Essays on the Forecasting Power of Implied Volatility Prithviraj Shyamal Banerjee

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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

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

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

LIST OF FIGURES

Figure 1: Mean Returns for the 12 B/M, Size and Beta Portfolios...... 34

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.

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 The notion of implied volatility was introduced by Schmalensee and Trippi (1978). 2 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. 4See 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)). 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 option- trading 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-to-

7 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.

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-by- minute 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 small- size 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-to- market 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 cross- sectional 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.

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

13 predictor of future realized volatility. 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

r i (1) σ tt +→ τ =α + βσt +εt

r where σ tt +→ τ is an asset’s realized volatility, calculated using returns from day t through

i t+ τ, and σ t 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 risk- free 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:

µ −r E[]λ < f (2) σ r

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):

µ−r E λ][ < f (3) α +βσi

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:

2 2 2 (4) ∆σ = (κ l (θ l − σ ) + F (θ ,ts |σ ))∆t + ξσ e 2 2 2 2 (5) σ t = (κ l (θ l − σ t−1 ) + F (θ ,ts |σ t −1 ))∆t + σ t −1 + ξσ t−1et

2 2 where F (θ ,ts |σ t −1 ) = κ s (θ ,ts − σ t −1 ) if σ > Θ 2 (6) F (θ ,ts |σ t−1 ) = 0 if σ ≤ Θ

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:

R −r E λ][ < f 2 2 2 (7) α + β κ (θll −σ ) + F(θ ,ts |σ ))∆t +σ

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:

2 2 1) σ > θl andσ > θ ,ts withσ > Θ

2 2 2) σ > θl andσ < θ ,ts withσ > Θ

2 3) σ > θl withσ < Θ , and

2 4) σ < θ l withσ < 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 mean-

15 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

2 below the short-term mean result in a positive value for κ (θ s −σ ) , 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. 17 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/

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 holding- period 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:

22 (8a) Rpt =α p +υpVIXt +ε pt 44 (8b) Rpt =α p +υpVIXt +ε pt

22 where R pt is the 22-day compounded future holding period excess returns at time t for

44 portfolio p, and R pt 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:

22 22 22 (9a) Rpt = α p +υ pVIXt + β p MKTt +γ p HMLt 22 22 +ς p SMBt + µ pUMDt +ε pt

R44 = α +υ VIX + β MKT 44 +γ HML44 pt p p t p t p t (9b) 44 44 +ς p SMBt + µ pUMDt +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.

22 44 HMLt and HMLt are the 22-day and 44-day geometric future returns, respectively, on the Fama and French (1993) HML factor formed by compounding the daily HML values.

22 44 SMBt and SMBt 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.

22 44 MKTt and MKTt 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.

22 44 UMDt and UMDt 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:

22 22 22 Rpt =α p +υ pVIXt + hp HDt + l p LDt + β pMKTt +γ p HMLt 22 22 (10a) +ς pSMBt + µ pUMDt +ε pt 44 44 44 Rpt =α p +υ pVIXt + hp HDt + l p LDt + β pMKTt +γ p HMLt

+ς SMB44 + µ UMD44 +ε p t p t 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 trading- days 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 = α + υ VIX + ε pt p p t pt (11) MKT 44 = α + υ VIX + ε pt p p t pt (12) SMB 22 = α + υ VIX + ε pt p p t pt (13) SMB 44 = α + υ VIX + ε pt p p t pt (14) HML 22 = α + υ VIX + ε pt p p t pt (15) HML 44 = α + υ VIX + ε pt p p t pt (16) UMD 22 = α + υ VIX + ε pt p p t pt (17) UMD 44 = α + υ VIX + ε pt p p t 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

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 book- to-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 44- day 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-to- market 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-to- market 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.

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.

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 High Be ta 4.50%

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

Figure 1-Continued

Panel B

5.00% Low Beta 44 Day Return Mid Beta High Beta 4.50%

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

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.

22-Day 44-Day

Returns Returns

VIX 0.031 0.056

(2.12)** (3.11)**

Constant 0.001 0.003

(0.17) (0.53)

Observations 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.

Table 2-Continued

22-Day Returns 44-Day Returns

Portfolio r11 r21 r31 r41 r51 r11 r21 r31 r41 r51

VIX 0.032 0.014 0.011 0.006 -0.021 0.145 0.101 0.089 0.081 0.034

(0.88) (0.51) (0.47) (0.27) (0.98) (2.54)* (2.35)* (2.57)* (2.23)* (1.00)

Constant -0.008 0.004 0.006 0.009 0.015 -0.033 -0.006 -0.002 0.004 0.015

(1.14) (0.75) (1.26) (1.95) (3.47)** (2.84)** (0.72) (0.26) (0.57) (2.11)*

Observations 4765 4765 4765 4765 4765 4744 4744 4744 4744 4744

Portfolio r12 r22 r32 r42 r52 r12 r22 r32 r42 r52

VIX 0.055 0.035 0.016 0.006 -0.010 0.156 0.127 0.082 0.062 0.053

(1.60) (1.22) (0.73) (0.27) (0.05) (3.50)** (3.41)** (2.85)** (2.14)* (1.67)

Constant -0.009 -0.002 0.005 0.008 0.009 -0.027 -0.015 0.000 0.004 0.006

(1.26) (0.29) (1.21) (1.83) (2.09)* (2.97)** (2.04)* (0.07) (0.76) (1.01)

Observations 4765 4765 4765 4765 4765 4744 4744 4744 4744 4744

Portfolio r13 r23 r33 r43 r53 r13 r23 r33 r43 r53

VIX 0.056 0.043 0.021 0.016 0.022 0.131 0.114 0.073 0.060 0.080

(1.78) (1.73) (1.00) (0.80) (1.03) (3.43)** (3.63)** (2.77)** (2.35)* (2.69)**

Constant -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) (2.47)* (1.66) (0.53) (0.68) (0.75)

Observations 4765 4765 4765 4765 4765 4744 4744 4744 4744 4744

Portfolio r14 r24 r34 r44 r54 r14 r24 r34 r44 r54

VIX 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)

Constant -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) (2.50)* (1.60) (0.05) (0.80) (1.19)

Observations 4765 4765 4765 4765 4765 4744 4744 4744 4744 4744

Portfolio r15 r25 r35 r45 r55 r15 r25 r35 r45 r55

VIX 0.047 0.019 0.026 0.013 0.001 0.077 0.033 0.055 0.022 0.012

(2.38)* (1.05) (1.55) (0.83) (0.03) (3.31)** (1.68) (2.73)** (1.18) (0.54)

Constant -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) (2.20)*

Observations 4765 4765 4765 4765 4765 4744 4744 4744 4744 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

r11 r21 r31 r41 r51 r15 r25 r35 r45 r55

VIX -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)

MKT 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)**

SMB 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)**

HML -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)**

UMD -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)**

Constant -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)

Observations 4765 4765 4765 4765 4765 4765 4765 4765 4765 4765

Table 3-Continued

Panel B: 44-Day Returns

r11 r21 r31 r41 r51 r15 r25 r35 r45 r55

VIX 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)

MKT 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)**

SMB 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)**

HML -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)**

UMD -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)**

Constant -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)

Observations 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.

Table 4-Continued

22-Day Returns 44-Day Returns

Low B/M, Small Size Low Beta 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%

High B/M, Small Size

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%

Low B/M, Big Size

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%

High B/M, Big Size

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%

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

22-Day 44-Day

Returns Returns

r111 r112 r113 r111 r112 r113

VIX 0.011 0.047 0.128 0.081 0.148 0.292

(0.45) (1.58) (2.69)** (2.51)* (4.00)** (4.66)**

Constant 0.009 0.001 -0.018 0.005 -0.009 -0.043

(1.85) (0.17) (1.93) (0.81) (1.24) (3.45)**

Observations 4765 4765 4765 4744 4744 4744

r121 r122 r123 r121 r122 r123

VIX 0.009 0.035 0.080 0.036 0.058 0.138

(0.46) (2.01)* (3.06)** (1.51) (3.28)** (4.15)**

Constant 0.004 0.001 -0.010 0.005 0.002 -0.016

(1.17) (0.02) (2.05)* (0.98) (0.57) (2.53)*

Observations 4765 4765 4765 4744 4744 4744

r211 r212 r213 r211 r212 r213

VIX 0.003 0.029 0.099 0.078 0.119 0.275

(0.12) (1.10) (2.28)* (2.33)* (3.18)** (4.63)**

Constant 0.014 0.008 -0.004 0.014 0.003 -0.024

(3.30)** (1.45) (0.51) (2.13)* (0.35) (2.04)*

Observations 4765 4765 4765 4744 4744 4744

r221 r222 r223 r221 r222 r223

VIX 0.010 0.035 0.061 0.053 0.078 0.133

(0.52) (2.05)* (2.34)* (2.21)* (3.77)** (3.87)**

Constant 0.007 0.003 -0.004 0.007 0.004 -0.011

(1.92) (0.77) (0.83) (1.40) (0.84) (1.57)

Observations 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.

r111 r112 R113 r121 r122 r123 VIX 0.002 0.027 0.059 -0.005 0.008 0.013

(0.26) (2.89)** (6.08)** (0.32) (1.12) (1.96)*

MKT 0.880 1.042 1.311 0.786 0.909 1.080

(48.87)** (55.36)** (56.83)** (21.51)** (34.83)** (70.60)**

SMB 0.745 0.829 1.162 0.028 -0.241 -0.160

(25.33)** (25.95)** (39.30)** (0.68) (8.16)** (6.47)**

HML 0.424 0.328 -0.377 0.367 0.263 -0.468

(16.37)** (10.55)** (10.39)** (8.86)** (7.17)** (20.07)**

UMD -0.084 -0.136 -0.443 -0.041 -0.087 -0.229

(4.05)** (5.48)** (14.40)** (1.22) (3.32)** (12.17)**

Constant 0.005 -0.001 -0.005 0.001 0.000 0.001

(3.23)** (0.49) (2.76)** (0.44) (0.25) (0.68)

Observations 4765 4765 4765 4765 4765 4765

r211 r212 r213 r221 r222 r223 VIX 0.002 0.022 0.064 0.008 0.017 0.031

(0.26) (3.16)** (5.65)** (0.55) (2.14)* (3.09)**

MKT 0.862 1.095 1.372 0.887 0.985 1.202

(51.63)** (61.02)** (59.94)** (20.89)** (44.27)** (55.63)**

SMB 0.809 0.855 1.267 0.052 -0.010 0.281

(29.60)** (24.95)** (34.87)** (1.14) (0.35) (9.15)**

HML 0.651 0.708 0.400 0.788 0.652 0.444

(27.21)** (23.90)** (10.47)** (16.28)** (18.13)** (11.52)**

UMD -0.129 -0.161 -0.365 -0.085 -0.219 -0.225

Table 6-Continued

r111 r112 R113 r121 r122 r123

(6.30)** (7.07)** (12.15)** (2.41)* (8.79)** (9.38)**

Constant 0.008 0.002 -0.003 0.000 0.000 -0.005

(6.48)** (1.06) (1.30) (0.04) (0.08) (2.24)*

Observations 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 r112 R113 r121 r122 r123 VIX 0.018 0.060 0.103 -0.003 0.007 0.020

(1.47) (4.15)** (6.40)** (0.10) (0.55) (1.68)

MKT 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

r111 r112 R113 r121 r122 r123

SMB 0.757 0.874 1.190 0.041 -0.223 -0.173

(19.00)** (21.08)** (30.52)** (0.87) (6.67)** (6.20)**

HML 0.439 0.344 -0.415 0.353 0.251 -0.444

(14.23)** (8.96)** (9.14)** (8.25)** (5.41)** (16.92)**

UMD -0.081 -0.155 -0.415 -0.084 -0.137 -0.196

(3.05)** (5.13)** (12.38)** (2.16)* (4.39)** (9.26)**

Constant 0.007 -0.002 -0.007 0.003 0.003 0.002

(2.61)** (0.62) (1.95) (0.44) (0.89) (0.75)

Observations 4744 4744 4744 4744 4744 4744

r211 r212 R213 r221 r222 r223 VIX 0.024 0.048 0.133 0.033 0.028 0.050

(1.99)* (4.01)** (7.42)** (1.15) (1.83) (2.89)**

MKT 0.874 1.065 1.316 0.854 0.913 1.153

(38.99)** (45.72)** (46.29)** (17.38)** (29.39)** (40.26)**

SMB 0.846 0.878 1.324 0.023 0.002 0.278

(23.61)** (19.61)** (27.10)** (0.45) (0.05) (6.15)**

HML 0.700 0.708 0.379 0.833 0.628 0.413

(23.76)** (20.27)** (7.95)** (14.91)** (15.11)** (8.04)**

UMD -0.140 -0.174 -0.363 -0.145 -0.275 -0.225

(6.06)** (6.30)** (10.42)** (3.55)** (8.87)** (7.11)**

Constant 0.013 0.003 -0.005 -0.003 0.003 -0.006

(5.19)** (1.23) (1.34) (0.44) (0.96) (1.57)

Observations 4744 4744 4744 4744 4744 4744

* significant at 5% level; ** significant at 1% level

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 44-

day 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%). Newey-

West 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

R111 r112 r113 r121 r122 r123 r211 r212 r213 r221 r222 r223 VIX 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)

HD 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)

LD 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)*

MKT 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 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)

Obs 574 574 574 574 574 574 574 574 574 574 574 574

Table 8-Continued

Panel B: High VIX for 44-Day Returns

R111 r112 r113 r121 r122 r123 r211 r212 r213 r221 r222 r223 VIX 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)

HD 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)**

LD 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)

MKT 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)**

SMB 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)**

HML 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)**

UMD 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)**

Cons 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)

Obs 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.

Table 9-Continued

22-Day Returns 44-Day Returns

MKT SMB HML UMD MKT SMB HML UMD

VIX 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)*

Constant -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)**

Observations 4765 4765 4765 4765 4744 4744 4744 4744

* significant at 5% level; ** significant at 1% level

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/

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 30 http://www.cboe.com/micro/vix/introduction.aspx 31 https://www.federalreserve.gov/releases 32 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/

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 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). 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, 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 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 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. 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. 36 Only firms with ordinary common equity (as classified by CRSP) are used. Thus, ADRs, REITS, and units of beneficial interest are excluded.

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 (2)

57 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:

22 Rpt = α p + vp VIXt+ ept (3)

44 R pt = α p + vp VIXt+ept (4)

22 44 R pt is the 22-day compounded future holding period excess returns for portfolio p and R pt 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.

Then, to estimate the forecasting power of only the risk component of VIX, I estimate the following regression:

22 Rpt = α p + sp VIXRISKt+ ept (5)

44 R pt = 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:

22 Rpt = α p + sp VIXSENTt+ ept (8)

44 R pt = 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:

22 Rpt = α p + rpVIXRISKt+ sp VIXSENTt+ept (10)

44 R pt = 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:

22 Rpt = α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt+ rp RIPOORt+ cpCCOR+ept (12)

44 R pt =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.

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-to- market 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).

Table 10-Continued

Panel A: 22-Day Return

Analystfiveret22 Analystfourret22 Analystthreeret22 Analysttworet22 Analystoneret22

Mean 0.010 0.010 0.012 0.016 0.022 Standard Deviation 0.063 0.073 0.076 0.076 0.070

Agefiveret22 Agefourret22 Agethreeret22 Agetworet22 Ageoneret22 Mean 0.015 0.022 0.022 0.023 0.012 Standard Deviation 0.045 0.059 0.070 0.079 0.095

Roefiveret22 Roefourret22 Roethreeret22 Roetworet22 Roeoneret22 Mean 0.012 0.013 0.015 0.018 0.020 Standard Deviation 0.057 0.058 0.058 0.063 0.072

Divfiveret22 Divfourret22 Divthreeret22 Divtworet22 Divoneret22 Mean 0.012 0.011 0.012 0.015 0.012 Standard Deviation 0.044 0.045 0.047 0.050 0.059 R111 R112 R113 R121 R122 R123 Mean 0.012 0.012 0.008 0.006 0.008 0.004 Standard Deviation 0.052 0.060 0.109 0.046 0.046 0.074

R211 R212 R213 R221 R222 R223 Mean 0.017 0.015 0.016 0.007 0.011 0.009 Standard Deviation 0.051 0.059 0.093 0.053 0.054 0.069

Table 10-Continued

Panel B: 44-Day Return

Analystfiveret44 Analystfourret44 Analystthreeret44 Analysttworet44 Analystoneret44 Mean 0.021 0.020 0.025 0.033 0.048 Standard Deviation 0.093 0.109 0.116 0.115 0.109

Agefiveret44 Agefourret44 Agethreeret44 Agetworet44 Ageoneret44 Mean 0.033 0.048 0.049 0.050 0.028 Standard Deviation 0.067 0.090 0.107 0.122 0.145

Roefiveret44 Roefourret44 Roethreeret44 Roetworet44 Roeoneret44 Mean 0.026 0.028 0.032 0.039 0.043 Standard Deviation 0.083 0.085 0.088 0.094 0.109

Divfiveret44 Divfourret44 Divthreeret44 Divtworet44 Divoneret44 Mean 0.023 0.023 0.024 0.031 0.025 Standard Deviation 0.064 0.068 0.069 0.073 0.086 R111 R112 R113 R121 R122 R123 Mean 0.027 0.026 0.016 0.014 0.016 0.004 Standard Deviation 0.077 0.087 0.162 0.067 0.064 0.111

R211 R212 R213 R221 R222 R223 Mean 0.037 0.033 0.034 0.016 0.023 0.017 Standard Deviation 0.079 0.089 0.140 0.078 0.078 0.098

Table 10-Continued

Panel C: Other Variables

VXO Rm-Rf SMB HML Mean 0.238 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’

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)

COEFFICIENT T-STAT INTERCEPT 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)

COEFFICIENT T-STAT INTERCEPT 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

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

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:

22 Rpt = α p + vp VIXt+ ept (3)

22 R pt 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.

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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET22 INTERCEPT -0.024 -1.490 AGEFIVERET22 INTERCEPT 0.004 0.360 VXO 0.145 1.950 VXO 0.048 0.970 ANALYSTFOURRET22 INTERCEPT -0.023 -1.270 AGEFOURRET22 INTERCEPT 0.001 0.050 VXO 0.138 1.650 VXO 0.089 1.410 ANALYSTTHREERET22 INTERCEPT -0.014 -0.740 AGETHREERET22 INTERCEPT -0.004 -0.250 VXO 0.108 1.250 VXO 0.111 1.490 ANALYSTTWORET22 INTERCEPT -0.011 -0.620 AGETWORET22 INTERCEPT -0.010 -0.530 VXO 0.112 1.380 VXO 0.136 1.630 ANALYSTONERET22 INTERCEPT 0.002 0.140 AGEONERET22 INTERCEPT -0.024 -1.140 VXO 0.081 1.120 VXO 0.151 1.530 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVERET22 INTERCEPT -0.002 -0.110 DIVFIVERET22 INTERCEPT 0.000 0.011 VXO 0.059 0.900 VXO 0.050 0.047 ROEFOURRET22 INTERCEPT -0.003 -0.200 DIVFOURRET22 INTERCEPT -0.002 0.011 VXO 0.068 1.030 VXO 0.054 0.048 ROETHREERET22 INTERCEPT 0.000 -0.010 DIVTHREERET22 INTERCEPT 0.002 0.012 VXO 0.063 0.970 VXO 0.043 0.053 ROETWORET22 INTERCEPT 0.001 0.040 DIVTWORET22 INTERCEPT 0.009 0.012 VXO 0.075 1.080 VXO 0.023 0.054 ROEONERET22 INTERCEPT -0.002 -0.090 DIVONERET22 INTERCEPT -0.004 0.014

VXO 0.090 1.170 VXO 0.065 0.064

* significant at 5% level; ** significant at 1% level

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

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT 0.006 0.450 VXO 0.026 0.430 R112 INTERCEPT -0.008 -0.590 VXO 0.086 1.360 R113 INTERCEPT -0.050 -1.930 VXO 0.244 2.020* R121 INTERCEPT -0.005 -0.450 VXO 0.047 0.980 R122 INTERCEPT -0.014 -1.420 VXO 0.091 2.120* R123 INTERCEPT -0.037 -2.250* VXO 0.174 2.370* R211 INTERCEPT 0.017 1.360 VXO -0.001 -0.010 R212 INTERCEPT 0.010 0.670 VXO 0.024 0.350 R213 INTERCEPT -0.028 -1.180 VXO 0.185 1.690 R221 INTERCEPT 0.013 1.110 VXO -0.023 -0.450 R222 INTERCEPT -0.003 -0.320 VXO 0.060 1.380 R223 INTERCEPT -0.029 -1.810 VXO 0.159 2.280* * significant at 5% level; ** significant at 1% level

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:

44 R pt = α p + vp VIXt+ept (4)

44 R pt is the 44-day compounded future holding period excess returns for portfolio p. VIX is the Friday’s VIX observation. 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.

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.

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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET44 INTERCEPT -0.058 -1.820 AGEFIVERET44 INTERCEPT 0.003 0.120

VXO 0.322 2.400* VXO 0.122 1.380 ANALYSTFOURRET44 INTERCEPT -0.066 -1.900 AGEFOURRET44 INTERCEPT -0.007 -0.250

VXO 0.355 2.400* VXO 0.223 2.000* ANALYSTTHREERET44 INTERCEPT -0.055 -1.540 AGETHREERET44 INTERCEPT -0.023 -0.720

VXO 0.328 2.180* VXO 0.294 2.280* ANALYSTTWORET44 INTERCEPT -0.049 -1.370 AGETWORET44 INTERCEPT -0.038 -1.090

VXO 0.336 2.270* VXO 0.363 2.510* ANALYSTONERET44 INTERCEPT -0.015 -0.450 AGEONERET44 INTERCEPT -0.068 -1.670

VXO 0.256 1.970* VXO 0.395 2.260*

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVERET44 INTERCEPT -0.019 -0.680 DIVFIVERET44 INTERCEPT -0.012 -0.570

VXO 0.183 1.560 VXO 0.141 1.670 ROEFOURRET44 INTERCEPT -0.021 -0.790 DIVFOURRET44 INTERCEPT -0.017 -0.790

VXO 0.201 1.830 VXO 0.166 1.870 ROETHREERET44 INTERCEPT -0.016 -0.560 DIVTHREERET44 INTERCEPT -0.009 -0.370

VXO 0.195 1.640 VXO 0.136 1.460

ROETWORET44 INTERCEPT -0.013 -0.430 DIVTWORET44 INTERCEPT 0.004 0.180 VXO 0.212 1.710 VXO 0.107 1.090 ROEONERET44 INTERCEPT -0.021 -0.620 DIVONERET44 INTERCEPT -0.024 -0.870 VXO 0.259 1.930 VXO 0.199 1.810

* significant at 5% level; ** significant at 1% level

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 R111 INTERCEPT -0.004 -0.150 VXO 0.124 1.190 R112 INTERCEPT -0.031 -1.150 VXO 0.232 2.150* R113 INTERCEPT -0.119 -2.450* VXO 0.553 2.680** R121 INTERCEPT -0.007 -0.380 VXO 0.084 1.080 R122 INTERCEPT -0.023 -1.230 VXO 0.155 2.220* R123 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 R213 INTERCEPT -0.087 -1.940 VXO 0.499 2.570** R221 INTERCEPT 0.019 0.920 VXO -0.017 -0.210 R222 INTERCEPT -0.011 -0.520 VXO 0.142 1.720 R223 INTERCEPT -0.064 -1.990* VXO 0.333 2.56*

* significant at 5% level; ** significant at 1% level

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:

22 Rpt = α p + sp VIXRISKt+ ept (5)

22 R pt 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).

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

PORTFOLIO 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 ANALYSTTHREERET22 INTERCEPT -0.044 -0.520 AGETHREERET22 INTERCEPT -0.057 -0.770

VIXRISK 0.056 0.640 VIXRISK 0.080 1.040 ANALYSTTWORET22 INTERCEPT -0.045 -0.550 AGETWORET22 INTERCEPT -0.084 -1.000

VIXRISK 0.061 0.720 VIXRISK 0.107 1.230 ANALYSTONERET22 INTERCEPT -0.040 -0.530 AGEONERET22 INTERCEPT -0.055 -0.580

VIXRISK 0.063 0.790 VIXRISK 0.068 0.680

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVERET22 INTERCEPT -0.006 -0.100 DIVFIVERET22 INTERCEPT -0.013 -0.270

VIXRISK 0.019 0.290 VIXRISK 0.024 0.510 ROEFOURRET22 INTERCEPT -0.023 -0.360 DIVFOURRET22 INTERCEPT -0.023 -0.460

VIXRISK 0.036 0.550 VIXRISK 0.035 0.680 ROETHREERET22 INTERCEPT -0.013 -0.200 DIVTHREERET22 INTERCEPT -0.019 -0.340

VIXRISK 0.028 0.420 VIXRISK 0.031 0.560 ROETWORET22 INTERCEPT -0.030 -0.430 DIVTWORET22 INTERCEPT 0.026 0.480

VIXRISK 0.049 0.680 VIXRISK -0.011 -0.210 ROEONERET22 INTERCEPT -0.029 -0.370 DIVONERET22 INTERCEPT -0.022 -0.330

VIXRISK 0.049 0.600 VIXRISK 0.034 0.500

* significant at 5% level; ** significant at 1% level

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

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT 0.021 0.350 VIXRISK -0.009 -0.140 R112 INTERCEPT -0.013 -0.200 VIXRISK 0.026 0.380 R113 INTERCEPT -0.124 -1.020 VIXRISK 0.133 1.050 R121 INTERCEPT -0.021 -0.450 VIXRISK 0.028 0.570 R122 INTERCEPT -0.067 -1.500 VIXRISK 0.075 1.650 R123 INTERCEPT -0.103 -1.370 VIXRISK 0.108 1.410 R211 INTERCEPT 0.037 0.650 VIXRISK -0.020 -0.350 R212 INTERCEPT 0.019 0.290 VIXRISK -0.003 -0.050 R213 INTERCEPT -0.127 -1.170 VIXRISK 0.144 1.280 R221 INTERCEPT 0.059 1.060 VIXRISK -0.052 -0.910 R222 INTERCEPT -0.049 -1.010 VIXRISK 0.060 1.220 R223 INTERCEPT -0.126 -1.750 VIXRISK 0.136 1.850

* significant at 5% level; ** significant at 1% level

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:

44 R pt = α p + sp VIXRISKt+ept (6)

44 R pt is the 44-day compounded future holding period excess returns for portfolio p. 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).

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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

ANALYSTFIVERET44 INTERCEPT -0.248 -1.840 AGEFIVERET44 INTERCEPT -0.072 -0.760

VIXRISK 0.269 1.970** VIXRISK 0.104 1.090

ANALYSTFOURRET44 INTERCEPT -0.239 -1.590 AGEFOURRET44 INTERCEPT -0.157 -1.340

VIXRISK 0.259 1.690 VIXRISK 0.205 1.710

ANALYSTTHREERET44 INTERCEPT -0.248 -1.620 AGETHREERET44 INTERCEPT -0.205 -1.510

VIXRISK 0.273 1.750 VIXRISK 0.254 1.840

ANALYSTTWORET44 INTERCEPT -0.253 -1.630 AGETWORET44 INTERCEPT -0.276 -1.800

VIXRISK 0.286 1.810 VIXRISK 0.326 2.090*

ANALYSTONERET44 INTERCEPT -0.195 -1.340 AGEONERET44 INTERCEPT -0.241 -1.440

VIXRISK 0.242 1.650 VIXRISK 0.269 1.570

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFICIENT T-STAT

ROEFIVERET44 INTERCEPT -0.107 -0.870 DIVFIVERET44 INTERCEPT -0.083 -0.940

VIXRISK 0.132 1.060 VIXRISK 0.106 1.180

ROEFOURRET44 INTERCEPT -0.142 -1.220 DIVFOURRET44 INTERCEPT -0.124 -1.270

VIXRISK 0.170 1.440 VIXRISK 0.147 1.490

ROETHREERET44 INTERCEPT -0.125 -0.980 DIVTHREERET44 INTERCEPT -0.109 -1.050

VIXRISK 0.156 1.200 VIXRISK 0.134 1.270

ROETWORET44 INTERCEPT -0.155 -1.150 DIVTWORET44 INTERCEPT -0.049 -0.480

VIXRISK 0.194 1.430 VIXRISK 0.079 0.760

ROEONERET44 INTERCEPT -0.177 -1.210 DIVONERET44 INTERCEPT -0.151 -1.170

VIXRISK 0.220 1.490 VIXRISK 0.175 1.360 * significant at 5% level; ** significant at 1% level

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

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.046 -0.390 VIXRISK 0.072 0.600 R112 INTERCEPT -0.130 -1.050 VIXRISK 0.156 1.240 R113 INTERCEPT -0.405 -1.890 VIXRISK 0.421 1.930 R121 INTERCEPT -0.034 -0.430 VIXRISK 0.048 0.580 R122 INTERCEPT -0.099 -1.230 VIXRISK 0.115 1.420 R123 INTERCEPT -0.200 -1.360 VIXRISK 0.205 1.390 R211 INTERCEPT -0.026 -0.220 VIXRISK 0.063 0.510 R212 INTERCEPT -0.097 -0.770 VIXRISK 0.130 1.000 R213 INTERCEPT -0.424 -2.100* VIXRISK 0.459 2.220* R221 INTERCEPT 0.080 0.830 VIXRISK -0.064 -0.660 R222 INTERCEPT -0.126 -1.220 VIXRISK 0.149 1.450 R223 INTERCEPT -0.301 -2.170* VIXRISK 0.319 2.280*

* significant at 5% level; ** significant at 1% leve

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

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:

22 Rpt = α p + sp VIXSENTt+ ept (8)

22 R pt 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.

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 COEFFICIENT T-STAT ANALYSTFIVERET22 INTERCEPT -0.144 -2.670** AGEFIVERET22 INTERCEPT -0.060 -1.640 VIXSENT 0.264 2.800** VIXSENT 0.129 2.020* ANALYSTfourRET22 INTERCEPT -0.150 -2.390* AGEFOURRET22 INTERCEPT -0.061 -1.260 VIXSENT 0.273 2.480* VIXSENT 0.141 1.670 ANALYSTTHREERET22 INTERCEPT -0.105 -1.630 AGETHREERET22 INTERCEPT -0.074 -1.290 VIXSENT 0.200 1.770 VIXSENT 0.164 1.640 ANALYSTTWORET22 INTERCEPT -0.098 -1.590 AGETWORET22 INTERCEPT -0.076 -1.200 VIXSENT 0.193 1.810 VIXSENT 0.169 1.520 ANALYSTONERET22 INTERCEPT -0.050 -0.940 AGEONERET22 INTERCEPT -0.143 -1.850 VIXSENT 0.123 1.320 VIXSENT 0.265 1.960* PORTFOLIO 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 INTERCEPT -0.071 -1.450 DIVTHREERET22 INTERCEPT -0.054 -1.380 VIXSENT 0.146 1.720 VIXSENT 0.112 1.650 ROETWORET22 INTERCEPT -0.061 -1.190 DIVTWORET22 INTERCEPT -0.044 -1.100 VIXSENT 0.136 1.510 VIXSENT 0.100 1.430 ROEONERET22 INTERCEPT -0.075 -1.300 DIVONERET22 INTERCEPT -0.073 -1.570 VIXSENT 0.162 1.610 VIXSENT 0.145 1.790

* significant at 5% level; ** significant at 1% level

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

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.042 -0.930 VIXSENT 0.093 1.190 R112 INTERCEPT -0.097 -2.040* VIXSENT 0.187 2.260* R113 INTERCEPT -0.229 -2.540* VIXSENT 0.404 2.570** R121 INTERCEPT -0.051 -1.500 VIXSENT 0.099 1.650 R122 INTERCEPT -0.085 -2.820** VIXSENT 0.158 3.030** R123 INTERCEPT -0.176 -3.210** VIXSENT 0.308 3.240** R211 INTERCEPT -0.015 -0.360 VIXSENT 0.055 0.750 R212 INTERCEPT -0.033 -0.650 VIXSENT 0.082 0.940 R213 INTERCEPT -0.142 -1.780 VIXSENT 0.270 1.930 R221 INTERCEPT -0.033 -0.850 VIXSENT 0.068 1.040 R222 INTERCEPT -0.067 -1.980* VIXSENT 0.134 2.290* R223 INTERCEPT -0.147 -2.710** VIXSENT 0.268 2.860**

* significant at 5% level; ** significant at 1% level

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:

44 R pt = α p + sp VIXSENTt+ept (9)

44 R pt is the 44-day compounded future holding period excess returns for portfolio p. 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).

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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET44 INTERCEPT -0.309 -3.320** AGEFIVERET44 INTERCEPT -0.141 -2.150*

VIXSENT 0.560 3.540** VIXSENT 0.295 2.690** ANALYSTFOURRET44 INTERCEPT -0.354 -3.330** AGEFOURRET44 INTERCEPT -0.151 -1.790

VIXSENT 0.636 3.520** VIXSENT 0.337 2.370* ANALYSTTHREERET44 INTERCEPT -0.294 -2.740** AGETHREERET44 INTERCEPT -0.198 -1.980*

VIXSENT 0.542 2.960** VIXSENT 0.420 2.480* ANALYSTTWORET44 INTERCEPT -0.269 -2.460* AGETWORET44 INTERCEPT -0.223 -1.960*

VIXSENT 0.514 2.770** VIXSENT 0.464 2.420* ANALYSTONERET44 INTERCEPT -0.167 -1.730 AGEONERET44 INTERCEPT -0.366 -2.640**

VIXSENT 0.363 2.250* VIXSENT 0.669 2.850**

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVERET44 INTERCEPT -0.182 -2.140* DIVFIVERET44 INTERCEPT -0.139 -2.110*

VIXSENT 0.352 2.460* VIXSENT 0.275 2.490* ROEFOURRET44 INTERCEPT -0.195 -2.330* DIVFOURRET44 INTERCEPT -0.157 -2.280*

VIXSENT 0.379 2.700** VIXSENT 0.306 2.670** ROETHREERET44 INTERCEPT -0.191 -2.210* DIVTHREERET44 INTERCEPT -0.138 -2.070*

VIXSENT 0.377 2.590* VIXSENT 0.277 2.480* ROETWORET44 INTERCEPT -0.162 -1.780 DIVTWORET44 INTERCEPT -0.120 -1.600

VIXSENT 0.341 2.220* VIXSENT 0.255 2.020* ROEONERET44 INTERCEPT -0.197 -1.930 DIVONERET44 INTERCEPT -0.188 -2.350*

VIXSENT 0.407 2.370* VIXSENT 0.361 2.700**

* significant at 5% level; ** significant at 1% level

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

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.133 -1.750 VIXSENT 0.271 2.130* R112 INTERCEPT -0.226 -2.740** VIXSENT 0.428 3.100** R113 INTERCEPT -0.492 -3.260** VIXSENT 0.862 3.370** R121 INTERCEPT -0.092 -1.460 VIXSENT 0.180 1.680 R122 INTERCEPT -0.143 -2.570** VIXSENT 0.269 2.930** R123 INTERCEPT -0.306 -2.930** VIXSENT 0.529 2.990** R211 INTERCEPT -0.092 -1.130 VIXSENT 0.219 1.590 R212 INTERCEPT -0.144 -1.560 VIXSENT 0.300 1.920 R213 INTERCEPT -0.378 -2.660** VIXSENT 0.699 2.890** R221 INTERCEPT -0.088 -1.180 VIXSENT 0.177 1.460 R222 INTERCEPT -0.148 -2.340* VIXSENT 0.292 2.810* R223 INTERCEPT -0.300 -3.050** VIXSENT 0.539 3.29**

* significant at 5% level; ** significant at 1% level

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:

22 Rpt = α p + rpVIXRISKt+ sp VIXSENTt+ept (10)

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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET22 INTERCEPT -0.130 -1.710 AGEFIVERET22 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* ANALYSTFOURRET22 INTERCEPT -0.101 -1.170 AGEFOURRET22 INTERCEPT -0.067 -0.990 VIXRISK -0.073 -0.880 VIXRISK 0.009 0.140 VIXSENT 0.313 2.700** VIXSENT 0.136 1.530 ANALYSTTHREERET22 INTERCEPT -0.076 -0.840 AGETHREERET22 INTERCEPT -0.080 -1.000 VIXRISK -0.043 -0.490 VIXRISK 0.009 0.120 VIXSENT 0.223 1.870 VIXSENT 0.159 1.520 ANALYSTTWORET22 INTERCEPT -0.076 -0.860 AGETWORET22 INTERCEPT -0.105 -1.170 VIXRISK -0.032 -0.360 VIXRISK 0.042 0.470 VIXSENT 0.211 1.840 VIXSENT 0.146 1.230 ANALYSTONERET22 INTERCEPT -0.057 -0.710 AGEONERET22 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVERET22 INTERCEPT -0.030 -0.450 DIVFIVERET22 INTERCEPT -0.032 -0.660 VIXRISK -0.056 -0.860 VIXRISK -0.037 -0.730 VIXSENT 0.167 1.860 VIXSENT 0.137 2.040* ROEFOURRET22 INTERCEPT -0.048 -0.700 DIVFOURRET22 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* ROETHREERET22 INTERCEPT -0.038 -0.550 DIVTHREERET22 INTERCEPT -0.037 -0.650 VIXRISK -0.048 -0.710 VIXRISK -0.025 -0.450 VIXSENT 0.172 1.920 VIXSENT 0.126 1.750 ROETWORET22 INTERCEPT -0.051 -0.690 DIVTWORET22 INTERCEPT 0.006 0.110 VIXRISK -0.015 -0.200 VIXRISK -0.073 -1.290 VIXSENT 0.144 1.500 VIXSENT 0.139 1.900 ROEONERET22 INTERCEPT -0.054 -0.660 DIVONERET22 INTERCEPT -0.046 -0.670 VIXRISK -0.030 -0.370 VIXRISK -0.040 -0.560 VIXSENT 0.178 1.670 VIXSENT 0.167 1.910

* significant at 5% level; ** significant at 1% level

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 COEFFICEINT T-STAT R111 INTERCEPT 0.003 0.040 VIXRISK -0.066 -1.030 VIXSENT 0.129 1.540 R112 INTERCEPT -0.046 -0.690 VIXRISK -0.076 -1.070 VIXSENT 0.228 2.510* R113 INTERCEPT -0.187 -1.460 VIXRISK -0.062 -0.510 VIXSENT 0.437 2.690** R121 INTERCEPT -0.037 -0.750 VIXRISK -0.021 -0.470 VIXSENT 0.110 1.790 R122 INTERCEPT -0.089 -1.990* VIXRISK 0.006 0.140 VIXSENT 0.154 2.800** R123 INTERCEPT -0.150 -1.960* VIXRISK -0.038 -0.460 VIXSENT 0.328 3.130** R211 INTERCEPT 0.025 0.410 VIXRISK -0.059 -0.950 VIXSENT 0.087 1.110 R212 INTERCEPT 0.003 0.040 VIXRISK -0.053 -0.760 VIXSENT 0.110 1.190 R213 INTERCEPT -0.163 -1.420 VIXRISK 0.031 0.280 VIXSENT 0.253 1.730

Table 17-Continued

PORTFOLIO COEFFICIENT T-STAT R221 INTERCEPT 0.041 0.730 VIXRISK -0.109 -1.730 VIXSENT 0.127 1.760 R222 INTERCEPT -0.068 -1.400 VIXRISK 0.001 0.020 VIXSENT 0.133 1.940 R223 INTERCEPT -0.162 -2.180* VIXRISK 0.022 0.270 VIXSENT 0.256 2.410* * 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:

44 R pt = α p + rpVIXRISKt + sp VIXSENTt+ept (11)

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).

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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET44 INTERCEPT -0.328 -2.410* AGEFIVERET44 INTERCEPT -0.117 -1.230 VIXRISK 0.028 0.190 VIXRISK -0.034 -0.320 VIXSENT 0.546 3.110** VIXSENT 0.312 2.510* ANALYSTFOURRET44 INTERCEPT -0.334 -2.240* AGEFOURRET44 INTERCEPT -0.201 -1.640 VIXRISK -0.029 -0.180 VIXRISK 0.071 0.540 VIXSENT 0.651 3.170** VIXSENT 0.301 1.890 ANALYSTTHREERET44 INTERCEPT -0.324 -2.090* AGETHREERET44 INTERCEPT -0.260 -1.860 VIXRISK 0.043 0.250 VIXRISK 0.088 0.570 VIXSENT 0.520 2.520* VIXSENT 0.375 1.940 ANALYSTTWORET44 INTERCEPT -0.323 -2.020* AGETWORET44 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 ANALYSTONERET44 INTERCEPT -0.240 -1.630 AGEONERET44 INTERCEPT -0.341 -1.990* VIXRISK 0.105 0.630 VIXRISK -0.035 -0.180 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT VIXSENT 0.310 1.650 VIXSENT 0.687 2.540*

Table 17-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

ROEFIVERET44 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*

ROEFOURRET44 INTERCEPT -0.198 -1.690 DIVFOURRET44 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*

ROETHREERET44 INTERCEPT -0.181 -1.420 DIVTHREERET44 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*

ROETWORET44 INTERCEPT -0.201 -1.470 DIVTWORET44 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*

ROEONERET44 INTERCEPT -0.233 -1.570 DIVONERET44 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*

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 COEFFICIENT T-STAT R111 INTERCEPT -0.090 -0.780 VIXRISK -0.061 -0.450 VIXSENT 0.302 2.030* R112 INTERCEPT -0.196 -1.650 VIXRISK -0.043 -0.300 VIXSENT 0.449 2.750** R113 INTERCEPT -0.527 -2.480* VIXRISK 0.051 0.230 VIXSENT 0.836 2.940** R121 INTERCEPT -0.064 -0.780 VIXRISK -0.041 -0.450 VIXSENT 0.200 1.630 R122 INTERCEPT -0.139 -1.750 VIXRISK -0.006 -0.060 VIXSENT 0.273 2.490* R123 INTERCEPT -0.280 -1.880 VIXRISK -0.037 -0.220 VIXSENT 0.547 2.690** R211 INTERCEPT -0.061 -0.490 VIXRISK -0.044 -0.320 VIXSENT 0.241 1.560 R212 INTERCEPT -0.142 -1.070 VIXRISK -0.004 -0.030 VIXSENT 0.302 1.720 R213 INTERCEPT -0.513 -2.500* VIXRISK 0.193 0.870 VIXSENT 0.602 2.200* R221 INTERCEPT 0.040 0.420 VIXRISK -0.184 -1.550 VIXSENT 0.269 1.890 R222 INTERCEPT -0.166 -1.650 VIXRISK 0.026 0.200 VIXSENT 0.279 2.130* R223 INTERCEPT -0.372 -2.580** VIXRISK 0.104 0.600 VIXSENT 0.487 2.450*

* 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:

22 Rpt = α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt+ rp RIPOORt+ cpCCOR+ept (12)

44 R pt =α p + vpVIXRISKt+ ap AAIIORt+ ip IIORt+ rp RIPOORt+ cpCCOR +ept (13)

44 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 pt 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET22 INTERCEPT 0.052 0.230 AGEFIVERET22 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFOURRET22 INTERCEPT 0.278 1.050 AGEFOURRET22 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* ANALYSTTHREERET22 INTERCEPT 0.182 0.620 AGETHREERET22 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 -0.227 -1.580 CCOR -0.301 -2.590** ANALYSTTWORET22 INTERCEPT 0.392 1.450 AGETWORET22 INTERCEPT 0.361 1.340 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 -0.333 -2.510* CCOR -0.345 -2.660* ANALYSTONERET22 INTERCEPT 0.269 1.150 AGEONERET22 INTERCEPT 0.404 1.060 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 Table 18-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVERET22 INTERCEPT 0.208 1.080 DIVFIVERET22 INTERCEPT 0.122 0.790 VIXRISK 0.019 0.290 VIXRISK 0.024 0.510 AAIIOR 0.027 1.550 AAIIOR 0.014 0.950 IIOR -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 ROEFOURRET22 INTERCEPT 0.191 0.960 DIVFOURRET22 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 ROETHREERET22 INTERCEPT 0.255 1.290 DIVTHREERET22 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 ROETWORET22 INTERCEPT 0.286 1.390 DIVTWORET22 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 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* ROEONERET22 INTERCEPT 0.311 1.290 DIVONERET22 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

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

PORTFOLIO COEFFICIENT T-STAT R111 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 R112 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* R113 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 R121 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 R122 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 R123 INTERCEPT -0.122 -0.390 VIXRISK 0.108 1.520 AAIIOR -0.012 -0.480

104

Table 18-Continued

PORTFOLIO COEFFICIENT T-STAT IIOR -0.162 -2.510* RIPOOR 0.086 3.450** CCOR -0.130 -0.830 R211 INTERCEPT 0.390 2.380* VIXRISK -0.020 -0.360 AAIIOR 0.042 2.560*

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)

PORTFOLIO COEFFICIENT T-STAT IIOR 0.024 0.580 RIPOOR 0.006 0.330 CCOR -0.206 -2.590** R212 INTERCEPT 0.291 1.460 VIXRISK -0.003 -0.050 AAIIOR 0.037 1.920 IIOR -0.015 -0.300 RIPOOR 0.026 1.090 CCOR -0.192 -1.960* R213 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* R221 INTERCEPT 0.174 0.980 VIXRISK -0.052 -0.940 AAIIOR 0.026 1.450 IIOR -0.003 -0.060

105

Table 18-Continued

PORTFOLIO COEFFICIENT T-STAT RIPOOR -0.028 -1.110 CCOR -0.048 -0.590 R222 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 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVERET44 INTERCEPT -0.119 -0.240 AGEFIVERET44 INTERCEPT 0.124 0.390 VIXRISK 0.251 1.980* VIXRISK 0.098 1.050 AAIIOR 0.033 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 -0.268 -1.030 CCOR -0.212 -1.290 ANALYSTFOURRET44 INTERCEPT 0.130 0.220 AGETHREERET44 INTERCEPT 0.150 0.360 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

106

Table 18-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

ANALYSTTWORET44 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

ANALYSTONERET44 INTERCEPT 0.204 0.410 AGEONERET44 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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

ROEFIVERET44 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

ROEFOURRET44 INTERCEPT 0.014 0.030 DIVFOURRET44 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

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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

ROETHREERET44 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

ROETWORET44 INTERCEPT 0.206 0.480 DIVTWORET44 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

ROEONERET44 INTERCEPT 0.183 0.360 DIVONERET44 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

* 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

PORTFOLIO COEFFICIENT T-STAT R111 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 R112 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 R113 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 R121 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 R122 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 R123 INTERCEPT -0.347 -0.480 VIXRISK 0.177 1.360 AAIIOR -0.034 -0.710

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 COEFFICIENT T-STAT IIOR -0.285 -2.020* RIPOOR 0.148 3.330** CCOR -0.141 -0.390 R211 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* R212 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 R213 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 R221 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 R222 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 R223 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

44-Day Return

VARIABLE SIGNIFICANT SIGN VIXRISK 3 POSITIVE AAIIOR 13 POSITIVE IIOR 5 NEGATIVE RIPOOR 19 POSITIVE CCOR 1 NEGATIVE

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-trading- day 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)).

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.

114 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 time- series 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:

22 RSDpt = α p + rpVIXt+ept (1)

22 where RSDpt 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. 40 Only firms with ordinary common equity (as classified by CRSP) are used. Thus, ADRs, REITS, and units of beneficial interest are excluded.

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:

22 RSDpt = 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.

22 RSDpt = 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.

22 RSDpt = α p + rpVIXRISKt+ ppLAGPORTt +mpLAGSP500t+ept (4)

22 RSDpt = 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.

22 RSDpt = α p + spVIXSENTt+ ppLAGPORTt +mpLAGSP500t+ept (6)

22 RSDpt = 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.

22 RSDpt = α p + rpVIXRISKt+ spVIXSENTt + ppLAGPORTt +mpLAGSP500t+ept (8)

22 RSDpt = 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:

22 RSDpt = α p + rpVIXt+ept (1)

22 RSDpt 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 COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.003 -0.210 AGEFIVESTD22 INTERCEPT 0.006 0.510 VIX 0.755 11.360** VIX 0.424 8.780** ANALYSTFOURSTD22 INTERCEPT 0.032 2.130* AGEFOURSTD22 INTERCEPT 0.007 0.580 VIX 0.592 8.870** VIX 0.447 8.460** ANALYSTTHREESTD22 INTERCEPT 0.053 3.580** AGETHREESTD22 INTERCEPT 0.009 0.660 VIX 0.465 6.880** VIX 0.488 7.880** ANALYSTTWOSTD22 INTERCEPT 0.056 4.130** AGETWOSTD22 INTERCEPT 0.011 0.760 VIX 0.364 5.780** VIX 0.513 7.740** ANALYSTONESTD22 INTERCEPT 0.045 3.830** AGEONESTD22 INTERCEPT -0.018 -0.980 VIX 0.283 5.220** VIX 0.730 7.960** PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 INTERCEPT 0.020 1.710 DIVFIVESTD22 INTERCEPT 0.025 2.220** VIX 0.490 9.160** VIX 0.419 8.310** ROEFOURSTD22 INTERCEPT 0.019 1.630 DIVFOURSTD22 INTERCEPT 0.051 3.420** VIX 0.494 9.260** VIX 0.309 4.870** ROETHREESTD22 INTERCEPT 0.030 2.600** DIVTHREESTD22 INTERCEPT 0.052 3.780** VIX 0.425 8.240** VIX 0.298 5.160** ROETWOSTD22 INTERCEPT 0.040 3.180** DIVTWOSTD22 INTERCEPT 0.049 3.730** VIX 0.397 7.250** VIX 0.326 5.800** ROEONESTD22 INTERCEPT 0.044 3.520** DIVONESTD22 INTERCEPT 0.049 2.880** VIX 0.399 7.130** VIX 0.383 5.310**

* significant at 5% level; ** significant at 1% level

128

Table 20-Continued

Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book- to-Market Equity, Size, and Beta on VIX

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT 0.045 3.630** VIX 0.313 5.750** R112 INTERCEPT 0.052 3.470** VIX 0.422 6.310** R113 INTERCEPT 0.036 1.860 VIX 0.915 10.230** R121 INTERCEPT 0.018 1.590 VIX 0.501 9.940** R122 INTERCEPT 0.016 1.290 VIX 0.564 9.200** R123 INTERCEPT 0.006 0.260 VIX 1.000 9.400** R211 INTERCEPT 0.046 4.420** VIX 0.229 5.190** R212 INTERCEPT 0.055 3.300** VIX 0.386 5.400** R213 INTERCEPT 0.059 2.790** VIX 0.691 7.770** R221 INTERCEPT 0.039 3.540** VIX 0.456 8.940** R222 INTERCEPT 0.015 1.170 VIX 0.598 9.960** R223 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:

22 RSDpt = α p + rpLAGSP500t+ept (2)

22 RSDpt 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT 0.067 5.830** AGEFIVESTD22 INTERCEPT 0.050 5.750** LAGSP500 0.625 8.930** LAGSP500 0.327 6.910**

ANALYSTFOURSTD22 INTERCEPT 0.084 6.990** AGEFOURSTD22 INTERCEPT 0.047 4.580** LAGSP500 0.506 7.390** LAGSP500 0.376 6.310**

ANALYSTTHREESTD22 INTERCEPT 0.090 7.390** AGETHREESTD22 INTERCEPT 0.052 4.280** LAGSP500 0.417 5.750** LAGSP500 0.421 5.960**

ANALYSTTWOSTD22 INTERCEPT 0.083 7.320** AGETWOSTD22 INTERCEPT 0.051 3.970** LAGSP500 0.339 4.880** LAGSP500 0.465 5.970**

ANALYSTONESTD22 INTERCEPT 0.066 6.490** AGEONESTD22 INTERCEPT 0.037 2.050** LAGSP500 0.262 4.090** LAGSP500 0.672 5.800**

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 INTERCEPT 0.069 7.160** DIVFIVESTD22 INTERCEPT 0.071 8.270** LAGSP500 0.385 6.660** LAGSP500 0.305 5.880**

ROEFOURSTD22 INTERCEPT 0.066 6.900** DIVFOURSTD22 INTERCEPT 0.082 8.320** LAGSP500 0.404 7.110** LAGSP500 0.245 4.380**

ROETHREESTD22 INTERCEPT 0.068 7.420** DIVTHREESTD22 INTERCEPT 0.081 8.320** LAGSP500 0.362 6.770** LAGSP500 0.238 4.430**

ROETWOSTD22 INTERCEPT 0.074 7.530** DIVTWOSTD22 INTERCEPT 0.081 8.600** LAGSP500 0.346 6.050** LAGSP500 0.260 4.810**

ROEONESTD22 INTERCEPT 0.078 7.460** DIVONESTD22 INTERCEPT 0.083 7.220** LAGSP500 0.347 5.540** LAGSP500 0.326 4.940**

* significant at 5% level; ** significant at 1% level

131

Table 21-Continued

Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book-to- Market Equity, Size, and Beta on Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT 0.070 7.440** LAGSP500 0.279 5.020** R112 INTERCEPT 0.091 8.030** LAGSP500 0.353 5.340** R113 INTERCEPT 0.104 6.310** LAGSP500 0.854 8.770** R121 INTERCEPT 0.060 6.570** LAGSP500 0.441 8.270** R122 INTERCEPT 0.074 7.320** LAGSP500 0.434 6.550** R123 INTERCEPT 0.102 5.470** LAGSP500 0.812 7.130** R211 INTERCEPT 0.070 8.830** LAGSP500 0.179 4.140** R212 INTERCEPT 0.092 7.420** LAGSP500 0.316 4.530** R213 INTERCEPT 0.117 7.110** LAGSP500 0.607 6.620** R221 INTERCEPT 0.069 7.670** LAGSP500 0.448 8.330** R222 INTERCEPT 0.077 7.390** LAGSP500 0.460 7.480** R223 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:

22 RSDpt = α p + rpVIXt+ mpLAGSP500t+ept (3)

22 RSDpt 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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.002 -0.130 AGEFIVESTD22 INTERCEPT 0.005 0.460 VIX 0.069 0.680 VIX 0.449 5.550** LAGSP500 0.698 6.410** LAGSP500 -0.030 -0.420 ANALYSTFOURSTD22 INTERCEPT 0.034 2.240* AGEFOURSTD22 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 ANALYSTTHREESTD22 INTERCEPT 0.055 3.770** AGETHREESTD22 INTERCEPT 0.011 0.780 VIX 0.134 1.090 VIX 0.412 3.670** LAGSP500 0.356 3.030** LAGSP500 0.093 0.770 ANALYSTTWOSTD22 INTERCEPT 0.059 4.360** AGETWOSTD22 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 ANALYSTONESTD22 INTERCEPT 0.047 4.020** AGEONESTD22 INTERCEPT -0.014 -0.720 VIX 0.198 2.020* VIX 0.518 3.090** LAGSP500 0.104 0.920 LAGSP500 0.260 1.320 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 INTERCEPT 0.020 1.680 DIVFIVESTD22 INTERCEPT 0.024 2.060* VIX 0.500 5.460** VIX 0.485 5.740** LAGSP500 -0.013 -0.140 LAGSP500 -0.080 -1.040 ROEFOURSTD22 INTERCEPT 0.020 1.670 DIVFOURSTD22 INTERCEPT 0.051 3.380** VIX 0.468 5.060** VIX 0.311 3.300** LAGSP500 0.032 0.350 LAGSP500 -0.002 -0.030 ROETHREESTD22 INTERCEPT 0.032 2.690** DIVTHREESTD22 INTERCEPT 0.052 3.770** VIX 0.371 4.070** VIX 0.296 3.490** LAGSP500 0.067 0.730 LAGSP500 0.002 0.030 ROETWOSTD22 INTERCEPT 0.041 3.310** DIVTWOSTD22 INTERCEPT 0.049 3.730** VIX 0.327 3.410** VIX 0.325 3.870** LAGSP500 0.085 0.860 LAGSP500 0.001 0.020 ROEONESTD22 INTERCEPT 0.045 3.630** DIVONESTD22 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 Book- to-Market Equity, Size, and Beta on VIX and Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT 0.046 3.830** VIX 0.245 2.990** LAGSP500 0.084 0.990 R112 INTERCEPT 0.053 3.540** VIX 0.380 3.580** LAGSP500 0.051 0.490 R113 INTERCEPT 0.043 2.210* VIX 0.622 3.810** LAGSP500 0.360 2.070* R121 INTERCEPT 0.020 1.790 VIX 0.404 4.960** LAGSP500 0.120 1.510 R122 INTERCEPT 0.016 1.220 VIX 0.597 6.320** LAGSP500 -0.041 -0.440 R123 INTERCEPT 0.007 0.300 VIX 0.964 6.320** LAGSP500 0.045 0.300 R211 INTERCEPT 0.046 4.390** VIX 0.238 3.400** LAGSP500 -0.010 -0.160 R212 INTERCEPT 0.056 3.330** VIX 0.366 3.250** LAGSP500 0.025 0.230 R213 INTERCEPT 0.062 2.950** VIX 0.559 3.840** LAGSP500 0.162 1.080 R221 INTERCEPT 0.044 4.010** VIX 0.257 3.130** LAGSP500 0.243 2.980** R222 INTERCEPT 0.014 1.070

135

Table 22-Continued

PORTFOLIO COEFFICIENT T-STAT VIX 0.636 5.810** LAGSP500 -0.046 -0.470 R223 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:

22 RSDpt = α p + rpVIXRISKt+ ppLAGPORTt +mpLAGSP500t+ept (4)

136 22 RSDpt 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.358 -4.450** AGEFIVESTD22 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 ANALYSTFOURSTD22 INTERCEPT -0.287 -3.350** AGEFOURSTD22 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 ANALYSTTHREESTD22 INTERCEPT -0.254 -2.810** AGETHREESTD22 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 ANALYSTTWOSTD22 INTERCEPT -0.201 -2.350* AGETWOSTD22 INTERCEPT -0.339 -4.570** VIXRISK 0.307 3.280** VIXRISK 0.436 5.240** LAGPORT 0.379 3.370** LAGPORT 0.376 4.130** LAGSP500 -0.083 -0.690 LAGSP500 -0.060 -0.610 ANALYSTONESTD22 INTERCEPT -0.179 -2.570* AGEONESTD22 INTERCEPT -0.456 -4.840** VIXRISK 0.269 3.490** VIXRISK 0.565 5.250** LAGPORT 0.300 3.070** LAGPORT 0.573 6.150** LAGSP500 -0.052 -0.560 LAGSP500 -0.216 -1.450 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 INTERCEPT -0.200 -2.900** DIVFIVESTD22 INTERCEPT -0.192 -3.020** VIXRISK 0.298 4.000** VIXRISK 0.289 4.250** LAGPORT 0.205 1.600 LAGPORT 0.324 3.270** LAGSP500 0.073 0.670 LAGSP500 -0.062 -0.760 ROEFOURSTD22 INTERCEPT -0.195 -2.750** DIVFOURSTD22 INTERCEPT -0.147 -2.130* VIXRISK 0.288 3.730** VIXRISK 0.238 3.290** LAGPORT 0.285 2.310* LAGPORT 0.506 5.590** LAGSP500 0.037 0.330 LAGSP500 -0.155 -2.090* ROETHREESTD22 INTERCEPT -0.173 -2.540* DIVTHREESTD22 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 0.024 0.230 LAGSP500 -0.145 -1.900 ROETWOSTD22 INTERCEPT -0.161 -2.210* DIVTWOSTD22 INTERCEPT -0.155 -2.440* 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 LAGSP500 -0.150 -2.350* ROEONESTD22 INTERCEPT -0.195 -2.550* DIVONESTD22 INTERCEPT -0.181 -2.220* VIXRISK 0.298 3.550**138 VIXRISK 0.280 3.220** LAGPORT 0.286 2.550* LAGPORT 0.519 5.430** LAGSP500 -0.007 -0.060 LAGSP500 -0.164 -1.800

Table 23-Continued

Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book-to- Market Equity, Size, and Beta on VIXRISK, Lagged Portfolio Standard Deviation, and Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.139 -2.330* VIXRISK 0.219 3.380** LAGPORT 0.424 4.200** LAGSP500 -0.056 -0.730 R112 INTERCEPT -0.166 -2.090* VIXRISK 0.275 3.240** LAGPORT 0.340 3.040** LAGSP500 -0.032 -0.310 R113 INTERCEPT -0.391 -3.290** VIXRISK 0.540 4.100** LAGPORT 0.392 3.560** LAGSP500 0.057 0.310 R121 INTERCEPT -0.234 -4.090** VIXRISK 0.322 5.040** LAGPORT 0.653 6.090** LAGSP500 -0.213 -2.270* R122 INTERCEPT -0.251 -3.730** VIXRISK 0.359 4.970** LAGPORT 0.445 4.480** LAGSP500 -0.119 -1.280 R123 INTERCEPT -0.576 -5.530** VIXRISK 0.751 6.480** LAGPORT 0.733 7.010** LAGSP500 -0.596 -3.610** R211 INTERCEPT -0.127 -2.520* VIXRISK 0.207 3.820** LAGPORT 0.390 3.850** LAGSP500 -0.093 -1.630 R212 INTERCEPT -0.187 -2.510* VIXRISK 0.291 3.640** LAGPORT 0.516 5.850**

139

Table 23-Continued

PORTFOLIO COEFFICIENT T-STAT LAGSP500 -0.172 -2.070* R213 INTERCEPT -0.353 -3.420** VIXRISK 0.500 4.390** LAGPORT 0.478 5.530** LAGSP500 -0.153 -1.120 R221 INTERCEPT -0.144 -2.160* VIXRISK 0.228 3.110** LAGPORT 0.289 3.170** LAGSP500 0.128 1.440 R222 INTERCEPT -0.253 -3.400** VIXRISK 0.364 4.520** LAGPORT 0.396 4.860** LAGSP500 -0.074 -0.790 R223 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:

22 RSDpt = α p + rpVIXRISKt+gpGARCHt +mpLAGSP500t+ept (5)

140

22 RSDpt 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.339 -4.270** AGEFIVESTD22 INTERCEPT -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 ANALYSTFOURSTD22 INTERCEPT -0.252 -3.150** AGEFOURSTD22 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 Table 24-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT LAGSP500 -0.120 -1.070 LAGSP500 -0.075 -0.820 ANALYSTTHREESTD22 INTERCEPT -0.189 -2.390* AGETHREESTD22 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 ANALYSTTWOSTD22 INTERCEPT -0.172 -2.360* AGETWOSTD22 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 LAGSP500 -0.031 -0.300 ANALYSTONESTD22 INTERCEPT -0.127 -2.070** AGEONESTD22 INTERCEPT -0.365 -4.030** VIXRISK 0.209 3.040** VIXRISK 0.455 4.450** GARCH 0.275 3.540** GARCH 0.415 3.930** LAGSP500 0.006 0.080 LAGSP500 0.029 0.190 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 INTERCEPT -0.208 -3.270** DIVFIVESTD22 INTERCEPT -0.178 -2.920* 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 ROEFOURSTD22 INTERCEPT -0.198 -3.070** DIVFOURSTD22 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 LAGSP500 -0.055 -0.770 ROETHREESTD22 INTERCEPT -0.160 -2.640** DIVTHREESTD22 INTERCEPT -0.117 -1.930 VIXRISK 0.245 3.660** VIXRISK 0.206 3.150** GARCH 0.404 4.300** GARCH 0.455 5.600** LAGSP500 -0.020 -0.240 LAGSP500 -0.102 -1.440 ROETWOSTD22 INTERCEPT -0.163 -2.490* DIVTWOSTD22 INTERCEPT -0.128 -2.100* 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* ROEONESTD22 INTERCEPT -0.173 -2.480* DIVONESTD22 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*

Table 24-Continued

142

Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book- to-Market Equity, Size, and Beta on VIXRISK, GARCH Forecast, and Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.074 -1.330 VIXRISK 0.145 2.340* GARCH 0.370 4.910** LAGSP500 0.037 0.520 R112 INTERCEPT -0.166 -2.340* VIXRISK 0.270 3.450** GARCH 0.466 5.530** LAGSP500 -0.101 -1.070 R113 INTERCEPT -0.360 -3.290** VIXRISK 0.498 4.060** GARCH 0.468 5.160** LAGSP500 0.018 0.110 R121 INTERCEPT -0.192 -3.690** VIXRISK 0.275 4.710** GARCH 0.517 6.170** LAGSP500 -0.081 -1.040 R122 INTERCEPT -0.237 -3.320** VIXRISK 0.344 4.490** GARCH 0.227 2.630** LAGSP500 0.075 0.860 R123 INTERCEPT -0.570 -5.880** VIXRISK 0.731 6.760** GARCH 0.840 7.880** LAGSP500 -0.643 -4.120** R211 INTERCEPT -0.071 -1.460 VIXRISK 0.144 2.760** GARCH 0.286 2.950** LAGSP500 -0.002 -0.040 R212 INTERCEPT -0.126 -1.790

143

Table 24-Continued

PORTFOLIO COEFFICIENT T-STAT

VIXRISK 0.222 2.880**

GARCH 0.499 7.220**

LAGSP500 -0.108 -1.310

R213 INTERCEPT -0.294 -3.020**

VIXRISK 0.431 3.990**

GARCH 0.500 6.910**

LAGSP500 -0.107 -0.830

R221 INTERCEPT -0.116 -1.760

VIXRISK 0.203 2.780**

GARCH 0.122 1.750

LAGSP500 0.251 3.120**

R222 INTERCEPT -0.236 -3.150**

VIXRISK 0.347 4.280**

GARCH 0.292 3.930**

LAGSP500 0.024 0.270

R223 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:

22 RSDpt = α p + rpVIXSENTt+ ppLAGPORTt +mpLAGSP500t+ept (6)

22 RSDpt 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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.147 -2.760** AGEFIVESTD22 INTERCEPT -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 ANALYSTFOURSTD22 INTERCEPT -0.104 -1.920 AGEFOURSTD22 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 ANALYSTTHREESTD22 INTERCEPT -0.063 -1.240 AGETHREESTD22 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 ANALYSTTWOSTD22 INTERCEPT -0.035 -0.740 AGETWOSTD22 INTERCEPT -0.061 -1.270 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 LAGSP500 0.108 1.130 ANALYSTONESTD22 INTERCEPT -0.026 -0.630 AGEONESTD22 INTERCEPT -0.030 -0.480 VIXSENT 0.175 2.170* VIXSENT 0.157 1.240 LAGPORT 0.223 2.420* LAGPORT 0.564 5.370** LAGSP500 0.060 0.760 LAGSP500 0.037 0.240 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 INTERCEPT -0.130 -2.980** DIVFIVESTD22 INTERCEPT -0.135 -3.260** 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 ROEFOURSTD22 INTERCEPT -0.114 -2.660** DIVFOURSTD22 INTERCEPT -0.094 -2.450* VIXSENT 0.355 4.130** 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 ROETHREESTD22 INTERCEPT -0.093 -2.340* DIVTHREESTD22 INTERCEPT -0.079 -2.160* VIXSENT 0.314 3.920** 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 ROETWOSTD22 INTERCEPT -0.083 -2.040* DIVTWOSTD22 INTERCEPT -0.078 -2.160* 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 LAGSP500 -0.077 -1.410 ROEONESTD22 INTERCEPT -0.065 -1.470 DIVONESTD22 INTERCEPT -0.098 -2.220* VIXSENT 0.274 3.090** 146 VIXSENT 0.339 3.930** LAGPORT 0.195 1.810 LAGPORT 0.364 4.170** LAGSP500 0.093 1.020 LAGSP500 -0.064 -0.930

Table 25-Continued

Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book- to-Market Equity, Size, and Beta on VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market Standard Deviation PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.053 -1.510 VIXSENT 0.225 3.210** LAGPORT 0.307 3.140** LAGSP500 0.022 0.360 R112 INTERCEPT -0.096 -2.030* VIXSENT 0.357 3.790** LAGPORT 0.203 1.950 LAGSP500 0.050 0.620 R113 INTERCEPT -0.115 -1.610 VIXSENT 0.414 2.910** LAGPORT 0.334 3.050** LAGSP500 0.241 1.510 R121 INTERCEPT -0.024 -0.690 VIXSENT 0.154 2.280* LAGPORT 0.638 5.820** LAGSP500 -0.092 -1.030 R122 INTERCEPT -0.110 -2.660** VIXSENT 0.358 4.520** LAGPORT 0.324 3.300** LAGSP500 0.013 0.150 R123 INTERCEPT -0.127 -1.790 VIXSENT 0.442 3.300** LAGPORT 0.645 5.810** LAGSP500 -0.260 -1.770 R211 INTERCEPT -0.033 -1.000 VIXSENT 0.185 2.840** LAGPORT 0.290 2.820** LAGSP500 -0.022 -0.440 R212 INTERCEPT -0.078 -1.610 VIXSENT 0.308 3.160** LAGPORT 0.408 4.460** LAGSP500 -0.083 -1.140 R213 INTERCEPT -0.111 -1.710 VIXSENT 0.414 3.240** LAGPORT 0.402 4.550** LAGSP500 0.013 0.110

147

Table 25-Continued

PORTFOLIO COEFFICIENT T-STAT R221 INTERCEPT 0.041 1.040 VIXSENT 0.040 0.540 LAGPORT 0.263 2.860** LAGSP500 0.256 3.030** R222 INTERCEPT -0.112 -2.140* VIXSENT 0.370 3.620** LAGPORT 0.235 2.480* LAGSP500 0.094 0.910 R223 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:

22 RSDpt = α p + rpVIXSENTt+ gpGARCHt +mpLAGSP500t+ept (7)

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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.138 -2.640** AGEFIVESTD22 INTERCEPT -0.073 -2.130* VIXSENT 0.402 4.050** VIXSENT 0.242 3.680** GARCH 0.348 3.470** GARCH 0.350 3.770** LAGSP500 0.112 1.050 LAGSP500 0.010 0.150 ANALYSTFOURSTD22 INTERCEPT -0.091 -1.750 AGEFOURSTD22 INTERCEPT -0.037 -0.940 VIXSENT 0.319 3.110** VIXSENT 0.166 2.110*

149

Table 26-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

GARCH 0.475 5.150** GARCH 0.394 3.680**

LAGSP500 -0.013 -0.140 LAGSP500 0.072 0.820

ANALYSTTHREESTD22 INTERCEPT -0.043 -0.890 AGETHREESTD22 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

ANALYSTTWOSTD22 INTERCEPT -0.022 -0.500 AGETWOSTD22 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

ANALYSTONESTD22 INTERCEPT -0.005 -0.110 AGEONESTD22 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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT

ROEFIVESTD22 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

ROEFOURSTD22 INTERCEPT -0.093 -2.190* DIVFOURSTD22 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**

150

Table 26-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT LAGSP500 0.068 0.890 LAGSP500 -0.044 -0.790 ROETHREESTD22 INTERCEPT -0.077 -1.970* DIVTHREESTD22 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 ROETWOSTD22 INTERCEPT -0.061 -1.510 DIVTWOSTD22 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 LAGSP500 -0.076 -1.430 ROEONESTD22 INTERCEPT -0.060 -1.370 DIVONESTD22 INTERCEPT -0.088 -2.090* VIXSENT 0.256 2.960** VIXSENT 0.311 3.840** GARCH 0.249 2.590** GARCH 0.437 6.370** LAGSP500 0.082 0.940 LAGSP500 -0.077 -1.240

Panel B: Regression Estimates of 22-day Future Realized Standard Deviation for the Twelve Portfolios Sorted on Book- to-Market Equity, Size, and Beta on VIXSENT, GARCH Forecast, and Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 INTERCEPT -0.035 -1.030 VIXSENT 0.185 2.760** GARCH 0.311 3.930** LAGSP500 0.060 1.000 R112 INTERCEPT -0.070 -1.570 VIXSENT 0.295 3.310** GARCH 0.360 4.260** LAGSP500 -0.015 -0.200 R113 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 COEFFICIENT T-STAT R121 INTERCEPT 0.002 0.050 VIXSENT 0.104 1.560 GARCH 0.522 6.020** LAGSP500 0.022 0.290 R122 INTERCEPT -0.119 -2.820** VIXSENT 0.379 4.670** GARCH 0.139 1.570 LAGSP500 0.158 2.000* R123 INTERCEPT -0.124 -1.830 VIXSENT 0.416 3.220** GARCH 0.738 6.290** LAGSP500 -0.297 -2.070* R211 INTERCEPT -0.018 -0.580 VIXSENT 0.155 2.460* GARCH 0.248 2.510* LAGSP500 0.021 0.430 R212 INTERCEPT -0.057 -1.240 VIXSENT 0.261 2.870** GARCH 0.436 6.120** LAGSP500 -0.066 -0.930 R213 INTERCEPT -0.072 -1.180 VIXSENT 0.328 2.740** GARCH 0.453 6.240** LAGSP500 0.028 0.250 R221 INTERCEPT 0.066 1.590 VIXSENT 0.000 0.000 GARCH 0.113 1.780 LAGSP500 0.372 5.050** R222 INTERCEPT -0.113 -2.220* VIXSENT 0.374 3.770** GARCH 0.188 3.170** LAGSP500 0.132 1.530 R223 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:

22 RSDpt = α p + rpVIXRISKt+ spVIXSENTt + ppLAGPORTt +mpLAGSP500t+ept (8)

22 RSDpt 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

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.487 -5.860** AGEFIVESTD22 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* ANALYSTFOURSTD22 INTERCEPT -0.396 -4.460** AGEFOURSTD22 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 ANALYSTTHREESTD22 INTERCEPT -0.339 -3.680** AGETHREESTD22 INTERCEPT -0.376 -4.890** VIXRISK 0.334 3.410** 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 LAGSP500 -0.090 -0.830 ANALYSTTWOSTD22 INTERCEPT -0.268 -2.990** AGETWOSTD22 INTERCEPT -0.402 -4.950** VIXRISK 0.281 3.040** VIXRISK 0.415 5.130** 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 LAGSP500 -0.121 -1.130 ANALYSTONESTD22 INTERCEPT -0.231 -3.170** AGEONESTD22 INTERCEPT -0.489 -4.510** VIXRISK 0.249 3.280** VIXRISK 0.554 5.230** VIXSENT 0.139 1.760 VIXSENT 0.084 0.680 LAGPORT 0.291 3.000** LAGPORT 0.576 6.160** LAGSP500 -0.100 154 -1.020 LAGSP500 -0.253 -1.500

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ROEFIVESTD22 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 ROEFOURSTD22 INTERCEPT -0.299 -4.250** DIVFOURSTD22 INTERCEPT -0.237 -3.470** VIXRISK 0.231 3.220** VIXRISK 0.179 2.810** 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** ROETHREESTD22 INTERCEPT -0.267 -3.940** DIVTHREESTD22 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** ROETWOSTD22 INTERCEPT -0.254 -3.440** DIVTWOSTD22 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** ROEONESTD22 INTERCEPT -0.281 -3.610** DIVONESTD22 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** 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 Book- to-Market Equity, Size, and Beta on VIXRISK, VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 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 R112 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 R113 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 R121 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** R122 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* R123 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 COEFFICIENT T-STAT R211 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* R212 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** R213 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 R221 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

PORTFOLIO ESTIMATE T-STAT R222 INTERCEPT -0.363 -4.680** VIXRISK 0.313 4.350** VIXSENT 0.312 3.240** LAGPORT 0.303 3.470**

Table 27-Continued

157 PORTFOLIO ESTIMATE T-STAT LAGSP500 -0.112 -1.16 R223 INTERCEPT -0.545 -5.100** VIXRISK 0.488 4.970** 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:

22 RSDpt = α p + rpVIXRISKt+ spVIXSENTt +gpGARCHt+ mpLAGSP500t+ept (9)

22 RSDpt 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 COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT ANALYSTFIVESTD22 INTERCEPT -0.466 -5.700** ROEFIVESTD22 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 ANALYSTFOURSTD22 INTERCEPT -0.353 -4.160** ROEFOURSTD22 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 LAGSP500 -0.083 -0.910 ANALYSTTHREESTD22 INTERCEPT -0.259 -3.150** ROETHREESTD22 INTERCEPT -0.247 -3.910** VIXRISK 0.263 3.030** VIXRISK 0.208 3.360** VIXSENT 0.188 1.950 VIXSENT 0.239 3.130** GARCH 0.450 5.140** GARCH 0.344 3.530**

Table 28-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT LAGSP500 -0.113 -1.060 LAGSP500 -0.073 -0.860

159 ANALYSTTWOSTD22 INTERCEPT -0.228 -2.900** ROETWOSTD22 INTERCEPT -0.238 -3.430** VIXRISK 0.249 3.120** VIXRISK 0.219 3.180** VIXSENT 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 ANALYSTONESTD22 INTERCEPT -0.166 -2.480* ROEONESTD22 INTERCEPT -0.257 -3.520** 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 PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT AGEFIVESTD22 INTERCEPT -0.321 -5.540** DIVFIVESTD22 INTERCEPT -0.303 -4.860** 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* LAGSP500 -0.074 -1.130 AGEFOURSTD22 INTERCEPT -0.315 -5.050** DIVFOURSTD22 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* AGETHREESTD22 INTERCEPT -0.346 -4.730** DIVTHREESTD22 INTERCEPT -0.208 -3.420** 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 -0.119 -1.160 LAGSP500 -0.166 -2.390* AGETWOSTD22 INTERCEPT -0.344 -4.420** DIVTWOSTD22 INTERCEPT -0.209 -3.480** 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**

Table 28-Continued

PORTFOLIO COEFFICIENT T-STAT PORTFOLIO COEFFICIENT T-STAT LAGSP500 -0.080 -0.700 LAGSP500 -0.178 -2.900** AGEONESTD22 INTERCEPT -0.374 -3.700** DIVONESTD22 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 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 Book- to-Market Equity, Size, and Beta on VIXRISK,VIXSENT, GARCH Forecast, and Lagged Market Standard Deviation

PORTFOLIO COEFFICIENT T-STAT R111 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 R112 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 R113 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 R121 INTERCEPT -0.219 -3.890**

Table 28-Continued

PORTFOLIO COEFFICIENT T-STAT VIXRISK 0.267 4.620** VIXSENT 0.069 1.100 GARCH 0.515 6.080** LAGSP500 -0.106 -1.350 R122 INTERCEPT -0.364 -5.150**

161 VIXRISK 0.297 4.280** VIXSENT 0.335 4.280** GARCH 0.179 1.980* LAGSP500 -0.017 -0.210 R123 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** R211 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 R212 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 COEFFICIENT T-STAT

R213 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

R221 INTERCEPT -0.106 -1.370

VIXRISK 0.207 2.830**

162 VIXSENT -0.028 -0.370

GARCH 0.122 1.770

LAGSP500 0.262 3.090**

R222 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

R223 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.

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