Slow Diffusion of Information and Price Momentum in Stocks: Evidence from Options Markets

Transcription

1 Slow Diffusion of Information and Price Momentum in Stocks: Evidence from Options Markets Zhuo Chen Andrea Lu November 10, 2014 Abstract This paper investigates the source of price momentum in the stock market using information from options markets. We provide direct evidence of the gradual information diffusion model in Hong and Stein (1999): momentum profits are larger for stocks whose information diffuses slowly into the stock market. We exploit the options markets to identify stocks with slow information diffusion speed. As informed traders trade options to realize the information that has not been fully incorporated in the stock price, we are able to enhance the momentum strategy by selecting winner/loser stocks with high growth/large drop in call option implied volatility. Our empirical strategy generates a risk-adjusted alpha of 1.8% per month over the period, during which the simple momentum strategy fails to perform. The results are robust to the impact of earnings announcement, transaction costs, industry concentration, and choice of options moneyness and time-to-maturity. Finally, our finding is not driven by existing stock- or option-related characteristics that are known the improve momentum. JEL Classification: G10, G11, G12, G13 Keywords: Momentum, Implied Volatility PBC School of Finance, Tsinghua University. chenzh@pbcsf.tsinghua.edu.cn. Tel: Department of Finance, The University of Melbourne. andrea.lu@unimelb.edu.au. Tel: For helpful comments and discussions, the authors thank Torben Andersen, Snehal Banerjee, Zhi Da, Stephen Figlewski, Kathleen Hagerty, Ravi Jagannathan, Robert Korajczyk, Chayawat Ornthanalai (discussant), Todd Pulvino, Costis Skiadas, Viktor Todorov, and participants at the 3 rd International Conference on Futures and Derivative Markets, the 2014 NFA Annual Conference, the 2014 PanAgora Crowell Memorial Prize Presentation, the 2013 FMA Doctoral Student Consortium, the 2013 Chicago Quantitative Alliance Fall Conference, the 2013 PKU-Tsinghua-Stanford Conference in Quantitative Finance, and the Kellogg finance baglunch. All errors remain ours 1

2 1 Introduction The diffusion of information plays a crucial role in explaining price momentum. Researchers attempt to understand momentum from investors process and reaction to firm-specific information, and how such information is conveyed into stock price. Among them, Hong and Stein (1999) propose a model that shows how slow diffusion of information and interaction of two types of investors, newswatchers and momentum traders, can explain price underreaction in the short run and overreaction in the median run. 1 A direct prediction of their model is that momentum should be stronger for stocks with slower information diffusion speed. In this paper, we provide empirical support for their theoretical prediction by identifying stocks information diffusion speed using options markets. We show that momentum profit concentrates in stocks with slow information diffusion speed. An enhanced momentum strategy that is constructed within such stocks perform well, even during periods when the simple momentum strategy fails to perform. Although the correct identification of information diffusion speed is important in explaining momentum, in reality it is easier said than done. Hong, Lim and Stein (2000) use size and analyst coverage to classify stocks into slow and fast diffusion groups. They find momentum effect is stronger for the slow diffusion group characterized by small size and low analyst coverage. However, size and analyst coverage are static firm-specific characteristics that do not change much over time, while information diffusion speed could be information-specific and time-varying. For example, the manager of a company tends to have a piece of positive information to be perceived by investors fast, but may try to delay the diffusion of another piece of negative information (Kothari, Shu, and Wysocki (2009)). Therefore, our goal is to 1 In their model setup, newswatchers trade stocks only based on fundamental information while momentum traders make their investment decisions solely based on forecasts from historical prices. As information slowly diffuses into the market, the stock price first experiences underreaction as newswatchers adjust to the new information, and then experiences overreaction as momentum traders attempt to profit from the previous price movement. 2

3 identify individual stocks information diffusion speed and construct the momentum portfolio using stocks with continued information diffusion in the holding period. We take advantage of the options markets to dynamically refine our momentum portfolio selection according to stocks information diffusion speed. Options markets provide an effective channel for price discovery and information diffusion (Manaster and Rendleman (1982)). Previous researchers find that informed traders may prefer options markets to the stock market for various reasons, such as embedded leverage of options (Black (1975), Frazzini and Pedersen (2012)), investors short sale constraints (Figlewski and Webb (1993)), transaction costs (Cox and Rubinstein (1985)), and so forth. Thus, options prices may contain material information that has not been fully reflected in stock prices. When a piece of information starts to diffuse into the market, option traders have informational advantage to distinguish whether the informational content has conveyed into the stock price. Billings and Jennings (2011) find that an increase in uncertainty-adjusted option prices prior to earnings announcements is positively related to the sensitivity between the stock market reaction and earnings announcements. Their finding indicates that option traders prefer options of those stocks with slower information diffusion speed regarding earnings announcements. We generalize their argument through out the course of information diffusion. When the information diffusion speed is slow, upon discovering more information to continue releasing in the stock market, they will realize their superior information in the options markets, causing options prices to change. Therefore, within those winner/loser stocks that have started their information diffusion process, trades in options markets allow us to identify those stocks with slower information diffusion speed and thus further price adjustment. Specifically, for winner stocks, if we also observe prices of call options increase or prices of put options decrease, it indicates that informed option traders believe that not all relevant information has released and there will be further price appreciation. The same logic applies to loser stocks: informed option traders can either sell call options or buy put options if they think that the negative 3

4 information associated with those loser stocks has not been fully incorporated in the stock prices. Based on the logic above, we use implied volatility growth of options to identify stocks information diffusion speed and construct the enhanced momentum portfolio. A large growth/decline in the call option implied volatility reflects informed option traders buy/sell position and their belief that positive/negative information will continue to convey into stock price. Thus to enhance the stock selection based on information diffusion speed, conditional on winner stocks, we long those with the largest growth in call option implied volatility. Similarly, conditional on loser stocks, we short those with the largest decline in call option implied volatility. Our enhanced momentum strategy generates a risk-adjusted alpha of 1.78% per month over the period, while a simple momentum strategy fails to perform during the same period. Moreover, Fama-MacBeth regression shows that the return spread is attributed to the interaction of the momentum effect and the correct identification of information diffusion speed with implied volatility growth. Similar improvement can be done using implied volatility growth of put options, i.e., longing winner stocks with the largest decline in put option implied volatility and shorting loser stocks with the largest increase in put option implied volatility. However, the size of the improvement is smaller. Our results are robust to a battery of alternatives. First, although it is well-known that options are more actively traded before earnings announcements, we find that the informativeness of implied volatility growth about stocks information diffusion is not limited to earnings announcements. Similar results can be found even if we exclude stocks that have earnings announcements in the holding month. Second, the profitability of the enhanced momentum strategy is robust in consideration of transaction costs. Third, we show that the good performance is not driven by industry momentum (Moskowitz and Grinblatt (1999)) or several stock-level characteristics (Bandarchuk and Hilscher (2012)). Fourth, the portfolio return remains significant if we use implied volatility growth of options that have time-to- 4

5 maturity equal to the holding period (two, three, or six months), while the magnitude of return is smaller. This result indicates that besides the correct identification of information diffusion speed, repeatedly updating the identification also contributes to the improvement. Finally, our results also hold if we use out-of-the-money options, control for the persistency of implied volatility, implement independent double sorting, and construct a value-weighted portfolio. Our paper adds to the momentum literature. 2 Although numerous papers have shown the existence of price momentum across asset classes, sample periods, and geographic markets, our paper, to the best of our knowledge, is the first to explain momentum profit using information from individual stock options. In addition, our paper is the first to document the poor performance of the simple momentum strategy for the most recent period (the OptionMetrics data range). However, by incorporating information from options markets, we are able to generate statistically significant raw/risk-adjusted returns for momentum strategy in the same period. Although many researchers find that momentum is stronger when uncertainty is higher, our finding is different from this uncertainty explanation. The high momentum profit is not due to mechanically finer sorting on more volatile stocks, but it is attributed to the selection of stocks with slow information diffusion speed. Our paper is also related to the growing research that studies the implication of options markets on equity returns. Our empirical approach of using growth of individual stock option implied volatility is similar to An et al. (2014), who find that the returns of stocks with a large first difference of call option implied volatility tend to rise in the next month, whereas 2 Papers documenting momentum effect include Jagadeesh and Titman (1993), (2001), (2012), Carhart (1997), Novy-Marx (2012), and Israel and Moskowitz (2013). Several papers also find that momentum effect exists in international markets (Asness et al. (2013), Asness (2011), Chui et al. (2010)). Many papers implement double sorting on firm-level characteristics to strengthen momentum profit (Hong et al (2000), Lee and Swaminathan (2000), Zhang (2006), Da et al. (2012), Hillert et al. (2012)). Bandarchuk and Hilscher (2012) provide a comprehensive summary of all the characteristic-based double-sorting strategies that are actually thinner sorting on more extreme returns. Papers that try to explain momentum effect include Daniel, Hirshleifer, and Subrahmanyam (1998), Johnson (2002), and Sagi and Seasholes (2007) 5

6 a large first difference in put option implied volatility predicts lower future returns. Our paper is different from An et al. s (2014) as our focus is on the role played by option implied volatility growth on identifying stocks information diffusion speed and how it interacts with the momentum effect. Fama-MacBeth regression also confirms that the outperformance of our double-sorted momentum strategy is not a simple linear summation of the momentum effect and the option effect. Besides An et al. (2014), many others have studied the predictive relationship between options markets and equity returns. Xing et al. (2010) find that volatility smirk defined as the difference between implied volatility of out-of-the-money put option and implied volatility of at-the-money call option has strong predictive power for future returns. Bali and Hovakimian (2009) find that realized volatility and implied volatility spread predicts lower future returns, whereas call and put implied volatility spread predicts higher future returns. Cremers and Weinbaum (2010) find that deviation from put-call parity predicts future stock returns. 3 The remainder of the paper is organized as follows. In Section 2 we describe the data. Section 3 presents the identification of slow information diffusion stocks and main empirical findings. We conduct a battery of robustness tests in Section 4. Section 5 concludes. 3 Other papers include Easley, O Hara and Srinivas (1998), who find that option volume contains superior information as informed traders may choose options markets over the stock market under some condition; Pan and Poteshman (2006), who find that the put-call option volume ratio has information content about future stock returns; Goyal and Saretto (2009), who find that stocks with a larger difference between historical realized volatility and at-the-money implied volatility have higher monthly returns; Johnson and So (2012), who show a negative relationship between option to stock trading volume ratio and future stock returns; Kehrle and Puhan (2013), who discover that option demand imbalance has predictive power for equity returns; Yan (2011), who finds that expected stock return is a function of the slope of option implied volatility smile; and Hu (2014), who finds that the stock market order imbalance induced by option transactions have strong cross-sectional predictive power for stock returns. There are also papers that study other implications of options markets on financial market or firm decisions: Cremers et al. (2008) study option implied volatility s predictive power on corporate bond; Roll et al. (2009) find that options trading is positively associated with firm values as well as information production; Stein and Stone (2012) study the impact of option implied volatility on firm s investment and hiring decisions; Vilkov and Xiao (2012) investigate the role of option implied volatility in predicting stocks extreme returns; Baltussen et al. (2012) find cross-sectional return prediction captured by higher second-order uncertainty using individual option vol-of-vol data; Cao et al. (2005) study the relationship between option volume and takeover announcement day returns; and Roll et al. (2010) suggest that the option/stock trading volume ratio relates positively with the post-announcement absolute returns. Acharya and Johnson (2007) also find evidence of significant incremental information revelation in the credit default swap market. 6

7 2 Data 2.1 Data overview Our data primarily come from two sources. The stock data are downloaded from the CRSP. We include all common stocks that are traded on NYSE, Amex, and Nasdaq. To ensure liquidity, we exclude stocks with market capitalization that are below the 10% NYSE cutoff or have price less than five dollars at the end of formation month. Data of implied volatility are from OptionMetrics Implied Volatility Surface. Our sample includes implied volatility of options written on stocks that also have data in CRSP. Because OptionMetrics data start in 1996, our final sample is from January 1996 to December [Insert Table 1] Table 1 presents the year-by-year descriptive statistics, including average number of stocks, average market size, and median market size. The average number of stocks in CRSP that satisfies the liquidity requirement is 2,762, across all years from 1996 to Nevertheless, the average number has gradually decreased from 3,564 in 1996 to 2,135 in Contrary to the decrease in the number of stocks, market size has increased significantly: the average size in 2011 is more than three and a half times than that in Not all stocks that pass the liquidity filter have listed option contracts; ones that do are often large in size. The CRSP-OptionMetrics-merged data set contains 1,536 stocks on average, covering more than half of the stocks in the CRSP data set. The average market capitalization in the merged data set is 6,741 million, which is about one and a half times larger than the average size of stocks in the CRSP data set. The median market capitalization is much smaller than the mean in both data sets. Note that the fraction of stocks with option contracts has expanded over time: only 15.8% CRSP stocks do not have options in 2011, whereas this number is 73.8% in Stocks with option contracts are less subject to the liquidity requirement: 7

8 almost half of all common stocks do not meet the liquidity requirement, whereas this rate is only 13% for stocks with option contracts. Overall, stocks we study in this paper are relatively large stocks that are typically considered to exhibit weaker momentum. 2.2 Data on option implied volatility OptionMetrics provides a comprehensive coverage of option data for U.S. equities. The Implied Volatility Surface covers almost 100% of equity options currently or historically listed on U.S. exchanges. The Implied Volatility Surface provides the implied volatility of standardized call and put options for each stock on a fixed grid in the time-to-expiration and moneyness coordinates. It considers expirations of 30, 60, 91, 122, 152, 182, 273, 365, 547, and 730 calendar days. Moneyness is measured in deltas, taking values from 0.20 to 0.80 with an increment of 0.05 (negative deltas for put options). The implied volatility of standardized option with a combination of expiration and moneyness is interpolated from implied volatilities of available listed option contracts with various maturities and strikes using a kernel smoothing technique. The implied volatility is computed using a pricing algorithm that is based on the Cox-Ross-Rubinstein binomial tree. Specifically, the option expiration period is dividend into N subperiods. 4 In each subperiod, the underlying stock s price is assumed to move either up or down, and the size of the movement is determined by the implied volatility and the length of the subperiod. The tree that contains all the possible security price movements is then built according to the current security price. The price of the option can be computed using backward computation. The model is run iteratively until the theoretical price of the option converges to its current market price. 5 The market price 4 The number of subperiods used is typically over 1, One advantage of this approach is that it correctly adjusts for the potential early exercise or future dividend payments. The security s current dividend yield, defined as the most recently announced dividend payment divided by the security s most recent closing price, is assumed to remain constant over the remaining life of the option. It is also assumed that the security pays dividends at specified predetermined times. When future dividend dates are not announced, OptionMetrics uses an extrapolation algorithm to project ex-dividend dates according to securities usual dividend payment frequency. 8

9 of the option used in the implied volatility computation is the settlement price. In case the settlement price is not available, the last traded price, or the midpoint of the closing bid and offer prices (in the order of availability), is taken as the price. The interpolated implied volatility, with a given combination of delta and maturity, is calculated as a weighted average of implied volatilities of all existing option contracts on that date, where the weights are functions of options Vegas and measures of the distance between the option and the target maturity and delta. An interpolated implied volatility is only included if there exists enough underlying option price data on that date. Computation is done using only the current available data without forward-looking bias. We use implied volatilities of call and put options with a delta of 0.5 (-0.5 for put) and time-to-maturity from one-month (30 days) to six-month (182 days). Options with a delta of 0.5 have two advantages. First, they have high trading volume as they are closest to atthe-money options. High liquidity means tighter bid-ask spreads and more accurate implied volatility interpolation. Second, although being close to at-the-money, options with a delta of 0.5 are slightly out-of-the-money so that the simple Put-Call Parity does not have to hold. Empirical deviation of put-call parity leaves room for us to explore the difference of information content between the call option implied volatility and put option implied volatility. In the robustness test, we also use implied volatility of call and put options with other moneyness and time-to-maturity. The variable we use to identify stocks information diffusion speed is option implied volatility growth, denoted by IV C and IV P for call and put options, respectively. The implied volatility growth is calculated over the last five trading days of each calendar month. Specifically, the implied volatility growth in month t is defined as the implied volatility on the last trading day of month t divided by the implied volatility five trading days earlier. For example, suppose the last trading day falls on a Wednesday, the growth is computed using the implied volatility of that day and the previous Wednesday. In case when the previous 9

10 Wednesday is a public holiday, we use the implied volatility of the nearest previous trading day. Table 2 presents summary statistics of option implied volatility growth. Average and standard deviation are computed from the monthly observations across all options and then averaged across 12 months within a year. The average implied volatility growth for call and put options with a delta of 0.5 and maturity of one month is 0.31% and 0.19%, respectively. Call option has a slightly higher cross-sectional dispersion in implied volatility growth relative to that of put option. This pattern also holds in longer maturity options. In addition, implied volatility growth of options with longer maturity exhibits lower cross-sectional average and standard deviation, consistent with the fact that long maturity options are less traded than short maturity options. [Insert Table 2] 3 Momentum strategy enhanced by options markets information 3.1 Performance of the traditional momentum strategy for the period We first examine the performance of a simple momentum strategy for the period. Momentum portfolios are constructed following the standard procedure described by Jegadeesh and Titman (1993). Specifically, we assign stocks into ten equal-weighted portfolios according to their past J-month cumulative returns and then hold the winner portfolio and short the loser portfolio for K months. We follow Jegadeesh and Titman (1993) to skip one month between the formation month and the holding month to mitigate the influence of 10

11 temporary price pressure due to high-frequency phenomena or bid-ask bounce. We construct the momentum portfolio using each of the two sets of stocks: the first is all U.S. common stocks traded on the three major exchanges that satisfy the liquidity requirement at the end of formation month. The second group is a subset of the first that contains stocks with listed option contracts. Table 3 presents monthly winner-minus-loser returns for various combinations of formation and holding periods. [Insert Table 3] Surprisingly, the traditional momentum strategy is only marginally profitable for the 1996 to 2011 period. 6 Panel A shows that the returns of various momentum portfolios are almost always insignificant. The return is only marginally significant when a combination of (J = 6,K = 1) is used for portfolio formation and holding. In Panel B, we report the results constructed over stocks with listed options: no return spread is significant while the magnitudes are all below 1% per month. This finding is in contradiction with common wisdom about momentum. A few reasons could explain the disappearance of momentum profit. First, our sample period contains a couple of crises that may lead to volatile momentum performance. Jegadeesh and Titman (2012) find that the raw return of the momentum strategy is % in 2009 when the market rebounded from the financial crisis. Daniel et al. (2013) also find that the momentum strategy could have a sharp performance decline as the market rebounds. Second, stocks with options are relatively large stocks that are associated with small momentum returns. Our finding is consistent with Hong et al. (2000), who find that the profitability of momentum strategies declines sharply with firm size. 6 Some papers study momentum in the most recent two decades. Israel and Moskowitz (2013) find that momentum strategy is still profitable for the period, but the monthly return is only about 70 bps. Novy-Marx (2012) finds that momentum strategy is much stronger if investors skip six months instead of one month after formation for the period. Ours is the first paper that looks at the period as the OptionMetrics data begin in

12 3.2 Identification of stocks information diffusion speed using implied volatility growth Hong and Stein (1999) propose a theoretical explanation for momentum. In their model, two groups of investors, newswatchers and momentum traders, interact in the stock market. Newswatchers trade stocks only based on information of future fundamentals, without relying on current or past prices. On the other hand, momentum traders trade solely on their price forecast formed using historical prices. As firm-specific information gradually diffuses into the stock market, prices first experience underreaction as newswatchers slowly adjust to such information. Prices then experience overreaction as momentum traders attempt to profit from the underreaction caused by newswatchers. Slow diffusion of information generates both underreaction and overreaction repeatedly, driving the price momentum. One important prediction of their paper is that stocks with slower information diffusion should exhibit more pronounced momentum. 7 Their story also implies that different pieces of news across stocks and time are heterogeneous in terms of information diffusion speed. The price of one stock could reflect firm-related information faster than the price of another stock. Alternatively, the price of one stock could reflect one piece of information faster than the other piece of information at a different time. Therefore, momentum traders can benefit if they construct the portfolio with stocks that have slow information diffusion speed, i.e., stocks whose prices have not fully incorporated the relevant information. We identify the speed of information diffusion using options markets. Compared to stocks static characteristics such as size or analyst coverage, options provide a more timely and precise identification in several ways. First, options provide a number of advantages that attract informed investors to realize their superior information in the options markets instead of the stock market. For example, leverage constrained investors could use options to invest with 7 Hong et al. (2000) test this prediction and find that momentum portfolios formed on small stocks or stocks with low analyst coverage deliver higher returns. 12

13 borrowed money. When a stock has short sale constraint, investors can also use options to express their negative view on the stock. Second, due to the benefit of options markets, researchers have empirically found that options markets could be a more informed channel for price discovery and information diffusion. 8 When sophisticated informed investors have positive private news on a company, they buy call options or sell put options if such information has not been reflected in the stock price. Therefore, call price appreciation or put price depreciation might convey informative content about informed traders view on the information diffusion stage of individual stocks. Third, Billings and Jennings (2011) find that pre earnings announcement option price change is positively related to option traders view on the sensitivity between the stock price reaction and the earnings announcements. For example, a large increase in call option price (or a large drop in put option price) implies informed option traders belief that the stock price will have a large increase to the potential positive earnings announcement, which is equivalent to saying that positive information is going to be diffused into the stock price. While the study of Billings and Jennings (2011) focuses on earnings announcements, the same logic could be applied to normal periods as well. We exploit the information of options markets to improve the momentum strategy. Past cumulative returns (momentum effect) of individual stocks could be used to detect stocks information diffusion, while possible future information diffusion and time-varying diffusion speed cannot be identified by only looking at such past returns. On the other hand, option prices reflect informed investors view on whether such information diffusion would continue being conveyed into stock prices. If we observe positive past cumulative return paired with call option price appreciation (put option price depreciation), it implies that option traders believe that the diffusion speed associated with the current piece of information is slow in the sense that it has started and will continue to diffuse in the stock market leading to further stock price increase. The same 8 Papers include but not limited to Easley et al. (1998); Chakravarty et al. (2004); Cao, Chen, and Griffin (2005); Chern et al. (2008) 13

14 applies to those loser stocks with negative past cumulative returns. Since option implied volatility is a monotonic mapping of option price, we identify the sign and magnitude of stocks information diffusion speed using option implied volatility growth. Notice that we do not exclude the possibility that informed investors could also trade on the stock market. What we assume here is that option traders are in general more sophisticated with better understanding on whether information diffusion would continue into the stock price. The identification of information diffusion speed helps to improve the price momentum in the stock market. To construct the enhanced momentum portfolio, we first sort stocks into ten groups based on their cumulative returns over the past six months. We fix the formation period to keep the number of strategies tractable. 9 The group of stocks with the highest past cumulative returns is the winner portfolio, and the one with the lowest past cumulative returns is the loser portfolio. These are stocks whose firm-specific good or bad information has already started diffusing into the stock market. We skip one month post the formation month. Instead of simply holding the winner portfolio (or shorting the loser portfolio), we take positions on a subset of stocks in the winner and loser pools that are more likely to experience continued information diffusion, as suggested by the options markets. Specifically, at the beginning of each month during the holding period, we sort stocks within the winner and loser pools into three groups, namely, slow, median, and fast, based on implied volatility growth over the most recent trading week. 10 They are named in this way because, given the detection of information diffusion, the likelihood of continuation in information diffusion is closely related to the diffusion speed. Stocks with slow (fast) information diffusion are more (less) likely to experience further information diffusion. Using call options, stocks with slow information diffusion are winners (or loser) stocks that option traders believe good (bad) news will continue to diffuse into the stock market, and thus ones with large (small) call 9 J =6 is also the formation period that delivers the highest return for the simple momentum strategy in the relevant sample period. 10 This is the last trading week of the previous month. In addition, to rule out the effect of extreme values, we winsorize the implied volatility growth at 1% and 99%. 14

15 option implied volatility growth. Using put options, stocks with slow information diffusion among winner (loser) stocks are the ones with small (large) growth in implied volatility. We construct equal-weighted winner-minus-loser momentum portfolio with this double sorting strategy by taking a long position in the refined winner stocks and a short position in the refined loser stocks. We hold the portfolio for one month and re-rank stocks based on implied volatility growth the next month during the holding period Empirical results Table 4 presents average monthly returns for the hedged winner-minus-loser portfolios (P10- P1) with holding period K = 1, 3, 6 using call option information. D F, D M, and D S represent portfolios constructed by selecting stocks with fast, median, and slow diffusion, respectively. Although our sample contains large stocks that usually exhibit smaller momentum effect, picking slow diffusion stocks within the winner and loser pools generates large momentum profit. When the holding period is one month, the average excess return for the refined momentum portfolio is 1.55% per month. 12 We also compute the risk-adjusted alphas relative to the CAPM, the Fama-French three-factor model, and a four-factor model of the Fama- French three factors plus the short-term reversal (STR) factor. 13 The alpha is 1.78% per month after controlling for all four risk factors, which is around 21% per year. Large and statistically significant returns remain for longer holding horizons. The risk-adjusted alpha is 1.25% per month when the holding period is six months. Panel B of Table 4 assesses the effect of selecting stocks with information diffusion continuation based on the call option 11 We keep the momentum ranking constant over the holding months and use dependent double sorting. We also consider the case in which we implement independent double sorting strategy. Our results are robust to different portfolio construction procedures. 12 The excess return for the momentum strategy using all NYSE/AMEX/NASDAQ stocks during the same period is 1.12% per month, and the excess return for the momentum strategy using stocks that have listed options is 0.94% per month. 13 Portfolios beta loadings and adjusted R 2 under this four-factor model are presented in Table A.1. Beta loadings and adjusted R 2 estimated under the CAPM or the Fama-French three-factor model are available upon request. 15

16 implied volatility growth. It reports the return difference of two winner/loser portfolios, one is constructed within stocks with slow information diffusion and the other is constructed within stocks with fast information diffusion. Taking the one-month holding period case as an example, winner stocks with large call option implied volatility growth earn a higher four-factor adjusted alpha of 55 bps per month than winner stocks with small call option implied volatility growth. Similar result is found for loser stocks and for longer holding horizons. [Insert Table 4] On the other hand, we do not observe the same pattern when sorting by put option implied volatility growth as presented in Table 5. Momentum portfolio constructed using stocks with slow information diffusion speed only generates a significant return when the holding period is short (K = 1), but not for longer holding horizons (K = 3 or K = 6). The magnitude of momentum profit is smaller than that generated by sorting on call implied volatility growth. Furthermore, the differences between D S (slow diffusion group) and D F (fast diffusion group) momentum portfolios are not significant as shown in the last row of Panel B of Table 5. Empirical results indicate that the put option seems to be less informative for identifying stocks information diffusion speed. [Insert Table 5] We provide empirical evidence on how identification of stocks future information diffusion helps refine stock selection within the winner and loser stocks. The enhanced momentum portfolio earns a risk-adjusted alpha over 20% per year by selecting winner/loser stocks with large growth/drop in call option implied volatility. Previous researchers have found the predictive power of options on stock returns. Our methodology is in line with theirs in terms of private information on companies fundamentals being first perceived by option traders. However, the outperfomance of our momentum strategy comes from the fact that we use 16

17 information embedded in options to dynamically identify stocks information diffusion speed. The return spread of our strategy is larger than that of a portfolio single-sorted on option implied volatility growth (Table A.2). We implement Fama-MacBeth regressions to examine whether the strong performance of the double-sorted momentum portfolio comes from the interaction of the past cumulative performance and the identification of slow information diffusion. The regression specification is as following: R i,t+1 = β 0 +β 1 P astreturn i,t +β 2 IV C(P ) i,t +β 3 P astreturn i,t IV ˆ C(P ) i,t +β 4 X i,t +ɛ i,t, (1) where ˆ IV C i,t = IV C i,t, ˆ IV P i,t = IV P i,t if P astreturn i,t > median(p astreturn i,t ); ˆ IV C i,t = IV C i,t, ˆ IV P i,t = IV P i,t if P astreturn i,t < median(p astreturn i,t ). The specification of IV ˆ C(P ) i,t is consistent with our stock selection procedure in the portfolio construction. X i,t consists of a list of control variables, including stock size, stock price, book-tomarket ratio, stock trading volume, number of analyst coverage, the maximum daily return, market beta, Amihud illiquidity measure, realized volatility, idiosyncratic volatility, options open interest growth, and options trading volume change. 14 Results are presented in Table 6. We find that while call option implied volatility growth has a strong predictive power on holding period return (Column (2)), past cumulative return does not (Column (3)), over the sample period of This finding is consistent with the predictive power of options documented in previous studies and the weak performance of a simple momentum strategy in the earlier section. However, the interaction of momentum and call option implied volatility growth plays an important role, as the coefficient estimate on the cross term 14 The open interest growth is calculated as the total open interest on the last trading day prior to the holding month divided by the value five trading days earlier. The option trading volume change is the total volume measured on the last trading day prior to the holding month minus the total volume five trading days earlier. We use the volume change instead of growth because of the presence of zero volume. Both open interest and volume are calculated using all call (put) options with maturities between 30 days and 365 days. We exclude short maturity options to avoid the potential mechanical changes near expiration. 17

18 β 3 is positive and statistically significant. Similar results are found when we use put options. The last two columns show the results when only winner and loser stocks (extreme stocks) are included in the sample. In case of call options, only the interaction term β 3 is significant, while neither past cumulative return or implied volatility growth has any predictive power alone. Results of Fama-MacBeth regressions imply that it is indeed the interaction between the momentum and implied volatility growth that contributes to the strong performance of our portfolio. To ensure that implied volatility growth is not related to other well-documented stock- or option-specific characteristics that can improve momentum effect, 15 we calculate the median of several characteristics for stocks in the double-sorted portfolios. We consider ten characteristics, including stock size, stock price, stock trading volume, stock analyst coverage, past cumulative return, realized volatility, idiosyncratic volatility, maximum daily return, option open interest growth, and option trading volume change. The median value of each characteristic within each double-sorted portfolio is presented in Table 7. Instead of displaying cells in terms of fast, medium, or slow (D F, D M, D S ), which involves different rankings for winner and loser stocks, we display cells according to the actual implied volatility growth (small, medium, and large). The portfolios that we pick for the long and short sides as part of the enhanced momentum portfolio are highlighted in bold. We see no obvious pattern in those characteristics across volatility growth sorted portfolios, indicating that stock selection based on implied volatility growth is not equivalent to selecting stocks based on these ten characteristics. In other words, by forming an enhanced momentum portfolio using implied volatility growth, we are not simply implementing a narrower sorting on more extreme winner or loser stocks based on these characteristics above. [Insert Table 7] 15 Bandarchuk and Hilscher (2012) provides a comprehensive summary of stock-level characteristics that can enhance momentum profit. 18

19 4 Robustness analysis In this section, we present a number of robustness tests. We examine the earnings announcement effect, the impact of transaction cost, the industry concentration of the momentum portfolio, and performance of portfolios that are refined using options with maturity matched with holding horizon. Other tests include using out-of-the-money options, constructing value-weighted portfolios, using monthly implied volatility growth, and examining the informational content of implied volatility growth. 4.1 Earnings announcement In the previous section, we show that the hedged winner-minus-lower portfolio enhanced with options markets information delivers a risk-adjusted alpha of 1.78% per month. The outperformance is attributed to the effective identification of stocks information diffusion speed using implied volatility growth. Meanwhile, it is well known that implied volatility increases significantly before earnings announcements. We examine whether our finding is caused by informational advantage of options traders around earnings announcements. We construct the enhanced momentum portfolio using stocks without earnings announcements in the holding month. Table 8 presents the monthly portfolio returns when the holding period is one month. 16 We find similar results for both unadjusted and risk-adjusted returns compared to the case where all stocks are used. Results are also unaffected if we use the put option implied volatility growth. [Insert Table 8] 16 Results with alternative holding periods are similar and available upon request. 19

20 4.2 Transaction cost Momentum strategy is known to have high turnover. Such high turnover also applies to our double sorting strategy. Taking the (J = 6,S = 1,K = 1) strategy as an example, only 10% of the stocks do not need to rebalance each month. In this section, we assess the profitability of the options improved momentum strategy after considering transaction costs. Due to the lack of data on realized transaction costs, we take an alternative approach by imposing a restriction on portfolio rebalancing. Specifically, each month, we rebalance x% of the largest stocks that needs rebalancing. We find that the performance of the option improved momentum strategy is robust to the imposed restriction. Table 9 presents the results on the call option improved momentum portfolios. 17 When 80% of the stocks are allowed to rebalance, the risk-adjusted alpha is 1.57% per month with a t-statistic of When we only allow a turnover of 20%, the alpha is 0.86% with a t-statistic of Similar results are also found for value-weighted portfolios. [Insert Table 9] 4.3 Industry concentration It is possible that our portfolio construction procedure actually results in selecting stocks with high industry concentration (Moskowitz and Grinblatt (1999)). To address this question, we compute industry concentration of the winner and the loser portfolios over time, and study its correlation with the portfolio return. We measure industry concentration using the Herfindahl-Hirschman Index (HHI) as expressed in Equation 2. HHI t = Σ Nt i=1 s2 i,t (2) 17 Results for the put options enhanced momentum portfolios are available upon request. 20

21 The HHI of a portfolio in a given month is computed as the sum of the squared stock share of industry i, s i,t, where s i,t is the fraction of stocks that belong to industry i. 18 As a result, the HHI takes a positive value from zero to one with a larger number indicating higher concentration. Panel A of Figure. 1 plots the time series of the HHIs for the winner and loser portfolios constructed using the call option-based benchmark strategy, in comparison to the HHIs of all qualifying stocks. We see that the HHIs for both the winner and the loser portfolios exhibit large time series variation, and such variation is more pronounced in the first half of the sample. Although both portfolios are less diversified relative to the portfolio constructed using all stocks, it is uncommon to see HHIs at extremely high levels: a vast majority of the sample has an HHI that is less than 0.5. Moreover, the correlations between the winner/loser portfolios HHIs and the return of the winner-minus-loser portfolio is 5.9% and 4.5%, respectively; the correlation between the HHIs of the winner/loser portfolio and the returns of the corresponding winner/loser portfolio is 1.7% and 5.9%. Similar results are found for portfolios sorted using put options implied volatility growth as shown in Panel B of Figure 1. [Insert Figure 1] 4.4 Lazy updating In the benchmark strategy, stocks are sorted into portfolios according to past cumulative return and option implied volatility growth. Options used are standardized call (put) options with 30-day-to-maturity and a delta of 0.5(-0.5). While the cumulative return rank hold 18 We classify stocks into ten major industry groups based on the first two digits of their SIC code: agriculture, forestry, and fishing ( ), mining ( ), construction ( ), manufacturing ( ), transportation, communications, electric, gas, and sanitary service ( ), wholesale trade ( ), retail trade ( ), finance, insurance, and real estate ( ), service ( ), and public administration ( ). 21

22 through out the holding months, the option-based sorting is implemented for each holding month. We can also match the holding horizon of the enhanced momentum portfolio with the maturity of options. Specifically, for any holding horizon, we sort winner and loser stocks only once according to implied volatility growth of options with the time-to-maturity that matches with the holding horizon. We present the results in Tables 10 and 11. When call option is used, raw excess return is 1.35% per month with a t-statistic of 2.04 for a two-month holding horizon (K = 2); the raw return is not significant for K = 3 or K = 6. Risk-adjusted alphas are all significant across different holding horizons. Two observations worth emphasizing. First, the lazy updating strategy yields lower momentum profit than the benchmark monthly updating strategy. The risk-adjusted alpha is 1.26%/0.98% per month for the 3/6- month holding horizon compared with 1.52%/1.25% under the benchmark strategy. Second, the power of the lazy updating strategy comes from different sides of winner/loser stocks compared to the timely updating strategy. Under the benchmark strategy, we find that the marginal contribution of selecting stocks with slow information diffusion speed is similar for winner and loser stocks. Under the lazy updating strategy, loser stocks with slow information diffusion (D S ) have a -0.66%/month lower return than the loser stocks identified to be fast diffusion (D F ), whereas the return difference is only 0.1%/month for the winner stocks. This finding suggests that the benefit of monthly updating concentrates more among winner stocks. [Insert Table 10 and Table 11] 4.5 Other robustness tests In addition, we also consider a number of other robustness tests. To keep the presentation succinct, we only present these tests in brief. Tables are included in the Appendix. Out-of-the-money options: We also use out-of-the-money options to identify stocks infor- 22

23 mation diffusion speed. We classify options into slightly out-of-the-money group (delta = 0.35, 0.40, or 0.45) and far our-of-the-money group (delta = 0.20, 0.25, or 0.30). The implied volatility for each group is calculated as the average value across options with three deltas. Double sorting on slightly OTM call option implied volatility growth further improves the momentum performance with a risk-adjusted alpha of 1.96% per month. On the other hand, momentum enhanced by far out-of-the-money option implied volatility growth does not deliver a return spread as large as the benchmark strategy. Detailed results are presented in Table A.3. Value-weighted: In the benchmark test, stocks are equally weighted within each portfolio. We also construct value-weighted momentum portfolios to check whether our results are driven by small stocks. We find that the momentum profit is even larger for value-weighted portfolios: the alphas are 1.73%, 1.96%, and 1.94% per month, respectively, for different holding horizons. Again, momentum profits are insignificant when the put option is used. Detailed results are presented in Table A.4. Monthly implied volatility growth: In the benchmark test, the implied volatility growth is computed over the last five trading days previous to the holding month. We also use implied volatility growth over the last month and find similar results with weaker magnitude. Detailed results can be found in Table A.5. Information content of implied volatility growth: We use a vector-autoregression (VAR) approach to examine whether our results are driven by the persistence of implied volatility. Each month, we regress the log growth of call (put) implied volatility on day t on the log growth rates of both call and put option implied volatilities on day t-1. Mean-reverting exists in implied volatility growth: there is a negative relation between implied volatility growth and its lagged value. 19 Persistency is less a concern for our study because information of option traders is not necessarily independent from day to day. However, as an extension, we 19 Results on the VAR regression using the full sample are presented in the Appendix Table A.6. 23