A Timing Momentum Strategy*

Robin K. Chou Department of Finance, National Chengchi University, Taiwan Risk and Insurance Research Center, National Chengchi University, Taiwan

Kuan-Cheng Ko** Department of Banking and Finance, National Chi Nan University, Taiwan September 2018

Chaonan Lin School of Management, Xiamen University, China

Nien-Tzu Yang Department of Business Management, National United University, Taiwan

Abstract We propose a timing momentum strategy by incorporating moving-average signals in the price momentum and show that the proposed strategy substantially outperforms the buy-and-hold strategy. The profitability of the timing momentum is enhanced when information uncertainty is high and cannot be captured by explanations associated with investor attention, information discreteness and growth options. Further investigations indicate that a major advantage of the timing momentum strategy is its time-invariant profitability across various time-series predictors and during periods of momentum crashes. Finally, the timing momentum is applicable to several momentum variables including industry returns, earnings surprises, 52-week high, and signed volume.

JEL Classification: G11; G12; G14; G15 Keywords: Moving average; Momentum investing; Return predictability; Information uncertainty

______* Chou acknowledges financial support from the Ministry of Science and Technology of Taiwan (grant number: MOST 102-2628-H-004-001) and from the National Natural Science Foundation of China (grant numbers: 71232004 and 71373296). ** Corresponding author. Email: [email protected]; Address: No. 1, Daxue Rd., Puli, 54561 Taiwan; Tel: 886-49-2910960 ext. 4695; Fax: 886-49-2914511. A Timing Momentum Strategy

Abstract We propose a timing momentum strategy by incorporating moving-average signals in the price momentum and show that the proposed strategy substantially outperforms the buy-and-hold strategy. The profitability of the timing momentum is enhanced when information uncertainty is high and cannot be captured by explanations associated with investor attention, information discreteness and growth options. Further investigations indicate that a major advantage of the timing momentum strategy is its time-invariant profitability across various time-series predictors and during periods of momentum crashes. Finally, the timing momentum is applicable to several momentum variables including industry returns, earnings surprises, 52-week high, and signed volume.

JEL Classification: G11; G12; G14; G15 Keywords: Moving average; Momentum investing; Return predictability; Information uncertainty

1 1. Introduction

One of the most puzzling phenomena in financial markets is the profitability of the intermediate-term momentum in stock returns firstly documented by Jegadeesh and

Titman (1993). Despite its soundness in both U.S. and international markets, 1 the momentum profit has been extensively demonstrated to exhibit predictable time-varying patterns by various conditioning variables. Chordia and Shivakumar (2002) document higher momentum profits in expansions than in recessions. Cooper, Gutierrez, and

Hameed (2004) indicate that the momentum strategy is profitable only following positive market returns because investor biases are more accentuated after market gains. Asem and

Tian (2010) further demonstrate that it is the market dynamic rather than the state of the market to account for the momentum profit. Wang and Xu (2015) and Avramov, Cheng, and Hameed (2016) show that momentum profits are more pronounced following periods of low market volatility and low market illiquidity. Antoniou, Doukas, and

Subrahmanyam (2013) and Stambaugh, Yu, and Yuan (2012) attribute momentum profits to higher level of investor sentiment. Daniel and Moskowitz (2016), on the other hand, observe infrequent and persistent strings of large negative momentum returns and show that this momentum crash is predictable by the occurrence of panic states.

One common feature of aforementioned studies is that the state variables used to predict momentum profits are all constructed on a market-wide or macroeconomic basis.

By highlighting the importance of the price information embedded in the market-wide index, Neely, Rapach, Tu, and Zhou (2014) document the usefulness of technical indicators in forecasting the U.S. equity risk premium. Their evidence suggests that

1 See, for example, Rouwenhorst (1998), Chan, Hameed, and Tong (2000), Jegadeesh and Titman (2001), Griffin, Ji, and Martin (2005) and Chui, Titman, and Wei (2010).

2 technical analysis captures information beyond that summarized by macroeconomic variables. Despite its soundness, the role of technical indicator in predicting momentum profits is rarely examined in the literature. The main objective of this paper is to fill up this gap.

We propose a timing momentum strategy by adopting a simple rule based on the information embedded in moving-average (MA) ratios to predict the proper timing in implementing the momentum strategy. According to the trading rule of MA signals, a buying or continuing to hold signal is implied when a short-term average price is greater than a relatively long-term average price. Based on this notion, our timing momentum strategy is constructed by combining the trading signals computed at the beginning of each holding month of momentum with the investment decision of that holding month. In particular, we compute the 20-day MAs for winner and loser portfolios using average daily prices of corresponding portfolios as the long-term average prices. To measure short-term prices, we use the closing prices of winner and loser portfolios on the day before the beginning of the holding month of momentum.

Our strategy is that, at the beginning of each holding month of momentum, we long the winner portfolio and hold for one month if its closing price at the end of previous month is greater than its past 20-day MA; otherwise we invest the money in the risk-free rate. On the contrary, we short sell the loser portfolio for one month only when its closing price at the end of previous month is smaller than the 20-day MA, otherwise we borrow the money at the risk-free rate. Over the sample period from January 1963 to December

2012, this timing momentum strategy generates an average profit of 1.994% per month, which is remarkably higher than the average profit of 0.566% for the standard

3 buy-and-hold strategy (with a significant difference of 1.428%). This pattern is also robust to the risk adjustment using the Fama and French (2015) five-factor model.

Taking a closer look at the components of the timing strategy, we find that the incremental profitability mainly comes from the short position of the loser portfolio.

Under the standard buy-and-hold (BH) strategy, the average return of the loser portfolio is 1.006%; that is, investors are subject to a huge loss when they short sell the loser portfolio. When the information of MA signals is incorporated, the average return of the loser portfolio shrinks to -0.290%; it means that investors can generate a slightly positive profit of 0.290% if they short sell the loser portfolio smartly. More importantly, because short selling is costly, investors may face a huge amount of borrowing fee if they continue to short sell the stock, say for example, for the six months of the holding period of momentum. Our strategy, however, is more flexible if the MA ratio suggests a stop shorting signal and the short position would be covered prior to the end of the holding period of the BH strategy. By doing so, investors only have to pay lower borrowing fee and earn higher profits in trading the short position.

MA signals also provide important implications to the January seasonality of momentum. The literature generally indicates significant reversals for momentum in

January months because of the tax-loss-selling effect on loser stocks (Jegadeesh and

Titman, 1993; Chan, Jegadeesh, and Lakonishok, 1996; George and Hwang, 2004;

Chordia and Shivakumar, 2006). We show that when MA signals are considered, the return to the loser portfolio reduces from 12.386% to 4.184% in January months, leading to an insignificant loss of -0.244% for the overall momentum strategy. As a comparison, the BH momentum return in January month is -6.409% in our sample. This evidence suggests that MA signals are useful in predicting the huge loss of the loser portfolio in

4 January and that the loss can be largely mitigated if some sophisticated investors are able to time the market in implementing the momentum strategy.

Our results are important to the literature of technical analysis. A growing number of studies have demonstrated the usefulness of technical analysis on some investment strategies. For example, Brown and Jennings (1989), Brock, Lakonishok, and LeBaron

(1992), Lo, Mamaysky, and Wang (2000) and Neely, Rapach, Tu, and Zhou (2014) all find that technical analysis adds value in investing stock or market returns. Han, Yang, and Zhou (2013) show that the MA indicator provides additional information in predicting the returns of the volatility portfolios. Han, Zhou, and Zhu (2016) construct a trend factor based on MA ratios and show that the factor outperforms factors that are associated with intermediate-term momentum and short- and long-term reversals. Our results, however, contribute to the literature of technical analysis by demonstrating the usefulness of technical analysis in momentum investing, an issue that has yet been examined in the literature.

Our study also provides important insights into the understanding of momentum.

Han, Yang, and Zhou (2013) argue that when stock returns are more volatile, firm fundamentals such as earnings and economic outlook are more likely to be imprecise, and hence investors tend to rely more heavily on the technical analysis. This argument suggests the importance of information uncertainty in inducing the predictability of MA signals. Also, motivated by Zhang’s (2006) observation that higher level of information uncertainty is associated with higher momentum returns, it is important to investigate whether information uncertainty plays an important role for the timing momentum profitability. Thus, we hypothesize that if momentum is induced because of information

5 uncertainty, there might be room for MA signals to provide incremental predictability for momentum.

We verify this conjecture by adopting a double sorting procedure to form momentum portfolios conditional on measures of information uncertainty. We find that stocks with higher information uncertainty generate remarkably higher timing momentum profits, and that the difference between the timing strategy and the BH strategy increases with the degree of information uncertainty. This finding suggests that information uncertainty is an important channel that drives the relation between MA signals and the predictability of momentum returns.

We also show that the profitability of the timing strategy cannot be explained by several cross-sectional determinants of the momentum phenomenon. In particular, the timing momentum profit is robust to subsamples partitioned by turnover, information discreteness, and growth options. This finding suggests that firm-specific attribute, investor over- and under-reaction do not account for the predictability of MA signals in identifying the proper timing of momentum investing.

Our findings regarding cross-sectional analyses of the timing momentum have an important implication to the momentum literature. The literature widely views momentum as an outcome of investor under- or over-reaction (Barberis, Shleifer, and

Vishny, 1998; Daniel, Hirshleifer, and Subrahmanyam, 1998; Hong and Stein, 1999).

Although our evidence in favor of information uncertainty might be consistent with the prediction of investor misreaction in explaining momentum, further analyses indicate that the timing momentum profitability is robust to measures of investor overreaction (e.g., turnover) and underreaction (e.g., information discreteness). This finding implies that it is unnecessary to particularly rely on investors’ misreaction to public information to explain

6 momentum. More importantly, our results suggest that in an environment with more uncertainty, technical indicators are useful to enhance the profitability of momentum.

Investors can thus benefit greatly from technical analyses in generating momentum profits in such situation.

We further study the time-series patterns of the timing momentum conditional on several time-varying predictors. The results indicate that the timing momentum profitability is invariant over different periods partitioned by business cycles, market states, market dynamics, market volatility, market liquidity, and investor sentiment. In addition, Daniel and Moskowitz (2016) identify infrequent but large losses for the standard momentum strategy during panic states, which is referred to as the momentum crash. Our timing strategy, however, generates significantly positive returns during panic states and is thus not subject to the momentum crash.

Finally, we apply the timing strategy to several momentum variables documented in the literature. The results indicate that our strategy is applicable to the industry, earnings,

52-week high, and signed volume momentum. That is, we observe remarkably higher profits when MA signals are combined with these variables. This evidence suggests the predictability of MA signals is not special to the traditional price momentum of

Jegadeesh and Titman (1993).

2. MA signals and momentum profits

2.1. The construction of the timing momentum strategy

We begin by introducing the construction of the timing momentum strategy. As in

Jegadeesh and Titman (1993), we measure the past performance for each stock by its average return over past 6 months. At the beginning of each month, stocks are ranked in

7 ascending order according to their past performance. Based on these rankings, we equally divide individual stocks into decile portfolios. Stocks with their past 6-month returns ranked in the top 10% constitute the winner portfolio, and those with 6-month past returns ranked in the bottom 10% constitute the loser portfolio. Each of the decile portfolios is constructed with equal weights and held for the next 6 months.2

To identify the proper timing in implementing the momentum strategy based on technical analysis, we follow Han, Yang, and Zhou (2013) to construct the MA timing

strategies for the ten decile portfolios. Let Pjd, denote the price of portfolio j on day d, which is the last trading day of the month. The L-day MA indicator of decile portfolio j on day d is defined as: PPPP  A  j,1,2,1, d Lj  d Lj dj d , (1) j,, d L L which is the average price of the past L days. In this proposal, the 20-day MA is the main indicator examined. Nevertheless, the 50-, 100-, and 200-day MAs are also investigated for robustness. A simple trading rule based on the constructed MA indicator is to invest

in the momentum decile portfolio j in month t, if the last closing price Pjt,1 is above

AjtL,1, on the last trading day of month t－1; and to invest in the risk-free asset otherwise. As a result, returns on the MA timing strategy for portfolio j can be described as follows:

Rj, t,; if P j , t 1 A j , t 1 Rj,, t L   (2) Rft, ,. otherwise

2 Jegadeesh and Titman (1993) find that the momentum strategy is profitable in intermediate-term period, ranging from 1 to 4 quarters. In this paper, we focus on 6-month formation and holding periods because it has been analyzed extensively in the literature. The results based on formation and holding periods of 3, 9, and 12 months are analyzed in untabulated tables and remain unchanged.

8 where Rj,t is the return of portfolio j in month t, and Rft, is the risk-free rate in month t.

After establishing the MA timing strategy, the return of Rj t,, L is then calculated for the

6-month holding period.

To construct the return of the timing momentum strategy (denoted as WMLMA, L ) based on the L-day MA indicator, we propose a zero-cost strategy by buying the winner

portfolio ( RW i n n e r t,, L ) and selling the loser ( RL o s e r t,, L ) portfolio. For a given month t, the strategy suggests a zero-cost long-short portfolio by buying the winner portfolio when its index price is higher than its MA indicator, and by short selling the loser portfolio when its index price is lower than its MA indicator, which can expressed as follows:

RRifWinner,,, PAand tLoser 1,, tWinner 1,, PA1,,,; t 1, LWinner t LLoser t LLose r t L  RRifWinner,,, PAand tf tWinner 1,, 1,,,; t PA1,, LWinner 1, t LLoser t LLoser t L WMLMA,, t L   (3) RRiff,,, tLoser 1,, PA tWinner, t LWinner t 1,,LLoser 1,,and 1, t PA LLoser t L  ;  0,. otherwise

where RWinnert, ( RLosert, ) is the return of the winner (loser) portfolio in month t,

PWinnertL,1, ( PLosertL,1, ) is the index price of the winner (loser) portfolio on the last trading

day of month t－1, and AWinnertL,1, ( ALosertL,1, ) is the L-day MA indicator of the winner

(loser) portfolio on the last trading day of month t－1. As in Jegadeesh and Titman

(1993), the strategy closes out the positions created 6 months before. For each month t, we calculate the momentum return (WMLMA,, t L ) as the equally weighted average of the month t returns from 6 separate WMLMA portfolios, each formed in one of the 6 consecutive months prior to month t.

9 To investigate the usefulness of the timing momentum strategy, we compare the return of the timing strategy with that of the BH strategy to see if the MA indicator provides additional information in improving the momentum profitability. To do so, we define a moving average portfolio (MAP) as the return difference between the two strategies, which can be expressed as follows:

MAPWMLWMLtL, MA,, tLt , (4)

where WMLt is the average return of the 6 separate BH momentum strategy in month t,

i.e., WMLRRtWinnertLosert,,. We hypothesize that if the MA indicator is able to provide additional information to predict the profitability of momentum, the average return of

MAP strategy would be significantly greater than zero.

To further examine whether the timing momentum exhibits abnormal returns, we perform time-series regressions of the WMLMA,, tL on the Fama-French (2015) five-factor model as follows:

WMLRRRRMA,, t L LL MKT,,,,,,,, MKT tL SMB SMB tL HML HML tL RMW RMW t

L,, CMACMAR tt , (5)

where RMKTt, is the excess return on the market portfolio in month t, RSMBt, , RHMLt, ,

RRMW, t , and RCMA, t are returns on the size, book-to-market, operating profitability, and investment factors in month t, respectively. We also perform the regressions by replacing

with and MAPt to obtain abnormal returns for the BH strategy and the difference between the two strategies.

2.2. Data

10 Our sample consists of all common stocks listed on NYSE, AMEX, and NASDAQ over the period from July 1963 to December 2012. We retrieve daily and monthly return data from the Center for Research in Security Prices (CRSP) database and accounting data from the COMPUSTAT database. The data on analyst forecasts are obtained from the Institutional Brokers’ Estimate System (I/B/E/S) database for the period from January

1980 to December 2012. The data on Fama and French’s (2015) five factors are downloaded from Kenneth French’s website.3

2.3. The profitability of the timing momentum strategy

Table 1 reports raw and Fama-French risk-adjusted returns for BH momentum, timing momentum, and MAPs. Because past studies indicate that the price momentum exhibits strong reversal in January months due to the tax-loss-selling effect, we also divide our sample into January-only and non-January observations, respectively. The full-period, January-only, and non-January momentum profits to the BH strategy, as reported in Panel A, are 0.566% (t-statistic = 2.53), -6.409% (t-statistic = -4.14), and

1.191% (t-statistic = 5.54) per month, respectively. These returns increase to 1.994%

(t-statistic = 6.99), -0.244% (t-statistic = -0.13), and 2.195% (t-statistic = 8.50) when MA signals are taken into consideration. The differences between timing and BH strategies, i.e. MAPs, are 1.428% (t-statistic = 4.48), 6.164% (t-statistic = 3.80), and 1.003%

(t-statistic = 3.29) for the full, January-only, and non-January periods, respectively.

[Insert Table 1 about here]

Taking a closer look at the returns of winner and loser portfolios, we find that the predictability of the timing momentum mainly comes from the loser portfolio, especially

3 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

11 in January months. For the BH strategy, the loser portfolio experiences a dramatic reversal in January months at 12.386% per month with a t-statistic of 5.85. This return largely reduces to 1.535% per month with a t-statistic of 2.08 when MA signals are taken into consideration. That is, considering MA signals enables one to avoid a dramatic loss of 10.851% in shorting loser stocks in January months. This finding suggests that MA indicator seems to better predict future declines than increases in prices, echoing with

Neely, Rapach, Tu, and Zhou’s (2014) observation that technical indicators typically detect declines in the equity risk premium.

We also show in Panel B that the results based on Fama-French risk adjustments are virtually similar to those based on raw returns. This finding confirms the robustness of our findings to the risk-based explanation, suggesting that the incremental explanatory ability of MA signals is not captured by the Fama-French (2015) five-factor model. To understand the information content embedded in MA signals in predicting momentum profits, we will examine several hypotheses that are associated with different sets of cross-sectional determinants in Section 3.

2.4. Results based on alternative lag lengths

The idea of the MA strategy is that an investor should hold a security when the security price is on an uninterrupted up trend, which is captured by the comparison between a short-term MA and a long-term MA. In this paper, the extreme short-term MA is represented by the last closing price in month t－1 and the relative long-term MA is represented by the 20-day MA. To examine whether the results are driven by a particular use of the MA indicator, we replicate the investigation by using 50-, 100-, and 200-day

MAs as alternative lag lengths. Table 2 gives the results.

12 [Insert Table 2 about here]

The timing momentum generates pronounced profits in all cases, but the magnitude of profits shrinks with the length of long-term MAs. In particular, the timing momentum profits are 1.882%, 1.377%, and 0.742% for 50-, 100-, and 200-day Mas, respectively.

This finding is also observed in Han, Yang, and Zhou (2013) and thus is not surprising because the trading information embedded in longer lag intervals may be cancelled out by the noisy information during this period. Despite the monotonically decreasing trend of the timing momentum profits, MA signals based on 200-day average prices still have substantial incremental power to predict the subsequent returns of the loser portfolio. This is observable from the significantly negative 200-day MAPs for the loser portfolio, which amounts to -0.238% (t-statistic = -2.44), -0.691% (t-statistic = -3.19), and -0.198%

(t-statistic = -1.99) for the full, January-only, and non-January periods, respectively. In untabulated results, we show that the risk-adjusted returns based on alternative lag lengths are quantitatively and statistically similar to the raw returns.4 To conclude, the overall results from Table 2 suggest the robustness of our findings across different lengths of long-term MAs.

3. The information content of MA signals

To understand the source underlying the profitability of the timing momentum, we investigate the roles of several cross-sectional determinants of momentum that have been documented in the literature. These variables are associated with explanations based on information uncertainty, investor attention, and growth options.

4 To conserve space, we only report the results based on raw returns in remaining tables. The results based on risk-adjusted returns are similar and available upon request.

13

3.1. Information uncertainty

The literature indicates the importance of information uncertainty in explaining cross-sectional variations of stock returns and momentum profits. Chan, Jegadeesh, and

Lakonishok (1996) attribute the return continuation to a gradual response to market information. Daniel, Hirshleifer, and Subrahmanyam (1998, 2001) and Hirshleifer (2001) propose that psychological biases are enhanced when uncertainty is high, resulting in subsequent return continuation. Zhang (2006) empirically adopts several measures of information uncertainty to observe the return pattern of the price momentum. These studies all suggest a positive relation between information uncertainty and momentum profits.

Emphasizing on the importance of MA signals, Han, Yang, and Zhou (2013) argue that when a stock’s price information is uncertain, its fundamentals such as earnings and economic outlook are more likely to be imprecise. In such case, fundamental analyses may be unreliable and hence investors tend to rely more heavily on technical analyses.

Motivated by this observation, we hypothesize that information uncertainty provides an important channel through which MA signals have impacts on momentum investing.

We adopt two measures of information uncertainty, namely analyst coverage and firm age, to investigate how they interact with MA signals in generating momentum profits. We consider analyst coverage because Hong, Lim, and Stein (2000) view higher analyst coverage as an indicator of less information asymmetry. Gleason and Lee (2003) show that firms with lower analyst coverage exhibit more pronounced post-revision price drift, while

Zhang (2006) document higher price momentum profits among firms with lower analyst coverage. Lam and Wei (2011) also point out that information uncertainty impedes

14 arbitrageurs from engaging in arbitrage activities to correct for potential mispricing. They use analyst coverage as a measure of limits-to-arbitrage to explain the asset growth anomaly. We follow these studies by defining analyst coverage (COV) as the number of analysts following a stock.

We consider firm age because Barry and Brown (1985) propose that firms with a long history have more information available to the market. Jiang, Lee, and Zhang (2005) and

Zhang (2006) both show that younger firms generate higher price momentum profits. We follow the literature by measuring firm age (AGE) as the number of years since the firm was first covered by the CRSP. Based on the two proxies, we measure the degree of information uncertainty by taking an inverse of COV and AGE (i.e., 1/COV and 1/AGE) so that higher value of the two variables represents higher information uncertainty.

We construct the timing momentum conditional on measures of information uncertainty. At the beginning of each month, we allocate stocks into quintiles according to their past 6-month returns. Within the winner and loser portfolios (highest and lowest quintiles), we subdivide stocks into three groups according to their values of 1/COV or

1/AGE. We then compute the 20-day MAs for winner and loser portfolios and obtain

returns of WMLMAtL,, based on the trading rules of Equation (3) for all 1/COV or 1/AGE groups. We hypothesize that if the profitability of the timing momentum is induced because of information uncertainty, we would observe significantly higher timing momentum profits among stocks with higher information uncertainty. Moreover, the incremental predictability of MA signals (i.e., MAPs) will also increase with information uncertainty.

Panels A and B of Table 3 confirm our prediction. Consistent with Zhang (2006), we first show that the momentum profits under the BH strategy increase monotonically with

15 the degree of information uncertainty. In addition, the incorporation of MA signals significantly enhances momentum profits, especially in the high information uncertainty group. The timing momentum profits are 0.636%, 1.083%, and 1.596% for low, median, and high 1/COV groups with a difference of 0.960% (t-statistic = 3.76) between high and low 1/COV groups. This results in MAPs of 0.197%, 0.257%, and 0.765% for low to high

1/COV groups and a significant difference of MAPs between high and low 1/COV groups at 0.567% (t-statistic = 2.17). These patterns remain similar when we use 1/AGE to measure the degree of information uncertainty, as presented in Panel B.

[Insert Table 3 about here]

These results indicate that information uncertainty enhances the precision of MA signals in predicting future momentum profits. Although prior studies attribute the explanatory ability of information uncertainty for momentum to investors’ overconfidence in estimating the precision of their information signals (Jiang, Lee, and

Zhang, 2005) or investors’ uncerreaction to public information (Zhang, 2006), our findings do not necessarily rely on investors’ irrational misreaction to information. We show in next subsection that the effectiveness of MA signals in momentum investing is irrelevant to investors’ over- and under-reaction.

3.2. Investor attention

Investor attention plays an important role in discriminating the underreaction explanation from the overreaction hypothesis in explaining momentum profits. Hou, Peng, and Xiong (2009) propose that investor attention is a necessary condition for overreaction, since investors can only overreact to information when they pay attention to a stock. In contrast, limited attention can cause investors to ignore useful information thus induces

16 subsequent underreaction. Using turnover as the proxy for investor attention, they empirically show that the price momentum profit increases monotonically with turnover.

Their finding thus implies supportive evidence in favor of the overreaction hypothesis in explaining price momentum profits.

By contrast, Da, Gurun, and Warachka (2014) develop and test the frog-in-the-pan

(FIP) hypothesis for momentum. By hypothesize that a series of frequent gradual changes attracts less attention than infrequent dramatic changes, they propose the information discreteness (ID) measure to identify the information flow embedded in stock prices.

Specifically, they define ID as sgn(PRET)[%neg %pos], where PRET is a firm’s cumulative return over past 12 months, and %neg and %pos denote the percentages of days with negative and positive returns during the same period. By construction, a higher value of ID signifies discrete information, and a lower value of ID signifies continuous information. Da, Gurun, and Warachka (2014) propose that investors tend to underreact to continuous information and hence momentum profits would be concentrated among stocks with low ID values. Their empirical results confirm this prediction and are infavor of investor underreaction in explaining the profitability of the price momentum.

We test over- and under-reaction hypotheses by using turnover and ID to interact with past 6-month returns in forming double-sorted portfolios, respectively. We follow

Hou, Peng, and Xiong (2009) by using the average monthly turnover over the prior year to measure a firm’s trading volume. We first allocate stocks into quintiles according to their past 6-month returns and subdivide stocks in winner and loser portfolios into three groups according to their values of turnover or ID. We then compute the 20-day MAs for

17 all winner and loser portfolios and obtain returns of WMLM A t,, L for all turnover or ID groups, respectively.

Panel C of Table 3 confirms Hou, Peng, and Xiong’s (2009) evidence that the profitability of the standard BH momentum strategy increases with turnover. The difference in the BH momentum profits between high and low turnover groups is 0.422% with a t-statistic of 2.89. When MA signals are considered, the momentum profits increase to 1.832%, 1.782%, and 1.515% for low, median, and high turnover groups with an insignificant difference of -0.320% (t-statistic = -1.45). As a result, the incremental effectiveness of MA signals in enhancing momentum profits (i.e., MAP) decreases with turnover. This finding suggests that the predictability of MA signals on momentum profits is not driven by the overreaction hypothesis.

Panel D of Table 3 reports the results based on the ID measure. Consistent with Da,

Gurun, and Warachka (2014), the momentum profit of the BH strategy decreases from

0.993% for the high ID group to 0.141% for the low ID group, with a significant difference of -0.852% (t-statistic = -5.90) between high and low ID groups. When MA signals are incorporated, the momentum profits significantly increase for all ID groups, with MAPs of 0.515%, 0.668%, and 0.651% for low, median, and high ID groups. This evidence indicates that the incremental effectiveness of MA signals for momentum is neutral to the flow of past information arrival, suggesting that the timing momentum profitability is unrelated to investors’ underreaction behavior induced by limited attention.

3.3. Growth options

18 Based on a real options model, Sagi and Seasholes (2007) establish the relation between firm-specific attributes and momentum. In their model, firms with higher growth options are shown to generate higher momentum profits because firms that performed well in the recent past are better poised to exploit their growth options. By using a firm’s market-to-book (MB) ratio as a proxy for growth options, they empirically demonstrate that firms with high MB ratios produce remarkably higher momentum profits than those with low MB ratios.

We consider the impact of growth options on the profitability of the timing momentum by repeating the two-way sorting procedure involving past 6-month returns and MB ratios. Analogously, we form 5 by 3 portfolios according to firms’ past 6-month returns and MB ratios, respectively. Panel E of Table 3 reports the returns of BH and timing momentum strategies conditional on MB ratios. The results can be summarized as follows: (i) the momentum profit of the BH strategy increases with MB ratios with a significant difference of 0.363% (t-statistic = 2.88) between high and low MB groups; (ii) the timing momentum profit is indistinguishable across MB groups, with corresponding values of 1.881%, 1.556%, and 1.594% for low, median, and high MB groups; and (iii) the incremental predictability of MA signals decreases with MB ratios, with MAP values of 1.555%, 1.055%, and 0.912% for low, median, and high MB groups and a difference of -0.647% (t-statistic = -3.68). This evidence indicates that growth options are not the main source to enhance the timing momentum profitability.

4. Time-varying patterns of the timing momentum

In this section, we investigate whether the timing momentum exhibits time-varying patterns across several conditioning variables that have been documented in the literature.

19 If MA signals play the dominant role in predicting future profitability of momentum, we expect that the timing momentum profits are consistent over time.

4.1. Business cycles

Chordia and Shivakumar (2002) and Griffin, Ji, and Martin (2003) both show that the profitability of the standard price momentum varies with common macroeconomic risk that is associated with business cycles. In particular, momentum profits are reliably positive and significant during expansionary periods, and are insignificantly negative during recessionary periods. Thus, it is interesting to examine whether the timing momentum profits are captured by macroeconomic risk. We address this issue by dividing our sample period into expansionary and recessionary periods according to the definition of NBER. We report the returns of BH and timing momentum strategies separately for expansionary and recessionary periods in Panel A of Table 4.

[Insert Table 4 about here]

Consistent with Chordia and Shivakumar (2002) and Griffin, Ji, and Martin (2003), we find that the profitability of the BH momentum strategy is concentrated in expansionary periods but not in recessionary periods. The corresponding returns are

0.770% (t-statistic = 4.11) and -0.656% (t-statistic = -0.66), respectively. When MA signals are taken into account, the momentum profits for expansionary and recessionary periods increase to 1.899% (t-statistic = 6.25) and 2.493% (t-statistic = 3.15), with corresponding MAPs of 1.129% (t-statistic = 3.68) and 3.149% (t-statistic = 2.72). This evidence indicates that the profitability of the timing momentum is unrelated to the exposure of macroeconomic risk and thus is robust to the business cycles.

20 4.2. Market states

Cooper, Gutierrez, and Hameed (2004) suggest that the profitability of momentum is associated with the state of the market because investor biases are more accentuated after market gains. They document a significantly positive momentum return following positive market returns, but a significantly negative momentum return following negative market returns. To examine whether returns on MAPs are associated with market conditions, we follow Cooper, Gutierrez, and Hameed (2004) by calculating the cumulative return of the CRSP value-weighted index over the past 36 months.5 If this return is positive, we define the state of the market as UP, otherwise it is classified as

DOWN. We split our sample period into UP and DOWN markets and report the returns of the BH strategy, the MA strategy, and MAPs for the two subperiods in Panel B of

Table 4.

We first confirm Cooper, Gutierrez, and Hameed’s (2004) finding that momentum profits are significantly positive only following UP markets. This result is robust across different lengths in identifying market states. We further show that the MA strategy generates significantly positive momentum profits in both UP and DOWN market states

(1.935% and 2.224%, respectively). The incremental power of MA signals (i.e., MAPs) in predicting momentum returns is particularly stronger following DOWN market states.

This finding suggests that the timing ability of MA signals is more useful following market declines and thus the timing momentum is unaffected by the state of market returns.

5 The results remain unchanged if we use the cumulative market return over the past 12 or 24 months to identify market states.

21 4.3. Market dynamics

Extending Cooper, Gutierrez, and Hameed’s (2004) finding, Asem and Tian (2010) propose that it is the dynamic of market states, rather than the market state itself, that predicts momentum profits. Their investigation is motivated by Daniel, Hirshleifer, and

Subrahmanyam’s (1998) model of investor overconfidence in driving momentum profits.

Specifically, they propose that the degree of overconfidence on the buying (selling) behavior is enhanced when the markets continue in the UP (DOWN) market state. As a result, the model predicts that momentum profits should be higher when the markets continue in the same state (from UP to UP or from DOWN to DOWN) than when they transit to a different state (from UP to DOWN or from DOWN to UP).

To explore the impact of market dynamics on our findings, we define whether a given month belongs to the condition of market continuation or transition as in Asem and

Tian (2010). At the beginning of each month t, we define past market performance by calculating past 12-month CRSP value-weighted index and classify the month as past UP

(DOWN) if this return is nonnegative (negative). Following past UP markets, we further classify month t as market continuation (transition) if the CRSP value-weighted return in the subsequent month is nonnegative (negative). Analogously, a market continuation

(transition) following DOWN markets is identified if the CRSP value-weighted return in the subsequent month is negative (nonnegative).

Confirming Asem and Tian’s (2010) results, we show in Panel C of Table 4 that the

BH momentum strategy is profitable only when the market continues in the same state, with an average return of 1.740% (t-statistic = 6.98). During market transitions, the BH strategy yields a significant loss of -1.198% per month with a t-statistic of -2.56. Our timing momentum strategy, however, generates a significant average return of 2.752%

22 (t-statistic = 8.86) during market continuations and an average return of 0.813%

(t-statistic = 1.57) during market transitions, indicating that the timing momentum profitability is robust regardless of the dynamic of the market. This finding also suggests that the MA signal is useful in identifying the proper investment timing to avoid the substantial loss of momentum when the market is in the transition stage.

4.4. Market volatility

Market volatility is another useful predictor of momentum profitability documented by Wang and Xu (2015) and Daniel and Moskowitz (2016). Motivated by the notion that the extreme market volatility during the financial crisis is followed by dramatic losses of momentum strategies, they propose that the price momentum is profitable following periods of low market volatility but not following periods of high market volatility. We follow Wang and Xu (2015) to calculate two sets of past market volatility. At the beginning of each month t, we calculate the short-term (long-term) market volatility by computing the standard deviation of CRSP value-weighted daily returns over month t−12 to month t−1 (month t−36 to month t−1). If the short-term market volatility is greater

(smaller) than the long-term market volatility, we define month t as high (low) market volatility.

Panel D of Table 4 presents the returns of BH and timing momentum strategies separately for periods of high and low market volatilities. We show that the timing momentum is profitable regardless of the state of market volatility while the BH momentum fails to generate significant profit when market volatility is high. This finding again confirms the robustness of timing momentum profitability to different states of market volatility.

23

4.5. Market liquidity

Avramov, Cheng, and Hameed (2016) empirically show that the BH momentum generates remarkably higher momentum profits in liquid market states than in illiquid market states, and that this phenomenon is robust to the inclusion of market return and volatility states. They also show that the impact of market liquidity is pervasive across the

U.S., Japan, and Eurozone markets. Although we have demonstrated the robustness of timing momentum profitability across different periods partitioned by market return and volatility states, it is important and interesting to study the impact of market liquidity on our results.

To investigate this issue, we follow Chordia, Subrahmanyam, and Tong (2014) and

Avramov, Cheng, and Hameed (2016) by employing Amihud’s (2002) measure of stock illiquidity (ILLIQ).6 We construct the market-wide measure of illiquidity, MKTILLIQ, as the value-weighted average of each stock’s value of ILLIQ. We identify a given month t as liquidity (illiquidity) market if the value of MKTILLIQ in month t−1 is lower (higher) than the median value of MKTILLIQ over the sample period. By dividing the whole sample period into subperiods of liquid and illiquidity market states, we show in Panel E of Table 4 that the timing momentum generates an average return of 2.069% (t-statistic =

4.48) in liquid market and an average return of 1.894% (t-statistic = 5.38) in illiquid market. This evidence thus suggests the robustness of our results controlling for the effect of market liquidity, which is an important time-series predictor of momentum.

n 6 t We define a stock’s ILLIQ in month t as R/( P N ) / n , where nt is the number of d 1 i,,, d i d i d t trading days in month t, Rid, is the absolute value of stock i’s return on day d of month t, Pi,d is stock i’s closing price on day d, and Ni,d is stock i’s number of shares traded on day 푑.

24

4.6. Investor sentiment

The literature widely documents evidence that investor sentiment plays a critical role in corporate and investor decision making. Stambaugh, Yu, and Yuan (2012) and

Antoniou, Doukas, and Subrahmanyam (2013) propose that the momentum phenomenon is enhanced when sentiment traders exert greater influences. They both show that momentum profits are higher following periods of high (i.e., optimistic) sentiment and insignificant following periods of low (i.e., pessimistic) sentiment. To consider the impact of investor sentiment on our results, we adopt the monthly sentiment index constructed by Baker and Wurgler (2006, 2007) to measure the degree of behavioral biases.7 We classify each month t of the holding period as following a high-sentiment month if the value of the sentiment index in month t−1 is above the median value for the sample period, and the low-sentiment month are those with below-median values. We then calculate the momentum profits separately for periods of high and low sentiment and report the results in Panel F of Table 4.

The result indicates that our timing momentum is not subject to the influence of investor sentiment because its profits are significantly positive following periods of both high and low sentiment (1.913% versus 2.325%). As a comparison, the BH momentum generates a return of 0.876% following high-sentiment periods and a return of 0.184% following low-sentiment periods. This finding suggests that the impact of investor sentiment is attenuated when MA signals are considered in momentum investing.

7 We obtain the sentiment index from Jeffrey Wurgler’s website (http://pages.stern.nyu.edu/~jwurgler/) and adopt the orthogonalized sentiment index with respect to a set of macroeconomic conditions as the conditioning variable.

25 4.7. Momentum crashes

A recent study of Daniel and Moskowitz (2016) points out that momentum experiences infrequent and persistent strings of negative profits which can be predictable and are referred to as the “momentum crashes”. They show that the crashes occur in panic states, that is, following market declines, when market volatility is high, and are contemporaneous with market rebounds. To explore whether our timing momentum exhibits substantial and infrequent losses as predicted by momentum crash, we follow

Daniel and Moskowitz (2016) by defining a given month t as panic state if: (i) the return to the CRSP value-weighted index over the 24 months ending in month t−1 is negative; (ii) the return to the value-weighted market index in month t is positive; and (iii) the variance of the daily returns on the CRSP value-weighted index calculated over the 126-days prior to month t is higher than the median of the time series. We define the remainder as normal states.

Consistent with Daniel and Moskowitz (2016), we show in Panel G of Table 4 that the BH momentum suffers from a huge loss of -5.323% per month in panic states and earns 1.005% (t-statistic = 5.60) in normal states. Surprisingly, this large loss in panic states can be simply avoided if one considers the MA signals of winner and loser portfolios.

In panic states, the average timing momentum profit is 2.923% (t-statistic = 2.00), which is remarkably higher in both magnitude and statistical significance than the profit of the BH momentum. Even in normal states, MA signals can substantially enhance the momentum profitability from 1.005% to 1.912%, which is almost double in magnitude.

To sum up, the time-series analyses based on several conditioning variables reveal consistent and robust profitability for the timing momentum across different time periods.

26 The results confirm the dominance of MA signals in predicting the profitability of momentum.

5. Applications to alternative momentum strategies

So far our analyses are implemented using the traditional price momentum of

Jegadeesh and Titman (1993). Since existing literature has proposed several momentum strategies, it is important and interesting to investigate whether our timing momentum strategies are applicable to these alternative momentum variables. We address this issue in this section.

5.1. The industry momentum

Moskowitz and Grinblatt (1999) argue that the momentum phenomenon in individual stock returns is driven by momentum in industry returns. They propose the industry momentum strategy by using past returns of industrial indices to evaluate past performance and identify winner and loser industries. Thus their strategy involves buying stocks belonging to past winner industries and short selling stocks belonging to past loser industries. We follow Moskowitz and Grinblatt (1999) by defining past performance of a stock as the value-weighted industry return over past 6 months of the industry to which the stock belongs. At the beginning of each month, stocks are ranked in ascending order according to the past performance of their industry and are divided into decile portfolios.

Stocks with their past 6-month industry returns ranked in the top 10% constitute the winner portfolio, and those with 6-month past industry returns ranked in the bottom 10% constitute the loser portfolio. We then apply Equation (3) to construct the timing strategy

27 for industry momentum. Panel A of Table 5 reports the returns to BH and timing strategies for the industry momentum and their difference.

[Insert Table 5 about here]

Over our sample period, the BH industry momentum generates an average return of

1.086% (t-statistic = 5.16), and this return is strengthened to 1.848% (t-statistic = 7.33) when MA signals are considered. That is, MA signals enhance the profitability of the industry momentum by 0.761% which is significant at the 1% level. This evidence indicates that the predictability of MA signals is not special to the price momentum but is also robust to the industry momentum.

5.2. The earnings momentum

The earnings momentum is initiated by Ball and Brown’s (1968) observation that stock returns continue in the same direction of earnings surprises for several months after earnings announcements. This anomaly is widely viewed as the evidence of investors’ underreaction to earnings surprises and has been documented as a pronounced and pervasive phenomenon in the U.S. stock market (Ball and Bartov, 1996; Chan, Jegadeesh, and Lakonishok, 1996; Barberis, Shleifer, and Vishny, 1998; Chordia and Shivakumar,

2006). Thus it is interesting and important to examine whether MA signals is useful to predict the time-varying profitability of the earnings momentum.

We follow Chan, Jegadeesh, and Lakonishok (1996) and Chordia and Shivakumar

(2006) by using standardized unexpected earnings (SUE) to measure a firm’s unexpected earnings surprise, which is defined as

eei, q i , q 4 SUEit,  , (6)  iq,

28 where eiq, is stock i’s earnings as of the most recent quarter, eiq,4 is stock i’s earnings

four quarters ago, and  iq, is the standard deviation of eei, q i , q 4 over past eight quarters. We then use SUE to evaluate a stock’s past performance and construct the earnings momentum in the same way we described above. Again, MA signals are incorporated to consider the proper investment timing in trading winner and loser portfolios.

Panel B of Table 5 indicates that MA signals are useful in enhancing the profitability of the earnings momentum as the difference between timing and BH strategies is 0.499%

(t-statistic = 2.16). This finding suggests that MA signals do provide useful information in identifying investment timing conditional on investors’ underreaction to earnings announcements.

5.3. The 52-week high momentum

Motivated by the theory of adjustment and anchoring biases proposed by Kahneman and Tversky (1979) and Kahneman, Slovic, and Tversky (1982), George and Hwang

(2004) propose a momentum strategy based on the nearness of stocks’ current prices to their 52-week high prices. They argue that the return continuation arises because of investors’ misreaction to individual stocks’ information conditional on their 52-week high (52WH) prices, which is most readily available to investors and serves as a good candidate of the anchor. For each month t, the 52WH ratio is defined as current price , in which current price is a stock’s price at the end of the month 52  week high price t−1, and 52-week high price is the highest price over past 52 weeks ending month t−1.

The higher value of 52WH indicates that the current price of a stock is closer to its

29 52-week high price, and the maximum possible value of 52WH is 1. The 52WH strategy is thus constructed by buying the top 10% stocks with the highest values of 52WH and short selling the bottom10% stocks with the lowest values of 52WH. We then examine whether MA signals provide incremental information in enhancing the profits of the

52WH momentum.

Panel C of Table 5 indicates that the standard 52WH strategy is less significant in our sample period, which amounts to 0.247% (t-statistic = 0.77) per month. When MA signals are considered, the profit of the 52WH momentum is substantially increased to

1.580% (t-statistic = 6.54) per month. This considerable increment in 52WH momentum profits thus confirms the credibility of MA signals in predicting return continuation associated with a firm’s 52WH information.

5.4. The signed volume momentum

Motivated by Daniel, Hirshleifer, and Subrahmanyam’s (1998) model of investor overconfidence, Byun, Lim, and Yun (2016) propose a measure of continuing overreaction (CO) using weighted signed volumes to capture the overreaction-driven momentum. In particular, CO is constructed based on the summation of weighted monthly signed volumes during the past 12 months, in which signed volume (SV) is defined as

voli,, t if R i t  0  SVi,, t00 if R i t (7)  voli,, t if R i t 0

30 where voli,t is stock i’s monthly dollar trading volume (defined as the sum of daily trading volume) within month t and Ri,t is stock i’s return in month t. The CO measure is then calculated as

sumwSVwSV(,,)Ni tNi t ,1,1 COit,  , (8) meanvolvol(,,) i,,1 tNi t where SVi,t is stock i’s signed volume in month t, N is the length of the formation period which equals 12 here, and wn is a weight that takes a value of N−n+1 in month N−n (i.e., wN = 1, wN−1 = 2, and w1 = N). We then use COi,t to identify winners (losers) that are ranked at the top (bottom) 10% with the highest (lowest) values of COi,t.

Although the profitability of the signed volume momentum (0.605% with a t-statistic of 3.55) is induced because of investor overconfidence, we show in Panel D of

Table 5 that this return can be amplified by the inclusion of MA signals. When MA signals are considered, the profit of the signed volume momentum is increased to 1.501%

(t-statistic = 7.22), which is significantly higher in magnitude of 0.896% (t-statistic =

3.63) than the BH strategy. Thus, MA signals are shown to contain information beyond investor overconfidence in explaining the momentum phenomenon.

6. Conclusions

Prior studies on momentum generally assume a buy-and-hold strategy with monthly rebalancing, and none of which had discussed the potential role of technical analysis in momentum investing. This study contributes to the literature by showing that the momentum return does exhibit predictable patterns by the MA signals, and that a combination of the momentum strategy and the MA indicator yields higher returns than the standard BH strategy. We find that the proposed timing momentum strategy generates

31 significantly higher returns than the BH momentum strategy, and that the credibility of

MA signals mainly comes from loser stocks. Moreover, the timing momentum strategy is not subject to the reversals in January months.

The impact of MA signals on momentum is positively correlated with information uncertainty. In particular, we observe significantly higher timing momentum profits among stocks with higher information uncertainty, i.e., lower analyst coverage and younger age.

Although our evidence in favor of information uncertainty might be consistent with the prediction of investor misreaction in explaining momentum, further analyses indicate that the timing momentum profitability is robust to measures of investor overreaction (e.g., turnover) and underreaction (e.g., information discreteness). An important implication is that it is unnecessary to particularly rely on investors’ misreaction to public information to explain momentum. MA signals are useful to enhance the profitability of momentum in an environment with more uncertainty. In such situation, investors can thus benefit greatly from technical analyses in generating momentum profits.

How good is the performance of the timing momentum? We show that its profitability is quite consistent over time and cannot be predicted by several time-varying conditioning variables such as business cycles, market states, market dynamics, market volatility, market liquidity, and investor sentiment. More surprisingly, the timing momentum is equally profitable in normal and panic states, and thus is free from the huge loss during periods of momentum crash. The results suggest the dominance of MA signals in predicting the profitability of momentum beyond several important conditioning variables.

Finally, we show that the effectiveness of MA signals is not special to the price momentum of Jegadeesh and Titman (1993). The timing strategy is applicable to several

32 momentum variables including industry returns, earnings surprises, 52-week high, and signed volume. This evidence indicates that MA signals contain information beyond investor underreaction, overconfidence, and anchoring biases in explaining the momentum phenomenon. Overall, the empirical results of this paper highlight the usefulness of technical analyses in momentum investing and thus have important contributions to the literature of both momentum and technical analysis.

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105-136.

39 Table 1: Returns to the buy-and-hold and timing momentum strategies

We follow Jegadeesh and Titman (1993) in constructing decile portfolios based on individual stocks’ past 6-month average returns. Stocks with their past 6-month returns ranked in the top 10% constitute the winner portfolio, and those with 6-month past returns ranked in the bottom 10% constitute the loser portfolio. The winner and loser portfolios are constructed with equal weights and held for the next 6 months. The BH strategy is defined as the difference in return between winner and loser portfolios held for 6 months with overlapping. We define the timing strategy as the difference in return between winner and loser portfolios conditional on MA signals. For each holding month t, we long the winner portfolio if its closing price in month t－1 is greater than its 20-day MA calculated on the last trading day of month t－1, otherwise we invest the money in the risk-free rate. On the contrary, we short sell the loser portfolio for month t only when its closing price in month t－1 is smaller than the 20-day MA, otherwise we borrow the money at the risk-free rate. MAP is the difference between timing and BH strategies. Panels A and B report the results based on raw returns and risk-adjusted returns using the Fama and French (2015) five-factor model, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. BH strategy Timing strategy MAP Portfolio All months Jan. Only Non-Jan. All months Jan. Only Non-Jan. All months Jan. Only Non-Jan. Panel A: Raw returns Winner 1.588 *** 5.977 *** 1.194 *** 1.706 *** 3.940 *** 1.505 *** 0.118 -2.037 *** 0.311 (4.52) (5.20) (3.33) (6.76) (4.40) (5.99) (0.61) (-3.09) (1.51) Loser 1.022 ** 12.386 *** 0.003 -0.288 4.184 ** -0.690 *** -1.310 *** -8.202 *** -0.692 ** (2.40) (5.85) (0.01) (-1.20) (2.37) (-3.09) (-4.18) (-5.14) (-2.39) Winner-Loser 0.566 ** -6.409 *** 1.191 *** 1.994 *** -0.244 2.195 *** 1.428 *** 6.164 *** 1.003 *** (2.53) (-4.14) (5.45) (6.99) (-0.13) (8.50) (4.48) (3.80) (3.29) Panel B: Fama-French risk-adjusted returns Winner 1.014 *** 2.498 *** 0.887 *** 1.364 *** 1.478 ** 1.308 *** 0.350 ** -1.020 ** 0.421 ** (9.37) (5.25) (7.93) (7.60) (2.44) (7.13) (2.13) (-2.06) (2.44) Loser 0.540 * 8.044 *** -0.263 -0.516 * 4.282 ** -0.952 *** -1.056 *** -3.762 *** -0.689 *** (1.76) (5.64) (-1.21) (-1.84) (2.58) (-5.77) (-4.80) (-3.02) (-3.10) Winner-Loser 0.474 -5.545 *** 1.150 *** 1.880 *** -2.804 2.260 *** 1.406 *** 2.742 * 1.110 *** (1.46) (-3.95) (4.50) (5.00) (-1.60) (7.64) (4.23) (1.88) (3.23)

40 Table 2: Timing momentum profits based on alternative lag lengths

We follow Jegadeesh and Titman (1993) in constructing decile portfolios based on individual stocks’ past 6-month average returns. Stocks with their past 6-month returns ranked in the top 10% constitute the winner portfolio, and those with 6-month past returns ranked in the bottom 10% constitute the loser portfolio. The winner and loser portfolios are constructed with equal weights and held for the next 6 months. We define the timing strategy as the difference in return between winner and loser portfolios conditional on MA signals. For each holding month t, we long the winner portfolio if its closing price in month t－1 is greater than its MA calculated on the last trading day of month t－1, otherwise we invest the money in the risk-free rate. On the contrary, we short sell the loser portfolio for month t only when its closing price in month t－1 is smaller than the MA, otherwise we borrow the money at the risk-free rate. MAP is the difference between timing and BH strategies, where the BH strategy is defined as in Table 1. Panels A to C report the returns based on 50-, 100-, and 200-day MAs, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Timing strategy MAP Portfolio All months Jan. Only Non-Jan. All months Jan. Only Non-Jan. Panel A: MA50 Winner 1.740 *** 3.969 *** 1.540 *** 0.154 -2.008 ** 0.347 (7.06) (4.60) (6.26) (0.71) (-2.23) (1.52) Loser -0.140 6.079 *** -0.697 *** -1.157 *** -6.307 *** -0.696 *** (-0.55) (3.17) (-2.76) (-4.14) (-4.88) (-2.66) Winner-Loser 1.882 *** -2.109 2.239 *** 1.311 *** 4.300 ** 1.043 *** (6.37) (-0.95) (8.00) (4.25) (2.65) (3.43) Panel B: MA100 Winner 1.666 *** 4.020 *** 1.456 *** 0.085 -1.957 ** 0.267 (6.58) (4.67) (5.81) (0.45) (-2.57) (1.34) Loser 0.288 8.339 *** -0.430 -0.718 *** -4.047 *** -0.421 * (1.04) (4.34) (-1.55) (-3.19) (-4.73) (-1.91) Winner-Loser 1.377 *** -4.318 ** 1.886 *** 0.803 *** 2.090 * 0.688 *** (5.09) (-2.15) (6.96) (3.12) (1.73) (2.61) Panel C: MA200 Winner 1.511 *** 4.397 *** 1.253 *** -0.068 -1.580 ** 0.067 (5.17) (5.30) (4.22) (-0.51) (-2.35) (0.49) Loser 0.768 ** 11.695 *** -0.205 -0.238 ** -0.691 *** -0.198 ** (2.02) (5.57) (-0.55) (-2.44) (-3.19) (-1.99) Winner-Loser 0.742 *** -7.297 *** 1.459 *** 0.171 -0.889 0.265 (2.72) (-3.85) (5.30) (1.06) (-1.21) (1.56)

41 Table 3: Timing momentum profits conditional on cross-sectional determinants

We follow Jegadeesh and Titman (1993) in constructing quintile portfolios based on individual stocks’ past 6-month average returns. Stocks with their past 6-month returns ranked in the top 20% constitute the winner portfolio, and those with 6-month past returns ranked in the bottom 20% constitute the loser portfolio. Within winner and loser portfolios, we subdivide stocks into three groups based on their cross-sectional determinants. The portfolios are constructed with equal weights and held for the next 6 months. The BH strategy is defined as the difference in return between winner and loser portfolios held for 6 months with overlapping. We define the timing strategy as the difference in return between winner and loser portfolios conditional on MA signals. For each holding month t, we long the winner portfolio if its closing price in month t－1 is greater than its 20-day MA calculated on the last trading day of month t－1, otherwise we invest the money in the risk-free rate. On the contrary, we short sell the loser portfolio for month t only when its closing price in month t－1 is smaller than the 20-day MA, otherwise we borrow the money at the risk-free rate. MAP is the difference between timing and BH strategies. In Panels A to E, the firm characteristics are 1/COV, 1/AGE, TURNOVER, ID, and MB respectively. COV is the number of analysts following. AGE is the number of years since the firm was first covered by the CRSP. TURNOVER is a firm’s average monthly turnover calculated over past 12 months. ID is a firm’s information discreteness defined by Da, Gurun, and Warachka (2014). MB is a firm’s market-to-book ratio. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Winner Loser Winner-Loser Portfolio BH Timing MAP BH Timing MAP BH Timing MAP Panel A: Portfolios sorted by 1/COV Low 1.460 *** 0.867 *** -0.593 *** 1.021 ** 0.231 -0.791 ** 0.439 0.636 ** 0.197 (3.94) (3.28) (-2.62) (2.09) (0.84) (-2.43) (1.44) (2.05) (0.55) 2 1.541 *** 1.094 *** -0.447 * 0.715 0.011 -0.704 * 0.826 *** 1.083 *** 0.257 (3.67) (3.55) (-1.85) (1.36) (0.04) (-1.92) (2.77) (3.34) (0.65) High 1.475 *** 1.246 *** -0.229 0.643 -0.350 -0.993 *** 0.832 *** 1.596 *** 0.765 ** (3.47) (4.05) (-1.00) (1.21) (-1.10) (-2.73) (3.02) (4.78) (2.05) High- Low 0.015 0.379 ** 0.364 *** -0.378 -0.581 *** -0.203 0.393 ** 0.960 *** 0.567 ** (0.09) (2.47) (3.01) (-1.62) (-2.75) (-0.89) (2.01) (3.76) (2.17) Panel B: Portfolios sorted by 1/AGE Low 1.562 *** 1.424 *** -0.137 1.160 *** 0.109 -1.052 *** 0.401 ** 1.314 *** 0.915 *** (5.80) (7.41) (-0.85) (3.58) (0.61) (-4.41) (2.20) (5.95) (3.68) 2 1.643 *** 1.741 *** 0.098 1.080 *** -0.181 -1.261 *** 0.562 *** 1.922 *** 1.359 *** (4.98) (7.19) (0.56) (2.84) (-0.82) (-4.81) (3.14) (7.58) (4.97) High 1.486 *** 1.690 *** 0.205 0.849 ** -0.320 -1.169 *** 0.637 *** 2.011 *** 1.374 *** (4.12) (6.86) (1.00) (2.07) (-1.34) (-4.22) (3.26) (7.30) (4.61) High- Low -0.076 0.266 ** 0.342 *** -0.316 ** -0.434 *** -0.118 0.241 ** 0.700 *** 0.460 *** (-0.55) (2.20) (3.02) (-2.01) (-3.45) (-0.88) (2.19) (4.27) (2.97)

42 Table 3 continued

Winner Loser Winner-Loser Portfolio BH Timing MAP BH Timing MAP BH Timing MAP Panel C: Portfolios sorted by TURNOVER Low 1.814 *** 1.856 *** 0.042 1.464 *** 0.025 -1.437 *** 0.350 ** 1.832 *** 1.479 *** (6.33) (8.73) (0.29) (4.30) (0.15) (-5.56) (2.08) (8.49) (5.87) 2 1.610 *** 1.590 *** -0.020 1.026 *** -0.193 -1.218 *** 0.584 *** 1.782 *** 1.198 *** (5.04) (6.70) (-0.12) (2.71) (-0.93) (-4.38) (3.09) (6.81) (4.09) High 1.183 *** 1.219 *** 0.036 0.410 -0.297 -0.704 ** 0.773 *** 1.515 *** 0.741 ** (3.29) (4.97) (0.17) (1.00) (-1.16) (-2.46) (3.64) (5.04) (2.38) High- Low -0.637 *** -0.643 *** -0.006 -1.059 *** -0.323 ** 0.735 *** 0.422 *** -0.320 -0.741 *** (-3.83) (-4.34) (-0.04) (-6.22) (-2.13) (4.87) (2.89) (-1.45) (-3.71) Panel D: Portfolios sorted by ID Low 1.611 *** 1.489 * ** -0.121 0.618 -0.018 -0.636 ** 0.993 *** 1.508 *** 0.515 ** (5.12) (5.84) (-0.87) (1.50) (-0.06) (-2.50) (4.67) (6.65) (2.08) 2 1.653 *** 1.585 *** -0.068 1.133 *** 0.397 -0.736 *** 0.520 *** 1.188 *** 0.668 *** (5.38) (6.15) (-0.54) (3.10) (1.52) (-3.17) (2.81) (5.41) (2.89) High 1.343 *** 1.334 *** -0.009 1.202 *** 0.543 ** -0.660 *** 0.141 0.792 *** 0.651 *** (4.09) (4.90) (-0.07) (3.58) (2.26) (-3.17) (0.86) (3.73) (3.08) High- Low -0.268 *** -0.155 * 0.113 * 0.584 *** 0.561 *** -0.023 -0.852 *** -0.716 *** 0.136 (-3.29) (-1.74) (1.72) (4.60) (5.61) (-0.23) (-5.90) (-5.23) (1.08) Panel E: Portfolios sorted by MB Low 1.850 *** 1.849 *** -0.001 1.522 *** -0.033 -1.555 *** 0.328 * 1.881 *** 1.555 *** (5.96) (7.95) (0.00) (3.97) (-0.18) (-5.57) (1.79) (8.57) (5.59) 2 1.605 *** 1.589 *** -0.016 1.104 *** 0.032 -1.071 *** 0.501 *** 1.556 *** 1.055 *** (5.26) (6.87) (-0.09) (3.19) (0.18) (-4.38) (2.61) (6.55) (4.11) High 1.300 *** 1.442 *** 0.142 0.620 -0.152 -0.770 *** 0.680 *** 1.594 *** 0.912 *** (3.77) (5.90) (0.73) (1.61) (-0.72) (-2.91) (3.51) (6.31) (3.35) High- Low -0.538 *** -0.395 *** 0.142 -0.900 *** -0.111 0.789 *** 0.363 *** -0.284 -0.647 *** (-3.48) (-2.78) (1.21) (-5.50) (-0.83) (5.34) (2.88) (-1.62) (-3.68)

43 Table 4: Time-series predictors and timing momentum profits

We follow Jegadeesh and Titman (1993) in constructing decile portfolios based on individual stocks’ past 6-month average returns. Stocks with their past 6-month returns ranked in the top 10% constitute the winner portfolio, and those with 6-month past returns ranked in the bottom 10% constitute the loser portfolio. The winner and loser portfolios are constructed with equal weights and held for the next 6 months. We define the timing strategy as the difference in return between winner and loser portfolios conditional on MA signals. For each holding month t, we long the winner portfolio if its closing price in month t－1 is greater than its MA calculated on the last trading day of month t－1, otherwise we invest the money in the risk-free rate. On the contrary, we short sell the loser portfolio for month t only when its closing price in month t－1 is smaller than the MA, otherwise we borrow the money at the risk-free rate. MAP is the difference between timing and BH strategies, where the BH strategy is defined as in Table 1. We then partition the sample period into different subperiods by various time-varying predictors and report the momentum profits separately for the subperiods. In Panels A to G, the time-varying predictors are business cycles, market states, market dynamics, market volatility, market illiquidity, investor sentiment, and normal/panic periods, respectively. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Portfolio BH Timing MAP BH Timing MAP Panel A: Momentum profits conditional on states of business cycles Expansionary periods Recessionary periods Winner 1.852 *** 1.767 *** -0.085 -0.127 1.223 * 1.350 ** (5.40) (7.02) (-0.43) (-0.11) (1.68) (2.17) Loser 1.083 *** -0.132 -1.215 *** 0.529 -1.270 -1.799 (2.82) (-0.56) (-4.20) (0.31) (-1.47) (-1.45) Winner-Loser 0.770 *** 1.899 *** 1.129 *** -0.656 2.493 *** 3.149 *** (4.11) (6.25) (3.68) (-0.66) (3.15) (2.72) Panel B: Momentum profits conditional on market states Up markets Down markets Winner 1.479 *** 1.606 *** 0.127 2.099 ** 2.140 *** 0.041 (4.22) (6.43) (0.61) (2.27) (3.08) (0.08) Loser 0.525 -0.329 -0.854 *** 3.526 ** -0.084 -3.610 *** (1.35) (-1.29) (-3.13) (2.51) (-0.14) (-3.15) Winner-Loser 0.954 *** 1.935 *** 0.981 *** -1.428 * 2.224 *** 3.652 *** (4.96) (6.47) (3.32) (-1.79) (2.80) (3.28) Panel C: Momentum profits conditional on market dynamics Market continuations Market transitions Winner 3.244 *** 2.545 *** -0.700 ** -0.949 0.398 1.347 *** (6.39) (7.71) (-2.34) (-1.52) (1.10) (3.40) Loser 1.505 *** -0.207 -1.712 *** 0.249 -0.415 -0.665 (2.79) (-0.71) (-4.81) (0.27) (-0.75) (-1.08) Winner-Loser 1.740 *** 2.752 *** 1.012 *** -1.198 ** 0.813 2.011 *** (6.98) (8.86) (2.64) (-2.56) (1.57) (3.49) Panel D: Momentum profits conditional on market volatility Low market volatility High market volatility Winner 1.563 *** 1.514 *** -0.050 1.594 *** 1.881 *** 0.287 (3.83) (5.18) (-0.21) (2.90) (4.96) (0.87) Loser 0.392 -0.412 -0.804 *** 1.660 ** -0.159 -1.820 *** (0.91) (-1.63) (-2.69) (2.29) (-0.37) (-3.38) Winner-Loser 1.172 *** 1.926 *** 0.754 ** -0.067 2.041 *** 2.107 *** (7.02) (6.05) (2.31) (-0.16) (4.29) (3.80)

44 Table 4 continued

Portfolio BH Timing MAP BH Timing MAP Panel E: Momentum profits conditional on market liquidity Liquid market Illiquid market Winner 1.891 *** 1.903 *** 0.012 1.266 *** 1.480 *** 0.214 (3.65) (4.92) (0.04) (2.88) (4.99) (0.81) Loser 1.113 * -0.166 -1.279 *** 0.899 -0.413 -1.312 *** (1.94) (-0.48) (-3.05) (1.52) (-1.23) (-3.03) Winner-Loser 0.778 ** 2.069 *** 1.291 *** 0.367 1.894 *** 1.527 *** (2.59) (4.48) (2.87) (1.12) (5.38) (3.33) Panel F: Momentum profits conditional on investor sentiment High sentiment Low sentiment Winner 1.156 ** 1.447 *** 0.291 2.116 *** 2.190 *** 0.074 (2.09) (3.82) (0.89) (4.52) (6.42) (0.28) Loser 0.280 -0.466 -0.746 * 1.932 *** -0.135 -2.067 *** (0.46) (-1.16) (-1.76) (2.96) (-0.40) (-4.24) Winner-Loser 0.876 *** 1.913 *** 1.036 ** 0.184 2.325 *** 2.141 *** (2.96) (4.19) (2.32) (0.48) (5.79) (4.19) Panel G: Momentum profits in normal/panic states Normal states Panic states Winner 1.156 *** 1.425 *** 0.268 7.318 *** 5.321 *** -1.996 *** (3.14) (5.59) (1.30) (9.91) (7.40) (-2.72) Loser 0.151 -0.487 * -0.638 ** 12.641 *** 2.398 ** -10.243 *** (0.38) (-1.89) (-2.35) (6.50) (2.28) (-5.47) Winner-Loser 1.005 *** 1.912 *** 0.907 *** -5.323 *** 2.923 * 8.246 *** (5.60) (6.58) (3.19) (-3.40) (2.00) (3.96)

45 Table 5: Alternative momentum strategies

We follow the literature to construct the industry momentum (Panel A), the earnings momentum (Panel B), the 52-week high momentum (Panel C), and the signed volume momentum (Panel D). Stocks with their corresponding values on each measure ranked in the top 10% constitute the winner portfolio, and those with corresponding values ranked in the bottom 10% constitute the loser portfolio. The winner and loser portfolios are constructed with equal weights and held for the next 6 months. We define the timing strategy as the difference in return between winner and loser portfolios conditional on MA signals. For each holding month t, we long the winner portfolio if its closing price in month t－1 is greater than its MA calculated on the last trading day of month t－1, otherwise we invest the money in the risk-free rate. On the contrary, we short sell the loser portfolio for month t only when its closing price in month t－1 is smaller than the MA, otherwise we borrow the money at the risk-free rate. MAP is the difference between timing and BH strategies. Numbers in the parentheses are the t-statistics calculated using the Newey-West (1987) robust standard errors. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Portfolio BH Timing MAP Panel A: The industry momentum Winner 1.828 *** 1.715 *** -0.113 (5.16) (6.95) (-0.58) Loser 0.742 ** -0.132 -0.874 *** (2.51) (-0.77) (-4.28) Winner-Loser 1.086 *** 1.848 *** 0.761 *** (5.16) (7.33) (3.42) Panel B: The earnings momentum Winner 1.720 *** 1.540 *** -0.180 (6.70) (8.05) (-1.22) Loser 0.744 *** 0.065 -0.679 *** (2.66) (0.40) (-3.32) Winner-Loser 0.977 *** 1.475 *** 0.499 ** (13.61) (6.76) (2.16) Panel C: The 52-week high momentum Winner 1.410 *** 1.284 *** -0.126 (6.47) (8.10) (-1.02) Loser 1.163 ** -0.295 -1.458 *** (2.54) (-1.26) (-4.10) Winner-Loser 0.247 1.580 *** 1.332 *** (0.77) (6.54) (3.85) Panel D: The signed volume momentum Winner 1.540 *** 1.378 *** -0.162 (5.71) (6.96) (-1.05) Loser 0.935 *** -0.123 -1.058 *** (2.94) (-0.70) (-4.59) Winner-Loser 0.605 *** 1.501 *** 0.896 *** (3.55) (7.22) (3.63)

46