-2.280*
VIXSENT
0.306
2.670**
INTERCEPT
-0.138
-2.070*
VIXSENT
0.277
2.480*
INTERCEPT
-0.120
-1.600
VIXSENT
0.255
2.020*
INTERCEPT
-0.188
-2.350*
VIXSENT
0.361
2.700**
Table 16-Continued
Panel D: Regression Estimates of 44-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXSENT
COEFFICIENT
T-STAT
INTERCEPT
-0.133
-1.750
VIXSENT
0.271
2.130*
INTERCEPT
-0.226
-2.740**
VIXSENT
0.428
3.100**
INTERCEPT
-0.492
-3.260**
VIXSENT
0.862
3.370**
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
-0.092
-1.460
VIXSENT
0.180
1.680
INTERCEPT
-0.143
-2.570**
VIXSENT
0.269
2.930**
INTERCEPT
-0.306
-2.930**
VIXSENT
0.529
2.990**
INTERCEPT
-0.092
-1.130
VIXSENT
0.219
1.590
INTERCEPT
-0.144
-1.560
VIXSENT
0.300
1.920
INTERCEPT
-0.378
-2.660**
VIXSENT
0.699
2.890**
INTERCEPT
-0.088
-1.180
VIXSENT
0.177
1.460
INTERCEPT
-0.148
-2.340*
VIXSENT
0.292
2.810*
INTERCEPT
-0.300
-3.050**
VIXSENT
0.539
3.29**
* significant at 5% level; ** significant at 1% level
92
Table 17
Regression Estimates of 22-day Future Returns of Portfolios on VIXRISK and VIXSENT
The table below shows the estimation results of equation (10) with weekly data from July 1996 to June 2005:
R 22
pt = α p + rpVIXRISKt + sp VIXSENTt +ept
R pt22
(10)
is the 22-day compounded future holding period excess returns for portfolio p. In panel A, Analystfiveret22 is the top
quintile portfolio formed by the number of analysts following the firm (obtained from IBES). Analystoneret22 is the bottom
quintile portfolio. Analystfourret22, analystthreeret22, and analysttworet22 are the fourth, third and second quintile portfolios,
respectively. Agefiveret22 is the 22-day return on the top quintile portfolio formed by the age of the firm. Ageoneret22 is the
bottom quintile portfolio. Agefourret22, agethreeret22, and agetworet22 are the fourth, third and second quintile portfolios,
respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP.
Divfiveret22 is the 22-day return on the top quintile portfolio formed by the dividend payout ratio of the firm. Divoneret22 is the
bottom quintile portfolio. Divfourret22, divthreeret22 and divtworet22 are the fourth, third and second quintile portfolios,
respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends
per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is
shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefiveret22 is the 22-day
return on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio.
Roefourret22, Roethreeret22 and Roetworet22 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. VIXRISK is the risk
component of VIX estimated with equation (2). VIXSENT is the sentiment component of VIX estimated with equation (7).
In Panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
93
Table 17-Continued
Panel A: Regression Estimates of 22-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIXRISK and VIXSENT
COEFFICIENT
PORTFOLIO
ANALYSTFIVERET22
ANALYSTFOURRET22
ANALYSTTHREERET22
ANALYSTTWORET22
ANALYSTONERET22
ROEFOURRET22
ROETHREERET22
ROETWORET22
ROEONERET22
PORTFOLIO
AGEFIVERET22
COEFFICIENT
T-STAT
INTERCEPT
-0.130
-1.710
INTERCEPT
-0.037
-0.740
VIXRISK
-0.021
-0.300
VIXRISK
-0.033
-0.680
VIXSENT
0.275
2.860**
VIXSENT
0.147
2.190*
INTERCEPT
-0.101
-1.170
VIXRISK
-0.073
-0.880
VIXSENT
0.313
2.700**
INTERCEPT
-0.076
-0.840
VIXRISK
-0.043
-0.490
AGEFOURRET22
AGETHREERET22
INTERCEPT
-0.067
-0.990
VIXRISK
0.009
0.140
VIXSENT
0.136
1.530
INTERCEPT
-0.080
-1.000
VIXRISK
0.009
0.120
VIXSENT
0.159
1.520
INTERCEPT
-0.105
-1.170
VIXSENT
0.223
1.870
INTERCEPT
-0.076
-0.860
VIXRISK
-0.032
-0.360
VIXRISK
0.042
0.470
VIXSENT
0.211
1.840
VIXSENT
0.146
1.230
AGETWORET22
INTERCEPT
-0.057
-0.710
INTERCEPT
-0.098
-0.950
VIXRISK
0.010
0.120
VIXRISK
-0.066
-0.640
VIXSENT
0.118
1.170
VIXSENT
0.300
2.080*
PORTFOLIO
ROEFIVERET22
T-STAT
AGEONERET22
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.030
-0.450
DIVFIVERET22
COEFFICIENT
T-STAT
INTERCEPT
-0.032
-0.660
VIXRISK
-0.056
VIXSENT
0.167
-0.860
VIXRISK
-0.037
-0.730
1.860
VIXSENT
0.137
2.040*
INTERCEPT
-0.048
-0.700
INTERCEPT
-0.044
-0.850
VIXRISK
-0.042
-0.640
VIXRISK
-0.028
-0.530
VIXSENT
0.175
1.900
VIXSENT
0.142
2.140*
INTERCEPT
-0.038
-0.550
VIXRISK
-0.048
-0.710
VIXSENT
0.172
1.920
INTERCEPT
-0.051
-0.690
VIXRISK
-0.015
VIXSENT
0.144
INTERCEPT
-0.054
-0.660
VIXRISK
-0.030
VIXSENT
0.178
DIVFOURRET22
DIVTHREERET22
INTERCEPT
-0.037
-0.650
VIXRISK
-0.025
-0.450
VIXSENT
0.126
1.750
INTERCEPT
0.006
0.110
-0.200
VIXRISK
-0.073
-1.290
1.500
VIXSENT
0.139
1.900
INTERCEPT
-0.046
-0.670
-0.370
VIXRISK
-0.040
-0.560
1.670
VIXSENT
0.167
1.910
DIVTWORET22
DIVONERET22
* significant at 5% level; ** significant at 1% level
94
Table 17-Continued
Panel B: Regression Estimates of 22-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXRISK and VIXSENT
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
COEFFICEINT
T-STAT
INTERCEPT
0.003
0.040
VIXRISK
-0.066
-1.030
VIXSENT
0.129
1.540
INTERCEPT
-0.046
-0.690
VIXRISK
-0.076
-1.070
VIXSENT
0.228
2.510*
INTERCEPT
-0.187
-1.460
VIXRISK
-0.062
-0.510
VIXSENT
0.437
2.690**
INTERCEPT
-0.037
-0.750
VIXRISK
-0.021
-0.470
VIXSENT
0.110
1.790
INTERCEPT
-0.089
-1.990*
VIXRISK
0.006
0.140
VIXSENT
0.154
2.800**
INTERCEPT
-0.150
-1.960*
VIXRISK
-0.038
-0.460
VIXSENT
0.328
3.130**
INTERCEPT
0.025
0.410
VIXRISK
-0.059
-0.950
VIXSENT
0.087
1.110
INTERCEPT
0.003
0.040
VIXRISK
-0.053
-0.760
VIXSENT
0.110
1.190
INTERCEPT
-0.163
-1.420
VIXRISK
0.031
0.280
VIXSENT
0.253
1.730
95
Table 17-Continued
COEFFICIENT
T-STAT
INTERCEPT
0.041
0.730
VIXRISK
-0.109
-1.730
VIXSENT
0.127
1.760
INTERCEPT
-0.068
-1.400
VIXRISK
0.001
0.020
VIXSENT
0.133
1.940
INTERCEPT
-0.162
-2.180*
VIXRISK
0.022
0.270
VIXSENT
0.256
2.410*
PORTFOLIO
R221
R222
R223
* significant at 5% level; ** significant at 1% level
Table 17-Continued
Regression Estimates of 44-day Future Returns of Portfolios on VIXSENT
The table below shows the estimation results of equation (11) with weekly data from July 1996 to June 2005:
R pt44
=
R pt44
is the 44-day compounded future holding period excess returns for portfolio p.
α p + rpVIXRISKt + sp VIXSENTt+ept
(11)
In Panel C, Analystfiveret44 is the top quintile portfolio formed by the number of analysts following the firm (obtained from
IBES). Analystoneret44 is the bottom quintile portfolio. Analystfourret44, analystthreeret44, and analysttworet44 are the fourth,
third and second quintile portfolios, respectively.Agefiveret44 are the 44-day return on the top quintile portfolio formed by the
age of the firm. Ageoneret44 is the bottom quintile portfolio. Agefourret44, agethreeret44, and agetworet44 are the fourth, third
and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the
firm has been on CRSP. Divfiveret44 is the 44-day return on the top quintile portfolio formed by the dividend payout ratio of the
96
firm. Divoneret44 is the bottom quintile portfolio. Divfourret44, divthreeret44 and divtworet44 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefiveret44 is the 44-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret44 is the bottom
quintile portfolio. Roefourret44, Roethreeret44 and Roetworet44 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. VIXRISK is
the risk component of VIX estimated with equation (2). VIXSENT is the sentiment component of VIX estimated with equation
(7).
In Panel D, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
Panel C: Regression Estimates of 44-day Future Returns of Portfolios Sorted Univariately by Number of Analysts, Age,
Profitability, and Dividend Payout on VIXRISK and VIXSENT
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.328
-2.410*
AGEFIVERET44
VIXRISK
0.028
VIXSENT
0.546
INTERCEPT
-0.334
-2.240*
VIXRISK
-0.029
VIXSENT
0.651
INTERCEPT
-0.324
-2.090*
VIXRISK
0.043
VIXSENT
0.520
PORTFOLIO
ANALYSTFIVERET44
ANALYSTFOURRET44
ANALYSTTHREERET44
ANALYSTTWORET44
ANALYSTONERET44
COEFFICIENT
T-STAT
INTERCEPT
-0.117
-1.230
0.190
VIXRISK
-0.034
-0.320
3.110**
VIXSENT
0.312
2.510*
INTERCEPT
-0.201
-1.640
-0.180
VIXRISK
0.071
0.540
3.170**
VIXSENT
0.301
1.890
INTERCEPT
-0.260
-1.860
0.250
VIXRISK
0.088
0.570
2.520*
VIXSENT
0.375
1.940
AGEFOURRET44
AGETHREERET44
INTERCEPT
-0.323
-2.020*
INTERCEPT
-0.332
-2.110*
VIXRISK
0.076
0.440
VIXRISK
0.156
0.900
VIXSENT
0.475
2.260*
VIXSENT
0.385
1.770
INTERCEPT
-0.240
-1.630
VIXRISK
0.105
0.630
COEFFICIENT
T-STAT
0.310
1.650
PORTFOLIO
VIXSENT
AGETWORET44
AGEONERET44
INTERCEPT
-0.341
-1.990*
VIXRISK
-0.035
-0.180
COEFFICIENT
T-STAT
0.687
2.540*
PORTFOLIO
VIXSENT
97
Table 17-Continued
PORTFOLIO
ROEFIVERET44
ROEFOURRET44
ROETHREERET44
ROETWORET44
ROEONERET44
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.160
-1.290
DIVFIVERET44
INTERCEPT
-0.125
-1.370
VIXRISK
-0.031
-0.230
VIXRISK
-0.020
-0.210
VIXSENT
0.368
2.300*
VIXSENT
0.285
2.310*
INTERCEPT
-0.198
-1.690
INTERCEPT
-0.167
-1.680
VIXRISK
0.003
0.020
VIXRISK
0.015
0.130
VIXSENT
0.377
2.330*
VIXSENT
0.298
2.240*
INTERCEPT
-0.181
-1.420
INTERCEPT
-0.149
-1.400
VIXRISK
-0.014
-0.100
VIXRISK
0.015
0.130
VIXSENT
0.384
2.320*
VIXSENT
0.269
2.100*
INTERCEPT
-0.201
-1.470
INTERCEPT
-0.090
-0.840
VIXRISK
0.055
0.370
VIXRISK
-0.043
-0.360
VIXSENT
0.313
1.800
VIXSENT
0.277
1.960*
INTERCEPT
-0.233
-1.570
INTERCEPT
-0.202
-1.570
VIXRISK
0.051
0.310
VIXRISK
0.020
0.130
VIXSENT
0.381
1.940
VIXSENT
0.351
2.210*
98
DIVFOURRET44
DIVTHREERET44
DIVTWORET44
DIVONERET44
Panel D: Regression Estimates of 44-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXRISK and VIXSENT
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
COEFFICIENT
T-STAT
INTERCEPT
-0.090
-0.780
VIXRISK
-0.061
-0.450
VIXSENT
0.302
2.030*
INTERCEPT
-0.196
-1.650
VIXRISK
-0.043
-0.300
VIXSENT
0.449
2.750**
INTERCEPT
-0.527
-2.480*
VIXRISK
0.051
0.230
VIXSENT
0.836
2.940**
INTERCEPT
-0.064
-0.780
VIXRISK
-0.041
-0.450
VIXSENT
0.200
1.630
INTERCEPT
-0.139
-1.750
VIXRISK
-0.006
-0.060
VIXSENT
0.273
2.490*
INTERCEPT
-0.280
-1.880
VIXRISK
-0.037
-0.220
VIXSENT
0.547
2.690**
INTERCEPT
-0.061
-0.490
VIXRISK
-0.044
-0.320
VIXSENT
0.241
1.560
INTERCEPT
-0.142
-1.070
VIXRISK
-0.004
-0.030
VIXSENT
0.302
1.720
INTERCEPT
-0.513
-2.500*
VIXRISK
0.193
0.870
VIXSENT
0.602
2.200*
INTERCEPT
0.040
0.420
VIXRISK
-0.184
-1.550
VIXSENT
0.269
1.890
INTERCEPT
-0.166
-1.650
VIXRISK
0.026
0.200
VIXSENT
0.279
2.130*
INTERCEPT
-0.372
-2.580**
VIXRISK
0.104
0.600
VIXSENT
0.487
2.450*
99
* significant at 5% level; ** significant at 1%
Table 18
Regression Estimates of 22-day and 44-day Future Returns of Portfolios on VIXRISK and the Orthogonal Sentiment
Measures
The table below shows the estimation results of equations (12) and (13) with weekly data from July 1996 to June 2005:
R 22
pt = α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt + rp RIPOORt+ cpCCOR+ept
(12)
R pt44 = α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt+ rp RIPOORt+ cpCCOR +ept
(13)
R pt22
is the 22-day compounded future holding period excess returns for portfolio p.
In panel A, Analystfiveret22 is the top quintile portfolio formed by the number of analysts following the firm (obtained from
IBES). Analystoneret22 is the bottom quintile portfolio. Analystfourret22, analystthreeret22, and analysttworet22 are the fourth,
third and second quintile portfolios, respectively. Agefiveret22 is the 22-day return on the top quintile portfolio formed by the
age of the firm. Ageoneret22 is the bottom quintile portfolio. Agefourret22, agethreeret22, and agetworet22 are the fourth, third
and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the
firm has been on CRSP. Divfiveret22 is the 22-day return on the top quintile portfolio formed by the dividend payout ratio of the
firm. Divoneret22 is the bottom quintile portfolio. Divfourret22, divthreeret22 and divtworet22 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefiveret22 is the 22-day return on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom
quintile portfolio. Roefourret22, Roethreeret22 and Roetworet22 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measure from July of year t to June of year t+1.
R pt44
is the
44-day compounded future holding period excess returns for portfolio p. Analystfiveret44 is the top quintile portfolio formed by
the number of analysts following the firm (obtained from IBES). Analystoneret44 is the bottom quintile portfolio.
Analystfourret44,
analystthreeret44,
and
analysttworet44
are
the
fourth,
third
and
second
quintile
portfolios,
respectively.Agefiveret44 are the 44-day return on the top quintile portfolio formed by the age of the firm. Ageoneret44 is the
bottom quintile portfolio. Agefourret44, agethreeret44, and agetworet44 are the fourth, third and second quintile portfolios,
respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP.
100
Divfiveret44 is the 44-day return on the top quintile portfolio formed by the dividend payout ratio of the firm. Divoneret44 is the
bottom quintile portfolio. Divfourret44, divthreeret44 and divtworet44 are the fourth, third and second quintile portfolios,
respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends
per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is
shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefiveret44 is the 44-day
return on the top quintile portfolio formed by the profitability of the firm. Roeoneret44 is the bottom quintile portfolio.
Roefourret44, Roethreeret44 and Roetworet44 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1.
In Panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and
portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1.
The returns on the portfolios are measured from July of year t to June of year t+1.
The future holding period returns are measured every Friday. I employ Newey and West (1987) standard errors to account for
residual correlation due to overlapping portfolio returns.
VIXRISK is the risk component of VIX estimated with equation (2).CCOR is the orthogonalized University of Michigan
Consumer Sentiment Index, AAIIOR is the orthogonalized percentage of bullish members minus the percentage of bearish
members as measured by American Association of Individual Investors survey, IIOR is the orthogonalized percentage of bullish
newsletters minus the percentage of bearish newsletters as measured by the Investors’ Intelligence survey, and RIPOOR is the
orthogonalized first day return on IPOs. All of the orthogonalized measures are obtained from the estimation of equation (1) and
are measured weekly. I expect the sign on the all of the orthogonalized sentiment proxies to be negative, since all the sentiment
proxies are positively correlated with the current level of sentiment, whereas VIX is negatively correlated with the current level
of sentiment. VIXRISK is estimated from equation 2(a).
PanelA: Regression Estimates of 22-day Future Returns of Portfolios Sorted Univariately by The Number of Analysts,
Age of the Firm, Profitability and Dividend Payout and on VIXRISK and the Orthogonal Sentiment Proxies
PORTFOLIO
ANALYSTFIVERET22
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
0.052
0.230
AGEFIVERET22
COEFFICIENT
T-STAT
INTERCEPT
0.163
1.070
VIXRISK
0.102
1.390
VIXRISK
0.032
0.640
AAIIOR
0.029
1.450
AAIIOR
0.026
1.760
IIOR
-0.108
-2.030*
IIOR
-0.020
-0.530
RIPOOR
0.048
2.020*
RIPOOR
0.015
0.890
CCOR
-0.175
-1.590
CCOR
-0.130
-1.750
101
Table 18-Continued
PORTFOLIO
ANALYSTFOURRET22
ANALYSTTHREERET22
ANALYSTTWORET22
ANALYSTONERET22
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
0.278
1.050
AGEFOURRET22
COEFFICIENT
T-STAT
INTERCEPT
0.236
1.190
VIXRISK
0.066
0.790
VIXRISK
0.070
1.060
AAIIOR
0.041
1.760
AAIIOR
0.031
1.560
IIOR
-0.103
-1.670
IIOR
-0.034
-0.700
RIPOOR
0.053
1.870
RIPOOR
0.046
1.850
CCOR
-0.289
-2.200*
CCOR
-0.222
-2.270*
INTERCEPT
0.182
0.620
INTERCEPT
0.340
1.430
VIXRISK
0.056
0.640
VIXRISK
0.080
1.030
AAIIOR
0.034
1.330
AAIIOR
0.034
1.490
IIOR
-0.094
-1.460
IIOR
-0.037
-0.650
RIPOOR
0.059
1.880
RIPOOR
0.059
2.020*
CCOR
-0.301
-2.590**
INTERCEPT
0.361
1.340
AGETHREERET22
CCOR
-0.227
-1.580
INTERCEPT
0.392
1.450
VIXRISK
0.061
0.720
VIXRISK
0.107
1.230
AAIIOR
0.036
1.370
AAIIOR
0.035
1.330
IIOR
-0.050
-0.800
IIOR
-0.041
-0.630
RIPOOR
0.062
2.020*
RIPOOR
0.077
2.270*
CCOR
-0.345
-2.660*
INTERCEPT
0.404
1.060
AGETWORET22
CCOR
-0.333
-2.510*
INTERCEPT
0.269
1.150
VIXRISK
0.063
0.780
VIXRISK
0.068
0.690
AAIIOR
0.040
1.670
AAIIOR
0.023
0.660
IIOR
-0.038
-0.660
IIOR
-0.089
-1.100
RIPOOR
0.062
2.070*
RIPOOR
0.076
1.940
CCOR
-0.254
-2.260*
CCOR
-0.372
-1.980*
102
AGEONERET22
Table 18-Continued
PanelA: Regression Estimates of 22-day Future Returns of Portfolios Sorted Univariately by The Number of Analysts,
Age of the Firm, Profitability and Dividend Payout and on VIXRISK and the Orthogonal Sentimnt Proxies (contd)
PORTFOLIO
ROEFIVERET22
ROEFOURRET22
ROETHREERET22
ROETWORET22
ROEONERET22
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
0.208
1.080
DIVFIVERET22
INTERCEPT
0.122
0.790
VIXRISK
0.019
0.290
VIXRISK
0.024
0.510
AAIIOR
IIOR
0.027
1.550
AAIIOR
0.014
0.950
-0.047
-1.000
IIOR
-0.027
-0.750
RIPOOR
0.027
1.180
RIPOOR
0.006
0.350
CCOR
-0.171
-1.790
CCOR
-0.097
-1.260
INTERCEPT
0.191
0.960
INTERCEPT
0.103
0.680
VIXRISK
0.036
0.550
VIXRISK
0.035
0.680
AAIIOR
0.026
1.410
AAIIOR
0.019
1.270
IIOR
-0.046
-0.930
IIOR
-0.032
-0.860
RIPOOR
0.038
1.620
RIPOOR
0.013
0.750
CCOR
-0.180
-1.840
CCOR
-0.101
-1.330
INTERCEPT
0.255
1.290
INTERCEPT
0.180
1.200
VIXRISK
0.028
0.420
VIXRISK
0.031
0.560
AAIIOR
0.037
1.970*
AAIIOR
0.029
1.940
IIOR
-0.043
-0.890
IIOR
-0.010
-0.270
RIPOOR
0.037
1.600
RIPOOR
0.008
0.420
CCOR
-0.211
-2.190*
CCOR
-0.131
-1.800
INTERCEPT
0.286
1.390
INTERCEPT
0.282
1.720
VIXRISK
0.049
0.670
VIXRISK
-0.011
-0.210
AAIIOR
0.033
1.610
AAIIOR
0.026
1.590
DIVFOURRET22
DIVTHREERET22
DIVTWORET22
IIOR
-0.031
-0.600
IIOR
-0.013
-0.310
RIPOOR
0.052
2.030*
RIPOOR
0.016
0.850
CCOR
-0.246
-2.460*
CCOR
-0.171
-2.130*
INTERCEPT
0.311
1.290
INTERCEPT
0.151
0.750
VIXRISK
0.049
0.600
VIXRISK
0.034
0.500
AAIIOR
0.031
1.310
AAIIOR
0.029
1.560
IIOR
-0.055
-0.930
IIOR
-0.049
-0.980
RIPOOR
0.075
2.430*
RIPOOR
0.025
1.110
CCOR
-0.288
-2.430*
CCOR
-0.148
-1.490
* significant at 5% level; ** significant at 1% level
103
DIVONERET22
Table 18-Continued
Panel B: Regression Estimates of 22-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXRISK and the Orthogonal Sentiment Proxies
COEFFICIENT
PORTFOLIO
R111
R112
R113
R121
R122
R123
T-STAT
INTERCEPT
0.204
1.210
VIXRISK
-0.009
-0.140
AAIIOR
0.029
1.770
IIOR
-0.036
-0.820
RIPOOR
0.025
1.140
CCOR
-0.147
-1.800
INTERCEPT
0.192
0.980
VIXRISK
0.026
0.390
AAIIOR
0.030
1.650
IIOR
-0.083
-1.680
RIPOOR
0.033
1.320
CCOR
-0.187
-1.960*
INTERCEPT
0.181
0.440
VIXRISK
0.133
1.070
AAIIOR
0.029
0.820
IIOR
-0.207
-2.200*
RIPOOR
0.117
2.590**
CCOR
-0.369
-1.850
INTERCEPT
0.128
0.630
VIXRISK
0.028
0.580
AAIIOR
0.006
0.370
IIOR
-0.011
-0.240
RIPOOR
0.004
0.190
CCOR
-0.094
-0.980
INTERCEPT
-0.076
-0.420
VIXRISK
0.075
1.730
AAIIOR
-0.001
-0.080
IIOR
-0.052
-1.280
RIPOOR
0.002
0.110
CCOR
-0.019
-0.210
INTERCEPT
-0.122
-0.390
VIXRISK
0.108
1.520
AAIIOR
-0.012
-0.480
104
Table 18-Continued
COEFFICIENT
T-STAT
IIOR
-0.162
-2.510*
RIPOOR
0.086
3.450**
CCOR
-0.130
-0.830
INTERCEPT
0.390
2.380*
VIXRISK
-0.020
-0.360
AAIIOR
0.042
2.560*
PORTFOLIO
R211
PanelB: Regression Estimates of 22-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity, Size,
and Beta on VIXRISK and the Orthogonal Sentiment Proxies (contd)
COEFFICIENT
T-STAT
IIOR
0.024
0.580
RIPOOR
0.006
0.330
CCOR
-0.206
-2.590**
INTERCEPT
0.291
1.460
VIXRISK
-0.003
-0.050
AAIIOR
0.037
1.920
PORTFOLIO
R212
R213
R221
IIOR
-0.015
-0.300
RIPOOR
0.026
1.090
CCOR
-0.192
-1.960*
INTERCEPT
0.318
0.970
VIXRISK
0.144
1.270
AAIIOR
0.048
1.630
IIOR
-0.084
-1.060
RIPOOR
0.082
2.240*
CCOR
-0.371
-2.340*
INTERCEPT
0.174
0.980
VIXRISK
-0.052
-0.940
AAIIOR
0.026
1.450
IIOR
-0.003
-0.060
105
Table 18-Continued
COEFFICIENT
T-STAT
RIPOOR
-0.028
-1.110
CCOR
-0.048
-0.590
INTERCEPT
0.110
0.550
VIXRISK
0.060
1.210
AAIIOR
0.006
0.300
IIOR
0.005
0.120
RIPOOR
0.006
0.260
CCOR
-0.095
-0.980
PORTFOLIO
R222
R223
INTERCEPT
0.122
0.470
VIXRISK
0.136
1.860
AAIIOR
0.025
1.050
IIOR
-0.078
-1.530
RIPOOR
0.071
2.940**
CCOR
-0.241
-1.790
* significant at 5% level; ** significant at 1% level
Panel A: Regression Estimates of 44-day Future Returns of Portfolios Sorted Univariately by The Number of Analysts,
Age of the Firm, Profitability and Dividend Payout on VIXRISK and the Orthogonal Sentiment Proxies
PORTFOLIO
ANALYSTFIVERET44
ANALYSTFOURRET44
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.119
-0.240
AGEFIVERET44
INTERCEPT
0.124
0.390
VIXRISK
0.251
AAIIOR
0.033
1.980*
VIXRISK
0.098
1.050
0.860
AAIIOR
0.049
1.770
IIOR
-0.225
-2.260*
IIOR
-0.087
-1.200
RIPOOR
0.120
3.080**
RIPOOR
0.067
2.170*
CCOR
-0.212
-1.290
INTERCEPT
0.150
0.360
CCOR
-0.268
-1.030
INTERCEPT
0.130
0.220
VIXRISK
0.242
1.660
VIXRISK
0.194
1.650
AAIIOR
0.074
1.730
AAIIOR
0.078
2.100*
IIOR
-0.258
-2.200*
IIOR
-0.145
-1.590
RIPOOR
0.127
2.520*
RIPOOR
0.117
2.400*
CCOR
-0.435
-1.460
CCOR
-0.347
-1.650
AGETHREERET44
106
Table 18-Continued
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
0.289
0.490
AGEFOURRET44
INTERCEPT
0.241
0.480
VIXRISK
0.274
1.780
VIXRISK
0.241
1.780
AAIIOR
0.090
1.890
AAIIOR
0.089
2.010*
IIOR
-0.188
-1.500
IIOR
-0.182
-1.670
RIPOOR
0.142
2.240*
RIPOOR
0.141
2.290*
CCOR
-0.523
-1.800
CCOR
-0.463
-1.840
INTERCEPT
0.204
0.410
INTERCEPT
0.371
0.440
VIXRISK
0.232
1.600
VIXRISK
0.250
1.540
AAIIOR
0.104
2.280*
AAIIOR
0.063
0.930
IIOR
-0.163
-1.470
IIOR
-0.255
-1.530
RIPOOR
0.141
2.190*
RIPOOR
0.155
1.780
CCOR
-0.431
-1.780
CCOR
-0.594
-1.430
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
0.065
0.160
DIVFIVERET44
INTERCEPT
0.081
0.260
VIXRISK
0.122
1.010
VIXRISK
0.101
1.150
AAIIOR
0.065
2.040*
AAIIOR
0.039
1.450
IIOR
-0.166
-1.860
IIOR
-0.098
-1.350
RIPOOR
0.083
2.070*
RIPOOR
0.041
1.200
CCOR
-0.246
-1.200
CCOR
-0.176
-1.090
INTERCEPT
0.014
0.030
INTERCEPT
0.032
0.100
VIXRISK
0.159
1.380
VIXRISK
0.140
1.450
AAIIOR
0.063
1.910
AAIIOR
0.039
1.380
IIOR
-0.166
-1.810
IIOR
-0.101
-1.350
RIPOOR
0.106
2.630**
RIPOOR
0.055
1.600
CCOR
-0.256
-1.180
CCOR
-0.184
-1.090
PORTFOLIO
ANALYSTTWORET44
ANALYSTONERET44
PORTFOLIO
ROEFIVERET44
ROEFOURRET44
AGEONERET44
DIVFOURRET44
107
Table 18-Continued
Panel A : Regression Estimates of 44-day Future Returns of Portfolios Sorted Univariately by the Number of Analysts,
Age of the Firm, Profitability and Dividend Payout and on VIXRISK and the Orthogonal Sentiment Proxies (Contd)
PORTFOLIO
ROETHREERET44
ROETWORET44
ROEONERET44
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
0.147
0.350
DIVTHREERET44
INTERCEPT
0.088
0.280
VIXRISK
0.147
1.150
VIXRISK
0.131
1.270
AAIIOR
0.085
2.500*
AAIIOR
0.058
2.140*
IIOR
-0.159
-1.710
IIOR
-0.076
-0.990
RIPOOR
0.102
2.390*
RIPOOR
0.050
1.350
CCOR
-0.321
-1.500
CCOR
-0.197
-1.250
INTERCEPT
0.206
0.480
INTERCEPT
0.264
0.770
VIXRISK
0.184
1.380
VIXRISK
0.076
0.730
AAIIOR
0.084
2.260*
AAIIOR
0.062
2.080*
IIOR
-0.140
-1.430
IIOR
-0.071
-0.840
RIPOOR
0.130
2.730**
RIPOOR
0.062
1.770
CCOR
-0.388
-1.800
CCOR
-0.272
-1.540
INTERCEPT
0.183
0.360
INTERCEPT
-0.046
-0.110
VIXRISK
0.205
1.410
VIXRISK
0.166
1.310
AAIIOR
0.087
1.940
AAIIOR
0.086
2.550*
IIOR
-0.197
-1.740
IIOR
-0.175
-1.950
RIPOOR
0.165
2.680**
RIPOOR
0.083
2.090*
CCOR
-0.438
-1.720
CCOR
-0.216
-1.020
DIVTWORET44
DIVONERET44
* significant at 5% level; ** significant at 1% level
108
Table 18-Continued
Panel B: Regression Estimates of 44-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity,
Size, and Beta on VIXRISK and the Orthogonal Sentiment Proxies
COEFFICIENT
T-STAT
INTERCEPT
0.121
0.340
VIXRISK
0.065
0.550
AAIIOR
0.072
2.270*
IIOR
-0.144
-1.810
RIPOOR
0.073
1.830
CCOR
-0.228
-1.240
INTERCEPT
-0.019
-0.050
VIXRISK
0.142
1.160
AAIIOR
0.079
2.290*
IIOR
-0.236
-2.700**
RIPOOR
0.096
2.080*
CCOR
-0.253
-1.250
INTERCEPT
-0.052
-0.060
VIXRISK
0.386
1.900
AAIIOR
0.057
0.840
IIOR
-0.417
-2.310*
RIPOOR
0.246
2.750**
CCOR
-0.581
-1.350
INTERCEPT
0.382
0.960
VIXRISK
0.046
0.580
AAIIOR
0.007
0.240
IIOR
0.000
0.000
RIPOOR
0.043
1.130
CCOR
-0.277
-1.340
INTERCEPT
-0.008
-0.020
VIXRISK
0.108
1.430
AAIIOR
-0.010
-0.340
IIOR
-0.084
-1.180
RIPOOR
0.028
0.740
CCOR
-0.106
-0.570
INTERCEPT
-0.347
-0.480
VIXRISK
0.177
1.360
AAIIOR
-0.034
-0.710
PORTFOLIO
R111
R112
R113
R121
R122
R123
109
Table 18-Continued
Panel B: Regression Estimates of 44-day Future Returns for the Twelve Portfolios Sorted on Book-to-Market Equity,
Size, and Beta on VIXRISK and the Orthogonal Sentiment Proxies (Contd)
PORTFOLIO
R211
R212
R213
R221
R222
R223
COEFFICIENT
T-STAT
IIOR
-0.285
-2.020*
RIPOOR
0.148
3.330**
CCOR
-0.141
-0.390
INTERCEPT
0.496
1.420
VIXRISK
0.065
0.550
AAIIOR
0.100
3.310**
IIOR
-0.038
-0.430
RIPOOR
0.048
1.260
CCOR
-0.378
-2.170*
INTERCEPT
0.179
0.420
VIXRISK
0.124
0.960
AAIIOR
0.083
2.350*
IIOR
-0.119
-1.230
RIPOOR
0.085
2.000*
CCOR
-0.294
-1.340
INTERCEPT
0.168
0.230
VIXRISK
0.440
2.180*
AAIIOR
0.098
1.770
IIOR
-0.258
-1.690
RIPOOR
0.189
2.730**
CCOR
-0.619
-1.730
INTERCEPT
0.024
0.070
VIXRISK
-0.068
-0.710
AAIIOR
0.032
0.850
IIOR
-0.081
-0.960
RIPOOR
0.017
0.320
CCOR
-0.021
-0.120
INTERCEPT
-0.041
-0.100
VIXRISK
0.145
1.420
AAIIOR
0.019
0.530
IIOR
-0.061
-0.730
RIPOOR
0.037
0.730
CCOR
-0.107
-0.500
INTERCEPT
0.076
0.150
VIXRISK
0.304
2.280*
AAIIOR
0.026
0.670
IIOR
-0.147
-1.610
RIPOOR
0.146
4.130**
CCOR
-0.400
-1.470
110
Table 19
Tabulation of Significant Variables with Signs in Table 9
This table summarizes the results of table 9.The first column lists the variables VIXRISK, AAIIOR, IIOR, RIPOOR and CCOR.
The second column shows the number of times the coefficient on the variable is significant. The third column shows the signs on
the significant coefficients.
22-Day Return
VARIABLE
SIGNIFICANT
SIGN
VIXRISK
0
AAIIOR
2
POSITIVE
IIOR
3
NEGATIVE
RIPOOR
11
POSITIVE
CCOR
15
NEGATIVE
VARIABLE
SIGNIFICANT
SIGN
VIXRISK
3
POSITIVE
AAIIOR
13
POSITIVE
IIOR
5
NEGATIVE
RIPOOR
19
POSITIVE
CCOR
1
NEGATIVE
44-Day Return
111
CHAPTER 4
FORECASTING FUTURE PORTFOLIO VOLATILITY: THE ROLE OF THE RISK AND
SENTIMENT COMPONENTS OF IMPLIED VOLATILITY
Introduction
There have been several attempts in the literature to forecast future realized volatility. One
stream of literature has used the GARCH type models to forecast volatility. Poon and Granger
(2003) list studies that compare the forecasting ability for future realized volatility of past
volatility and GARCH forecasts. The conclusions from these studies are mixed. Recently, there
has been growing interest in using implied volatility from option prices as a forecast of future
realized volatility. The underlying belief is that if option markets are informationally efficient,
then implied volatility should contain all relevant information about future realized volatility,
and no other additional information matters.
The current approach to test the effectiveness of different forecasts of volatility is to use
encompassing regressions of future realized volatility on a proxy for implied volatility, and some
time series forecast of future realized volatility (such as a GARCH type forecast), to see if the
coefficient on the implied volatility forecast is positive and significant, and if there is additional
significance of the coefficient on the GARCH forecast. Lamoureux and Lastrapes (1993)
examine stock options and find that implied volatility is an inefficient predictor of future realized
volatility, since there is information in past volatility, in addition to that contained in implied
volatility, that is useful in forecasting future realized volatility. On the other hand, Christensen
and Prabhala (1998), using longer sample periods and non-overlapping data, find that implied
volatility subsumes the information content of past volatility. Fleming, Ostidiek and Whaley
112
(1995) find that VIX has forecasting ability for the future realized volatility of the S&P 100.
Blair, Poon and Taylor (2001) find that VIX subsumes information in high-powered low
frequency data in forecasting future realized volatility.
Prior literature has also addressed the question of whether sentiment has forecasting power for
future realized volatility, with mixed results. Brown (1999) finds that individual investor
sentiment, as measured by the American Association of Individual Investors survey, is related to
the volatility of closed-end fund discounts. Lee, Jiang and Indro (2002) employ a GARCH-M
model to test if the Investors’ Intelligence Survey measure of sentiment has impact on
conditional volatility and expected returns. They find that when sentiment becomes bullish,
volatility falls and vice versa. On the other hand, Wang, Keswani and Taylor (2005) find that a
technical measure of sentiment, the ARMS ratio, has limited forecasting ability for realized
volatility after controlling for the leverage effect.
So, both implied volatility and some sentiment proxies have forecasting powers for future
realized volatility. However, as I show in my second essay, implied volatility as proxied by VIX
may be decomposed into a risk component and sentiment component. These two components
may have distinct forecasting powers for future realized volatility. In this essay I examine the
forecasting power for future realized volatility of the risk component of implied volatility, the
sentiment component of implied volatility, and a forecast of volatility based on prior market
volatility or prior portfolio volatility, or both. There are three contributions in this essay. One, I
use the decomposition of implied volatility into risk and sentiment components, developed with
the methodologies in my second essay, to forecast future realized volatilities of portfolios sorted
by various important characteristics, rather than the market volatility. Two, I compare the
forecasting power of the risk and sentiment components of implied volatility, rather than total
implied volatility. Three, I compare the risk and sentiment components of implied volatility with
other forecasts of future volatility including lagged realized volatility and GARCH forecasts.
113
Data
Univariate sorting
To better understand the relation between VIX as a sentiment proxy and future portfolio standard
deviations, I sort all firms into quintiles by the number of analysts following the firm, age of the
firm, dividend payout ratio of the firm, and profitability of the firm, respectively. The 22-tradingday realized standard deviations on these portfolios, from July 1996 through June 2005, are the
dependent variables in the time-series regressions37. I obtain the daily risk-free rates from
Kenneth French’s website.
The number of analysts following the firm is obtained from IBES. Sorting firms by age, dividend
payout and profitability are done in the manner followed by Baker and Wurgler (2006). The age
of the firm is measured by the number of years (to the nearest month) the firm has been on
CRSP. Dividend payout is calculated as dividends (D) divided by book value of equity (BE).
Dividends (D) is dividends per share at the ex date (Item 26 of Compustat) times shares
outstanding (Item 25 of Compustat). Book value of equity (BE) is shareholders equity (Item 60
of Compustat)) plus balance sheet deferred taxes (Item 35 of Compustat)).
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book
value of equity (BE). Earnings (E) are calculated as income before extraordinary items (Item 18
of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus preferred
dividends (Item 19 of Compustat)).
Multivariate sorting
I use the 22-day realized standard deviations of the excess returns (returns less the risk-free rate)
on twelve portfolios formed on size, book-to-market equity, and beta as dependent variables in
the time-series regressions38. The twelve portfolios are formed in the Fama and French (1993)
style. Specifically, at the end of June of each year t from 1996 to 2005, I independently sort
37
I use 22-day standard deviation as this corresponds to the one-month horizon .
38
I use 22-day standard deviations to correspond to the forecasting horizon of VIX.
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NYSE stocks on CRSP by beta, size (market value of equity), and book-to-market equity.39
Book value of equity is for fiscal year end t-1 and is defined as the COMPUSTAT book value of
shareholders’ equity, plus balance sheet deferred-taxes and investment tax credits, if available,
minus the book value of preferred stock. Depending on availability, the redemption, liquidation,
or par value (in that order) is used to estimate the value of preferred stock. Market value of
equity (ME) is measured at the end of June of year t. Book-to-market equity is the ratio of the
book value of equity divided by the market value of equity (BE/ME). Beta is measured at the
end of June of year t by estimating the market model over the prior 200 trading days. The CRSP
value-weighted index is the market proxy.
I use the NYSE breakpoints for ME, book-to-market equity, and beta to allocate NYSE, AMEX
and Nasdaq stocks to two size, two book-to-market, and three beta categories.40 The size and
BE/ME breakpoint is the 50th percentile and beta breakpoints are the 30th and 70th NYSE
percentiles. I construct twelve portfolios from the intersection of the size, book-to-market
equity, and beta categories and calculate the daily value-weighted returns on these portfolios
from July of year t through June of year t+1. The 22-trading-day realized standard deviations on
these twelve portfolios, from 1996 through June 2005, are the dependent variables in the timeseries regressions. I obtain the daily risk-free rates from Kenneth French’s website.
Methodology
To examine the forecasting power for future realized volatility of VIX, I estimate the following
equation for each of the portfolios with weekly data:
RSD pt22 = α p + rpVIXt+ept
(1)
where RSDpt22 is the 22-day future realized volatility is estimated for each of the portfolios. VIX is
the Friday’s VIX observation.
39
Similar to Fama and French (1993), I delete negative book equity firms, financial firms, and utilities.
Only firms with ordinary common equity (as classified by CRSP) are used. Thus, ADRs, REITS, and units of
beneficial interest are excluded.
40
115
To examine the forecasting power for future realized volatility of past realized market volatility,
I estimate the following equation for each of the portfolios:
RSD pt22 = α p + mpLAGSP500t+ept
(2)
where LAGSP500 is the standard deviation of the S&P 500 index over the previous 22 days from
day t, where day t is the date of observation of VIX.
To compare the forecasting powers for future realized volatility of VIX and realized market
volatility, I estimate the following equation for each of the portfolios.
RSD pt22 = α p + rpVIXt+ mpLAGSP500t+ept
(3)
I expect the coefficient on VIX to be positive and significant. If implied volatility subsumes all
other information, then the coefficient on LAGSP500 should not be significant once VIX is
included.
I then compare the forecasting power for future realized volatility of the risk component of VIX,
the lagged market realized volatility, and a portfolio based forecast of future volatility. I use two
portfolio based forecasts of future realized volatilities. The first is the lagged portfolio standard
deviation of each portfolio. The second is a GARCH forecast of volatility for each of the
portfolios. Since the average correlation coefficient between these two forecasts is high (0.83), I
estimate the following equations separately.
RSD pt22 = α p + rpVIXRISKt+ ppLAGPORTt +mpLAGSP500t+ept
(4)
RSD pt22 = α p + rpVIXRISKt+gpGARCHt +mpLAGSP500t+ept
(5)
VIXRISK is the risk component of VIX estimated from equation (2) in essay two. LAGPORT is
the standard deviation of the respective portfolio over the previous 22 days from day t, where
day t is the date of observation of VIX. GARCH is the next day’s forecast of standard deviation
116
for each of the respective portfolios calculated using GARCH (1, 1) parameters estimated over
the previous 22 days from day t, where day t is the date of observation of VIX.
I expect the coefficient on the risk component of VIX to be positive and significant. If implied
volatility subsumes all other information, then the coefficient on LAGPORT or GARCH and
LAGSP500 should not be significant once VIXRISK is included.
To compare the forecasting power for future realized volatility of the sentiment component of
VIX, and the market standard deviation, and the two forecasts of future volatility, I estimate the
following equations for each of the portfolios.
RSD pt22 = α p + spVIXSENTt+ ppLAGPORTt +mpLAGSP500t+ept
(6)
RSD pt22 = α p + spVIXSENTt+ gpGARCHt +mpLAGSP500t+ept
(7)
VIXSENT is the sentiment component of VIX estimated from equation (7) in essay two.
If sentiment has forecasting power future volatilities, the coefficient on the sentiment component
of VIX should be positive and significant.
Finally, I compare the forecasting power for future realized volatility of the risk component of
VIX, the sentiment component of VIX, the two forecasts of future volatility, and lagged market
standard deviation. I estimate the following equations for each of the portfolios.
RSD pt22 = α p + rpVIXRISKt+ spVIXSENTt + ppLAGPORTt +mpLAGSP500t+ept
(8)
RSD pt22 = α p + rpVIXRISKt+ spVIXSENTt + gpGARCHt +mpLAGSP500t+ept
(9)
If implied volatility subsumes all other information, then only the coefficient on VIXRISK and
the coefficient on VIXSENT should be significant. Additionally, if markets are efficient, the
sentiment component of VIX should not show predictive power and VIXRISK should subsume
all other information.
117
Results
Table 1 shows the output from the regression of the realized standard deviation of the portfolios
on VIX. Panel A shows the estimation results for the portfolios sorted univariately by number of
analysts, age, profitability, and dividend payout ratio of the firm. For the univariately sorted
portfolios, all of the coefficients on VIX are positive and significant.
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIX are positive and significant, and the
magnitude of the coefficients increases as we move from the low beta to the high beta portfolio
for the small size portfolios.
From the results in this table, we see that VIX has explanatory power for future realized
volatilities for all portfolios, and its forecasting power is greater for high beta portfolios than for
low beta portfolios for small size portfolios.
Table 2 shows the output from the regression of realized standard deviation of the portfolios on
the lagged realized standard deviation of the S&P 500 index. Panel A shows the estimation
results for the portfolios sorted univariately by number of analysts, age, profitability, and
dividend payout ratio of the firm. For the univariately sorted portfolios, all the coefficients on the
standard deviation of the S&P 500 index are positive and significant.
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios also, all the coefficients on the lagged market standard deviation are
positive and significant.
From the results in this table, we see that the lagged market volatility has explanatory power for
future realized volatilities for all portfolios.
118
Table 3 shows the output from the regression of realized standard deviation of the portfolios on
VIX and the lagged realized standard deviation of the S&P 500 index. Panel A shows the
estimation results for the portfolios sorted univariately by number of analysts, age, profitability,
and dividend payout ratio of the firm. All the coefficients on VIX are positive and all but four of
the coefficients are significant. All of the coefficients on the lagged market standard deviation
are positive and four of the coefficients are significant.
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. All of the coefficients on VIX are positive and significant. Three coefficients on the lagged
market standard deviation are negative; however, none of them are significant. Two of the
positive coefficients on the lagged market standard deviation are significant.
This table shows that for the univariately sorted portfolios in panel A and for the portfolios
sorted by book-to-market equity, size, and beta in panel B, the number of significant coefficients
on VIX (sixteen in panel A and twelve in panel B) is greater than the number of significant
coefficients on the lagged market standard deviation (four in panel A and in two panel B). So, in
terms of the number of significant coefficients, VIX has more forecasting power for future
realized volatility than the lagged market standard deviation. The coefficients on VIX increase in
magnitude from the low beta to the high beta portfolios for all portfolios in panel B.
Table 4 shows the output from the regression of the realized standard deviation of the portfolios
on the risk component of VIX, the lagged portfolio standard deviation, and the lagged realized
standard deviation of the S&P 500 index. Panel A shows the estimation results for the portfolios
sorted univariately by number of analysts, age, profitability, and dividend payout ratio of the
firm. For the univariately sorted portfolios, all of the coefficients on VIXRISK and all but one of
the coefficients on the lagged portfolio standard deviation are positive and significant. Sixteen of
the coefficients on the lagged market standard deviation are negative, and two of them are
significant with negative signs. Four of coefficients on the lagged market standard deviation are
positive, but none of them are significant.
119
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIXRISK and on the lagged portfolio
standard deviation are positive and significant. Ten of the coefficients on the lagged market
standard deviation are negative, and three of them are significant with negative signs. Two of the
coefficients on the lagged market standard deviation are positive, but none of them are
significant.
This table shows that for the univariately sorted portfolios in panel A, the number of significant
coefficients on VIXRISK (twenty) is greater than the number of significant coefficients on the
lagged portfolio standard deviation (nineteen). So, in terms of the number of significant
coefficients, VIXRISK has a little more forecasting power than the lagged portfolio standard
deviation. For the portfolios sorted by book-to-market equity, size, and beta in panel B, the
number of significant coefficients on VIXRISK (twelve) is equal to the number of significant
coefficients on the lagged portfolio standard deviation (twelve). So, in terms of the number of
significant coefficients, VIXRISK and the lagged portfolio standard deviation have identical
forecasting powers. In both panels, the lagged market volatility has fewer significant coefficients
(two in panel A and three in panel B) than either VIXRISK or the lagged portfolio standard
deviation, and so, in terms of the number of significant coefficients, the lagged market standard
deviation has lower forecasting power than VIXRISK and the lagged portfolio standard
deviation. Also, in most cases the signs of the coefficients on the lagged market standard
deviation are negative.
Table 5 shows the output from the regression of realized standard deviation of the portfolios on
the risk component of VIX, the GARCH forecast of volatility for the respective portfolio, and the
lagged realized standard deviation of the S&P 500 index. Panel A shows the estimation results
for the portfolios sorted univariately by number of analysts, age, profitability, and dividend
payout ratio of the firm. For the univariately sorted portfolios, all of the coefficients on
VIXRISK are positive, and all of them are significant. All of the coefficients on the GARCH
forecast are positive and significant. Seventeen of the coefficients on lagged market standard
deviation are negative, and two are significant. None of the positive coefficients are significant.
120
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIXRISK are positive and significant. All of
the coefficients on the GARCH forecast are positive and all but one is significant. Seven
coefficients on the lagged market standard deviation have negative signs. One coefficient is
significant with a negative sign and one coefficient is significant with a positive sign.
This table shows that for the univariately sorted portfolios in panel A, the number of significant
coefficients on VIXRISK (twenty) is equal to the number of significant coefficients on the
GARCH forecast (twenty). So, in terms of the number of significant coefficients, VIXRISK and
the GARCH forecast have identical forecasting powers. For the portfolios sorted univariately by
book-to-market equity, size, and beta in panel B, the number of significant coefficients on
VIXRISK (twelve) is more than the number of significant coefficients on the GARCH forecast
(eleven). So, in terms of the number of significant coefficients, VIXRISK has a little more
forecasting power than the GARCH forecast. In both panels, the number of significant
coefficients on the lagged market standard deviation (two in panel A and two in panel B) is
lower than the number of significant coefficients on the GARCH forecast and the lagged market
volatility. So, in terms of the number of significant coefficients, the lagged market standard
deviation has much lower forecasting power than VIXRISK and the GARCH forecast. Also, in
most cases, the signs of the coefficients on the lagged market standard deviation are negative.
Table 6 shows the output from the regression of realized standard deviation of the portfolios on
the sentiment component of VIX, the lagged portfolio standard deviation, and the lagged realized
standard deviation of the S&P 500 index. Panel A shows the estimation results for the portfolios
sorted univariately by number of analysts, age, profitability, and dividend payout ratio of the
firm. For the univariately sorted portfolios, all of the coefficients on VIXSENT are positive, and
all but one of the coefficients is significant. All the coefficients on LAGPORT are positive and
fourteen coefficients are significant. Five of the coefficients on the lagged market standard
deviation are negative but none of them are significant, and one of the coefficients is significant
with a positive sign.
121
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIXSENT are positive, and all but one of the
coefficients is significant. All the coefficients on LAGPORT are positive and all but one of the
coefficients is significant. Four of the coefficients on the lagged market standard deviation are
negative, and one of the coefficients is significant with a positive sign.
This table shows that for the univariately sorted portfolios in panel A, the number of significant
coefficients on VIXSENT (nineteen) is more than the number of significant coefficients on the
lagged portfolio standard deviation (fourteen). So, in terms of the number of significant
coefficients, VIXSENT has more forecasting power than the lagged portfolio standard deviation.
For the portfolios sorted by book-to-market equity, size, and beta in panel B, the number of
significant coefficients on VIXSENT (eleven) is equal to the number of significant coefficients
on the lagged portfolio standard deviation (eleven). So, in terms of the number of significant
coefficients, the forecasting powers of VIXSENT and the lagged portfolio standard deviation are
identical. In both panels, the number of significant coefficients on the lagged market standard
deviation (one in panel A and one in panel B) is lower than the number of significant
coefficients on VIXSENT and the lagged portfolio standard deviation. So, in terms of the
number of significant coefficients, the lagged market volatility has much lower forecasting
power than VIXSENT and the lagged portfolio standard deviation. Also, in most cases the signs
of the coefficients on the lagged market standard deviation are negative.
Table 7 shows the output from the regression of realized standard deviation of the portfolios on
the sentiment component of VIX, the GARCH forecast of volatility for the respective portfolio,
and the lagged realized standard deviation of the S&P 500 index. Panel A shows the estimation
results for the portfolios sorted univariately by number of analysts, age, profitability, and
dividend payout ratio of the firm. For the univariately sorted portfolios, all of the coefficients on
VIXSENT are positive, and all but two of them are significant. All of the coefficients on the
GARCH forecast are positive and significant, and all but two of them are significant. Five of the
122
coefficients on the lagged market standard deviation are negative, and none of the coefficients
are significant.
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIXSENT are positive and all but two are
significant. All of the coefficients on the GARCH forecasts are positive and all but one is
significant. Four coefficients on the lagged market standard deviation have negative signs. One
coefficient is significant with a negative sign and two coefficients are significant with positive
signs.
This table shows that for the univariately sorted portfolios in panel A, the number of significant
coefficients on VIXSENT (eighteen) is equal to the number of significant coefficients on the
GARCH forecast (eighteen). So, in terms of the number of significant coefficients, VIXSENT
and the GARCH forecast have identical forecasting powers. For the portfolios sorted univariately
by book-to-market equity, size, and beta in panel B, the number of significant coefficients on
VIXSENT (ten) is less than the number of significant coefficients on the GARCH forecast
(eleven). So, in terms of the number of significant coefficients, the GARCH forecast has a little
more forecasting power than VIXSENT. In both panels, the number of significant coefficients on
the lagged market standard deviation (none in panel A and three in panel B) is lower than the
number of significant coefficients on VIXSENT and the GARCH forecast. So, in terms of the
number of significant coefficients, the lagged market volatility has much lower forecasting
power than VIXSENT and the GARCH forecast.
Table 8 shows the output from the regression of realized standard deviation of the portfolios on
the risk component of VIX, the sentiment component of VIX, the lagged portfolio standard
deviation, and the lagged realized standard deviation of the S&P 500 index. Panel A shows the
estimation results for the portfolios sorted univariately by number of analysts, age, profitability,
and dividend payout ratio of the firm. For the univariately sorted portfolios, all of the coefficients
on VIXRISK are positive, and all of them are significant. All of the coefficients on VIXSENT
are positive, and all but four of them are significant. All the coefficients on LAGPORT are
123
positive and all but two of them are significant. Nineteen of the coefficients on the lagged market
standard deviation are negative, and five of the coefficients are significant with negative signs.
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIXRISK are positive, and all of them are
significant. All of the coefficients on VIXSENT are positive, and all but four of them are
significant. All the coefficients on LAGPORT are positive and all of them are significant. Eleven
of the coefficients on lagged market standard deviation are negative, and five of the coefficients
are significant with negative signs.
This table shows that for both the univariately sorted portfolios in panel A, VIXRISK has the
highest number of significant coefficients (twenty), followed by the number of significant
coefficients on lagged portfolio standard deviation (eighteen), and followed by the number of
significant coefficients on VIXSENT (sixteen). So, in terms of the number of significant
coefficients, VIXRISK has the most forecasting power, followed by the lagged portfolio standard
deviation, and finally by VIXSENT. For the portfolios sorted by book-to-market equity, size, and
beta in panel B, the number of significant coefficients on VIXRISK (twelve) is equal to the
number of significant coefficients on the lagged portfolio standard deviation (twelve) but greater
than the number of significant coefficients on VIXSENT (eight). So, in terms of the number of
significant coefficients, VIXRISK and the lagged portfolio standard deviation have identical
forecasting powers, followed by VIXSENT. In both panels, the lagged market volatility has
fewer significant coefficients (five in panel A and five in panel B) and hence lower forecasting
power than the other variables.
Table 9 shows the output from the regression of the realized standard deviation of the portfolios
on the risk component of VIX, the sentiment component of VIX, the GARCH forecast of
volatility for the respective portfolio, and the lagged realized standard deviation of the S&P 500
index. Panel A shows the estimation results for the portfolios sorted univariately by number of
analysts, age, profitability, and dividend payout ratio of the firm. For the univariately sorted
portfolios, all of the coefficients on VIXRISK are positive, and all of them are significant. All of
the coefficients on VIXSENT are positive, and all but seven of them are significant. All of the
124
coefficients on GARCH are positive and significant. Nineteen of the coefficients on the lagged
market standard deviation have negative signs, and five of them are significant with negative
signs.
Panel B shows the estimation results for the portfolios sorted by book-to-market equity, size, and
beta. For these portfolios, all of the coefficients on VIXRISK are positive and significant. All of
the coefficients on VIXSENT are positive, and all but two of them are significant. All the
coefficients on GARCH are positive and all but one of them is significant. Eleven of the
coefficients on the lagged market standard deviation are negative. Two of the coefficients are
significant with negative signs and one is significant with a positive sign.
This table shows that for the univariately sorted portfolios in panel A, the number of significant
coefficients on VIXRISK(twenty) is equal to the number of significant coefficients on the
GARCH forecast (twenty), followed by the number of significant coefficients on VIXSENT
(thirteen). So, in terms of the number of significant coefficients, VIXRISK and the GARCH
forecast have identical forecasting powers, followed by VIXSENT. For the portfolios sorted by
book-to-market equity, size, and beta in panel B, VIXRISK has the highest number of significant
coefficients (twelve), followed by the GARCH forecast (eleven), and followed by VIXSENT
(ten). So, in terms of the number of significant coefficients, VIXRISK has a little more
forecasting power than the GARCH forecast, followed by VIXSENT, and finally by the lagged
portfolio standard deviation. In both panels, the lagged market volatility has fewer significant
coefficients (five in panel A and three in panel B) and hence lower forecasting power than the
other variables.
Conclusion
In this essay, I compare the forecasting power for future realized volatility of the risk and
sentiment components of VIX, a GARCH forecast of future realized volatility, the lagged
portfolio volatility, and the lagged market volatility. The results suggest that the risk and
sentiment components of VIX, the GARCH forecast, and the lagged portfolio volatility all play
125
significant incremental roles in forecasting future realized volatility. When the risk and sentiment
components of implied volatility, the lagged portfolio standard deviation, and the lagged market
standard deviation are included in the regression, the risk component of VIX has the most
forecasting power, followed by the lagged portfolio standard deviation, and finally by the
sentiment component of implied volatility. When the risk and sentiment components of implied
volatility, the GARCH forecast, and the lagged market standard deviation are included in the
regression, the risk component of VIX and the GARCH forecast have nearly identical forecasting
powers, followed by the sentiment component of VIX. Market volatility plays a lesser role in
both sets of regressions, and the coefficients on the lagged market volatility often have negative
signs.
The findings of this essay expand previous volatility forecasting literature. From these results, it
appears imperative to decompose implied volatility into risk and sentiment components for
forecasting future volatility, since each component plays a significant role in forecasting future
realized volatility. However, the risk component of VIX plays a greater role than the sentiment
component in forecasting future volatilities of all portfolios, including those portfolios sorted to
capture effects of sentiment. This implies that sentiment has lower forecasting power for future
realized volatility than risk does. The two other forecasts of volatility, namely the lagged
portfolio standard deviation and the GARCH forecast also play significant roles in forecasting
future volatility, and the presence of the risk and sentiment components of implied volatility does
not encompass their significance. The GARCH forecast and the risk component of VIX have
nearly identical forecasting powers. In the separate regressions containing the risk and sentiment
components of VIX and the respective volatility forecast (the lagged portfolio standard deviation
and the GARCH forecast), both the lagged portfolio standard deviation and the GARCH forecast
have more forecasting power than the sentiment component of VIX, again implying that
sentiment plays a lesser role in forecasting future realized volatility than risk does.
126
Table 20
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIX
The table below shows the estimation results of equation (1) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXt+ept
RSD 22
pt
(1)
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIX is the Friday’s VIX observation. In panel A, analystfivestd22 is the top quintile portfolio formed by the number of analysts
following the firm (obtained from IBES). Analystonestd22 is the bottom quintile portfolio. Analystfourstd22, analystthreestd22,
and analysttwostd22 are the fourth, third and second quintile portfolios, respectively. Agefivestd22 is the top quintile portfolio
formed by the age of the firm. Ageonestd22 is the bottom quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are
the fourth, third and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the
nearest month) the firm has been on CRSP. Divfivestd22 is the top quintile portfolio formed by the dividend payout ratio of the
firm. Divonestd22 is the bottom quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefivestd22 is the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio.
Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. In panel B, portfolio R111
represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and portfolio R223 is high
B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1. The returns on the
portfolios are measured from July of year t to June of year t+1.The future holding period returns are measured every Friday. I
employ Newey and West (1987) standard errors to account for residual correlation due to overlapping portfolio returns.
127
Table 20-Continued
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIX
PORTFOLIO
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.003
-0.210
AGEFIVESTD22
VIX
0.755
11.360**
INTERCEPT
0.032
2.130*
VIX
0.592
8.870**
ANALYSTTHREESTD22
INTERCEPT
0.053
3.580**
VIX
0.465
6.880**
ANALYSTTWOSTD22
INTERCEPT
0.056
4.130**
VIX
0.364
5.780**
ANALYSTONESTD22
INTERCEPT
0.045
3.830**
VIX
0.283
5.220**
COEFFICIENT
T-STAT
PORTFOLIO
ROEFIVESTD22
INTERCEPT
0.020
1.710
VIX
0.490
9.160**
ROEFOURSTD22
INTERCEPT
0.019
1.630
ANALYSTFIVESTD22
ANALYSTFOURSTD22
PORTFOLIO
VIX
0.494
9.260**
ROETHREESTD22
INTERCEPT
0.030
2.600**
VIX
0.425
8.240**
ROETWOSTD22
INTERCEPT
0.040
3.180**
VIX
0.397
7.250**
ROEONESTD22
INTERCEPT
0.044
3.520**
VIX
0.399
7.130**
COEFFICIENT
T-STAT
INTERCEPT
0.006
0.510
VIX
0.424
8.780**
INTERCEPT
0.007
0.580
VIX
0.447
8.460**
AGETHREESTD22
INTERCEPT
0.009
0.660
VIX
0.488
7.880**
AGETWOSTD22
INTERCEPT
0.011
0.760
VIX
0.513
7.740**
AGEONESTD22
INTERCEPT
-0.018
-0.980
VIX
0.730
7.960**
COEFFICIENT
T-STAT
DIVFIVESTD22
INTERCEPT
0.025
2.220**
VIX
0.419
8.310**
DIVFOURSTD22
INTERCEPT
0.051
3.420**
VIX
0.309
4.870**
INTERCEPT
0.052
3.780**
VIX
0.298
5.160**
INTERCEPT
0.049
3.730**
VIX
0.326
5.800**
AGEFOURSTD22
DIVTHREESTD22
DIVTWOSTD22
DIVONESTD22
* significant at 5% level; ** significant at 1% level
128
INTERCEPT
0.049
2.880**
VIX
0.383
5.310**
Table 20-Continued
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIX
COEFFICIENT
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
T-STAT
INTERCEPT
0.045
3.630**
VIX
0.313
5.750**
INTERCEPT
0.052
3.470**
VIX
0.422
6.310**
INTERCEPT
0.036
1.860
VIX
0.915
10.230**
INTERCEPT
0.018
1.590
VIX
0.501
9.940**
INTERCEPT
0.016
1.290
VIX
0.564
9.200**
INTERCEPT
0.006
0.260
VIX
1.000
9.400**
INTERCEPT
0.046
4.420**
VIX
0.229
5.190**
INTERCEPT
0.055
3.300**
VIX
0.386
5.400**
INTERCEPT
0.059
2.790**
VIX
0.691
7.770**
INTERCEPT
0.039
3.540**
VIX
0.456
8.940**
INTERCEPT
0.015
1.170
VIX
0.598
9.960**
INTERCEPT
0.012
0.640
VIX
0.845
9.750**
* significant at 5% level; ** significant at 1% level
129
Table 21
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on Lagged Market Standard Deviation
The table below shows the estimation results of equation (2) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpLAGSP500t+ept
RSD 22
pt
(2)
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
LAGSP500 is the standard deviation of the S&P 500 index over the previous 22 days from day t, where day t is the date of
observation of VIX. In panel A, analystfivestd22 is the top quintile portfolio formed by the number of analysts following the
firm (obtained from IBES). Analystonestd22 is the bottom quintile portfolio. Analystfourstd22, analystthreestd22, and
analysttwostd22 are the fourth, third and second quintile portfolios, respectively. Agefivestd22 is the top quintile portfolio
formed by the age of the firm. Ageonestd22 is the bottom quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are
the fourth, third and second quintile portfolios, respectively. The age of the firm is measured by the number of years (to the
nearest month) the firm has been on CRSP. Divfivestd22 is the top quintile portfolio formed by the dividend payout ratio of the
firm. Divonestd22 is the bottom quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third and second
quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefivestd22 is the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio.
Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and second quintile portfolios, respectively. Profitability is
measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated
as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus
preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. In panel B, portfolio R111
represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and portfolio R223 is high B/M,
high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1. The returns on the portfolios
are measured from July of year t to June of year t+1.The future holding period returns are measured every Friday. I employ
Newey and West (1987) standard errors to account for residual correlation due to overlapping portfolio returns.
130
Table 21-Continued
PanelA: Regression Estimates of 22-day Future Realized Standard Deviation of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on Lagged Market Standard Deviation
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
0.067
5.830**
AGEFIVESTD22
LAGSP500
0.625
8.930**
INTERCEPT
0.084
6.990**
LAGSP500
0.506
7.390**
INTERCEPT
0.090
7.390**
LAGSP500
0.417
5.750**
ROEFOURSTD22
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
AGETHREESTD22
INTERCEPT
0.083
7.320**
LAGSP500
0.339
4.880**
INTERCEPT
0.066
6.490**
LAGSP500
0.262
4.090**
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
0.069
7.160**
DIVFIVESTD22
LAGSP500
0.385
6.660**
INTERCEPT
0.066
6.900**
LAGSP500
0.404
7.110**
INTERCEPT
0.068
7.420**
LAGSP500
0.362
6.770**
INTERCEPT
0.074
7.530**
LAGSP500
0.346
6.050**
INTERCEPT
0.078
7.460**
LAGSP500
0.347
5.540**
PORTFOLIO
ROEFIVESTD22
AGEFOURSTD22
* significant at 5% level; ** significant at 1% level
131
AGETWOSTD22
AGEONESTD22
DIVFOURSTD22
DIVTHREESTD22
DIVTWOSTD22
DIVONESTD22
COEFFICIENT
T-STAT
INTERCEPT
0.050
5.750**
LAGSP500
0.327
6.910**
INTERCEPT
0.047
4.580**
LAGSP500
0.376
6.310**
INTERCEPT
0.052
4.280**
LAGSP500
0.421
5.960**
INTERCEPT
0.051
3.970**
LAGSP500
0.465
5.970**
INTERCEPT
0.037
2.050**
LAGSP500
0.672
5.800**
COEFFICIENT
T-STAT
INTERCEPT
0.071
8.270**
LAGSP500
0.305
5.880**
INTERCEPT
0.082
8.320**
LAGSP500
0.245
4.380**
INTERCEPT
0.081
8.320**
LAGSP500
0.238
4.430**
INTERCEPT
0.081
8.600**
LAGSP500
0.260
4.810**
INTERCEPT
0.083
7.220**
LAGSP500
0.326
4.940**
Table 21-Continued
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book-toMarket Equity, Size, and Beta on Lagged Market Standard Deviation
COEFFICIENT
T-STAT
INTERCEPT
0.070
7.440**
LAGSP500
0.279
5.020**
INTERCEPT
0.091
8.030**
LAGSP500
0.353
5.340**
INTERCEPT
0.104
6.310**
LAGSP500
0.854
8.770**
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
0.060
6.570**
LAGSP500
0.441
8.270**
INTERCEPT
0.074
7.320**
LAGSP500
0.434
6.550**
INTERCEPT
0.102
5.470**
LAGSP500
0.812
7.130**
INTERCEPT
0.070
8.830**
LAGSP500
0.179
4.140**
INTERCEPT
0.092
7.420**
LAGSP500
0.316
4.530**
INTERCEPT
0.117
7.110**
LAGSP500
0.607
6.620**
INTERCEPT
0.069
7.670**
LAGSP500
0.448
8.330**
INTERCEPT
0.077
7.390**
LAGSP500
0.460
7.480**
INTERCEPT
0.093
6.410
LAGSP500
0.687
7.830
* significant at 5% level; ** significant at 1% level
132
Table 22
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIX and Lagged Market Standard
Deviation
The table below shows the estimation results of equation (3) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXt+ mpLAGSP500t+ept
RSD 22
pt
(3)
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIX is the Friday’s VIX observation. LAGSP500 is the standard deviation of the S&P 500 index over the previous 22 days from
day t, where day t is the date of observation of VIX. In panel A, analystfivestd22 is the top quintile portfolio formed by the
number of analysts following the firm (obtained from IBES). Analystonestd22 is the bottom quintile portfolio. Analystfourstd22,
analystthreestd22, and analysttwostd22 are the fourth, third and second quintile portfolios, respectively. Agefivestd22 is the top
quintile portfolio formed by the age of the firm. Ageonestd22 is the bottom quintile portfolio. Agefourstd22, agethreestd22, and
agetwostd22 are the fourth, third and second quintile portfolios, respectively. The age of the firm is measured by the number of
years (to the nearest month) the firm has been on CRSP. Divfivestd22 is the top quintile portfolio formed by the dividend payout
ratio of the firm. Divonestd22 is the bottom quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third
and second quintile portfolios, respectively. Dividend payout is calculated as dividends (D) divided by book value of equity (BE).
Dividends (D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat).
Book value of equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of
Compustat). Roefivestd22 is the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile
portfolio. Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and second quintile portfolios, respectively.
Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity (BE). Earnings
(E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of
Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year based on data for the
fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. In panel B,
portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and portfolio
R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1. The returns
on the portfolios are measured from July of year t to June of year t+1.The future holding period returns are measured every
Friday. I employ Newey and West (1987) standard errors to account for residual correlation due to overlapping portfolio returns.
133
Table 22-Continued
PanelA: Regression Estimates of 22-day Future Realized Standard Deviation of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIX and Lagged Market Standard Deviation
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
INTERCEPT
ROEFOURSTD22
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
T-STAT
PORTFOLIO
-0.130
AGEFIVESTD22
INTERCEPT
COEFFICIENT
T-STAT
0.005
0.460
VIX
0.069
0.680
VIX
0.449
5.550**
LAGSP500
0.698
6.410**
LAGSP500
-0.030
-0.420
INTERCEPT
0.034
2.240*
INTERCEPT
0.008
0.660
VIX
0.100
0.860
VIX
0.400
4.060**
LAGSP500
0.510
4.340**
LAGSP500
0.057
0.550
INTERCEPT
0.055
3.770**
VIX
0.134
1.090
LAGSP500
0.356
3.030**
INTERCEPT
0.059
4.360**
AGEFOURSTD22
AGETHREESTD22
AGETWOSTD22
INTERCEPT
0.011
0.780
VIX
0.412
3.670**
LAGSP500
0.093
0.770
INTERCEPT
0.014
0.950
VIX
0.141
1.170
VIX
0.380
3.060**
LAGSP500
0.248
2.250*
LAGSP500
0.163
1.180
INTERCEPT
0.047
4.020**
INTERCEPT
-0.014
-0.720
AGEONESTD22
VIX
0.198
2.020*
VIX
0.518
3.090**
LAGSP500
0.104
0.920
LAGSP500
0.260
1.320
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
0.020
1.680
DIVFIVESTD22
INTERCEPT
0.024
2.060*
PORTFOLIO
ROEFIVESTD22
COEFFICIENT
-0.002
VIX
0.500
5.460**
VIX
0.485
5.740**
LAGSP500
-0.013
-0.140
LAGSP500
-0.080
-1.040
INTERCEPT
0.020
1.670
INTERCEPT
0.051
3.380**
DIVFOURSTD22
VIX
0.468
5.060**
VIX
0.311
3.300**
LAGSP500
0.032
0.350
LAGSP500
-0.002
-0.030
INTERCEPT
0.032
2.690**
VIX
0.371
4.070**
LAGSP500
0.067
0.730
INTERCEPT
0.041
3.310**
VIX
0.327
3.410**
LAGSP500
0.085
0.860
INTERCEPT
0.045
3.630**
DIVTHREESTD22
DIVTWOSTD22
DIVONESTD22
INTERCEPT
0.052
3.770**
VIX
0.296
3.490**
LAGSP500
0.002
0.030
INTERCEPT
0.049
3.730**
VIX
0.325
3.870**
LAGSP500
0.001
0.020
INTERCEPT
0.050
2.930**
VIX
0.332
3.240**
VIX
0.334
3.070**
LAGSP500
0.082
0.740
LAGSP500
0.060
0.640
134
Table 22-Continued
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIX and Lagged Market Standard Deviation
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
R221
R222
COEFFICIENT
T-STAT
INTERCEPT
0.046
3.830**
VIX
0.245
2.990**
LAGSP500
0.084
0.990
INTERCEPT
0.053
3.540**
VIX
0.380
3.580**
LAGSP500
0.051
0.490
INTERCEPT
0.043
2.210*
VIX
0.622
3.810**
LAGSP500
0.360
2.070*
INTERCEPT
0.020
1.790
VIX
0.404
4.960**
LAGSP500
0.120
1.510
INTERCEPT
0.016
1.220
VIX
0.597
6.320**
LAGSP500
-0.041
-0.440
INTERCEPT
0.007
0.300
VIX
0.964
6.320**
LAGSP500
0.045
0.300
INTERCEPT
0.046
4.390**
VIX
0.238
3.400**
LAGSP500
-0.010
-0.160
INTERCEPT
0.056
3.330**
VIX
0.366
3.250**
LAGSP500
0.025
0.230
INTERCEPT
0.062
2.950**
VIX
0.559
3.840**
LAGSP500
0.162
1.080
INTERCEPT
0.044
4.010**
VIX
0.257
3.130**
LAGSP500
0.243
2.980**
INTERCEPT
0.014
1.070
135
Table 22-Continued
COEFFICIENT
PORTFOLIO
R223
T-STAT
VIX
0.636
5.810**
LAGSP500
-0.046
-0.470
INTERCEPT
0.013
0.670
VIX
0.812
5.960**
LAGSP500
0.041
0.330
* significant at 5% level; ** significant at 1% level
Table 23
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, Lagged Portfolio Standard
Deviation, and Lagged Market Standard Deviation
The table below shows the estimation results of equation (4) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXRISKt+ ppLAGPORTt +mpLAGSP500t+ept
136
(4)
RSD 22
pt
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIXRISK is the risk component of VIX estimated from equation (2) in essay two. LAGPORT is the standard deviation of the
respective portfolio over the previous 22 days from day t, where day t is the date of observation of VIX. VIXSENT is the
sentiment component of VIX estimated from equation (7) in essay two. LAGSP500 is the standard deviation of the S&P 500
index over the previous 22 days from day t, where day t is the date of observation of VIX. In panel A, analystfivestd22 is the top
quintile portfolio formed by the number of analysts following the firm (obtained from IBES). Analystonestd22 is the bottom
quintile portfolio. Analystfourstd22, analystthreestd22, and analysttwostd22 are the fourth, third and second quintile portfolios,
respectively. Agefivestd22 is the top quintile portfolio formed by the age of the firm. Ageonestd22 is the bottom quintile
portfolio. Agefourstd22, agethreestd22, and agetwostd22 are the fourth, third and second quintile portfolios, respectively. The
age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP. Divfivestd22 is the top
quintile portfolio formed by the dividend payout ratio of the firm. Divonestd22 is the bottom quintile portfolio. Divfourstd22,
divthreestd22 and divtwostd22 are the fourth, third and second quintile portfolios, respectively. Dividend payout is calculated as
dividends (D) divided by book value of equity (BE). Dividends (D) is dividends per share at the ex date (Item 26 of Compustat)
times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is shareholders equity (Item 60 of Compustat) plus
balance sheet deferred taxes (Item 35 of Compustat). Roefivestd22 is the top quintile portfolio formed by the profitability of the
firm. Roeoneret22 is the bottom quintile portfolio. Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and
second quintile portfolios, respectively. Profitability is measured by the ratio of return on equity, which is earnings (E) divided by
book value of equity (BE). Earnings (E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income
statement deferred taxes (Item 50 of Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are
formed each year based on data for the fiscal year t-1.
The equally-weighted returns on the portfolios are measured from July of year t to June of year t+1. In panel B, portfolio R111
represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high beta, and portfolio R223 is high B/M,
high size, and high beta. The portfolios are formed each year based on data for the fiscal year t-1. The returns on the portfolios
are measured from July of year t to June of year t+1.The future holding period returns are measured every Friday. I employ
Newey and West (1987) standard errors to account for residual correlation due to overlapping portfolio returns.
Table 23-Continued
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIXRISK, Lagged Portfolio Standard Deviation, and
Lagged Market Standard Deviation
137
Table 23-Continued
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
COEFFICIENT
ROEFOURSTD22
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
PORTFOLIO
AGEFIVESTD22
COEFFICIENT
T-STAT
INTERCEPT
-0.358
-4.450**
INTERCEPT
-0.261
-4.700**
VIXRISK
0.473
5.370**
VIXRISK
0.346
5.730**
LAGPORT
0.486
4.190**
LAGPORT
0.421
4.620**
LAGSP500
-0.121
-0.890
LAGSP500
-0.117
-1.800
INTERCEPT
-0.287
-3.350**
INTERCEPT
-0.292
-4.740**
VIXRISK
0.403
4.270**
VIXRISK
0.379
5.540**
LAGPORT
0.489
4.790**
LAGPORT
0.326
3.350**
LAGSP500
-0.139
-1.140
LAGSP500
-0.049
-0.560
INTERCEPT
-0.254
-2.810**
INTERCEPT
-0.307
-4.280**
VIXRISK
0.369
3.730**
VIXRISK
0.401
5.020**
LAGPORT
0.491
4.510**
LAGPORT
0.319
3.220**
LAGSP500
-0.163
-1.330
LAGSP500
-0.032
-0.300
INTERCEPT
-0.201
-2.350*
INTERCEPT
-0.339
-4.570**
VIXRISK
0.307
3.280**
VIXRISK
0.436
5.240**
AGEFOURSTD22
AGETHREESTD22
AGETWOSTD22
LAGPORT
0.379
3.370**
LAGPORT
0.376
4.130**
LAGSP500
-0.083
-0.690
LAGSP500
-0.060
-0.610
INTERCEPT
-0.179
-2.570*
INTERCEPT
-0.456
-4.840**
VIXRISK
0.269
3.490**
VIXRISK
0.565
5.250**
AGEONESTD22
LAGPORT
0.300
3.070**
LAGPORT
0.573
6.150**
LAGSP500
-0.052
-0.560
LAGSP500
-0.216
-1.450
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.200
-2.900**
DIVFIVESTD22
INTERCEPT
-0.192
-3.020**
VIXRISK
0.298
4.000**
VIXRISK
0.289
4.250**
PORTFOLIO
ROEFIVESTD22
T-STAT
LAGPORT
0.205
1.600
LAGPORT
0.324
3.270**
LAGSP500
0.073
0.670
LAGSP500
-0.062
-0.760
INTERCEPT
-0.195
-2.750**
INTERCEPT
-0.147
-2.130*
VIXRISK
0.288
3.730**
VIXRISK
0.238
3.290**
DIVFOURSTD22
LAGPORT
0.285
2.310*
LAGPORT
0.506
5.590**
LAGSP500
0.037
0.330
LAGSP500
-0.155
-2.090*
INTERCEPT
-0.173
-2.540*
INTERCEPT
-0.144
-2.290*
VIXRISK
0.264
3.540**
VIXRISK
0.233
3.460**
LAGPORT
0.296
2.530*
LAGPORT
0.503
5.210**
LAGSP500
-0.145
-1.900
INTERCEPT
-0.155
-2.440*
DIVTHREESTD22
LAGSP500
0.024
0.230
INTERCEPT
-0.161
-2.210*
VIXRISK
0.256
3.210**
VIXRISK
0.242
3.600**
LAGPORT
0.266
2.300*
LAGPORT
0.534
6.590**
LAGSP500
0.031
0.280
INTERCEPT
-0.195
-2.550*
VIXRISK
0.298
LAGPORT
LAGSP500
DIVTWOSTD22
LAGSP500
-0.150
-2.350*
INTERCEPT
-0.181
-2.220*
138
3.550**
VIXRISK
0.280
3.220**
0.286
2.550*
LAGPORT
0.519
5.430**
-0.007
-0.060
LAGSP500
-0.164
-1.800
DIVONESTD22
Table 23-Continued
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book-toMarket Equity, Size, and Beta on VIXRISK, Lagged Portfolio Standard Deviation, and Lagged Market Standard
Deviation
COEFFICIENT
T-STAT
INTERCEPT
-0.139
-2.330*
VIXRISK
0.219
3.380**
LAGPORT
0.424
4.200**
LAGSP500
-0.056
-0.730
INTERCEPT
-0.166
-2.090*
VIXRISK
0.275
3.240**
LAGPORT
0.340
3.040**
LAGSP500
-0.032
-0.310
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
INTERCEPT
-0.391
-3.290**
VIXRISK
0.540
4.100**
LAGPORT
0.392
3.560**
LAGSP500
0.057
0.310
INTERCEPT
-0.234
-4.090**
VIXRISK
0.322
5.040**
LAGPORT
0.653
6.090**
LAGSP500
-0.213
-2.270*
INTERCEPT
-0.251
-3.730**
VIXRISK
0.359
4.970**
LAGPORT
0.445
4.480**
LAGSP500
-0.119
-1.280
INTERCEPT
-0.576
-5.530**
VIXRISK
0.751
6.480**
LAGPORT
0.733
7.010**
LAGSP500
-0.596
-3.610**
INTERCEPT
-0.127
-2.520*
VIXRISK
0.207
3.820**
LAGPORT
0.390
3.850**
LAGSP500
-0.093
-1.630
INTERCEPT
-0.187
-2.510*
VIXRISK
0.291
3.640**
LAGPORT
0.516
5.850**
139
Table 23-Continued
PORTFOLIO
R213
R221
R222
R223
COEFFICIENT
T-STAT
LAGSP500
-0.172
-2.070*
INTERCEPT
-0.353
-3.420**
VIXRISK
0.500
4.390**
LAGPORT
0.478
5.530**
LAGSP500
-0.153
-1.120
INTERCEPT
-0.144
-2.160*
VIXRISK
0.228
3.110**
LAGPORT
0.289
3.170**
LAGSP500
0.128
1.440
INTERCEPT
-0.253
-3.400**
VIXRISK
0.364
4.520**
LAGPORT
0.396
4.860**
LAGSP500
-0.074
-0.790
INTERCEPT
-0.397
-3.960**
VIXRISK
0.541
4.960**
LAGPORT
0.442
4.300**
LAGSP500
-0.117
-0.800
Table 24
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, GARCH Forecast, and Lagged
Market Standard Deviation
The table below shows the estimation results of equation (5) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXRISKt+gpGARCHt +mpLAGSP500t+ept
140
(5)
RSD 22
pt
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIXRISK is the risk component of VIX estimated from equation (2) in essay two. GARCH is the one-day ahead forecast of
standard deviation calculated using rolling 22-day GARCH (1,1) parameter estimates. LAGSP500 is the standard deviation of the
S&P 500 index over the previous 22 days from day t, where day t is the date of observation of VIX. In panel A, analystfivestd22
is the top quintile portfolio formed by the number of analysts following the firm (obtained from IBES). Analystonestd22 is the
bottom quintile portfolio. Analystfourstd22, analystthreestd22, and analysttwostd22 are the fourth, third and second quintile
portfolios, respectively. Agefivestd22 is the top quintile portfolio formed by the age of the firm. Ageonestd22 is the bottom
quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are the fourth, third and second quintile portfolios, respectively.
The age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP. Divfivestd22 is the top
quintile portfolio formed by the dividend payout ratio of the firm. Divonestd22 is the bottom quintile portfolio. Divfourstd22,
divthreestd22 and divtwostd22 are the fourth, third and second quintile portfolios, respectively. Dividend payout is calculated as
dividends (D) divided by book value of equity (BE). Dividends (D) is dividends per share at the ex date (Item 26 of Compustat)
times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is shareholders equity (Item 60 of Compustat) plus
balance sheet deferred taxes (Item 35 of Compustat). Roefivestd22 is the top quintile portfolio formed by the profitability of the
firm. Roeoneret22 is the bottom quintile portfolio. Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and
second quintile portfolios, respectively. Profitability is measured by the ratio of return on equity, which is earnings (E) divided by
book value of equity (BE). Earnings (E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income
statement deferred taxes (Item 50 of Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are
formed each year based on data for the fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of
year t to June of year t+1. In panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low
size, and high beta, and portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data
for the fiscal year t-1. The returns on the portfolios are measured from July of year t to June of year t+1.The future holding period
returns are measured every Friday. I employ Newey and West (1987) standard errors to account for residual correlation due to
overlapping portfolio returns.
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIXRISK, GARCH Forecast, and Lagged Market
Standard Deviation
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
INTERCEPT
COEFFICIENT
T-STAT
PORTFOLIO
-0.339
-4.270**
AGEFIVESTD22
INTERCEPT
COEFFICIENT
T-STAT
-0.242
-4.350**
VIXRISK
0.451
5.170**
VIXRISK
0.326
5.370**
GARCH
0.461
4.390**
GARCH
0.418
4.590**
LAGSP500
-0.063
-0.490
LAGSP500
-0.101
-1.420
INTERCEPT
-0.252
-3.150**
INTERCEPT
-0.268
-4.580**
VIXRISK
0.358
4.020**
VIXRISK
0.352
5.340**
GARCH
0.541
6.070**
GARCH
0.440
4.600**
141
AGEFOURSTD22
Table 24-Continued
COEFFICIENT
T-STAT
LAGSP500
-0.120
-1.070
INTERCEPT
-0.189
-2.390*
PORTFOLIO
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
ROEFOURSTD22
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
AGETHREESTD22
COEFFICIENT
T-STAT
LAGSP500
-0.075
-0.820
INTERCEPT
-0.288
-4.310**
VIXRISK
0.289
3.300**
VIXRISK
0.377
5.030**
GARCH
0.468
5.540**
GARCH
0.415
4.550**
LAGSP500
-0.053
-0.510
LAGSP500
-0.073
-0.760
INTERCEPT
-0.172
-2.360*
INTERCEPT
-0.288
-4.130**
VIXRISK
0.270
3.320**
VIXRISK
0.376
4.720**
GARCH
0.443
5.150**
GARCH
0.413
4.670**
LAGSP500
-0.081
-0.810
INTERCEPT
-0.127
-2.070**
VIXRISK
0.209
GARCH
LAGSP500
PORTFOLIO
ROEFIVESTD22
PORTFOLIO
INTERCEPT
AGETWOSTD22
LAGSP500
-0.031
-0.300
INTERCEPT
-0.365
-4.030**
3.040**
VIXRISK
0.455
4.450**
0.275
3.540**
GARCH
0.415
3.930**
0.006
0.080
LAGSP500
0.029
0.190
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
-0.208
-3.270**
DIVFIVESTD22
-0.178
-2.920*
AGEONESTD22
INTERCEPT
VIXRISK
0.303
4.340**
VIXRISK
0.273
4.140**
GARCH
0.344
3.130**
GARCH
0.266
4.030**
LAGSP500
-0.011
-0.120
LAGSP500
-0.004
-0.060
INTERCEPT
-0.198
-3.070**
INTERCEPT
-0.111
-1.640
VIXRISK
0.289
4.060**
VIXRISK
0.201
2.820**
GARCH
0.411
4.490**
GARCH
0.381
4.200**
LAGSP500
-0.036
-0.390
INTERCEPT
-0.160
-2.640**
VIXRISK
0.245
GARCH
LAGSP500
INTERCEPT
DIVFOURSTD22
LAGSP500
-0.055
-0.770
INTERCEPT
-0.117
-1.930
3.660**
VIXRISK
0.206
3.150**
0.404
4.300**
GARCH
0.455
5.600**
-0.020
-0.240
LAGSP500
-0.102
-1.440
-0.163
-2.490*
INTERCEPT
-0.128
-2.100*
DIVTHREESTD22
DIVTWOSTD22
VIXRISK
0.254
3.500**
VIXRISK
0.211
3.240**
GARCH
0.388
4.500**
GARCH
0.542
7.840**
LAGSP500
-0.035
-0.380
LAGSP500
-0.123
-1.990*
INTERCEPT
-0.173
-2.480*
INTERCEPT
-0.168
-2.230*
VIXRISK
0.270
3.480**
VIXRISK
0.261
3.240**
GARCH
0.295
2.800**
GARCH
0.558
7.600**
LAGSP500
0.020
0.190
LAGSP500
-0.152
-1.990*
DIVONESTD22
Table 24-Continued
142
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIXRISK, GARCH Forecast, and Lagged Market Standard Deviation
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
COEFFICIENT
T-STAT
INTERCEPT
-0.074
-1.330
VIXRISK
0.145
2.340*
GARCH
0.370
4.910**
LAGSP500
0.037
0.520
INTERCEPT
-0.166
-2.340*
VIXRISK
0.270
3.450**
GARCH
0.466
5.530**
LAGSP500
-0.101
-1.070
INTERCEPT
-0.360
-3.290**
VIXRISK
0.498
4.060**
GARCH
0.468
5.160**
LAGSP500
0.018
0.110
INTERCEPT
-0.192
-3.690**
VIXRISK
0.275
4.710**
GARCH
0.517
6.170**
LAGSP500
-0.081
-1.040
INTERCEPT
-0.237
-3.320**
VIXRISK
0.344
4.490**
GARCH
0.227
2.630**
LAGSP500
0.075
0.860
INTERCEPT
-0.570
-5.880**
VIXRISK
0.731
6.760**
GARCH
0.840
7.880**
LAGSP500
-0.643
-4.120**
INTERCEPT
-0.071
-1.460
VIXRISK
0.144
2.760**
GARCH
0.286
2.950**
LAGSP500
-0.002
-0.040
INTERCEPT
-0.126
-1.790
143
Table 24-Continued
PORTFOLIO
R213
R221
R222
R223
COEFFICIENT
T-STAT
VIXRISK
0.222
2.880**
GARCH
0.499
7.220**
LAGSP500
-0.108
-1.310
INTERCEPT
-0.294
-3.020**
VIXRISK
0.431
3.990**
GARCH
0.500
6.910**
LAGSP500
-0.107
-0.830
INTERCEPT
-0.116
-1.760
VIXRISK
0.203
2.780**
GARCH
0.122
1.750
LAGSP500
0.251
3.120**
INTERCEPT
-0.236
-3.150**
VIXRISK
0.347
4.280**
GARCH
0.292
3.930**
LAGSP500
0.024
0.270
INTERCEPT
-0.372
-3.760**
VIXRISK
0.511
4.720**
GARCH
0.398
5.050**
LAGSP500
-0.031
-0.260
144
Table 25
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXSENT, Lagged Portfolio Standard
Deviation, and Lagged Market Standard Deviation
The table below shows the estimation results of equation (6) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXSENTt+ ppLAGPORTt +mpLAGSP500t+ept
RSD 22
pt
(6)
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIXSENT is the sentiment component of VIX estimated from equation (7) in essay two. LAGPORT is the standard deviation of
the respective portfolio over the previous 22 days from day t, where day t is the date of observation of VIX. LAGSP500 is the
standard deviation of the S&P 500 index over the previous 22 days from day t, where day t is the date of observation of VIX. In
panel A, analystfivestd22 is the top quintile portfolio formed by the number of analysts following the firm (obtained from IBES).
Analystonestd22 is the bottom quintile portfolio. Analystfourstd22, analystthreestd22, and analysttwostd22 are the fourth, third
and second quintile portfolios, respectively. Agefivestd22 is the top quintile portfolio formed by the age of the firm. Ageonestd22
is the bottom quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are the fourth, third and second quintile
portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on
CRSP. Divfivestd22 is the top quintile portfolio formed by the dividend payout ratio of the firm. Divonestd22 is the bottom
quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third and second quintile portfolios, respectively.
Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends per share at the
ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is shareholders
equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefivestd22 is the top quintile
portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio. Roefourstd22, Roethreestd22 and
Roetwostd22 are the fourth, third and second quintile portfolios, respectively. Profitability is measured by the ratio of return on
equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated as income before extraordinary
items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus preferred dividends (Item 19
of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1. The equally-weighted returns on
the portfolios are measured from July of year t to June of year t+1. In panel B, portfolio R111 represents low B/M, low size, and
low beta, portfolio R113 is low B/M, low size, and high beta, and portfolio R223 is high B/M, high size, and high beta. The
portfolios are formed each year based on data for the fiscal year t-1. The returns on the portfolios are measured from July of year
t to June of year t+1.The future holding period returns are measured every Friday. I employ Newey and West (1987) standard
errors to account for residual correlation due to overlapping portfolio returns.
145
Table 25-Continued
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIXSENT, Lagged Portfolio Standard Deviation, and
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
INTERCEPT
ROEFOURSTD22
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
T-STAT
PORTFOLIO
-2.760**
AGEFIVESTD22
INTERCEPT
COEFFICIENT
T-STAT
-0.082
-2.280*
VIXSENT
0.421
4.130**
VIXSENT
0.259
3.690**
LAGPORT
0.336
2.890**
LAGPORT
0.300
2.710**
LAGSP500
0.098
0.860
LAGSP500
0.030
0.430
INTERCEPT
-0.104
-1.920
INTERCEPT
-0.063
-1.530
VIXSENT
0.357
3.310**
VIXSENT
0.218
2.700**
LAGPORT
0.388
3.730**
LAGPORT
0.260
2.420*
LAGSP500
0.009
0.090
LAGSP500
0.106
1.230
AGEFOURSTD22
INTERCEPT
-0.063
-1.240
INTERCEPT
-0.067
-1.460
VIXSENT
0.280
2.760**
VIXSENT
0.235
2.570**
LAGPORT
0.407
3.760**
LAGPORT
0.262
2.460*
LAGSP500
-0.021
-0.220
LAGSP500
0.126
1.310
INTERCEPT
-0.035
-0.740
INTERCEPT
-0.061
-1.270
AGETHREESTD22
AGETWOSTD22
VIXSENT
0.219
2.360*
VIXSENT
0.222
2.330*
LAGPORT
0.300
2.830**
LAGPORT
0.341
3.480**
LAGSP500
0.040
0.420
INTERCEPT
-0.026
-0.630
VIXSENT
0.175
LAGPORT
LAGSP500
INTERCEPT
PORTFOLIO
ROEFIVESTD22
COEFFICIENT
-0.147
LAGSP500
0.108
1.130
INTERCEPT
-0.030
-0.480
2.170*
VIXSENT
0.157
1.240
0.223
2.420*
LAGPORT
0.564
5.370**
0.060
0.760
LAGSP500
0.037
0.240
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
-0.130
-2.980**
DIVFIVESTD22
INTERCEPT
-0.135
-3.260**
AGEONESTD22
VIXSENT
0.394
4.560**
VIXSENT
0.408
4.920**
LAGPORT
0.006
0.050
LAGPORT
0.065
0.650
LAGSP500
0.199
2.410*
LAGSP500
0.076
1.090
INTERCEPT
-0.114
-2.660**
INTERCEPT
-0.094
-2.450*
VIXSENT
0.355
4.130**
DIVFOURSTD22
VIXSENT
0.326
4.390**
LAGPORT
0.118
1.010
LAGPORT
0.346
4.130**
LAGSP500
0.155
1.820
LAGSP500
-0.087
-1.450
INTERCEPT
-0.093
-2.340*
INTERCEPT
-0.079
-2.160*
VIXSENT
0.314
3.920**
DIVTHREESTD22
VIXSENT
0.294
4.020**
LAGPORT
0.160
1.450
LAGPORT
0.361
3.890**
LAGSP500
0.114
1.440
LAGSP500
-0.079
-1.210
INTERCEPT
-0.083
-2.040*
INTERCEPT
-0.078
-2.160*
DIVTWOSTD22
VIXSENT
0.304
3.740**
VIXSENT
0.288
4.020**
LAGPORT
0.148
1.370
LAGPORT
0.399
4.860**
LAGSP500
0.110
1.240
INTERCEPT
-0.065
-1.470
LAGSP500
-0.077
-1.410
INTERCEPT
-0.098
-2.220*
VIXSENT
0.274
3.090** 146
VIXSENT
0.339
3.930**
LAGPORT
LAGSP500
0.195
1.810
LAGPORT
0.364
4.170**
0.093
1.020
LAGSP500
-0.064
-0.930
DIVONESTD22
Table 25-Continued
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market Standard
Deviation
PORTFOLIO
R111
R112
R113
R121
R122
R123
R211
R212
R213
COEFFICIENT
T-STAT
INTERCEPT
-0.053
-1.510
VIXSENT
0.225
3.210**
LAGPORT
0.307
3.140**
LAGSP500
0.022
0.360
INTERCEPT
-0.096
-2.030*
VIXSENT
0.357
3.790**
LAGPORT
0.203
1.950
LAGSP500
0.050
0.620
INTERCEPT
-0.115
-1.610
VIXSENT
0.414
2.910**
LAGPORT
0.334
3.050**
LAGSP500
0.241
1.510
INTERCEPT
-0.024
-0.690
VIXSENT
0.154
2.280*
LAGPORT
0.638
5.820**
LAGSP500
-0.092
-1.030
INTERCEPT
-0.110
-2.660**
VIXSENT
0.358
4.520**
LAGPORT
0.324
3.300**
LAGSP500
0.013
0.150
INTERCEPT
-0.127
-1.790
VIXSENT
0.442
3.300**
LAGPORT
0.645
5.810**
LAGSP500
-0.260
-1.770
INTERCEPT
-0.033
-1.000
VIXSENT
0.185
2.840**
LAGPORT
0.290
2.820**
LAGSP500
-0.022
-0.440
INTERCEPT
-0.078
-1.610
VIXSENT
0.308
3.160**
LAGPORT
0.408
4.460**
LAGSP500
-0.083
-1.140
INTERCEPT
-0.111
-1.710
VIXSENT
0.414
3.240**
LAGPORT
0.402
4.550**
LAGSP500
0.013
0.110
147
Table 25-Continued
COEFFICIENT
PORTFOLIO
R221
R222
R223
T-STAT
INTERCEPT
0.041
1.040
VIXSENT
0.040
0.540
LAGPORT
0.263
2.860**
LAGSP500
0.256
3.030**
INTERCEPT
-0.112
-2.140*
VIXSENT
0.370
3.620**
LAGPORT
0.235
2.480*
LAGSP500
0.094
0.910
INTERCEPT
-0.143
-2.160
VIXSENT
0.458
3.670**
LAGPORT
0.361
3.560**
LAGSP500
0.067
0.510
Table 26
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXSENT, GARCH Forecast, and Lagged
Market Standard Deviation
The table below shows the estimation results of equation (7) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXSENTt+ gpGARCHt +mpLAGSP500t+ept
RSD 22
pt
(7)
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIXSENT is the sentiment component of VIX estimated from equation (7) in essay two. GARCH is the one-day ahead forecast
148
of standard deviation calculated using rolling 22-day GARCH (1,1) parameter estimates. LAGSP500 is the standard deviation of
the S&P 500 index over the previous 22 days from day t, where day t is the date of observation of VIX. In panel A,
analystfivestd22 is the top quintile portfolio formed by the number of analysts following the firm (obtained from IBES).
Analystonestd22 is the bottom quintile portfolio. Analystfourstd22, analystthreestd22, and analysttwostd22 are the fourth, third
and second quintile portfolios, respectively. Agefivestd22 is the top quintile portfolio formed by the age of the firm. Ageonestd22
is the bottom quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are the fourth, third and second quintile
portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on
CRSP. Divfivestd22 is the top quintile portfolio formed by the dividend payout ratio of the firm. Divonestd22 is the bottom
quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third and second quintile portfolios, respectively.
Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends (D) is dividends per share at the
ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of equity (BE) is shareholders
equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat). Roefivestd22 is the top quintile
portfolio formed by the profitability of the firm. Roeoneret22 is the bottom quintile portfolio. Roefourstd22, Roethreestd22 and
Roetwostd22 are the fourth, third and second quintile portfolios, respectively. Profitability is measured by the ratio of return on
equity, which is earnings (E) divided by book value of equity (BE). Earnings (E) are calculated as income before extraordinary
items (Item 18 of Compustat) plus income statement deferred taxes (Item 50 of Compustat) minus preferred dividends (Item 19
of Compustat). The quintile portfolios are formed each year based on data for the fiscal year t-1. The equally-weighted returns on
the portfolios are measured from July of year t to June of year t+1. In panel B, portfolio R111 represents low B/M, low size, and
low beta, portfolio R113 is low B/M, low size, and high beta, and portfolio R223 is high B/M, high size, and high beta. The
portfolios are formed each year based on data for the fiscal year t-1. The returns on the portfolios are measured from July of year
t to June of year t+1.The future holding period returns are measured every Friday. I employ Newey and West (1987) standard
errors to account for residual correlation due to overlapping portfolio returns.
Table 26-Continued
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIXSENT, GARCH Forecast, and Lagged Market
Standard Deviation
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.138
-2.640**
AGEFIVESTD22
COEFFICIENT
T-STAT
INTERCEPT
-0.073
-2.130*
VIXSENT
0.402
4.050**
VIXSENT
0.242
3.680**
GARCH
LAGSP500
0.348
3.470**
GARCH
0.350
3.770**
0.112
1.050
LAGSP500
0.010
0.150
INTERCEPT
-0.091
-1.750
INTERCEPT
-0.037
-0.940
VIXSENT
0.319
3.110**
VIXSENT
0.166
2.110*
AGEFOURSTD22
149
Table 26-Continued
COEFFICIENT
T-STAT
COEFFICIENT
T-STAT
GARCH
0.475
5.150**
GARCH
0.394
3.680**
LAGSP500
-0.013
-0.140
LAGSP500
0.072
0.820
INTERCEPT
-0.043
-0.890
INTERCEPT
-0.051
-1.120
VIXSENT
0.227
2.340*
VIXSENT
0.199
2.220*
GARCH
0.427
4.960**
GARCH
0.390
4.020**
LAGSP500
0.031
0.380
LAGSP500
0.064
0.710
INTERCEPT
-0.022
-0.500
INTERCEPT
-0.045
-1.000
VIXSENT
0.183
2.080*
VIXSENT
0.186
2.050*
GARCH
0.401
4.740**
GARCH
0.418
4.500**
LAGSP500
0.012
0.140
LAGSP500
0.090
0.920
INTERCEPT
-0.005
-0.110
INTERCEPT
0.000
-0.010
VIXSENT
0.129
1.590
VIXSENT
0.085
0.730
GARCH
0.253
3.230**
GARCH
0.431
3.950**
LAGSP500
0.076
1.050
LAGSP500
0.230
1.480
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.116
-2.700**
DIVFIVESTD22
INTERCEPT
-0.129
-3.150
VIXSENT
0.358
4.240**
VIXSENT
0.391
4.850**
GARCH
0.200
1.840
GARCH
0.122
1.960*
LAGSP500
0.091
1.070
LAGSP500
0.054
0.910
INTERCEPT
-0.093
-2.190*
INTERCEPT
-0.095
-2.550*
VIXSENT
0.305
3.640**
VIXSENT
0.331
4.590**
GARCH
0.291
3.050**
GARCH
0.278
4.080**
PORTFOLIO
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
PORTFOLIO
ROEFIVESTD22
ROEFOURSTD22
PORTFOLIO
AGETHREESTD22
AGETWOSTD22
AGEONESTD22
150
DIVFOURSTD22
Table 26-Continued
COEFFICIENT
T-STAT
LAGSP500
0.068
0.890
INTERCEPT
-0.077
-1.970*
PORTFOLIO
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
PORTFOLIO
DIVTHREESTD22
COEFFICIENT
T-STAT
LAGSP500
-0.044
-0.790
INTERCEPT
-0.077
-2.210*
VIXSENT
0.274
3.490**
VIXSENT
0.292
4.230**
GARCH
0.309
3.230**
GARCH
0.351
4.720**
LAGSP500
0.049
0.670
LAGSP500
-0.070
-1.130
INTERCEPT
-0.061
-1.510
INTERCEPT
-0.071
-2.040*
VIXSENT
0.252
3.130**
VIXSENT
0.268
3.970**
GARCH
0.292
3.340**
GARCH
0.436
6.230**
LAGSP500
0.051
0.650
INTERCEPT
-0.060
-1.370
VIXSENT
0.256
GARCH
LAGSP500
DIVTWOSTD22
LAGSP500
-0.076
-1.430
INTERCEPT
-0.088
-2.090*
2.960**
VIXSENT
0.311
3.840**
0.249
2.590**
GARCH
0.437
6.370**
0.082
0.940
LAGSP500
-0.077
-1.240
DIVONESTD22
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIXSENT, GARCH Forecast, and Lagged Market Standard Deviation
COEFFICIENT
T-STAT
INTERCEPT
-0.035
-1.030
VIXSENT
0.185
2.760**
GARCH
0.311
3.930**
LAGSP500
0.060
1.000
INTERCEPT
-0.070
-1.570
PORTFOLIO
R111
R112
R113
VIXSENT
0.295
3.310**
GARCH
0.360
4.260**
LAGSP500
-0.015
-0.200
INTERCEPT
-0.100
-1.430
VIXSENT
0.370
2.690**
GARCH
0.433
4.670**
LAGSP500
0.170
1.160
151
Table 26-Continued
PORTFOLIO
R121
R122
R123
R211
R212
R213
R221
R222
R223
INTERCEPT
COEFFICIENT
T-STAT
0.002
0.050
VIXSENT
0.104
1.560
GARCH
0.522
6.020**
LAGSP500
0.022
0.290
INTERCEPT
-0.119
-2.820**
VIXSENT
0.379
4.670**
GARCH
0.139
1.570
LAGSP500
0.158
2.000*
INTERCEPT
-0.124
-1.830
VIXSENT
0.416
3.220**
GARCH
0.738
6.290**
LAGSP500
-0.297
-2.070*
INTERCEPT
-0.018
-0.580
VIXSENT
0.155
2.460*
GARCH
0.248
2.510*
LAGSP500
0.021
0.430
INTERCEPT
-0.057
-1.240
VIXSENT
0.261
2.870**
GARCH
0.436
6.120**
LAGSP500
-0.066
-0.930
INTERCEPT
-0.072
-1.180
VIXSENT
0.328
2.740**
GARCH
0.453
6.240**
LAGSP500
0.028
0.250
INTERCEPT
0.066
1.590
VIXSENT
0.000
0.000
GARCH
0.113
1.780
LAGSP500
0.372
5.050**
INTERCEPT
-0.113
-2.220*
VIXSENT
0.374
3.770**
GARCH
0.188
3.170**
LAGSP500
0.132
1.530
INTERCEPT
-0.125
-1.880
Table 26-Continued
152
PORTFOLIO
COEFFICIENT
T-STAT
VIXSENT
0.417
3.350**
GARCH
0.339
4.240**
LAGSP500
0.129
1.210
Table 27
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, VIXSENT, Lagged Portfolio
Standard Deviation, and Lagged Market Standard Deviation
The table below shows the estimation results of equation (8) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXRISKt+ spVIXSENTt + ppLAGPORTt +mpLAGSP500t+ept (8)
RSD 22
pt
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIXRISK is the risk component of VIX estimated from equation (2) in essay two. VIXSENT is the sentiment component of VIX
estimated from equation (7) in essay two. LAGPORT is the standard deviation of the respective portfolio over the previous 22
days from day t, where day t is the date of observation of VIX. LAGSP500 is the standard deviation over the previous 22 days
from day t, where day t is the date of observation of VIX. In panel A, Analystfivestd22 is the 22-day standard deviation on the
top quintile portfolio formed by the number of analysts following the firm (obtained from IBES). Analystonestd22 is the bottom
quintile portfolio. Analystfourstd22, analystthreestd22, and analysttwostd22 are the fourth, third and second quintile portfolios,
respectively. Agefivestd22 is the 22-day standard deviation on the top quintile portfolio formed by the age of the firm.
Ageonestd22 is the bottom quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are the fourth, third and second
quintile portfolios, respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been
on CRSP. Divfivestd22 is the 22-day standard deviation on the top quintile portfolio formed by the dividend payout ratio of the
firm. Divonestd22 is the bottom quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third and second
quintile portfolios, respectively Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
Roefivestd22 is the 22-day standard deviation on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is
the bottom quintile portfolio. Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and second quintile portfolios,
respectively. Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity
(BE). Earnings (E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred
153
taxes (Item 50 of Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year
based on data for the fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of
year t+1. In panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high
beta, and portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal
year t-1. The returns on the portfolios are measured from July of year t to June of year t+1.The future holding period returns are
measured every Friday. I employ Newey and West (1987) standard errors to account for residual correlation due to overlapping
portfolio returns.
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIXRISK, VIXSENT,Lagged Portfolio Standard
Deviation, and Lagged Market Standard Deviation
Table 27-Continued
COEFFICIENT
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
ANALYSTTHREESTD22
ANALYSTTWOSTD22
ANALYSTONESTD22
T-STAT
PORTFOLIO
AGEFIVESTD22
COEFFICIENT
T-STAT
INTERCEPT
-0.487
-5.860**
INTERCEPT
-0.339
-5.770**
VIXRISK
0.419
5.240**
VIXRISK
0.316
5.560**
VIXSENT
0.353
3.700**
VIXSENT
0.208
3.180**
LAGPORT
0.427
3.600**
LAGPORT
0.348
3.630**
LAGSP500
-0.195
-1.500
LAGSP500
-0.153
-2.320*
INTERCEPT
-0.396
-4.460**
INTERCEPT
-0.355
-5.420**
VIXRISK
0.357
3.970**
VIXRISK
0.357
5.340**
VIXSENT
0.299
2.870**
VIXSENT
0.166
2.140*
LAGPORT
0.457
4.320**
LAGPORT
0.308
3.160**
LAGSP500
-0.224
-1.830
LAGSP500
-0.101
-1.090
AGEFOURSTD22
INTERCEPT
-0.339
-3.680**
VIXRISK
0.334
3.410**
AGETHREESTD22
INTERCEPT
-0.376
-4.890**
VIXRISK
0.376
4.810**
VIXSENT
0.230
2.290*
VIXSENT
0.180
2.030*
LAGPORT
0.476
4.300**
LAGPORT
0.304
3.070**
LAGSP500
-0.238
-1.950
INTERCEPT
-0.268
-2.990**
VIXRISK
0.281
3.040**
VIXSENT
0.179
1.960
VIXSENT
0.164
1.790
LAGPORT
0.369
3.270**
LAGPORT
0.371
4.130**
LAGSP500
-0.145
-1.170
INTERCEPT
-0.231
-3.170**
VIXRISK
0.249
VIXSENT
0.139
LAGPORT
LAGSP500
AGETWOSTD22
LAGSP500
-0.090
-0.830
INTERCEPT
-0.402
-4.950**
VIXRISK
0.415
5.130**
LAGSP500
-0.121
-1.130
INTERCEPT
-0.489
-4.510**
3.280**
VIXRISK
0.554
5.230**
1.760
VIXSENT
0.084
0.680
0.291
3.000**
LAGPORT
0.576
6.160**
-0.100
-1.020
154
LAGSP500
-0.253
-1.500
AGEONESTD22
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
INTERCEPT
-0.314
-4.610**
DIVFIVESTD22
INTERCEPT
-0.306
-4.860**
VIXRISK
0.230
3.460**
VIXRISK
0.216
3.690**
VIXSENT
0.348
4.190**
VIXSENT
0.360
4.540**
LAGPORT
0.098
0.800
LAGPORT
0.159
1.530
LAGSP500
0.025
0.250
LAGSP500
-0.084
-1.090
INTERCEPT
-0.299
-4.250**
INTERCEPT
-0.237
-3.470**
VIXRISK
0.231
3.220**
VIXRISK
0.179
2.810**
PORTFOLIO
ROEFIVESTD22
ROEFOURSTD22
ROETHREESTD22
ROETWOSTD22
ROEONESTD22
DIVFOURSTD22
VIXSENT
0.310
3.680**
VIXSENT
0.289
4.060**
LAGPORT
0.200
1.590
LAGPORT
0.418
4.570**
LAGSP500
-0.013
-0.120
LAGSP500
-0.209
-2.930**
INTERCEPT
-0.267
-3.940**
INTERCEPT
-0.227
-3.620**
VIXRISK
0.215
3.100**
VIXRISK
0.184
3.060**
VIXSENT
0.275
3.490**
VIXSENT
0.257
3.610**
LAGPORT
0.233
1.980*
LAGPORT
0.426
4.400**
LAGSP500
-0.036
-0.370
LAGSP500
-0.198
-2.670**
INTERCEPT
-0.254
-3.440**
INTERCEPT
-0.237
-3.870**
VIXRISK
0.210
2.830**
VIXRISK
0.196
3.150**
VIXSENT
0.268
3.400**
VIXSENT
0.250
3.530**
LAGPORT
0.218
1.890
LAGPORT
0.464
5.340**
LAGSP500
-0.036
-0.330
LAGSP500
-0.203
-3.270**
INTERCEPT
-0.281
-3.610**
INTERCEPT
-0.273
-3.370**
VIXRISK
0.262
3.250**
VIXRISK
0.219
2.730**
VIXSENT
0.235
2.690**
VIXSENT
0.295
3.520**
DIVTHREESTD22
DIVTWOSTD22
DIVONESTD22
LAGPORT
0.265
2.330*
LAGPORT
0.447
4.580**
LAGSP500
-0.082
-0.710
LAGSP500
-0.219
-2.490*
Table 27-Continued
155
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIXRISK, VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market
Standard Deviation
PORTFOLIO
R111
R112
R113
R121
R122
R123
COEFFICIENT
T-STAT
INTERCEPT
-0.201
-3.410**
VIXRISK
0.184
2.940**
VIXSENT
0.189
2.710**
LAGPORT
0.370
3.560**
LAGSP500
-0.097
-1.290
INTERCEPT
-0.269
-3.380**
VIXRISK
0.215
2.740**
VIXSENT
0.315
3.410*
LAGPORT
0.267
2.390*
LAGSP500
-0.094
-0.940
INTERCEPT
-0.523
-4.120**
VIXRISK
0.493
3.900**
VIXSENT
0.345
2.490*
LAGPORT
0.382
3.490**
LAGSP500
-0.065
-0.350
INTERCEPT
-0.279
-4.600**
VIXRISK
0.308
4.960**
VIXSENT
0.113
1.840
LAGPORT
0.661
6.210**
LAGSP500
-0.263
-2.770**
INTERCEPT
-0.366
-5.390**
VIXRISK
0.314
4.740**
VIXSENT
0.308
4.090**
LAGPORT
0.380
3.820**
LAGSP500
-0.185
-2.100*
INTERCEPT
-0.706
-6.200**
VIXRISK
0.703
6.290**
VIXSENT
0.341
2.730**
LAGPORT
0.721
6.930**
LAGSP500
-0.710
-4.290**
Table 27-Continued
156
PORTFOLIO
R211
R212
R213
R221
COEFFICIENT
T-STAT
INTERCEPT
-0.180
-3.580**
VIXRISK
0.181
3.490**
VIXSENT
0.153
2.370*
LAGPORT
0.347
3.280**
LAGSP500
-0.132
-2.310*
INTERCEPT
-0.276
-3.600**
VIXRISK
0.245
3.280**
VIXSENT
0.261
2.740**
LAGPORT
0.459
4.890**
LAGSP500
-0.232
-2.760**
INTERCEPT
-0.479
-4.380**
VIXRISK
0.450
4.210**
VIXSENT
0.343
2.810**
LAGPORT
0.449
5.080**
LAGSP500
-0.254
-1.800
INTERCEPT
-0.149
-1.970*
VIXRISK
0.226
3.120**
VIXSENT
0.014
0.190
LAGPORT
0.291
3.230**
LAGSP500
0.122
1.310
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIXRISK, VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market
Standard Deviation (Contd)
PORTFOLIO
R222
ESTIMATE
T-STAT
-0.363
-4.680**
VIXRISK
0.313
4.350**
VIXSENT
0.312
3.240**
LAGPORT
0.303
3.470**
INTERCEPT
Table 27-Continued
157
PORTFOLIO
R223
ESTIMATE
T-STAT
LAGSP500
-0.112
INTERCEPT
-0.545
-5.100**
0.488
4.970**
VIXRISK
-1.16
VIXSENT
0.388
3.360**
LAGPORT
0.419
4.100**
LAGSP500
-0.24
-1.65
Table 28
Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, VIXSENT, GARCH Forecast,
and Lagged Market Standard Deviation
The table below shows the estimation results of equation (9) with weekly data from July 1996 to June 2005:
RSD pt22 = α p + rpVIXRISKt+ spVIXSENTt +gpGARCHt+ mpLAGSP500t+ept
RSD 22
pt
(9)
is the 22-day future realized standard deviation for portfolio p from day t, where t is the date of observation of VIX.
VIXRISK is the risk component of VIX estimated from equation (2) in essay two. VIXSENT is the sentiment component of VIX
estimated from equation (7) in essay two. GARCH is the one-day ahead forecast of standard deviation calculated using rolling
22-day GARCH (1,1) parameter estimates. LAGSP500 is the standard deviation over the previous 22 days from day t, where day
t is the date of observation of VIX. In panel A, Analystfivestd22 is the 22-day standard deviation on the top quintile portfolio
formed by the number of analysts following the firm (obtained from IBES). Analystonestd22 is the bottom quintile portfolio.
Analystfourstd22, analystthreestd22, and analysttwostd22 are the fourth, third and second quintile portfolios, respectively.
Agefivestd22 is the 22-day standard deviation on the top quintile portfolio formed by the age of the firm. Ageonestd22 is the
bottom quintile portfolio. Agefourstd22, agethreestd22, and agetwostd22 are the fourth, third and second quintile portfolios,
respectively. The age of the firm is measured by the number of years (to the nearest month) the firm has been on CRSP.
Divfivestd22 is the 22-day standard deviation on the top quintile portfolio formed by the dividend payout ratio of the firm.
Divonestd22 is the bottom quintile portfolio. Divfourstd22, divthreestd22 and divtwostd22 are the fourth, third and second
quintile portfolios, respectively Dividend payout is calculated as dividends (D) divided by book value of equity (BE). Dividends
(D) is dividends per share at the ex date (Item 26 of Compustat) times shares outstanding (Item 25 of Compustat). Book value of
equity (BE) is shareholders equity (Item 60 of Compustat) plus balance sheet deferred taxes (Item 35 of Compustat).
158
Roefivestd22 is the 22-day standard deviation on the top quintile portfolio formed by the profitability of the firm. Roeoneret22 is
the bottom quintile portfolio. Roefourstd22, Roethreestd22 and Roetwostd22 are the fourth, third and second quintile portfolios,
respectively. Profitability is measured by the ratio of return on equity, which is earnings (E) divided by book value of equity
(BE). Earnings (E) are calculated as income before extraordinary items (Item 18 of Compustat) plus income statement deferred
taxes (Item 50 of Compustat) minus preferred dividends (Item 19 of Compustat). The quintile portfolios are formed each year
based on data for the fiscal year t-1. The equally-weighted returns on the portfolios are measured from July of year t to June of
year t+1. In panel B, portfolio R111 represents low B/M, low size, and low beta, portfolio R113 is low B/M, low size, and high
beta, and portfolio R223 is high B/M, high size, and high beta. The portfolios are formed each year based on data for the fiscal
year t-1. The returns on the portfolios are measured from July of year t to June of year t+1.The future holding period returns are
measured every Friday. I employ Newey and West (1987) standard errors to account for residual correlation due to overlapping
portfolio returns.
PanelA: Regression Estimates of 22-day Future Realized Standard Deviations of Portfolios Sorted Univariately by
Number of Analysts, Age, Profitability, and Dividend Payout on VIXRISK,VIXSENT, GARCH Forecast, and Lagged
Market Standard Deviation
PORTFOLIO
ANALYSTFIVESTD22
ANALYSTFOURSTD22
ANALYSTTHREESTD22
COEFFICIENT
T-STAT
PORTFOLIO
INTERCEPT
-0.466
-5.700**
ROEFIVESTD22
COEFFICIENT
T-STAT
INTERCEPT
-0.320
-4.870**
VIXRISK
0.402
5.090**
VIXRISK
0.252
4.050**
VIXSENT
0.339
3.650**
VIXSENT
0.313
3.940**
GARCH
0.403
3.970**
GARCH
0.255
2.300*
LAGSP500
-0.136
-1.150
LAGSP500
-0.067
-0.690
INTERCEPT
-0.353
-4.160**
INTERCEPT
-0.291
-4.360**
VIXRISK
0.319
3.810**
VIXRISK
0.246
3.740**
VIXSENT
0.270
2.740**
VIXSENT
0.261
3.220**
GARCH
0.509
5.480**
GARCH
0.339
3.470**
LAGSP500
-0.197
-1.730
INTERCEPT
-0.259
-3.150**
VIXRISK
0.263
VIXSENT
GARCH
ROEFOURSTD22
LAGSP500
-0.083
-0.910
INTERCEPT
-0.247
-3.910**
3.030**
VIXRISK
0.208
3.360**
0.188
1.950
VIXSENT
0.239
3.130**
0.450
5.140**
GARCH
0.344
3.530**
ROETHREESTD22
Table 28-Continued
PORTFOLIO
LAGSP500
COEFFICIENT
T-STAT
-0.113
-1.060
PORTFOLIO
LAGSP500
159
COEFFICIENT
T-STAT
-0.073
-0.860
ANALYSTTWOSTD22
ANALYSTONESTD22
INTERCEPT
-0.228
-2.900**
VIXRISK
0.249
VIXSENT
INTERCEPT
-0.238
-3.430**
3.120**
VIXRISK
0.219
3.180**
0.146
1.700
VIXSENT
0.213
2.750**
GARCH
0.430
4.930**
GARCH
0.335
3.680**
LAGSP500
-0.129
-1.220
LAGSP500
-0.081
-0.840
INTERCEPT
-0.166
-2.480*
INTERCEPT
-0.257
-3.520**
AGEFOURSTD22
AGETHREESTD22
AGETWOSTD22
ROEONESTD22
VIXRISK
0.196
2.900**
VIXRISK
0.240
3.240**
VIXSENT
0.101
1.270
VIXSENT
0.221
2.620**
GARCH
0.261
3.230**
GARCH
0.274
2.660**
LAGSP500
-0.026
-0.300
LAGSP500
-0.052
-0.480
COEFFICIENT
T-STAT
PORTFOLIO
COEFFICIENT
T-STAT
-0.321
-5.540**
DIVFIVESTD22
-0.303
-4.860**
PORTFOLIO
AGEFIVESTD22
ROETWOSTD22
INTERCEPT
INTERCEPT
VIXRISK
0.301
5.270**
VIXRISK
0.215
3.800**
VIXSENT
0.200
3.290**
VIXSENT
0.352
4.620**
GARCH
0.359
4.250**
GARCH
0.165
2.610**
LAGSP500
-0.145
-2.100*
INTERCEPT
-0.315
-5.050**
LAGSP500
-0.074
-1.130
INTERCEPT
-0.214
-3.180**
VIXRISK
0.337
5.140**
VIXRISK
0.147
2.390*
VIXSENT
0.119
1.560
VIXSENT
0.304
4.390**
GARCH
0.405
4.060**
GARCH
0.315
4.110**
LAGSP500
-0.101
-1.120
LAGSP500
-0.133
-2.000*
INTERCEPT
-0.346
-4.730**
INTERCEPT
-0.208
-3.420**
DIVFOURSTD22
DIVTHREESTD22
VIXRISK
0.358
4.910**
VIXRISK
0.161
2.800**
VIXSENT
0.150
1.740
VIXSENT
0.263
3.950**
GARCH
0.397
4.290**
GARCH
0.391
5.110**
LAGSP500
-0.166
-2.390*
INTERCEPT
-0.209
-3.480**
LAGSP500
-0.119
-1.160
INTERCEPT
-0.344
-4.420**
VIXRISK
0.360
4.650**
VIXRISK
0.171
2.860**
VIXSENT
0.140
1.590
VIXSENT
0.237
3.590**
GARCH
0.404
4.520**
GARCH
0.476
6.580**
COEFFICIENT
T-STAT
LAGSP500
-0.178
-2.900**
DIVTWOSTD22
Table 28-Continued
PORTFOLIO
AGEONESTD22
COEFFICIENT
T-STAT
LAGSP500
-0.080
-0.700
INTERCEPT
-0.374
-3.700**
INTERCEPT
-0.257
-3.400**
VIXRISK
0.452
4.410**
VIXRISK
0.210
2.850**
VIXSENT
0.024
0.210
VIXSENT
0.271
3.470**
GARCH
0.416
3.930**
GARCH
0.496
6.760**
160
PORTFOLIO
DIVONESTD22
LAGSP500
0.019
0.120
LAGSP500
-0.212
-2.800**
Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Bookto-Market Equity, Size, and Beta on VIXRISK,VIXSENT, GARCH Forecast, and Lagged Market Standard Deviation
PORTFOLIO
R111
R112
R113
R121
COEFFICIENT
T-STAT
INTERCEPT
-0.136
-2.380*
VIXRISK
0.123
2.040*
VIXSENT
0.165
2.450*
GARCH
0.322
3.940**
LAGSP500
-0.005
-0.070
INTERCEPT
-0.252
-3.470**
VIXRISK
0.227
3.070**
VIXSENT
0.251
2.910**
GARCH
0.403
4.610**
LAGSP500
-0.151
-1.570
INTERCEPT
-0.478
-4.030**
VIXRISK
0.458
3.910**
VIXSENT
0.305
2.290*
GARCH
0.453
4.940**
LAGSP500
-0.082
-0.480
INTERCEPT
-0.219
-3.890**
Table 28-Continued
PORTFOLIO
R122
COEFFICIENT
T-STAT
VIXRISK
0.267
4.620**
VIXSENT
0.069
1.100
GARCH
0.515
6.080**
LAGSP500
-0.106
-1.350
INTERCEPT
-0.364
-5.150**
161
R123
R211
R212
VIXRISK
0.297
4.280**
VIXSENT
0.335
4.280**
GARCH
0.179
1.980*
LAGSP500
-0.017
-0.210
INTERCEPT
-0.691
-6.420**
VIXRISK
0.689
6.680**
VIXSENT
0.315
2.620**
GARCH
0.828
7.820**
LAGSP500
-0.749
-4.820**
INTERCEPT
-0.124
-2.410*
VIXRISK
0.128
2.590**
VIXSENT
0.138
2.240*
GARCH
0.249
2.410*
LAGSP500
-0.043
-0.770
INTERCEPT
-0.211
-2.830**
VIXRISK
0.189
2.610**
VIXSENT
0.230
2.580**
GARCH
0.453
6.230**
LAGSP500
-0.168
-1.980*
Table 28-Continued
PORTFOLIO
R213
R221
COEFFICIENT
T-STAT
INTERCEPT
-0.396
-3.790**
VIXRISK
0.395
3.830**
VIXSENT
0.269
2.340*
GARCH
0.470
6.270**
LAGSP500
-0.182
-1.360
INTERCEPT
-0.106
-1.370
VIXRISK
0.207
2.830**
162
R222
R223
VIXSENT
-0.028
-0.370
GARCH
0.122
1.770
LAGSP500
0.262
3.090**
INTERCEPT
-0.356
-4.590**
VIXRISK
0.299
4.130**
VIXSENT
0.324
3.450**
GARCH
0.228
3.890**
LAGSP500
-0.045
-0.520
INTERCEPT
-0.507
-4.790**
VIXRISK
0.464
4.710**
VIXSENT
0.350
3.000**
GARCH
0.364
4.530**
LAGSP500
-0.128
-1.080
163
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BIOGRAPHICAL SKETCH
EDUCATION
Ph.D. in Finance, Florida State University, expected 2008.
M.S. in Finance, Boston College, 2004.
M.Com with Specialization in Finance, University of Calcutta, 1999.
RESEARCH INTERESTS
Security Analysis and Portfolio Management, Derivatives and Risk Management, Behavioral
Finance and Corporate Finance.
TEACHING INTERESTS
Investments, Corporate Finance, Financial Markets, Econometrics.
COURSES TAUGHT
QMB 3200:Quantitative Methods in Business
FIN 3244:Financial Markets and Institutions
WORKING PAPERS
“Decomposing Implied Volatility: Sentiment and Risk”, May. 2006 – Job Market Paper.
“Implied Volatility and Future Portfolio Returns”, with James S. Doran and David R. Peterson,
Nov. 2006.
“Behavioral Finance: Are the Disciples Profiting from the Doctrine?” With Colbrin Wright and
Vaneesha Boney, August 2004.
170