A risk-return explanation of the momentum-reversal “anomaly”

Journal of Empirical Finance 35 (2016) 68–77

Contents lists available at ScienceDirect

Journal of Empirical Finance journal homepage: www.elsevier.com/locate/jempfin

A risk-return explanation of the momentum-reversal “anomaly” G. Geoffrey Booth a,1, Hung-Gay Fung b,2, Wai Kin Leung c,⁎ a b c

Eli Broad Graduate School of Management, Michigan State University, 645 West Shaw Lane, East Lansing, MI 48824-1121, USA College of Business Administration, University of Missouri, St. Louis, One University Blvd., St. Louis, MO 63121, USA Nottingham University Business School China, University of Nottingham Ningbo, 199 Taikang East Road, Ningbo 315100, China

a r t i c l e

i n f o

Article history: Received 16 July 2015 Received in revised form 4 October 2015 Accepted 6 October 2015 Available online 23 October 2015 JEL classification: G12 Keywords: Asset pricing Stock returns Momentum Market capitalization

a b s t r a c t This study investigates the nature of the momentum-reversal phenomenon exhibited by U.S. stock returns from 1962 to 2013. We use cumulative future returns of long–short portfolios, which are formed using prior returns as benchmarks, after portfolio formation to analyze the well-documented momentum-reversal pattern. Contrary to many previous studies our results demonstrate that there is no momentum-reversal anomaly. We show that size (market capitalization), which is often considered a proxy for risk, eventually dominates momentum's initial effect, causing stock prices and, hence, returns to move in the opposite direction. We demonstrate that this latter price movement is likely to be related to institutional trading. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Investment practitioners and academicians have long searched for time series patterns in stock prices and trading strategies to exploit them. Whether these price patterns actually exist is a hotly debated topic. Many believe that these patterns are an example of a type of apophenia that involves seeing patterns that do not exist in a sequence of random numbers. Others suggest that price patterns exist temporarily but disappear as a result of investors profitably exploiting the observed relationship. Still others accept that a blending of these two notions may account for the observed stock price patterns, but maintain that only a few of the patterns are indeed real and last long enough to allow profits to be earned by strategically constructed investment plans. One such pattern falling into the last category is price momentum-reversal. Price momentum occurs when a stock's price moves in the same direction for a recognizable period of time. Stocks with a recent history of over-performance are labeled as winners while those with one of underperformance are named losers. Profits are obtained by strategically creating long–short portfolios by simultaneously taking a long position in winner stocks and a short position in loser stocks during the momentum phase and then unwinding the position when this phase ends. A reversal occurs when the long–short portfolio experiences opposite return behavior in the long run; i.e., winners become losers and vice versa. The profitability of this long–short strategy

⁎ Corresponding author. Tel.: +86 574 88180325. E-mail addresses: [email protected] (G. Geoffrey Booth), [email protected] (H.-G. Fung), [email protected] (W.K. Leung). 1 Tel.: +1 517 884 2986. 2 Tel.: +1 314 516 6374.

http://dx.doi.org/10.1016/j.jempfin.2015.10.007 0927-5398/© 2015 Elsevier B.V. All rights reserved.

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

69

Table 1 Summary statistics. Year

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2013

No. of stocks in sample Mean value of institutional investor ratio Percentage of stocks with no institutional investors Maximum market capitalization Mean market capitalization Minimum market capitalization Maximum institutional trading Mean institutional trading Minimum institutional trading No. of institutional traders

2166

2409

5256

5024

6409

6853

8360

8468

6885

6642

6669

NA

NA

NA

0.109

0.152

0.196

0.258

0.280

0.370

0.409

0.391

NA

NA

NA

0.310

0.196

0.119

0.061

0.054

0.065

0.025

0.196

20,380

28,429

31,025

41,468

75,820

67,527

95,492

524,352

367,495

290,960

401,730

195.5

182.9

152.2

231.4

298.7

458.2

683.7

2059.8

2416.1

2334.4

3547.2

0.063

0.189

0.008

0.033

0.025

0.035

0.005

0.070

0.280

0.584

0.228

NA

NA

NA

999.5

1459.2

1797.7

2990.6

229,274.3

9074.7

16,050.4

13,927.6

NA

NA

NA

9.3

17.1

25.6

36.8

239.5

134.7

159.5

201.3

NA

NA

NA

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

NA

NA

NA

2132

3623

3919

6201

6582

5749

5984

5138

Notes: In each month from January 1963 to December 2013 we find from NYSE, AMEX, NASDAQ, and NYSE Arca stocks the market capitalization of each stock on the last day of each month, the monthly turnover by adding the daily turnover in each month and the monthly return. In each quarter from 1980 onward we retrieve from the WRDS Institutional (13f) Holdings data the institutional investor ratio (shares held by institutional investors/share outstanding at end of quarter) and the institutional trading (value of shares newly bought by institutional investors in that quarter provided they already held shares in the previous quarter). All values except return are in millions of dollars. We report here the June values for each year.

has been documented in numerous studies of U.S. stocks using a variety of techniques to determine which stocks are winners and which are losers (e.g., George and Hwang, 2004; Jegadeesh and Titman, 1993; Novy-Marx, 2012).3 Price reversals have also been empirically identified (e.g., De Bondt and Thaler, 1987; Jegadeesh and Titman, 2001). Numerous attempts have been made to explain why momentum exists and why the accompanying long–short strategy may be profitable. Rational actions do not seem to explain momentum adequately nor do various firm characteristics (e.g., Bandarchuk and Hilscher, 2013; Conrad and Kaul, 1998; Johnson, 2002; Sagi and Seasholes, 2007). Transaction costs are also unable to explain adequately the phenomenon (e.g., Korajczyk and Sadka, 2004; Lehmann, 1990; Lesmond et al., 2004). Jegadeesh and Titman (2001), however, show that momentum profits may be the result of delayed overreactions of information that are subsequently reversed. This behavioral explanation is supported by a large number of overreaction/under-reaction studies (e.g., Antoniou et al., 2013; Barberis et al., 1998; Chan et al., 1996; Daniel et al., 1998; De Bondt and Thaler, 1987; Frazzini, 2006; Grinblatt and Han, 2005; Hong and Stein, 1999; Hong et al., 2000; Lu, 2014). Although it may be possible to obtain important insights into financial phenomena using a behavioral approach, we contend that the well-documented pattern of momentum-reversal may be more simply explained using the traditional risk-return paradigm. We support our conjecture by demonstrating that the observed momentum pattern is strongly related to the pervasive influence of firm size as measured by market capitalization, which, as Berk (1995) suggests, is a ubiquitous proxy for risk. Our supposition rests on the notion that large institutional traders tend to take significant positions in the stocks of large companies instead of small ones, because the stocks of smaller firms are often less attractive purchases as a result of various attributes of these stocks such as short-selling restrictions, lack of market depth, and information asymmetry, all of which contribute to some aspect of risk. Our analysis is based on the double-sort procedure that is used by many of the studies cited above. This procedure constructs portfolios of stocks that are identified by returns and other characteristics. Portfolios are used to minimize or possibly even eliminate the idiosyncratic effects of individual stocks. The stocks are then sorted by returns or other characteristic. After sorting, the stocks are divided into quantiles, with quintiles and deciles being the most frequently used segmentation schemes. The stocks in each quantile are then sorted again using a characteristic that is not used in the first sort. To ensure that our data cover many stock price cycles and represent a deep market, we consider U.S. stocks that are traded on four domestic exchanges for a 52 year period beginning with the first month in 1962. Our data for individual firms consist of stock

3 Similarly, momentum has been documented in other asset classes in the U.S. as well as in various other markets throughout the world (e.g., Asness et al., 2013: Bhojrai and Swaninathan, 2006; Moskowitz et al., 2012: Rouwenhorst, 1998). Industry momentum has also been reported (e.g., Moskowitz and Grinblatt, 1999).

70

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

returns, size as measured by market capitalization and institutional trading. For reasons to be discussed later (see Section 3) we first sort using returns and form quintiles. We then sort our return quintiles using a characteristic derived from our data. Finally, we construct various long–short portfolios based on our constructed portfolios and assess their relative strategic performance. Our analysis makes two meaningful contributions to the understanding of momentum. First, the observed momentum-price reversal pattern puzzle is largely related to firm size, which serves as a proxy for risk. Our results are robust across size differences in the long and short positions of stocks in the strategic portfolios regardless of the portfolio formation technique used. They also are generally consistent with the literature indicating that, on average, small firms yield more positive returns than large firms (e.g., Banz, 1981; Fama and French, 1992). Second, we show that institutional investors appear to trade primarily the stocks of large firms, which leads to lower returns as a result of not exploiting the small-firm effect. We also show that their trading behavior is consistent with the observed momentum-reversal pattern found in our long–short portfolios. Our results provides additional insights into the trading of institutional investors whose routine actions appear not to follow momentum, in contrast to the behavior suggested in the extant trading literature (e.g., Nofsinger and Sias, 1999; Yan Zhang, 2009). 2. Data sources and description Our data consist of stock price, return and volume (including institutional trading) data from four U.S. stock exchanges (AMEX, NASDAQ, NYSE, NYSE Arca) spanning a 52-year period beginning in January 1962 and ending in December 2013. With the exception of institutional trading all of our data are supplied by the Center for Research in Security Prices (CRSP). We obtain the institutional trading information from Thomson Reuter, Institutional Trading (13F). All of the information is downloaded from Wharton Research Data Services (WRDS). For each month in the data sample, we retrieve the monthly return and the market capitalization of each stock on the last day of the month. For each quarter after 1980 (previous data are not available), we download for each stock the shares held by institutional investors, the number of shares outstanding at end of quarter, and the institutional trading volume (the value of shares newly bought by institutional investors in that quarter, provided they held shares in the previous quarter) for that quarter. We define the institutional investor ratio to be the shares held by institutional investors divided by the number of shares outstanding at end of quarter. Table 1 provides select summary statistics of the variables in five year intervals from 1965 to 2010 and 2013. All observations are for the month of June. By way of illustration, in June 2013, there are 6669 stocks. The stock with the largest capitalization is valued at $401.7 billion and the smallest has a market value of $228 thousand. The average market capitalization for these stocks is $3.5 billion. The average of the institutional investor ratio is 0.391, while 19.6% of the stocks are not owned by institutions. From the beginning of our sample, the number of stocks, institutional trading activity and market capitalization has noticeably increased, although the values for these variables peaked around the turn of the 21st century.4 3. Method of analysis The standard approach to investigate the various issues surrounding momentum is to construct portfolios of stocks that tend to over-perform or underperform over time. Over-performing stocks are labeled winners and underperforming stocks are dubbed losers. To quantify performance some measure of return is selected. This measure is used to rank the stocks. The ranked stocks are then segmented into quantiles, with quintiles and deciles being the most common groupings. Winner stocks are those in the top quantile and loser stocks are in the bottom quantile. The winner and loser portfolios are then strategically combined to create long–short trading strategies. For example, one strategy might be longing the winners and shorting the losers. This portfolio formation procedure can be extended to consider other stock characteristics than performance such as market capitalization. Thus the portfolio construction rubric can be designed so that the performance to be examined is associated only with the stocks associated with that characteristic. For example, a trading strategy might be longing large capitalization winners and shorting small capitalization losers. To implement the approach, there are at least three important issues to resolve. First, there is no agreed upon metric to identify which stocks are winners and which ones are losers. For example, Jegadeesh and Titman (1993) use the return obtained in the prior month as the winner–loser criterion, and Novy-Marx (2012) relies on the previous 2–6 and 7–12 months return. George and Hwang (2004), however, employ the price ratio (the closing price at a particular time divided the prior-period closing price), while Moskowitz et al. (2012) use past returns scaled by a risk factor. Each approach has its merits. Second, there is disagreement as to whether returns or a stock characteristic should be the focus of the first sort. In most studies, returns are used in the first sort. Bandarchuk and Hilscher (2013), however, propose the opposite and sort by a firmcharacteristic first and then sort by returns. Sorting first by returns guarantees that stocks will be correctly classified as winners or losers. Sorting second by returns provides no such guarantee. In other words, the first sort provides an unconditional ranking while the second sort gives in a conditional ranking with the ranking from the first sort being the conditioning agent. Thus, the order of the sort is determined by the purpose of the analysis. Third, the appropriate way to measure the future returns of the winner–loser portfolio after portfolio formation is also subject to debate. Many prior studies use the Jegadeesh and Titman (1993) approach to evaluate future returns (e.g., George and Hwang, 4 Institutional trading activity was especially large at this time, which was partially due to the boom in the technology industry. For example, during the second quarter of June 2010, 1038 Fund managers increased shares in Intel Corp. by 6.7 billion shares at a total cost of approximately $229 billion.

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

71

Table 2 Sorting for global winners and losers. Panel A. First sort by previous 6-month return Quintile

Average previous 6-month return

Global loser in 103 sorts

Global winner in 103 sorts

1 Lowest 103 0 2 2nd lowest 0 0 3 Medium 0 0 4 2nd highest 0 0 5 Highest 0 103 Total 103 103 Note: Starting from December 1962, we sort all stocks into quintiles by their previous 6-month return. We do this every 6 months, which results in a total of 103 sorts from December 1962 to December 2013. If the average previous 6-month return of a quintile is the lowest (highest) among the five quintiles in a sort, we call it global loser (winner) in that sort. For each quintile we calculate the number of sorts of that group being a global loser (winner) in all 103 sorts. Panel B. First sort by market capitalization Quintile

Average market capitalization

Global loser in 103 sorts

Global winner in 103 sorts

1 2 3 4 5 Total

Lowest 2nd lowest Medium 2nd highest Highest

78 2 0 1 22 103

1 14 19 24 45 103

Note: Starting from December 1962, we sort all stocks into quintiles by their market capitalization. We do this every 6 months, which results in a total of 103 sorts from December 1962 to December 2013. If the average previous 6-month return of a group is the lowest (highest) among the five quintiles in a sort, we call it global loser (winner) in that sort. For each quintile we calculate the number of sorts of that group being a global loser (winner) in all 103 sorts.

2004; Jegadeesh and Titman, 2001). Although the Jegadeesh and Titman (1993) approach is appealing because it skirts issues associated with overlapping returns (Moskowitz and Grinblatt, 1999), it uses monthly rebalancing. Thus, it does not track the original winner–loser portfolio throughout a certain “defined” holding period. A more intuitive approach is taken by Carhart (1997) who tracks the stock performance through the holding period. For our empirical analysis, we use Jegadeesh and Titman's (1993) approach to form our winner–loser portfolios. We do two double sorts: We sort first by returns and then by characteristic. We also sort in the reverse sorting order in order to examine whether the sorting order makes a difference. To measure our post-portfolio formation performance, we use the continuously compounded cumulative return. We rationalize this measure by noting that typical investors seek the highest possible overall return after adjusting for their risk preferences. We use 3-, 6-, 9- and 12-month previous returns to sort stocks and we calculate the cumulative 3-, 6-, 9-, 12-, 24-, 36-, 48- and 60-month future returns. Our initial starting point is January 1, 1963, allowing us to use 1962 as the initial basis for our portfolio formation.5 For our institutional trading measure, we sum the value of shares newly bought by institutional investors in that quarter provided they already held shares in the previous quarter for the next 3, 6, 9, 12, 24, 36, 48 and 60 months after portfolio formation. 4. Results and discussion 4.1. Nature of sorting portfolios Recall that the double-sort approach involves either (1) sorting firms by firm characteristics into groups and then sorting firms within each group by returns or (2) sorting firms by returns to form portfolios and then sorting firms within each group by firm characteristic. Before we detail the sort strategies, we need to define not only winner and loser portfolios and but also price momentum and reversal. We continue to use the previous 6-month return and future 6-month return approach to illustrate our method. First, we use the previous 6-month return to sort all stocks into quintiles. Within these quintiles, the quintile that has the highest (lowest) average return is called a global winner (loser) portfolio. If this global winner (loser) portfolio continues to be a global winner (loser) portfolio as determined by the average future 6-month returns, we label this phenomenon “price momentum.” If, instead, the global winner (loser) portfolio does not continue to be the global winner (loser) portfolio as determined by the average future 6-month return, we call this “price reversal.” Panel A of Table 2 provides a summary of the results from first sorting by returns and Panel B provides similar data associated with first sorting by size (market capitalization).6 In each panel we present the quintiles in ascending order. Turning first to Panel A, as expected all of the sorts correctly place the global losers and winners in Quintiles 1 and 5, respectively. This, however, is not 5 To illustrate our return calculations, assume that we first sort stocks according to their returns in the previous six months and we want to determine their return in the next six months. If the future return calculation begins on January 1, 1963, the portfolios are formed on December 31, 1962 based on cumulative return from July 1, 1962 to December 31, 1962. The next 6-month cumulative return is the return from January 1, 1963 to June 30, 1963. The portfolio is then rebalanced on June 30 using the previous cumulative return from previous January 1, 1963 to June 30, 1963. This process continues until the data's end. 6 We also use implied volatility, volume and momentum strength (as defined by Bandarchuk and Hilscher, 2013) as the first sort for firm characteristic with the second sort being returns. The results (not reported) are similar and further confirm that this kind of sorting does not provide global winner and loser portfolios.

72

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

Table 3 Loser/Big–Loser/Small strategy results. Length of sort periods

Long–short size ratio

Number of months in the future 3

6

12

24

36

48

60

−0.0697 (−6.41) −0.0759 (−6.95) −0.0777 (−7.06) −0.0821 (−7.33)

−0.1523 (−6.21) −0.1541 (−6.27) −0.1659 (−6.62) −0.1717 (−6.87)

−0.3929 (−5.72) −0.4018 (−5.97) −0.4011 (−5.79) −0.4071 (−5.68)

−0.9001 (−3.58) −0.9193 (−3.84) −0.9229 (−3.70) −0.9235 (−3.81)

−0.9918 (−3.68) −1.0269 (−3.81) −1.0915 (−3.82) −1.0217 (−3.64)

−1.4935 (−3.82) −1.4371 (−3.81) −1.3621 (−3.65) −1.4671 (−3.78)

−1.8336 (−3.57) −1.5646 (−3.65) −1.5951 (−3.41) −1.5703 (−3.44)

Median of difference of cumulative returns (signed rank test) 3 242.5 −0.0362 z-Stat (12.41) (−5.32) 6 232.1 −0.0471 z-Stat (12.41) (−5.85) 9 210.2 −0.0592 (12.41) (−6.20) z-Stat 12 205.9 −0.0565 z-Stat (12.41) (−6.51)

−0.1144 (−5.56) −0.1211 (−5.45) −0.1239 (−5.81) −0.1238 (−6.07)

−0.2713 (−5.49) −0.2979 (−5.45) −0.2808 (−5.52) −0.2884 (−5.44)

−0.3541 (−3.94) −0.5034 (−3.94) −0.3799 (−3.94) −0.4923 (−3.97)

−0.5087 (−3.05) −0.5529 (−3.34) −0.6607 (−3.20) −0.6507 (−3.20)

−1.2349 (−2.90) −1.25 (−2.90) −1.1234 (−2.98) −1.293 (−2.98)

−1.5461 (−2.60) −1.6447 (−2.50) −1.2483 (−2.60) −1.3157 (−2.70)

Mean of difference of sum of institutional trading 3 318.9 t-Stat (17.53) 6 301.2 t-Stat (17.36) 9 282.7 t-Stat (17.56) 12 278.9 t-Stat (18.52)

7821.3 (2.69) 4199.3 (6.79) 6724.9 (4.25) 9567.0 (1.86)

2851.9 (7.34) 4965.6 (2.68) 4354.4 (4.96) 3834.0 (5.65)

2874.0 (6.76) 2810.6 (6.37) 3501.3 (3.61) 4297.3 (4.14)

2459.5 (2.65) 1567.6 (5.89) 1611.3 (5.30) 2822.3 (3.21)

1390.4 (8.03) 1855.2 (4.13) 2569.1 (3.24) 1685.8 (3.35)

1628.6 (2.14) 1063.9 (3.82) 951.5 (3.58) 1154.9 (3.08)

Mean of difference of cumulative returns (t-test) 3 318.9 t-Stat (17.53) 6 301.2 t-Stat (17.36) 9 282.7 t-Stat (17.56) 278.9 12 t-Stat (18.52)

19,441.9 (2.24) 8990.4 (3.28) 11,739.9 (3.69) 8564.8 (4.90)

Notes: We sort in descending order our sample stocks by previous 3-, 6-, 9- or 12-month returns using the Jegadeesh and Titman (1993) method into quintiles. Loser stocks are those in the lowest return quintile. We then sort in descending order the Loser stocks into quintiles using market capitalization. Big (Small) stocks are those in the highest (lowest) size quintile. Loser/Big (Loser/Small) is the group of stocks with lowest (lowest) return and biggest (smallest) market capitalization among the Loser stocks. We then create a long short portfolio using these two stock groups and report below the results for cumulative return (using both t-test and non-parametric signed rank test), and institutional trades from three to 60 months after portfolio formation. Selected months are presented below. For the Long–Short Size Ratio, the t-statistics (z-statistics) of testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalization of the long portfolio is equal to the short portfolio.

the case when the first sort is based on market capitalization. As shown in Panel B, only 78 global losers fall into Quintile 1 and 45 global winners are in Quintile 5. If no quintile can be declared a winner or loser by average previous 6-month return in all 103 sorts, discussing whether it is a price momentum or reversal by further looking at its average future 6-month return is not very meaningful because any result derived from this comparison is not directly related to price momentum-reversal analysis. Hence, the results in Table 2 suggest that momentum-reversal analysis requires a first sort by returns and a second sort, if required, by firm-characteristic sort and not the reverse. 4.2. Comparison of momentum and the small-firm effect We refer to the quintiles containing the largest and the smallest firms as Big and Small, respectively. We create two longshort portfolios, i.e., Loser/Big–Loser/Small and Winner/Big–Winner/Small. We present the results associated with each of these investment strategies in Tables 3 and 4. Because the return classification categories are the same in each table, we can examine the impact of size on momentum trading on each return segment. Nevertheless, it is possible that the Winner–Loser portfolio may in some circumstances embed the momentum and the firm size effects. Thus, we differentiate their relative importance and interactions by creating four additional strategic portfolios: (1) long the Winner/Small portfolio and short the Loser/Small portfolio (Table 5), (2) long the Winner/Big portfolio and short the Loser/Small portfolio (Table 6), (3) long the Winner/Small portfolio and short the Loser/Big portfolio (Table 7), and (4) long the Winner/Big portfolio and short the Loser/Big portfolio (Table 8). 4.2.1. Momentum and the small-firm effect Table 3 reports the return results of buying the Loser/Big portfolio and selling the Loser/Small portfolio (i.e., Loser/Big–Loser/ Small strategy). Our results in the first panel show that the cumulative mean returns of the portfolio, which are calculated using continuous compounding, are all negative and statistically significant for all of the holding periods following portfolio

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

73

Table 4 Winner/Big–Winner/Small strategy results. Length of sort periods

Long–short size ratio

Number of months in the future 3

6

12

24

36

48

60

−0.0122 (−1.61) −0.0148 (−2.25) −0.0125 (−2.02) −0.0145 (−2.40)

−0.047 (−2.91) −0.0373 (−2.44) −0.0387 (−2.73) −0.0379 (−2.74)

−0.1158 (−2.76) −0.0905 (−2.59) −0.0867 (−2.54) −0.0943 (−2.81)

−0.2756 (−2.34) −0.1981 (−2.10) −0.2133 (−2.03) −0.2557 (−2.06)

−0.5128 (−2.30) −0.3517 (−2.04) −0.3563 (−2.08) −0.4512 (−2.21)

−0.4729 (−1.98) −0.446 (−2.19) −0.4499 (−2.29) −0.4857 (−2.85)

−0.5198 (−2.39) −0.4489 (−2.19) −0.3155 (−1.94) −0.4441 (−2.02)

Median of difference of cumulative return (signed rank test) 3 220.9 0 z-Stat (12.41) (−0.45) 6 209.0 −0.0044 z-Stat (12.41) (−1.46) 9 197.1 −0.0073 (12.41) (−1.46) z-Stat 12 195.2 −0.0096 z-Stat (12.41) (−1.69)

−0.0127 (−2.15) −0.0186 (−1.62) −0.0309 (−2.23) −0.0265 (−2.14)

−0.0654 (−2.39) −0.0359 (−1.94) −0.0524 (−2.07) −0.0678 (−2.47)

−0.0247 (−1.68) −0.047 (−1.17) −0.0195 (−1.49) −0.0853 (−1.74)

−0.3262 (−2.15) −0.0442 (−1.44) −0.1728 (−1.73) −0.1914 (−2.15)

−0.3958 (−1.80) −0.3973 (−1.88) −0.4773 (−1.96) −0.5178 (−2.27)

−0.2697 (−2.09) −0.2712 (−1.99) −0.1732 (−1.48) −0.0841 (−1.27)

Mean of difference of sum of institutional trading 3 268.1 t-Stat (19.40) 6 250.5 t-Stat (19.15) 9 239.4 t-Stat (18.76) 12 235.4 t-Stat (18.85)

1920.0 (7.52) 2003.5 (6.02) 1566.7 (8.98) 1476.9 (9.82)

2386.8 (4.37) 1762.5 (6.46) 1480.4 (4.04) 1291.9 (7.88)

1335.6 (5.95) 1021.2 (9.06) 1010.4 (7.70) 1083.7 (9.14)

729.9 (8.64) 683.7 (6.83) 597.6 (7.57) 712.8 (6.79)

606.0 (7.58) 545.8 (6.31) 493.2 (7.44) 545.9 (7.46)

598.6 (3.86) 528.0 (4.44) 523.8 (4.61) 606.8 (3.69)

Mean of difference of cumulative return (t-test) 3 268.1 t-Stat (19.40) 6 250.5 t-Stat (19.15) 9 239.4 t-Stat (18.76) 235.4 12 t-Stat (18.85)

3841.0 (6.89) 3092.2 (5.18) 2255.2 (7.32) 1906.1 (10.70)

Notes: We sort in descending order our sample stocks by previous 3-, 6-, 9- or 12-month returns using the Jegadeesh and Titman (1993) method into quintiles. Winner stocks are those in the highest return quintile. We then sort in descending order the Winner stocks into quintiles using market capitalization. Big (Small) stocks are those in the highest (lowest) size quintile. Winner/Big (Winner/Small) is the group of stocks with highest return and biggest (smallest) market capitalization among the Winner stocks. We then create a long short portfolio using these two stock groups and report below the results for cumulative return (using both t-test and non-parametric signed rank test), and institutional trades from three to 60 months after portfolio formation. Selected months are presented below. For Long–Short Size Ratio, the t-statistics (z-statistics) of testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalization of the long portfolio is equal to the short portfolio.

formation. This pervasive negative pattern suggests that shorting the smallest firms in this strategic portfolio will incur losses in the short and long term. Of course, the reverse strategy (i.e., Loser/Small–Loser/Big) will result in positive returns for the portfolio. The second column of Table 3 shows the ratio of the market capitalization of the long portfolio to the short portfolio (hereafter referred to as the Long–Short Size Ratio), enabling us to measure the relative size of the two portfolios.7 The mean returns test results indicate that in every case the Long–Short Size Ratio is economically and statistically greater than one, indicating that the size of firms in the long portfolio (Loser/Big) is, on average, much larger in terms of size than the short portfolio (Loser/ Small). These results not only suggest that the small-firm effect may dominate the momentum effect, but also reinforce the importance of the small-firm effect as shown, e.g., by Banz (1981) and Fama and French (1992). The second panel in Table 3 presents the median returns of the winner and loser portfolios that are equal. The median results are negative and mostly significant, according to the signed rank test (z-test), and are generally consistent with the t-tests in first panel. In the second column of this panel, the Long–Short Size Ratio is based on the median sizes of the winner–loser portfolios rather than the mean sizes that are used in the first panel. The z-statistic indicates again that the capitalization of the long portfolio is much bigger than the short portfolio based on median returns.8 Prior studies have demonstrated that either institutional investors are either better informed or their trades are motivated by previous returns (i.e., momentum trading). We investigate the impact of this phenomenon on our results by examining how institutional investors who have investments in the long and short positions balance their trading positions. To this end, we obtain a ratio of institutional trades in the long position to that of the short position. We compute the institutional trade ratio in the performance month from that of the month of portfolio formation and examine the relative trading position by institutional investors

7 For the ratio of Long–Short Size Ratio, the t-statistics (z-statistics) from testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalizations of the long and short portfolio are equal. If the ratio is greater (smaller) than one, the long (short) portfolio's market capitalization is larger than that of the short (long) portfolio. 8 In the rest of the panels containing the “median of difference of cumulative returns” in Tables 4–8, we similarly compute the ratio of the Long–Short Size Ratio using on median returns.

74

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

Table 5 Winner/Small–Loser/Small strategy results. Length of sort periods

Long–short size ratio

Number of months in the future 3

6

12

24

36

48

60

−0.0458 (−5.67) −0.0428 (−4.34) −0.0432 (−4.16) −0.0395 (−3.75)

−0.0743 (−3.51) −0.0712 (−3.03) −0.075 (−3.01) −0.0793 (−3.30)

−0.2078 (−3.98) −0.2434 (−3.65) −0.2557 (−3.61) −0.2525 (−3.47)

−0.6454 (−3.51) −0.7447 (−3.29) −0.7604 (−3.37) −0.7141 (−3.64)

−0.4726 (−2.32) −0.5869 (−2.91) −0.6862 (−3.48) −0.4961 (−2.75)

−1.0799 (−3.43) −1.1795 (−2.87) −1.101 (−2.66) −1.0457 (−2.54)

−1.3003 (−3.12) −1.0093 (−2.43) −1.2854 (−2.52) −1.0341 (−2.44)

Median of difference of cumulative return (signed rank test) 3 2.4 −0.0287 z-Stat (11.98) (−5.05) 6 3.0 −0.018 z-Stat (12.29) (−3.72) 9 3.5 −0.0156 (12.34) (−3.05) z-Stat 12 3.8 −0.0121 z-Stat (12.37) (−2.78)

−0.027 (−3.13) −0.0163 (−2.16) −0.0099 (−1.80) −0.0235 (−2.33)

−0.1259 (−4.12) −0.0906 (−3.67) −0.0942 (−3.57) −0.1147 (−3.58)

−0.322 (−3.97) −0.3451 (−3.51) −0.2419 (−3.83) −0.3133 (−3.89)

−0.0691 (−1.78) −0.4436 (−2.53) −0.4148 (−3.10) −0.3378 (−2.72)

−0.9414 (−2.82) −1.0893 (−2.12) −0.6235 (−2.27) −0.4544 (−2.51)

−0.9828 (−2.50) −0.726 (−2.09) −0.6261 (−2.60) −0.6328 (−2.40)

21.2 (2.79) 16.6 (4.11) 31.1 (3.71) 49.7 (1.87)

6.1 (4.01) 10.5 (4.45) 23.6 (4.55) 25.9 (4.32)

14.7 (4.99) 19.3 (4.45) 26.3 (2.95) 20.9 (4.19)

17.0 (3.86) 15.5 (5.65) 23.3 (4.00) 21.1 (4.12)

11.5 (3.50) 18.3 (4.32) 23.3 (3.26) 14.0 (3.20)

12.2 (3.48) 15.1 (3.91) 14.5 (3.52) 13.4 (4.08)

Mean of difference of cumulative return (t-test) 3 2.6 t-Stat (15.49) 6 3.2 t-Stat (18.12) 9 3.7 t-Stat (20.32) 4.2 12 t-Stat (22.31)

Mean of difference of sum of institutional trading 3 2.6 t-Stat (15.49) 6 3.2 t-Stat (18.12) 9 3.7 t-Stat (20.32) 12 3.2 t-Stat (22.31)

35.1 (1.6) 42.1 (1.92) 44.2 (3.77) 46.5 (4.33)

Notes: We sort in descending order our sample stocks by previous 3-, 6-, 9- or 12-month returns using the Jegadeesh and Titman (1993) method into quintiles. Winner (loser) stocks are those in the highest (lowest) return quintile. We then sort in descending order the Winner (loser) stocks into quintiles using market capitalization. Small stocks are those in the lowest size quintile. Winner/Small (Loser/Small) is the group of stocks with highest (lowest) return and smallest market capitalization among the Winner (Loser) stocks. We then create a long short portfolio using these two stock groups and report below the results for cumulative return (using both t-test and non-parametric signed rank test), and institutional trades from three to 60 months after portfolio formation. Selected months are presented below. For the Long–Short Size Ratio, the t-statistics (z-statistics) of testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalization of the long portfolio is equal to the short portfolio.

(i.e., the investment amount of institutional investors in the long position to the short position less one) are reported in the third panel of Table 3 (under “institutional” trades).9 These ratios are quite large and positive, suggesting that institutional investors invest largely in large firms and do not necessarily follow momentum trading behavior. Table 4 presents the performance results of the Winner/Big–Winner/Small investment strategy. Again, the results demonstrate the small-firm effect the in short portfolio dominates the returns of the long position. Over various holding periods, the cumulative returns of this long–short portfolio are negative and significant. Trades of institutional investors in the long position with larger firms are much larger than the small firms in the short portfolio.

4.2.2. “Net” momentum and the small-firm effect Table 5 presents the performance of Winner/Small–Loser/Small strategy. This table contains the results of a strategy minimizes the impact of large firms on momentum trading by focusing only on small capitalization stocks. The size of the winner (long) portfolio is on average slightly larger than the loser (short) portfolio. This consistent result indicates that the positive price momentum effect is overwhelmed by the small-firm effect of the loser portfolio (in the short portfolio). It also implies that a reverse trading strategy yields significant positive returns. The ratio of the long position relative to the short position by institutional investors is always positive and significant, suggesting that institutional investors are investing in larger firms. Table 6 reports the returns of Winner/Big–Loser/Small strategy. This table contains the results of a strategy that focuses on return and size opposites and, thus, reflects the combined impact of the two factors. Again, we find negative and significant returns for the performance months. These results are consistent and significant in the short and long term, implying that the reverse strategy yields consistently positive and significant results. The ratio of trades by institutional investors in the long and short position is positive and significant, indicating that trading activity of institutional investors in large stocks.

9

In Table 3 and other remaining tables, the institutional investor variable is computed using data from 1980 onward reported in Table 1.

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

75

Table 6 Winner/Big–Loser/Small strategy results. Length of sort periods

Long–short size ratio

Number of months in the future 3

Mean of difference of cumulative return (t-test) 3 717.5 t-Stat (15.26) 6 863.8 t-Stat (14.05) 9 986.5 t-Stat (13.76) 1096.3 12 t-Stat (14.44)

6

12

24

36

48

60

−0.058 (−4.69) −0.0575 (−4.36) −0.0557 (−4.08) −0.054 (−3.94)

−0.1213 (−4.08) −0.1085 (−3.55) −0.1136 (−3.58) −0.1172 (−3.78)

−0.3236 (−4.09) −0.3339 (−3.85) −0.3423 (−3.78) −0.3468 (−3.87)

−0.921 (−3.31) −0.9428 (−3.19) −0.9736 (−3.17) −0.9698 (−3.37)

−0.9854 (−3.28) −0.9386 (−3.23) −1.0425 (−3.35) −0.9473 (−3.22)

−1.5528 (−3.08) −1.6255 (−3.14) −1.5509 (−2.85) −1.5314 (−2.86)

−1.8201 (−3.35) −1.4581 (−3.39) −1.6009 (−3.05) −1.4781 (−3.08)

Median of difference of cumulative return (signed rank test) 3 546.2 −0.0213 z-Stat (12.41) (−3.53) 6 669.9 −0.021 z-Stat (12.41) (−3.39) 9 703.2 −0.0241 (12.41) (−2.81) z-Stat 12 775.3 −0.0289 z-Stat (12.41) (−2.72)

−0.0674 (−3.41) −0.0367 (−2.54) −0.0341 (−2.61) −0.0528 (−2.79)

−0.1616 (−3.81) −0.1666 (−3.76) −0.1532 (−3.67) −0.1354 (−3.85)

−0.5442 (−3.38) −0.3563 (−3.30) −0.2728 (−3.13) −0.3319 (−3.62)

−0.7201 (−2.67) −0.4813 (−2.58) −0.6689 (−2.86) −0.5049 (−2.96)

−1.3727 (−2.35) −1.1285 (−2.59) −0.9609 (−2.59) −0.7277 (−2.67)

−1.6059 (−2.70) −1.1459 (−2.60) −1.0645 (−2.70) −1.1712 (−2.60)

Mean of difference of sum of institutional trading 3 717.5 t-Stat (15.26) 6 863.8 t-Stat (14.05) 9 986.5 t-Stat (13.76) 12 1096.3 t-Stat (14.44)

34,129.3 (3.87) 35,100.1 (4.56) 61,600.5 (3.19) 62,872.5 (4.11)

29,611.7 (3.55) 17,001.2 (6.86) 43,273.0 (2.24) 56,089.5 (1.86)

9413.1 (4.95) 14,000.2 (5.02) 21,394.8 (5.29) 24,451.2 (5.15)

14,677.7 (5.39) 17,482.2 (5.39) 18,793.2 (5.19) 19,337.5 (5.11)

13,098.0 (3.81) 12,536.0 (3.68) 14,462.1 (3.66) 17,260.5 (3.63)

8257.6 (2.89) 13,210.0 (2.50) 13,108.7 (2.44) 9732.6 (2.45)

6974.4 (4.21) 8997.3 (2.58) 8418.2 (2.95) 8216.9 (3.75)

Notes: We sort in descending order our sample stocks by previous 3-, 6-, 9- or 12-month returns using the Jegadeesh and Titman (1993) method into quintiles. Winner (Loser) stocks are those in the highest (lowest) return quintile. We then sort in descending order the Winner (Loser) stocks into quintiles using market capitalization. Small stocks are those in the lowest size quintile. Winner/Big (Loser/Small) is the group of stocks with highest (lowest) return and smallest market capitalization among the Winner (Loser) stocks. We then create a long short portfolio using these two stock groups and report below the results for cumulative return (using both t-test and non-parametric signed rank test), and institutional trades from three to 60 months after portfolio formation. Selected months are presented below. For the Long–Short Size Ratio, the t-statistics (z-statistics) of testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalization of the long portfolio is equal to the short portfolio.

Table 7 shows the returns of the Winner/Small–Loser/Big strategy. The analysis also focuses on return and size opposites. In this scenario, the size of the winner firms (either based on the mean return or medium return) is much smaller than that of the loser firms as indicated in the second column and the t-tests. The ratio of the Long–Short Size Ratio is close to zero (due to rounding, such as 0.002) because the long portfolio is much smaller than the short portfolio (either in mean value or medium value). All cumulative returns are positive and significant, reflecting the positive effect of momentum factor and the positive small-firm effect of the winner portfolio. An analysis of institutional trades in the long and short positions suggests that the institutional investors invest relatively more in the short position with larger firm size. In this case, the institutional investors earned significant positive returns. Finally, Table 8 presents the returns of the Winner/Big–Loser/Big strategy. This strategy consists of relatively large firms, although of different sizes, in order to minimize the effect of small firm on momentum profits. Returns are positive and significant within one year. The absence of the small-firm effect in this strategic portfolio explains reasonably well the return behaviors because of the positive initial price momentum effect. Once again the ratios of the long and short positions of institutional investors are positive, confirming our previous observation that institutional investors tend to invest in large firms. 5. Conclusions Our study uses all the U.S. stock returns from four exchanges (NYSE, AMEX, NASDAQ and NYSE Arca) from January 1962 through December 2013 to investigate the momentum pattern of the U.S. stocks. In addition replicating and extending the results of past studies that show a positive short-term price momentum effect but long-term price reversals, our analysis provides several noteworthy results. We do not invoke behavioral models to explain the momentum pattern. Instead, we use several long–short portfolios to show that the momentum pattern is largely attributable to the interaction of the price momentum and the market capitalization and other size related effects. For example, our results using strategic portfolios that involve a combination of long and short portfolios

76

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

Table 7 Winner/Small–Loser/Big strategy results. Length of sort periods

Long–short size ratio

Number of months in the future 3

Mean of difference of cumulative return (t-test) 3 0.00 t-Stat (−676.2) 6 0.00 t-Stat (−650.6) 9 0.00 t-Stat (−477.0) 12 0.00 t-Stat (−432.2)

6 0.0239 (2.64) 0.0331 (3.65) 0.0346 (3.85) 0.0426 (4.62)

Median of difference of cumulative return (signed rank test) 3 0.00 0.0255 z-Stat (−12.41) (3.01) 6 0.00 0.0381 z-Stat (−12.41) (4.39) 9 0.00 0.0454 z-Stat (−12.41) (4.79) 12 0.00 0.0432 z-Stat (−12.41) (5.61)

12

24

36

48

60

0.078 (4.60) 0.0829 (4.85) 0.091 (5.51) 0.0925 (5.82)

0.1852 (3.97) 0.1584 (4.17) 0.1454 (3.77) 0.1547 (3.71)

0.2547 (1.93) 0.1746 (1.67) 0.1626 (1.44) 0.2094 (1.55)

0.5192 (2.37) 0.44 (2.34) 0.4053 (2.52) 0.5256 (2.47)

0.4136 (3.09) 0.2576 (1.69) 0.2611 (2.34) 0.4214 (3.19)

0.5333 (1.91) 0.5553 (1.68) 0.3098 (1.16) 0.5362 (2.11)

0.065 (4.45) 0.0709 (4.64) 0.0886 (5.47) 0.0861 (5.56)

0.1495 (4.32) 0.2105 (4.18) 0.1562 (4.24) 0.1389 (4.71)

0.2243 (2.35) 0.2016 (2.30) 0.2213 (2.25) 0.2126 (2.62)

0.3359 (2.63) 0.2793 (2.20) 0.3389 (2.44) 0.3339 (2.58)

0.3252 (2.59) 0.0311 (1.18) 0.2252 (2.04) 0.4594 (2.51)

0.3235 (1.89) 0.5128 (1.58) 0.3249 (1.07) 0.6953 (1.89)

Mean of difference of sum of institutional trading 3 0.00 −0.9973 −0.9959 −0.9967 −0.994 t-Stat (−676.2) (−2191) (−1578) (−1696) (−1260) 6 0.00 (−0.9947) (−0.9933) (−0.9954) (−0.99) (−488.8) t-Stat (−650.6) (−949.1) (−724.0) (−1211) 9 0.00 (−0.9939) (−0.9919) (−0.9929) (−0.9876) t-Stat (−477.0) (−1215) (−782.2) (−1007) (−404.1) 12 0.00 (−0.9932) (−0.9925) (−0.9911) (−0.992) t-Stat (−432.2) (−1213) (−912.7) (−692.4) (−776.1)

−0.991 (−659.4) (−0.9832) (−160.1) (−0.9821) (−216.8) (−0.9894) (−487.9)

−0.9914 (−583.5) (−0.9859) (−246.8) (−0.9826) (−166.3) (−0.9846) (−172.0)

−0.9888 (−501.8) (−0.9833) (−303.6) (−0.9812) (−255.1) (−0.9849) (−300.7)

Notes: We sort in descending order our sample stocks by previous 3-, 6-, 9- or 12-month returns using the Jegadeesh and Titman (1993) method into quintiles. Winner (Loser) stocks are those in the highest (lowest) return quintile. We then sort in descending order the Winner (Loser) stocks into quintiles using market capitalization. Big (Small) stocks are those in the highest (lowest) size quintile. Winner/Small (Loser/Big) is the group of stocks with highest (lowest) return and smallest (biggest) market capitalization among the Winner (Loser) stocks. We then create a long short portfolio using these two stock groups and report below the results for cumulative return (using both t-test and non-parametric signed rank test), and institutional trades from three to 60 months after portfolio formation. Selected months are presented below. For the Long–Short Size Ratio, the t-statistics (z-statistics) of testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalization of the long portfolio is equal to the short portfolio.

demonstrate that the size effect appears to dominate the price momentum effect in their performance. To illustrate, regardless of the different winner–loser portfolio category used, when the size category is the smallest in the short portfolio, the cumulative returns of these portfolio (after portfolio formation) are consistently negative and significant, demonstrating the dominant small-firm effect. Further, when the firm size in the long portfolio is smallest, the overall strategic return is positive with no negative price reversals. In addition, in a strategic portfolio that longs the stocks of large firms that have experienced superior returns and shorts the stocks of small firms characterized by poor past performance, the long portfolio continues to underperform the short portfolio, showing significant short- and long-term price reversals. This result differs from previous literature but shows support for short-term momentum and long-term price reversals. In sum, we show small capitalization stocks outperform the large capitalization stocks. Moreover, we demonstrate that institutional investors tend to invest in large firms, regardless of various winner–loser portfolio combinations. This finding is not consistent with the results of many studies that suggest the momentum trading behavior of institutional investors. Our results, however, do confirm the observation that institutional investors tend to invest in large firms. We contribute to the momentum literature by showing that the small-firm effect dominates price momentum in the long run and explaining the so-called momentum-price reversal anomaly. Because we rely on the notion that the small-firm effect is a proxy for risk, our explanation is rooted in the traditional risk-return framework. Thus, behavioral reasons for this so-called anomaly, although intriguing, are not needed, particularly if Occam's Razor, which urges the acceptance of the simplest explanation, is invoked.

Acknowledgments We thank Richard Baillie (Editor) and anonymous reviewer for their insightful comments and suggestions. We also thank Jot Yau and seminar participants at the University of Missouri—St. Louis, University of Nottingham Ningbo, National Kaohsiung First University of Science and Technology, Fengchia University, and Harbin Institute of Technology for helpful discussions and input.

G. Geoffrey Booth et al. / Journal of Empirical Finance 35 (2016) 68–77

77

Table 8 Winner/Big–Loser/Big strategy results. Length of sort periods

Long–short size ratio

Number of months in the future 3

6

12

24

36

48

60

0.0117 (1.67) 0.0183 (2.31) 0.0221 (2.58) 0.0281 (3.20)

0.031 (2.33) 0.0456 (3.11) 0.0523 (3.24) 0.0545 (3.54)

0.0693 (2.04) 0.0679 (1.93) 0.0587 1.63 0.0604 (1.71)

−0.0209 (−0.23) −0.0236 (−0.24) −0.0507 (−0.49) −0.0463 (−0.48)

0.0064 (0.06) 0.0883 (0.77) 0.0489 (0.43) 0.0744 (0.62)

−0.0592 (−0.32) −0.1884 (−1) −0.1889 (−0.86) −0.0643 (−0.32)

0.0135 (0.07) 0.1065 (0.51) −0.0057 (−0.03) 0.0922 (0.44)

Median of difference of cumulative return (signed rank test) 3 2.1 0.0159 z-Stat (8.86) (2.66) 6 3.1 0.0297 z-Stat (9.76) (4.50) 9 3.3 0.032 z-Stat (10.49) (4.90) 12 3.8 0.0331 z-Stat (10.86) (5.37)

0.0362 (2.99) 0.0465 (3.81) 0.0602 (3.96) 0.0647 (4.04)

0.0925 (2.99) 0.0816 (2.85) 0.1006 (2.61) 0.104 (2.92)

0.0385 (0.55) 0.11 (0.63) 0.1315 (0.36) 0.1488 (0.44)

0.005 (0.31) 0.0716 (1.3) 0.0842 (0.83) 0.0876 (0.69)

−0.1618 (−0.55) 0.0135 (−0.55) −0.1703 (−0.55) −0.0803 (−0.08)

−0.0027 (0.05) −0.053 (−0.15) −0.1066 (−0.36) −0.0862 (0.05)

Mean of difference of sum of institutional trading 3 4.0 t-Stat (9.01) 6 4.9 t-Stat (9.77) 9 6.2 t-Stat (9.56) 12 7.0 (9.80) t-Stat

3.78 (6.50) 5.22 (5.50) 8.25 (6.14) 8.33 (5.66)

3.02 (5.22) 4.75 (4.11) 6.26 (4.53) 8.17 (5.48)

5.14 (5.34) 8.16 (4.56) 10.36 (4.45) 7.64 (3.94)

6.75 (4.09) 9.52 (3.61) 10.46 (3.98) 6.51 (3.55)

4.53 (3.15) 7.33 (2.70) 8.74 (2.35) 8.03 (2.27)

6.59 (3.08) 7.53 (4.18) 9.59 (3.76) 7.51 (2.96)

Mean of difference of cumulative return (t-test) 3 4.0 t-Stat (9.01) 6 4.9 t-Stat (9.77) 9 6.2 t-Stat (9.56) 12 7.0 t-Stat (9.80)

2.67 (8.17) 4.52 (8.51) 6.76 (8.11) 8.10 (8.00)

Notes: We sort in descending order our sample stocks by previous 3-, 6-, 9- or 12-month returns using the Jegadeesh and Titman (1993) method into quintiles. Winner (Loser) stocks are those in the highest (lowest) return quintile. We then sort in descending order the Winner (Loser) stocks into quintiles using market capitalization. Big stocks are those in the highest size quintile. Winner/Big (Loser/Big) is the group of stocks with highest (lowest) return and biggest (biggest) market capitalization among the Winner (Loser) stocks. We then create a long short portfolio using these two stock groups and report below the results for cumulative return (using both t-test and non-parametric signed rank test), and institutional trades from three to 60 months after portfolio formation. Selected months are presented below. For the Long–Short Size Ratio, the t-statistics (z-statistics) of testing whether the mean (median) of the ratio equals one is equivalent to testing if the market capitalization of the long portfolio is equal to the short portfolio.

References Antoniou, C., Doukas, J.A., Subrahmanyan, A., 2013. Cognitive dissonance, sentiment and momentum. J. Financ. Quant. Anal 48 (1), 245–275. Asness, C.S., Moskowitz, T.J., Pedersen, L.H., 2013. Value and momentum everywhere. J. Financ. 68 (3), 929–985. Bandarchuk, P., Hilscher, J., 2013. Sources of momentum profits: evidence on the irrelevance of characteristics. Rev. Financ. 17 (2), 809–845. Banz, R.W., 1981. The relationship between returns and market value of common stocks. J. Financ. Econ. 9 (1), 3–18. Barberis, N., Shleifer, A., Vishny, R., 1998. A model of investor sentiment. J. Financ. Econ. 49 (3), 307–343. Berk, J.B., 1995. A critique of size related anomalies. Rev. Financ. Stud. 8 (2), 275–286. Bhojraj, S., Swaminathan, B., 2006. Macromomentum: returns predictability in international equity indices. J. Bus. 79 (1), 429–451. Chan, L.K., Jegadeesh, N., Lakonishok, J., 1996. Momentum strategies. J. Financ. 51 (5), 1681–1713. Carhart, M.M., 1997. On persistence in mutual fund performance. J. Financ. 52 (1), 57–81. Conrad, J., Kaul, G., 1998. An anatomy of trading strategies. Rev. Financ. Stud. 11 (3), 489–519. Daniel, K., Hirshleifer, D., Subrahmanyam, A., 1998. Investor psychology and security market under- and overreactions. J. Financ. 53 (6), 1839–1886. De Bondt, W.F.M., Thaler, R., 1987. Further evidence on investor overreaction and stock market seasonality. J. Financ. 42 (3), 557–581. Fama, E., French, K., 1992. The cross-section of expected stock returns. J. Financ. 47 (2), 427–465. Frazzini, A., 2006. The disposition effect and underreaction to news. J. Financ. 61 (4), 2017–2046. George, T.J., Hwang, C.Y., 2004. The 52-week high and momentum investing. J. Financ. 9 (5), 2145–2176. Grinblatt, M., Han, B., 2005. Prospect theory, mental accounting, and momentum. J. Financ. Econ. 78 (2), 311–339. Hong, H., Stein, J.C., 1999. A unified theory of underreaction, momentum trading and overreaction in asset markets. J. Financ. 54 (6), 2143–2184. Hong, H., Lim, T., Stein, J.C., 2000. Bad news travels slowly: size, analyst coverage, and the profitability of momentum strategies. J. Financ. 55 (1), 265–295. Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: implications for stock market efficiency. J. Financ. 48 (1), 65–91. Jegadeesh, N., Titman, S., 2001. Profitability of momentum strategies: an evaluation of alternative explanations. J. Financ. 56 (2), 699–720. Johnson, T., 2002. Rational momentum effects. J. Financ. 57 (2), 585–608. Korajczyk, R., Sadka, R., 2004. Are momentum profits robust to trading costs? J. Financ. 59 (3), 1039–1082. Lehmann, B., 1990. Fads, martingales, and market efficiency. Q. J. Econ. 105 (1), 1–28. Lesmond, D., Schill, M., Zhou, C., 2004. The illusory nature of momentum profits. J. Financ. Econ. 71 (2), 349–380. Lu, Z., 2014. Can Cash Flow Expectations Explain Momentum and Reversal? (Available at SSRN: http://ssrn.com/abstract-2442127.) Moskowitz, T.J., Grinblatt, M., 1999. Do industries explain momentum? J. Financ. 54 (4), 1249–1290. Moskowitz, T.J., Ooi, Y., Pedersen, L.H., 2012. Time series momentum. J. Financ. Econ. 104 (2), 228–250. Nofsinger, J., Sias, R.W., 1999. Herding and feedback trading by institutional and individual investors. J. Financ. 54 (6), 2263–2295. Novy-Marx, R., 2012. Is momentum really momentum? J. Financ. Econ. 103 (3), 429–453. Rouwenhorst, K.G., 1998. International momentum strategies. J. Financ. 53 (1), 267–284. Sagi, J., Seasholes, M., 2007. Firm-specific attributes and the cross section of momentum. J. Financ. Econ. 84 (2), 389–434. Yan, X.M., Zhang, Z., 2009. Institutional investors and equity returns: are short-term institutions better informed? Rev. Financ. Stud. 22 (2), 893–924.