Notes: Quintile portfolios are constructed every month by sorting stocks on each **option**-**implied** **volatility** measure at the end of the previous month. Call-put **implied** **volatility** spread ( CPIV ) is the difference between the average **implied** **volatility** of at-the-money calls and minus the average **implied** **volatility** of at-the-money puts. **Implied** **volatility** skew ( IVSKEW ) is the difference between the average **implied** **volatility** of out-of-the- money puts and minus the average **implied** **volatility** of at-the-money calls. “Above-minus-below” ( AMB ) is the difference between the average **implied** **volatility** of options whose strike prices are above the current underlying price and minus the mean average **implied** **volatility** of options whose strike prices are below the current underlying price. “Out-minus-at” of calls ( COMA ) is the difference between the average **implied** **volatility** of out-of-the-money calls and minus the average **implied** **volatility** of at-the-money calls. “Out-minus- at” of puts ( POMA ) is the difference between the average **implied** **volatility** of out-of-the-money puts and minus the average **implied** **volatility** of at-the-money puts. Realized-**implied** **volatility** spread ( RVIV ) is the difference between the realized **volatility** (i.e. the annualized standard deviation of daily returns over the previous month) and minus the average of at-the-money call and put **implied** volatilities. Quintile 1 (5) denotes the portfolio of stocks with the lowest (highest) **option**-**implied** **volatility** measure. The Jensen’s alphas are reported in rows labeled “Alpha”. The column “5-1” refers to the arbitrage portfolio with a long position in portfolio 5 and a short position in portfolio 1. The row “**Return**” documents data about raw returns on portfolios, and the row “Alpha” shows data about Jensen’s alpha with respect to Fama-French three factor model. P-values reported in Exhibit 3 are calculated using Newey-West method to control for serial correlation. Hereafter, *, **, and *** denote for significance at 10%, 5% and 1% level, respectively.

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In term of “industry effect”, a few papers have also found that some industry portfolios may be able to lead the **stock** market (Eleswarapu and Ashish, 1996 and Pollet, 2002). In particular, Pollet (2002) finds that oil can predict **stock** returns and most interestingly that the Norwegian **stock** market (which is dominated by oil) leads the world **stock** market. His finding regarding the Norwegian market fits especially nicely with our gradual- information-diffusion hypothesis since the Norwegian market is likely to be off the radar screen of investors who trade the world market index. Hong, Torous and Valkanov (2007) investigate whether the returns of industry portfolios are able to predict the movements of **stock** markets. Their finding is that out of thirty-four industry portfolios in the U.S., fourteen including commercial real estate, petroleum, metal, transportation, utilities, retail and financial can predict the **stock** market by up to two months. Importantly, the ability of an industry to lead the market is strongly correlated with its propensity to forecast indicators of economic activity such as industrial production growth. When they extend their analysis to the eight largest **stock** markets outside of the U.S., the findings are remarkably similar patterns. These findings indicate that markets incorporate information contained in industry returns about their fundamentals only with a lag because information diffuses gradually across asset markets. The logic of their hypothesis suggests that the gradual diffusion of information across asset markets ought to be pervasive. As a result, they would expect to find cross- asset **return** **predictability** in many contexts beyond industry portfolios and the broad market index. The key to finding such cross-**predictability** is to first identify sets of assets whose payoffs are likely correlated. As such, other contexts for interesting empirical work include looking at whether returns of stocks from one industry predict those in another or at stocks and the options listed on them. Indeed, a number of papers following theirs have taken up this task and found confirming results. For instance, Menzly and Oguzhan (2004) find that industry returns do lead and lag each other according to their place in the supply chain and Pan and Poteshman (2004) find that information may diffuse slowly from **option** markets to **stock** markets as **option** volume seems to be able to predict **stock** price movements. But much more work remains to be done on this topic.

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identical to the Black Scholes formula apart from replacing the risk free rate with the **return** on the underlying **stock** (that is, the risk free is supplemented with the risk premium). Our approach is also broadly consistent with Shefrin (2008) who provides a systematic treatment of how behavioral assumptions impact the pricing kernel at the heart of modern asset pricing theory. 4) We provide a number of testable predictions of the model and summarize existing evidence. Existing evidence strongly supports the analogy approach. 5) Duan and Wei (2009) use daily **option** quotes on the S&P 100 index and its 30 largest component stocks, to show that, after controlling for the underlying asset’s total **volatility**, a higher amount of systematic risk leads to a higher level of **implied** **volatility** and a steeper slope of the **implied** **volatility** curve. In the analogy **option** pricing model, higher risk premium on the underlying for a given level of total **volatility** generates this result. As risk premium is related to systematic risk, this prediction of the analogy model is quite intriguing. 6) Our approach is also an example of behavioralization of finance. Shefrin (2010) argues that finance is in the midst of a paradigm shift, from a neoclassical based framework to a psychologically based framework. Behavioralizing finance is the process of replacing neoclassical assumptions with behavioral

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Table 2 shows the correlation matrix of monthly ﬁrm-level **option**-**implied** **measures** and control variables. The ex-ante **option**-**implied** dividend yield (IDY) and the corrected dividend-price ratio (DP c ) from Golez (2014) are positively correlated and the correlation coeﬃcient is 0.746. They are, in fact, very similar **measures**. The only diﬀerence is that the **implied** dividend yield (IDY) captures both the expected **return** and expected dividend growth by construction while the corrected dividend-price ratio (DP c ) represents only the expected **return** by subtracting the expected dividend growth term from the historical dividend price ratio. Thus, the **implied** dividend yield is still a noisy proxy for the expected **return**. However, we consider the **implied** dividend yield, hoping that it can be cleaner measure than the historical dividend yield in that the historical dividend yield includes the realized dividend which is noisy by nature. On the other hand, the corrected dividend- price ratio (DP c ) is still a noisy proxy for the expected **return** because measuring the dividend growth term is subject to estimation errors and model mis-speciﬁcation embedded in the procedure by Golez (2014). Therefore, we consider both the **implied** dividend yield (IDY) and the corrected dividend-price ratio (DP c ) in our analysis.

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In this table, we report the results of various **stock** characteristics: size (SIZE), book-to-market (BTM), momentum (MOM), model-free **implied** **volatility** (MFIV), model-free **implied** skewness (MFIS), call-put- **volatility** spread (CPVS), and **implied**-realized-**volatility** spread (IRVS) to explain the cross section of returns. For each sample, on a daily basis, we sort the stocks by a particular characteristic, form the long-short decile portfolio, and hold this period for a particular holding period (one week, two weeks, or one month). Below, we show the annualized mean holding **return** for each decile-based portfolio and in the parenthesis the p-value for the hypothesis that the mean **return** is not different from zero. The p-values are based on the Newey and West (1987) autocorrelation-adjusted standard errors with the lag equal to the number of overlapping periods in portfolio holding.

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Several studies on other index options have been carried out using the same sampling procedure as Christensen and Prabhala (1998). Hansen (2001) analyses the information content of options on the Danish KFX share index. This **option** market is very illiquid compared to the OEX options market. It is shown that when error-in- variable problem is controlled by instrumental variable techniques, call **implied** **volatility** still contains more information about future realized **volatility** than historical **volatility** in such an illiquid **option** market. More recently, Shu and Zhang (2003) examine the options on S&P 500 index, and also report that **implied** **volatility** outperforms the subsequently historical index **return** **volatility**. Szakmary et al (2003) examine 35 futures options markets across eight separate exchanges and find that for a large majority of the commodities studied, **implied** **volatility** is a better predictor of future realized **volatility** than historical **volatility**.

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Note: This table shows regression results for Model (1). 22 firms in total are involved. This table presents coefficients and t-statistics of the Fama-Macbeth procedure. The extreme returns in each month are defined as the biggest and the smallest firm returns. Probit regressions of the likelihood of a firm having extreme **stock** returns in the following year are involved in this procedure. Different sample set are regressed, respectively. And the results are shown in three different columns. **Implied** is the monthly **implied** **volatility** from Canadian **option** price collected form Bloomberg. Price is the firm price. Volume is the log of the monthly volume calculated as the average number of shares traded in the previous month (in millions). BM is the book-to-market ratio. Age is the firm age in months. All observations are collected and computed based on available data from 2001 to 2014 and must have data for all **measures**.

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Regarding the **predictability** of IV itself, we run the CPA test for the squared forecast error. Table 4 reports the p-values for testing the null hypothesis of equal predictive ability between the row and column models.Rejection of the null hypothesis is indicated by the superscripts + and −. A positive (negative) sign indicates that the row (column) model is outperformed by the column (row) model. There are 9 cases (out of 18) in which we reject the null hypothesis that the random walk and the ARMA-type models perform equally well. In these cases, the + sign denotes the ARMA models performs better than the random walk. This suggests that there is a predictable pattern in the dynamics of **implied** **volatility** indices, which is in line with the results of Konstantinidi et al. (2008). When the predictive ability of the random walk is tested against the asymmetric ARMA models, the latter performs significantly better than the random walk at the 1% level. The importance of asymmetry found in-sample carries over to the out-of-sample analysis. When the model under consideration is an ARMA model that takes into account the contemporaneous asymmetric effect - ARMAX, ARIMAX, ARFIMAX models - always outperforms not only the random walk, but also the symmetric ARMA models. In these cases, the null hypothesis of equal predictive ability is always rejected at the 1% level.

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Adrian and Fronzoni (2005) have adopted the concept of learning in the estimation of beta coefficients. They believe that the traditional OLS ignores previous errors in training investors and this may result in CAPM failure in practice. Their model **measures** the effect of long-term learning, as a non- observable variable, on beta coefficients through state- space model. Assuming non-constant beta coefficients, Huang and Hueng (2007) used state-space model and examined conditional CAPM model. They found that there is a positive and a negative relation between risk and **return** in prosperity and depression conditions, respectively. Das et al.. (2010) estimated CAPM beta coefficients using Kalman filter. They found that the estimation of beta coefficients using Kalman filter promotes the accuracy of this model in forecasting **return**. Nieto et al. (2014) compared OLS, GARCH and Kalman filter in Mexico **stock** exchange and found that Kalman filter shows a better performance in estimating beta coefficients compared with other techniques. In a PhD thesis, Fux et al. (2014) studied **return** **predictability** and structure modeling. According to their findings, the investor can increase its idealistic level up to 1.2%, compared with OLS- based predictions, using dynamic averaging models where instabilities, time-varying coefficients and non- reliability are taken into account. In their study, under the title of "can oil price help forecasting the U.S. **stock**; evidence from dynamic averaging model" Naser and Alaali (2015) studied the power of oil price and other macro-economic and macro-financial variables, including industrial production index, interest rate,

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Our empirical results so far support the existence of condi- tional herding in the equity market. In this context, condi- tional herding refers to the fact that, during certain periods, the cross-sectional dispersion of **stock** returns is systemati- cally lower than what would have been expected given the magnitude of the market **return**. These periods of conditional herding, when investors are significantly more likely to clus- ter around the market consensus as they price individual stocks, are characterized by higher **implied** **volatility**, more negative **implied** skewness, and higher trading activity in puts, particularly OTM contracts. However, the fundamental relationship between cross-sectional dispersion and the mar- ket **return** does not seem to change when we account for these **option**-related variables. In other words, even when we control for the effect of **option** variables in the herding speci- fication, CSAD is still found to be positively related to the magnitude of index returns, as theory would suggest, rejecting the hypothesis of strong herding.

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Exhibit 3 contains an empirical **volatility** skew obtained from S&P 500 index call **option** price quotes recorded on 2 December 1993 for options expiring in February 1994. In Exhibit 3, the horizontal axis **measures** **option** moneyness as the percentage difference between a dividend- adjusted **stock** index level and a discounted strike price. Positive (negative) moneyness corresponds to in-the-money (out-of-the-money) options with low (high) strike prices. The vertical axis **measures** **implied** standard deviation values. Solid marks represent **implied** volatilities calculated from observed **option** prices using the Black-Scholes formula. Hollow marks represent **implied** volatilities calculated from observed **option** prices using the Jarrow- Rudd formula. The Jarrow-Rudd formula uses a single skewness parameter and a single kurtosis parameter across all price observations. The skewness parameter and the kurtosis parameter are estimated by a procedure described in the empirical results section below. There are actually 1,354 price quotes used to form this graph, but the number of visually distinguishable dots is smaller.

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Despite the increasing popularity of the V IX, measurement errors in its construction have been noted by Jiang & Tian (2005). The common problem inherent in the computation of the V IX as well as other **measures** of model-free **implied** **volatility** is that only a discrete set of strikes is actually traded in the market and that very low and high strikes are usually absent. To account for measurement errors induced by the limited number of strikes, Jiang & Tian (2005) apply the cubic spline method to interpolate between existing strikes and exploit a ‡at extrapolation scheme to infer **option** prices beyond the truncation point. Andersen & Bondarenko (2007) address the issue induced by the discrete set of strikes via the positive convolution approximation method proposed by Bondarenko (2003). Although interpolation and extrapolation techniques are widely accepted, it remains unclear how such techniques a¤ect the performance of **implied** volatilities in predicting future returns and realized **volatility**. In addition, there appears to be no consensus on the roles played by the OTM call and put options in the forecast of future **volatility** and returns. Jackwerth (2000), Jones (2006) and Bates (2008) suggest that the OTM put options may be irrelevant to known risk factors a¤ecting **stock** returns. Using a cubic spline interpolation and ‡at extrapolation methods, Dotsis & Vlastakis (2016) also …nd that the OTM put options, especially deep OTM puts, do not contain important information with respect to equity **volatility** risk. They also show that the OTM call options subsume all useful information embedded in the OTM puts for forecasting future realized **volatility**. However, Andersen et al. (2015) show that the left tail risk, driving a substantial part of the OTM put **option** dynamics, exhibits strong predictive power for future excess market returns over long horizons.

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It has been documented that the **implied** **volatility** of **stock** exhibits **predictability** of **stock** returns. Bali and Hovakimian [1] examines if the difference of realized and **implied** **volatility** of firms can forecast the cross- section of future **stock** **return**. They indicate a significant negative association between **volatility** spread and ex- pected **return**. Bali and Hovakimian [1] also identify that the difference of call-put **implied** **volatility** can predict the future **return**. Extensive studies have been made in investigating relation of **volatility** and future **return**. Ang et al. [2] show that the idiosyncratic **volatility** relative to Fama and French [3] model of individual **stock** is nega- tively associated with its future **return**. But the study generally uses the historical **stock** price **volatility** to de- velop expectation of future **return**. Similarly, Bali and Cakici [4] employ 60 months of **stock** returns observa- tions to develop one-month ahead future **volatility**. Bali and Hovakimian [1] further examine the relation between the expected future **volatility** proxied by **implied** volatil- ity and cross section of expected **return**. In contrast to these studies, I contribute to the literature by examining the market expectation of the required rate of **return** of individual **stock** and investigate if the rate of **return** im- plied by **stock** options exhibits **predictability** of the cross section of expected **return**.

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This study aims to contribute to the existing literature on **volatility** **measures**, **volatility** risk and **stock** **return** **predictability** in a number of ways. First, to our knowledge, it is the first research analyzing the effect of differ- ent idiosyncratic **volatility** **measures** for a period that involves both the dotcom bubble and the recent financial crisis. This will shed light on the relation between idiosyncratic **volatility** and **stock** prices in periods when S&P500 dropped at least 20 percent. Second, the empirical findings will disclose more information on the accu- racy of different **volatility** **measures**. Third, this research will extend the work of [2] by including and analyzing firm-specific characteristics. Fourth, we control for possible short-sale constraints and liquidity issues effect on **stock** returns.

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We select one call and one put for each **stock** in each month of the sample period. All options have expirations of one month and moneyness close to one (these are the same options that were used to generate the **implied** volatilities used in Table 2). We hold these options till expiration. The returns on options are computed from the mid-point opening price (MidP) and from the effective bid-ask spread (ESPR), estimated to be equal to 50%, 75%, and 100% of the quoted spread (QSPR). The closing price of options is equal to the terminal payoff of the **option** depending on the **stock** price and the strike price of the **option**. The delta-hedged portfolios are constructed by buying (or shorting) appropriate shares of underlying **stock**. The hedge ratio for these portfolios is calculated using the current IV estimate. We sort stocks independently into deciles based on based on the **implied** **volatility** forecasts from Table 2 and into terciles based on **stock** options’ liquidity characteristics. For **volatility** sorts, decile ten is predicted to have the highest (positive) increase in **implied** **volatility** while decile one is predicted to have the lowest (negative) decrease in **implied** **volatility**. For **stock** options liquidity sorts, we consider groups based on the average quoted bid-ask spread of all the options series traded in the previous month, as well as groups based on daily average dollar volume of all the options series traded in the previous month. The monthly returns on options (or delta-hedged portfolios) are averaged across all the stocks in any particular sub-group. Panel A considers returns on long-short 10–1 straddles portfolio while Panel B considers returns on long-short 10–1 delta-hedged calls/puts. The table then reports the average **return** and the associated t-statistic (in parenthesis) of this continuous time-series of monthly returns in each of the three **stock** options’ liquidity sub-groups. The sample period is from January 1996 to May 2005.

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Our sample represents the US equity **option** market by comprising the **stock** options traded at the American **Stock** Exchange and the Chicago Board Options Exchange (CBOE) for the period from January 2001 to De- cember 2010. The data to undertake the research was collected from different sources. 1) The daily **implied** vo- latility for each individual company and the **option** open interest were collected from Tick Data and **Option** Me- trics; 2) **Stock** returns, share prices, and the number of shares outstanding are from Tick Data and CRSP and eq- uity book value are from Tick Data and Compustat; 3) daily returns for the the Carhart (1997) momentum factor (UMD) and three Fama and French (1993) factors (MKT, SMB, HML) were collected from Kenneth French’s website.

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Another policy implication of the market efficiently pricing in **volatility** is that speculators provide a stabilising influence on the foreign exchange market. Since speculators can buy or sell **volatility** through currency options which are efficiently priced, then policy makers should worry less about their role in determining exchange rates. Indeed there is a danger that the introduction of a “Tobin tax” on foreign exchange transactions could interfere with the efficiency and price discovery process in the foreign exchange market.

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i.e. the Black-Scholes model (BS). The conclusions we draw from the above comparison are sum- marized as following. First, all models appear to perform very poorly in pricing options, especially the long-term ITM options which are the most expensive ones. The Black-Scholes model based on historical **volatility** tends to systematically underprice deep ITM options but overprice deep OTM op- tions. Since the simulation results in the next section suggest the existence of a non-zero risk premium for the stochastic **volatility**, the overall overpricing of all SV models may be due to our assumption of zero risk premium for conditional **volatility**. As Lamoureux & Lastrapes (1993) point out, only if in- vestors are risk-neutral, or if the instantaneous **volatility** is uncorrelated with aggregate consumption and, therefore, is uncorrelated with marginal utility of wealth, is the **option** price irrelevant to the risk- preference. In the case of a negative market price of risk for stochastic **volatility**, the observed **option** prices will be lower than the risk-neutral prices, ceteris paribus. Second, the effect of stochastic in- terest rates on **option** prices is minimal in both cases of stochastic asset **return** **volatility** and constant asset **return** **volatility**, i.e. the differences between the general model and submodels 1 and those be- tween submodels 2 and 3 are negligible. Third, even though the pricing errors are relatively smaller for the SV models, they do not clearly outperform the Black-Scholes model as expected and actually share similar patterns of mispricing as the Black-Scholes model, i.e. underpricing of ITM options and overpricing of OTM options. While the asymmetric SV models do outperform all other models for pricing short-term options, overall they still tend to have very high relative **option** pricing errors. Fi- nally, as an alternative measure to gauge the **option** pricing errors, we further calculate the **implied** Black-Scholes **volatility** from model **option** prices for alternative models. The **implied** Black-Scholes **volatility** is believed to be less sensitive to the degree of moneyness and length of maturity. A careful look at the **implied** Black-Scholes **volatility** of the asymmetric SV model prices together with those of symmetric SV model prices and Black-Scholes model prices, as reported in Figure 7, reveals that the **implied** Black-Scholes **volatility** curve of the asymmetric model prices against maturity has a cur- vature closer to the **implied** Black-Scholes **volatility** from observed market **option** prices, suggesting such pricing biases may be easier to correct.

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In February 2000, Datastream enhanced the options models and provided new options sensitivities to the existing options coverage. This enhancement has been produced in partnership with MB Risk Management (MBRM) using their world famous UNIVOPT – Universal Options Add In software which is regarded by many dealers and risk managers as the industry standard **option** pricing and risk management system.

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Table 5 presents the results of out-of-sample tests for the null of equal **predictability** between the two models. In this case, the two models are non-nested and the DMW test can be used with standard normal critical values. The Fed model with Taylor rule fundamentals outperforms the original Fed model when the initial forecast starts in 1989. This period coincides with the Great Moderation, the period of significant decline in overall macroeconomic **volatility** (including lower **volatility** of inflation and output) since the mid-1980s, where the U.S. monetary policy is successfully characterized by a variant of the Taylor rule. The Fed model with Taylor rule fundamentals outperforms the original Fed model with at least one measure of the output gap for window sizes with the first forecast dates in September 1989, November 1991, and August 1994. Since most of the empirical evidence is consistent with the hypothesis that the Fed adopted some variant of the Taylor rule starting in the mid-1980s, our findings indicate that Taylor rule fundamentals contain additional predictive information for **stock** returns.

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