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Attention bias and 52-Week High Price Momentum
Abstract
In this paper, we propose a simple modification of 52-week high price momentum
strategy. We show that the 52-week high momentum profits based on stocks with a
recent 52-week high price and slow-accumulation closing price are significantly higher
than the stocks with a distant 52-week high price and rapid-accumulation closing price.
The Fama-French three-factor alpha of our modified 52-week high momentum strategy
is larger than twice of original George and Hwang (2004) momentum strategy.
JEL: G11, G12, G14
Keywords: 52-week, attention, recency, anchor, momentum
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1. Introduction
Investors’ cognitive bias has been widely documented to play an important role in
determining asset prices, for example, Barber and Odean (2008), Hou, Peng, and Xiong
(2009), Hirshleifer, Lim, and Teoh (2012), and Li and Yu (2012). We explore the
hypothesis that behavioral anchoring bias interacts with attention bias.
George and Hwang (2004) indicate that investors use the 52-week high as an
anchor when assessing the up-trend stock price. The anchoring bias leads to investors
to underreact to good news about the stocks whose prices are near their 52-week high
prices. For example, when good news in the prior year pushes a stock’s closing price
near a new 52-week high, traders are reluctant to bid the price of the stock higher even
if the information warrants it. As a result, they underreact to good news. When the
information eventually prevails, and the price goes up, momentum occurs. They
confirm that a momentum strategy based on the nearness of current closing price to its
52-week high price can earn significantly positive abnormal returns. The momentum is
denoted as GH momentum.
In this paper, first, according to Bhootra and Hur (2013), we construct a recency
ratio (RR) to measure the distance to the past 52-week high price. Bhootra and Hur
(2013) show that anchoring bias is stronger for stocks with recent 52-week high price
than stocks with the distant 52-week high price. The stocks that attain the 52-week high
price in the recent past significantly outperform the stocks that attain the 52-week price
in the distant past. Since investors pay too much attention to the anchor (anchoring bias),
investors underreact to the positive (negative) news about the stocks whose prices are
near (far from) their 52-week high price. The timing of 52-week high price (i.e., the
anchor) affects the profitability of GH momentum.
Second, following Da, Gurun, and Warachka (2014), we create an information
discreteness (ID) measure to proxy for investors’ attention. Specifically, we use the
percentage of positive daily returns relative negative daily returns to estimate
information discreteness (i.e., accumulation of formation-period return or closing price)
that captures the relative frequency of small signals. Da, Gurun, and Warachka (2014)
document that investors are inattentive to information arriving continuously in small
amounts, which is denoted as the frog in the pan (FIP) hypothesis. Specifically, a series
of frequent gradual changes attracts less attention than infrequent dramatic changes.
The profits of Jegadeesh and Titman (1993) price momentum for stocks with
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continuous information, are higher than stocks with discrete information. Because of
investors’ under (or limited) attention to the dynamic changes of price, the investors
tend to underreact to continuous information. We argue that the accumulation of closing
price affects the profitability of GH momentum.
GH measure is the ratio of closing price to the 52-week high price. Recency ratio
affects GH measure through the timing of 52-week high price, i.e., the denominator of
GH measure, while the information discreteness influences GH measure by the
accumulation of closing price, i.e., numerator the of GH measure. Moreover, recency
ratio is positively associated with the level of investors’ attention and is negatively
associated with the level of investors’ underreaction, while in contrast, information
discreteness is negatively associated with the level of investors’ attention and is
positively associated with the level of investors’ underreaction. Combining these two
attention-bias related measures, we hypothesize that stocks whose 52-week high price
occur in the recent past and their closing prices have gradually moved up will have a
higher magnitude of underreaction than stocks whose 52-week high price occur in the
distant past and their closing prices have dramatically moved up. That is, if both the
recency hypothesis and frog in the pan hypothesis hold, then RR and ID should enhance
the GH momentum.
The results confirm our conjectures. First, the GH momentum is the stronger
in stocks with continuous price accumulation than stocks with discrete price
accumulation. The alpha (Fama-French three-factor model) of GH momentum in
continuous information is 1.89% with t-statistics of 12.32, and the alpha of GH
momentum in stocks with discrete information is 1.64% with t-statistics of 13.10.
The alpha of spread in GH momentum between continuous information and
discrete information is 0.25% with t-statistics of 3.31. Further, the GH momentum
is the stronger in the recent 52-week high group than in the distant 52-week high
group. The alpha of GH momentum in stocks with recent 52-week high is 1.72%
with t-statistics of 13.94, and the alpha of GH momentum in distant 52-week high
is 1.51% with t-statistics of 12.20. The alpha of spread in GH momentum between
recent and distant 52-week high groups is 0.21% with t-statistics of 1.69. Consistent
with our hypothesis that the GH momentum strategy is higher for stocks with a recent
52-week high price and having the closing price gradually changed than for stocks with
a distant 52-week high price and having the closing price suddenly changed.
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Moreover, we test whether one subsumes or dominates the other. Specifically, we
explore the interaction between rerecncy ratio and information discreteness on GH
momentum by independently forming triple sorting portfolios. Interestingly, the results
indicate that after controlling for recency ratio, the information discreteness can
improve GH momentum only for stocks with moderate recency ratio. On the other hand,
after controlling for information discreteness, the recency ratio can improve GH
momentum only for stocks with moderate information discreteness. The limited
attention hypothesis provides the following explanation.1 If the RR is relatively high,
i.e., the timing of 52-week high price is very close to the current time, since investors
pay too much attention to 52-week high price, the relative importance of the how a
closing price is formed will be neglected. As a result, investors’ attention to how the
closing price is formed (quick or slow) might be indifferent. On the other hand, when
the RR is relatively low, i.e., the timing of 52-week high price is far from the current
time, investors pay too little attention to the stock. As a result, the accumulation process
of closing price will also be neglected and induce indifferent attention toward how the
closing price is formed (quick or slow). Similarly, when the ID is relatively high, i.e.,
the closing price changes quickly, investors are significantly attracted by the sudden
changes of closing price. As a result, too much attention to the current closing price will
mitigate the relative importance of the timing of 52-week high price. Moreover, when
the ID is relatively low, i.e., the closing price changes slowly, investors pay little
attention to the stocks whenever the timing of 52-week high price is recent or distant.
We modify the GH measure by summing the GH, RR, and -ID to simultaneously
incorporating recency ratio and information discreteness into account, and document
that the modified GH ratio (MGH) greatly improves the performance of original GH
momentum. The alpha of MGH is 2.01% and statistically significant with t-statistic
of 14.51. Particularly, the alpha of MGH momentum is larger than twice of GH
momentum strategy.
Our paper is related to two strands of literature: The literature on 52-week high
price momentum and the literature on investor behavior bias. The paper contributes to
the literature in threefold. First, no study introduces and compares different types of
1 Many studies show that Investor’s attention is a limited cognitive resource which can prevent them
from immediately processing all available information (Hirshleifer and Teoh 2003; Sims 2003; Peng and
Xiong 2006).
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limited attention bias at the same time. Second, we investigate how the anchoring bias
and attention bias interacts with each other. Third, we show that combing two types of
attention biases can significantly enhance the profit of a 52-week high price momentum
strategy.
2. Literature reviews
2.1. The anchoring hypothesis
Tversky and Kahneman (1974) suggest that individuals who use one of the most
common heuristics (anchoring and adjustment) to make estimates, start from an initial
value (the anchor) and adjust this upwards or downwards to account for the
information they have available. George and Hwang (2004) have documented that
investors tend to use 52-week high price as an important reference point in
decision making. They argue that the profitability of 52-week high strategy arises
because investors are reluctant to bid up the price of stocks trading near their 52-
week high price beyond the 52-week high, even if positive information warrants
a higher valuation. On the other hand, investors are unwilling to bid down the price
of stocks in response to negative information, when these stocks are trading at
prices far below the 52-week peak price. As the true information is eventually
realized, the subsequent prices are corrected. The price momentum occurs.
2.2. The attention-bias hypothesis
Much psychological literature establishes that there are limits to the central cognitive-
processing capacity of the human brain. In the finance area, many participants,
particularly individual investors, can devote only limited attention to their portfolios. For
example, Peng and Xiong (2006) show that the limited attention of investors cause
investors to process more market-wide information than firm-specific information.
Similarly, Li and Yuan (2012) indicate that market-wide attention-grabbing events cause
investors to pay increased attention to their portfolios, thereby increasing trading activity
and, in turn, influencing stock prices.
Bhootra and Hur (2013) show that anchoring bias appears to be negatively related
to the distance of the anchor. They argue that the investors’ reluctance to bid up the
price of a stock in response to positive information would be particularly strong
when the stock has recently traded at an elevated price. If investors put more weight
on recent information due to the recency bias, then the straightforward implication
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is that their tendency to underreact would be significantly stronger when the 52-
week high occurred recently. On the other hand, if the 52-week high occurred early
during the year, the investors’ response to information is likely to be relatively more
complete, resulting in weaker underreaction. As a result, investors’ over attention to
the anchor will cause a serious anchoring bias, i.e., underreaction.
On the other hand, Da, Gurun, and Warachka (2014) show that a series of gradual
changes attracts less attention than sudden dramatic changes. They document a frog-in-
the-pan (FIP) hypothesis that originates from investors’ under attention. This hypothesis
predicts that investors are less attentive to information arriving continuously in small
amounts than to information with the same cumulative stock price implications that
arrives in large amounts at discrete time points. The FIP hypothesis predicts that ID has
a conditional relationship with momentum.
3. Portfolio results
The data of the sample period is from January 1965 to December 2017. The relevant
firm-level accounting data are drawn from COMPUSTAT. Stocks listed on the NYSE,
the AMEX and the NASDAQ with ordinary common equity (security type 10 or 11
from Center for Research in Security Prices (CRSP)) are included. The firms must have
valid monthly returns over the past 12 months. We exclude stocks with price less than
$5 at the end of the portfolio formation month to prevent from illiquid trading. Further,
we also exclude stocks with the smallest NYSE market capitalization decile. The Fama
and French three factors are downloaded from the Kenneth French’s website.2
According to George and Hwang (2004), at the end of each month t, we use the
price ratio of the closing price to the previous 12-month high price as the sorting index
to sort stocks into deciles. We denote this as GH momentum. The price adjusted for
stock splits and dividends using CRSP price adjustment factor. The winner (loser)
portfolio defined as stocks with the highest 10% (lowest) GH ratio.
GHt = Closing Pricet
52−week high price (1)
For the comparison purpose, we also measure JT (Jegadeesh and Titman, 1993)
momentum profits. JT portfolios are constructed as follows. For each month t, we sort
2 Please refer to the Kenneth French’s website:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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all stocks into deciles by their cumulative raw returns during the previous 12 months.
We skip one month between portfolio formation and holding period to avoid the effects
of bid-ask bounce, price pressure, and any lagged reaction.
Following Da, Gurun, and Warachka (2014), we calculate information
discreteness (ID) to proxy for the speed of stock prices. The ID is determined by the
sign of daily returns and ignores the magnitude by equally weighting each observed
return. The ID is denoted as follows.
ID = sgn(PRET) × [%neg −%pos ], (2)
where PRET is the cumulative return during the formation period. sgn(PRET) is
denoted as the sign of PRET. sgn(PRET) = 1 if PRET > 0 and sgn(PRET) = -1 if PRET
< 0. %neg and %pos are the percentage of days during the formation period with
positive and negative returns.
The higher ID implies discrete information and lower ID implies continuous
information. For example, for winner stocks, their PRET is high. A high percentage of
positive returns (%pos > %neg) means that PRET is constructed by many small
movements of positive returns. From Eq (2), a high percentage of positive return for
winner stock suggests a low value in ID implying the continuous information. In the
extreme case, if a series of daily returns are all positive, then ID will be a minimum
value of -1. On the other hand, if only a few positive returns contribute to PRET of
winner stock, then ID is closing to +1 and the information is discrete.
Following Bhootra and Hur (2013), at the end of each month, we estimate the
recency ratio, RR, for each stock as follows:
RR = 1 - number of days since 52−week high price
364 (3)
The recency ratio is adversely related to the number of days since the 52-week
high price. In extreme case, the number of days since the 52-week high price is 0 if the
closing price at time t is the 52-week high price and the RR ratio equal to 1. At the end
of each month, the stocks with the highest 10% RR are classified as winner portfolio,
and the lowest 10% RR of the firms are allocated as loser portfolio.
The portfolios are held for six overlapping months. The portfolio returns are
equally weighted. We construct a zero-investment portfolio by buying the top ten
percentile winner and selling the bottom ten percentile loser stocks. The overlapping
holding period implies time diversification. That is, for each month t, one-sixth of
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stocks need to be replaced with new winners and losers.
We begin our analysis by examining the results of portfolios formed on JT,
GH, and RR measures. Table 1 of Panel A reports the average monthly returns
over the 6-month holding period. Consistent with GH, we find evidence of strong
momentum based on the nearness of the current price to 52-week high price. The
GH loser portfolio earns a return of 0.62% per month, while the winner portfolio
has a return of 1.35% per month. The spread of 0.73% between loser and winner
portfolio returns is statistically significant with a t-statistic of 3.31. The
corresponding Fama and French (1993) alpha is 1.03% and also statistically
significant with a t-statistic of 5.03.
We find evidence of strong momentum based on RR measure as well. The RR
loser portfolio earns a return of 0.76% per month, while the RR winner portfolio
return is 1.36% per month. The corresponding difference of 0.60% per month (t-
statistic = 4.69) and the alpha of 0.78% (t-statistic = 6.32) are statistically
significant at the 1% level. The significant JT momentum profits are also
documented. The JT loser portfolio earns a return of 0.53% per month, while the
JT winner portfolio return is 1.40% per month. The corresponding difference of
0.87% per month (t-statistic = 4.09) and the alpha of 1.14% (t-statistic = 5.58) are
statistically significant at the 1% level.
As indicated by prior research, the loser stocks tend to experience positive
return in January, and therefore, the zero-cost winner minus loser portfolio tends to
earn much higher return after excluding the January returns. To examine the impact
of January seasonality, we report the returns to JT, GH, and RR based momentum
strategies separately for January and non-January months in Panels B and C of
Table 1. The results confirm that the loser stocks earn higher positive returns in
January, and thus induce negative momentum profits in January. The non-January
momentum returns are particularly pronounced, especially for excluding large
positive January returns of losers; the winner portfolio returns are similar with or
without exclusion of January returns. The JT strategy generates a monthly return of
1.07% with an alpha of 1.31%; GH strategy earns a monthly return of 0.97% with
an alpha of 1.23%, and the RR strategy generates a monthly return of 0.75% with
an alpha of 0.90%.
[Table 1 Here]
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We investigate the profitability of a strategy that uses information of 52-week
high price as well as the information discreteness. The stocks are independently
sorted into five by five portfolios based on information discreteness (ID) and
52-week high price (GH). The results of these tests are reported in Table 2. For
each of the five ID portfolios (continuous to discrete information), we report the
raw and risk-adjusted returns to GH winner and loser portfolios and the difference
in returns between winner and loser portfolios. The results show that the profits of
GH momentum are the stronger in low information discreteness (continuous) group
of than in high information discreteness (discrete) group. For example, the raw
returns (alpha) of GH momentum profits in low information discreteness are 1.60%
(1.89%) with t-statistics of 9.26 (12.32) and the raw returns (alpha) of GH
momentum profits in high information discreteness are 1.38% (1.64%) with t-
statistics of 8.87 (13.10). The raw (alpha) spread of the momentum profits between
low (continuous) and high (Discrete) ID groups is 0.22% (0.25%) with t-statistics
of 2.81 (3.31). In sum, we show that the profitability of GH momentum strategy
can be significantly enhanced by conditioning on the information discreteness.
[Table 2 Here]
We explore the profitability of a strategy that uses information of 52-week
high price as well as the recency ratio. The stocks are independently sorted into
five by five portfolios based on recency ratio (RR) and 52-week high price
(GH). The results of these tests are reported in Table 3. For each of the five RR
portfolios (Distant to Recent information). Consistent with Bhootra and Hur (2013),
the results show that the profits of GH momentum are the stronger in the recent
group than in the distant group. For example, the raw returns (alpha) of GH
momentum profits in recent RR are 1.45% (1.72%) with t-statistics of 9.82 (13.94)
and the raw returns (alpha) of GH momentum profits in distant RR are 1.21%
(1.51%) with t-statistics of 8.16 (12.20). The raw (alpha) spread of the momentum
profits between recent RR and distant RR groups is 0.24% (0.21%) with t-statistics
of 1.92 (1.69). In sum, we show that the profitability of GH momentum strategy
can be significantly enhanced by conditioning on the recency of 52-week high price.
[Table 3 Here]
In addition to separately investigating the impact of recency ratio and information
discreteness on GH momentum, we explore the interaction between recency ratio and
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information discreteness on GH momentum by forming independent triple sorting
portfolios in Table 4. Several interesting findings of Table 4 are summarized as follows.
First, after controlling for recency ratio, the information discreteness can improve GH
momentum only for stocks with moderate recency ratio. After controlling for
information discreteness, the recency ratio can improve GH momentum only for stocks
with moderate information discreteness. For example, the alpha of GH momentum
profit for stocks with low ID (high RR) of 0.84% (0.92%) is significantly higher than
alpha of GH momentum profit for stocks with high ID (low RR) of 73% (73%).
However, the improvement only for stocks with moderate recency ratio (information
discreteness), that is, the Middle RR (Middle ID).
The above results are aligned with the limited attention hypothesis that investor’s
attention is a limited cognitive resource which can prevent them from immediately
processing all available information (Hirshleifer and Teoh 2003; Sims 2003; Peng and
Xiong 2006). Recency ratio affects GH ratio through the timing of 52-week high price,
i.e., the denominator of GH ratio, while the information discreteness influences GH
ratio by the formation of closing price, i.e., numerator the of GH ratio. If the RR is
relatively high, i.e., the timing of 52-week high price is very close to the current time,
investors will commit a serious recency bias. The serious recency bias (too much
attention to 52-week high price) mitigates the relative importance of the formation of
closing price. That is, when the timing of 52-week high price is close to the current time,
the investors’ attention to how the closing price is formed (quick or slow) might be
indifferent. On the other hand, when the RR is relatively low, i.e., the timing of 52-
week high price is far from the current time, investors commit less recency bias. In
contrast, the investor might have a distant bias. The distant bias also mitigates the
relative importance of the formation of closing price because investors pay too little
attention to the stock. As a result, when the timing of 52-week high price is far from the
current time, the investors’ attention to how the closing price is formed (quick or slow)
is also indifferent. The analysis of the influence of ID on RR is in a similar manner.
When the ID is relatively high, i.e., the closing price changes quickly, investors are
significantly attracted by the sudden changes of closing price. As a result, too much
attention to the current closing price will mitigate the relative importance of the timing
of 52-week high price. Moreover, when the ID is relatively low, i.e., the closing price
changes slowly, investors will pay very little attention to the stocks whenever the timing
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of 52-week high price is recent or distant. Furthermore, we document that the GH
momentum is greatly improved by incorporating recency ratio and information
discreteness into account.
Second, when we look at extreme cases, the GH momentum performance is greatly
improved by incorporating the recency ratio and information discreteness into account.
Specifically, consistent with our hypothesis that the profitability of 52-week high
momentum strategy is higher for stocks with a recent 52-week high price and having
the closing price gradually changed than for stocks with a distant 52-week high price
and having the closing price suddenly changed. For instance, the alpha of GH
momentum profit for stocks with low ID and high RR of 0.97% is significantly higher
than that for stocks with high ID and low RR of 83%. The monthly alpha between these
two extreme portfolios is 0.14% with t-statistics of 1.93, around 1.68% a year.
[Table 4 Here]
The anchor of the 52-week high price is associated with investors’ underreaction.
We have shown that RR is positively related to the magnitude of underreaction and, ID
is negatively correlated with the magnitude of underreaction. As a result, we construct
a new modified GH measure which is defined as:
MGH = GH + RR – ID, (4)
where GH, RR, and ID are defined the same as previously mentioned. The measure
MGH simultaneously incorporates anchoring bias and two limited attention bias
measures into account. The performance of decile portfolios based on MGH is shown
in Table 5.
We find evidence of strong momentum based on the MGH. The loser portfolio
earns a return of 0.25% per month, while the winner portfolio has a return of 1.99%
per month. The spread of 1.74% in loser and winner portfolio returns is statistically
significant with a t-statistic of 11.03. The corresponding Fama and French (1993)
alpha is 2.01% and also statistically significant with a t-statistic of 14.51.
Particularly, the Fama-French three-factor alpha of MGH momentum is larger than twice of
original GH momentum strategy. The performance of January and non-January months
are shown in Panels B and C of Table 5. Similarly, the results confirm that the loser
stocks earn higher positive returns in January, and thus induce negative momentum
profits in January. The non-January momentum returns are particularly pronounced,
especially for excluding large positive January returns of losers; the winner
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portfolio returns are similar with or without exclusion of January returns. The
strategy generates a monthly return of 1.96% with a Fama–French alpha of 2.19%.
[Table 5 Here]
4. Cross-sectional regression results
To compare the profitability among different momentum strategy, we estimate the
contributions of the various portfolios formed in month t – j to the month t return by
estimating the following cross-sectional regression:
Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtJTHi,t−j+b4.jtJTLi,t−j+b5.jtRRHi,t−j+b6.jtRRLi,t−j+b7.jtGHHi,t−j+
b8.jtGHLi,t−j+b8.jtMGHHi,t−j+b9.jtMGHLi,t−j+eit, (5)
where Rit is the return of stock i in month t; SIZEi,t−1 is the natural logarithm of stock
i's market capitalization at the end of previous month; JTHi,t−j equals one if stock i’s
past performance over the 12-month period (t–j–12, t–j) is in the top 30% when
measured by JT’s performance criterion, and is zero otherwise; JTLi,t−j equals one if
stock i’s past performance over the period (t–j–12, t–j) is in the bottom 30% when
measured by JT’s performance criterion, and is zero otherwise. The rest of variables are
defined similarly.
Table 6 indicates that the presence of short-term return reversals: the
coefficients on past month returns are significantly negative. The negative
relationship between firm size and f u tu re returns is also documented. As for
momentum strategy, we find significant JT, GH, RR, and MGH momentum. The
returns on GH’s winner minus loser strategy is 0.22% per month (t-statistic =
11.13). When the January month is excluded from the sample, the momentum
profits of these three strategies are enhanced.
[Table 6 Here]
We examine the role of recency ratio in profitability of momentum by modifying
Fama and MacBeth cross-sectional regression of George and Hwang (2004) and
Bhootra and Hur (2013) as follows.
Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtGHHi,t−j+b4.jtGHLi,t−j+b5.jtRRHi,t−j+b6.jtRRLi,t−j+b7.jtRRHi,t−
j*GHHi,t−j+b8.jtRRHi,t−j*GHLi,t−j+b9.jtRRLi,t−j*GHHi,t−j+b10.jtRRLi,t−j*GHLi,t−j+eit, (6)
where RR is the recency ration defined in Equation (3). RRH (RRL) is a dummy
variable that equals 1 for 30% of the stocks with the highest (lowest) recency ratio at
the end of month t - j, and is 0 otherwise. Table 7 shows that the GH momentum strategy
is more significant in stocks with high RR than stocks with low RR. For example, the
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interactive term GHH*RRH is significantly positive at 1% level of significance, the
term GHL*RRH is insignificantly negative. The difference between in coefficients on
GHH*RRH and GHL*RRH is 0.15% with t-statistics of 5.02. The difference between
coefficients GHH*RRL and GHL*RRL is 0.04% with t-statistics of 1.96. We conduct
a difference-in-difference test, i.e., the difference of (GHH*RRH - GHL*RRH) -
(GHH*RRL - GHL*RRL) of 0.10% with t-statistics of 4.31, confirming that GH
momentum profits are significantly higher in stocks with high RR. The non-January
results also indicate the same conclusion.
[Table 7 Here]
We also examine whether information discreteness affects the profitability of 52-
week momentum strategy. The ID is defined by Equation (2). IDH (IDL) is a dummy
variable that equals 1 for 30% of the stocks with the highest (lowest) ID ratio at the end
of month t - j, and is 0 otherwise.
Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtGHHi,t−j+b4.jtGHLi,t−j+b5.jtIDHi,t−j+b6.jtIDLi,t−j+b7.jtIDHi,t−j*
GHHi,t−j+b8.jtIDHi,t−j*GHLi,t−j+b9.jtIDLi,t−j*GHHi,t−j+b10.jtIDLi,t−j*GHLi,t−j+eit, (7)
where ID is the information discreteness defined in Equation (2). IDH (IDL) is a
dummy variable that equals 1 for 30% of the stocks with the highest (lowest)
information discreteness at the end of month t - j, and is 0 otherwise.
Table 8 shows that the GH momentum strategy is more significant in stocks with
low ID than stocks with high ID. For example, the difference in coefficients on
GHH*IDL and GHL*IDL is 0.15% with t-statistics of 5.12. The difference in
coefficients GHH*IDH and GHL*IDH is 0.05% with t-statistics of 1.62. A difference-
in-difference test, i.e., difference between (GHH*IDL - GHL*IDL) - (GHH*IDH -
GHL*IDH) of 0.10% with t-statistics of 2.64, confirming the evidence that the
performance GH momentum is also driven by ID. The non-January results also indicate
the same conclusion.
[Table 8 Here]
We explore the interaction between recency ratio (RR) and information
discreteness (ID) on GH momentum. The joint test of two explanations are adopted by
the following equation.
Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtGHHi,t−j+b4.jtGHLi,t−j+b5.jtRRHi,t−j+b6.jtRRLi,t−j+b7.jtIDHi,t−j
+b8.jtIDLi,t−j+b9.jtIDHi,t−j*RRHi,t−j*GHHi,t−j+b10.jtIDHi,t−j*RRHi,t−j*GHLi,t−j+b11.jtIDHi,t−j*RRLi,
t−j*GHHi,t−j+b12.jtIDHi,t−j*RRLi,t−j*GHLi,t−j+b12.jtIDLi,t−j*RRHi,t−j*GHHi,t−j+b14.jtIDLi,t−j*RRHi,
t−j*GHLi,t−j+b15.jtIDLi,t−j*RRLi,t−j*GHHi,t−j+ b16.jtIDLi,t−j*RRLi,t−j* GHLi,t−j +eit,
(8)
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The results are shown in Table 9. Since there are too many coefficients in Eq. (8),
we only report the interaction coefficients, and the rest of the unreported coefficients
are quite similar to previous results. First, after controlling for information discreteness,
the recency ratio (RR) can enhance 52-week high momentum profits only for stocks
with high ID group. The result is consistent with average raw returns in Panel A of Table
4.3 For example, the coefficient of GHIDHRR is 0.14% with t-statistics of 2.77 and
coefficient of GHIDLRR is 0.05% with t-statistics of 0.97. On the other hand, after
controlling for recency ratio, the information discreteness add a very limited
contribution to the profitability of 52-week high price momentum. Specifically, the
coefficient of GHIDRRH is -0.03% with t-statistics of -0.39 and coefficient of
GHIDRRL is 0.06% with t-statistics of 1.38. The results are consistent with our
conjecture that because of the investors’ limited attention, the ID and RR are
particularly stronger in stocks with moderate attention. We compare 52-week high
momentum profits for stocks with distant 52-week high anchor and continuous closing
price formation to stocks with recent 52-week high anchor and discrete closing price
formation. The average difference-in-difference between GH momentum in low ID and
high RR group and GH momentum in high ID and low RR group is 0.11% with t-
statistics of 2.27, suggesting that adding information of RR and ID significantly
enhances the GH momentum.
[Table 9 Here]
5. Conclusion
This paper explores the roles of two attention-bias related variables, i.e., distance of the
anchor and information discreteness, in explaining anchoring bias of 52-week high
price momentum strategy. The anchoring bias, i.e., investors viewing the 52-week high
price as a reference point, leads to investors to underreact to good news about the stocks
whose prices are near their 52-week high price (George and Hwang 2004). We show
that both attention-bias measures, i.e., a distance of the anchor and information
discreteness, simultaneously affect the profitability of 52-week high strategies.
Specifically, the 52-week high momentum profits based on stocks with recent 52-week
high price and slow-accumulation closing price (or low information discreteness) is
3 The results of Panel B of Table 4 suggest that RR (ID) can affect alpha of GH momentum only in
stocks with moderate ID (RR). However, we use raw return to estimate coefficients in Table 9.
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significantly higher than the stocks with distant 52-week high price and rapid-
accumulation closing price (high information discreteness). The Fama-French three
factor alpha of a modified 52-week high momentum strategy incorporating recency and
information discreteness is about twice as large for original GH momentum strategy.
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References
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Table 1. Monthly performance of momentum strategy The sample period is from January 1965 to December 2017. We exclude the stocks with price
less than $5 and stocks below NYSE minimum decile market capitalization. The stocks are
sorted into decile portfolios based on JT, GH, and RR measures. Momentum is defined as a
zero-cost portfolio that long-buy top winner portfolio and short-sell loser portfolio. The JT is
denoted as the cumulative prior 12-month raw return excluding the most recent month. GH is
the ratio of current price to 52-week high price. Recency ratio (RR), is defined as 1 – number of
days since 52-week high price/364. The monthly average raw returns and Fama and French
(1993)’s alpha of each momentum portfolio during all periods are provided Panels A and B.
Panel C provides the Fama and French (1993)’s alpha excluding January. t-statistics are in
parentheses. The monthly raw returns and Fama and French (1993)’s alpha of each momentum
portfolio are provided. t-statistics are in parentheses.
JT GH RR
Loser Winner WML Loser Winner WML Loser Winner WML
Panel A: All periods
Raw returns 0.533 1.402 0.869 0.618 1.351 0.733 0.760 1.364 0.604 (1.78) (4.76) (4.09) (1.92) (6.32) (3.31) (3.40) (6.40) (4.69)
FF3 alpha -0.813 0.326 1.139 -0.670 0.360 1.030 -0.437 0.344 0.781 (-6.09) (3.12) (5.58) (-4.68) (4.47) (5.03) (-5.32) (5.57) (6.32)
Panel B: January
Raw returns 3.602 2.229 -1.373 3.336 1.456 -1.881 2.499 1.545 -0.954 (2.82) (2.15) (-1.72) (2.27) (1.98) (-1.58) (2.81) (1.96) (-2.15)
FF3 alpha 0.240 -0.133 -0.373 -0.056 -0.331 -0.275 -0.008 -0.430 -0.422 (0.38) (-0.29) (-0.42) (-0.07) (-0.95) (-0.25) (-0.03) (-1.68) (-0.85)
Panel C: Excluding January
Raw returns 0.254 1.327 1.072 0.371 1.341 0.970 0.602 1.347 0.745 (0.84) (4.32) (4.91) (1.15) (6.00) (4.54) (2.63) (6.09) (5.60)
FF3 alpha -0.543 0.771 1.310 -0.384 0.848 1.229 -0.084 0.822 0.902 (-4.12) (7.04) (6.35) (-2.84) (10.42) (6.26) (-0.98) (12.85) (7.18)
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Table 2 Independent double sorts on information discreteness and 52-
week high price momentum The sample period is from January 1965 to December 2017. We exclude the stocks with price
less than $5 and stocks below NYSE minimum decile market capitalization. The stocks are
independently sorted into 5 by 5 portfolios based on information discreteness (ID) and 52-week
high price (GH). ID is determined by the sign of daily returns and ignores the magnitude by equally
weighting each observed return. ID = sgn(PRET) × [%neg −%pos ] where PRET is the cumulative
return during the formation period. sgn(PRET) is denoted as the sign of PRET. sgn(PRET) = 1 if PRET
> 0 and sgn(PRET) = -1 if PRET < 0. %neg and %pos are the percentage of days during the formation
period with positive and negative returns. GH is the ratio of current price to 52-week high price.
CMD denotes that the momentum profit of Continuous portfolio minus the momentum profit
of Discrete portfolio. The monthly average raw returns and Fama and French (1993)’s alpha of
each momentum portfolio during all periods are provided in Panels A and B. Panel C provides
the Fama and French (1993)’s alpha excluding January. t-statistics are in parentheses.
Panel A: Raw returns
Continuous 2 3 4 Discrete
Loser 0.227 0.419 0.454 0.502 0.363
(0.76) (1.44) (1.59) (1.76) (1.25)
Winner 1.824 1.803 1.823 1.781 1.743
(9.07) (9.20) (9.32) (9.28) (9.03)
CMD
WML 1.597 1.384 1.369 1.279 1.380 0.217
(9.26) (8.48) (8.76) (8.30) (8.87) (2.81) Panel B: FF3 alpha
Loser -1.080 -0.893 -0.861 -0.787 -0.901
(-8.98) (-8.05) (-8.58) (-8.00) (-9.40)
Winner 0.807 0.782 0.811 0.764 0.733
(13.91) (15.00) (15.36) (14.57) (13.24)
CMD
WML 1.887 1.675 1.672 1.552 1.635 0.253
(12.32) (11.76) (12.46) (12.04) (13.10) (3.31) Panel C: Exclude January FF3 alpha
Loser -1.199 -1.017 -0.958 -0.868 -0.972
(-10.76) (-9.67) (-9.78) (-9.28) (-10.55)
Winner 0.859 0.833 0.870 0.807 0.772
(14.43) (15.70) (16.12) (15.01) (13.59)
CMD
WML 2.059 1.850 1.828 1.675 1.744 0.314
(14.28) (13.61) (13.95) (13.56) (14.27) (4.18)
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Table 3 Independent double sorts on recency ratio and 52-week high price
momentum The sample period is from January 1965 to December 2017. We exclude the stocks with price
less than $5 and stocks below NYSE minimum decile market capitalization. The stocks are
independently sorted into 5 by 5 portfolios based on recency ratio (RR) and 52-week high price
(GH). Recency ratio (RR), is defined as 1 – number of days since 52-week high price/364. GH is the
ratio of current price to 52-week high price. RMD denotes that the momentum profit of Recent
portfolio minus the momentum profit of Distant portfolio. The monthly average raw returns
and Fama and French (1993)’s alpha of each momentum portfolio during all periods are
provided in Panels A and B. Panel C provides the Fama and French (1993)’s alpha excluding
January. t-statistics are in parentheses.
Panel A: Raw returns
Distant 2 3 4 Recent
Loser 0.356 0.406 0.502 0.443 0.524
(1.24) (1.39) (1.69) (1.49) (1.76)
Winner 1.571 1.613 1.748 1.891 1.977
(8.19) (8.30) (8.98) (9.41) (9.45)
RMD
WML 1.214 1.207 1.246 1.448 1.453 0.238 (8.16) (7.73) (7.65) (9.48) (9.82) (1.92) Panel B: FF3 alpha
Loser -1.002 -0.900 -0.777 -0.806 -0.713
(-8.20) (-7.55) (-6.57) (-8.20) (-6.24)
Winner 0.509 0.554 0.711 0.889 1.011
(7.32) (9.09) (11.94) (15.36) (13.35)
RMD
WML 1.510 1.454 1.488 1.695 1.724 0.214 (12.20) (11.17) (11.17) (13.80) (13.94) (1.69) Panel C: Exclude January FF3 alpha
Loser -1.122 -1.009 -0.877 -0.855 -0.649
(-9.41) (-8.86) (-7.80) (-8.80) (-5.50)
Winner 0.523 0.576 0.751 0.936 1.094
(7.17) (9.07) (12.31) (15.72) (14.47)
RMD
WML 1.646 1.584 1.629 1.792 1.743 0.098 (13.88) (12.69) (12.71) (14.73) (13.84) (0.78)
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Table 4 Independent triple sorts on recency ratio, information
discreteness, and 52-week high price The sample period is from January 1965 to December 2017. We exclude the stocks with price
less than $5 and stocks below NYSE minimum decile market capitalization. The stocks are
independently sorted into 3 by 3 by3 portfolios based on recency ratio (RR), information
discreteness (ID), and and 52-week high price (GH). Recency ratio (RR), is defined as 1 – number of
days since 52-week high price/364. ID is determined by the sign of daily returns and ignores the
magnitude by equally weighting each observed return. ID = sgn(PRET) × [%neg −%pos ] where
PRET is the cumulative return during the formation period. sgn(PRET) is denoted as the sign of PRET.
sgn(PRET) = 1 if PRET > 0 and sgn(PRET) = -1 if PRET < 0. %neg and %pos are the percentage of
days during the formation period with positive and negative returns. GH is the ratio of current price
to 52-week high price. The monthly average raw returns and Fama and French (1993)’s alpha
of long winner and short loser portfolio during all periods are provided in Panels A and B. t-
statistics are in parentheses.
Panel A: Raw returns
Low RR Middle RR High RR RRHML
Low ID 1.066 1.045 1.161 0.095
(8.70) (8.24) (9.77) (1.15)
Middle ID 0.902 0.916 1.092 0.190
(8.11) (7.81) (9.28) (2.45)
High ID 0.989 0.951 1.141 0.152
(9.25) (7.94) (9.57) (1.98)
High RR & Low ID
- Low RR & high ID
IDLMH 0.076 0.094 0.020 0.171
(1.47) (1.71) (0.30) (2.13)
Panel B: FF3 alpha Low RR Middle RR High RR RRHML
Low ID 0.901 0.842 0.970 0.069
(8.65) (7.56) (9.43) (0.82)
Middle ID 0.728 0.720 0.922 0.193
(7.69) (7.15) (9.07) (2.44)
High ID 0.828 0.727 0.943 0.115
(9.29) (7.19) (9.20) (1.49)
High RR & Low ID
- Low RR & high ID
IDLMH 0.073 0.115 0.026 0.142
(1.39) (2.07) (0.39) (1.93)
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Table 5. Monthly performance of modified 52-week high price momentum
strategy The sample period is from January 1965 to December 2017. We exclude the stocks with price
less than $5 and stocks below NYSE minimum decile market capitalization. The stocks are
sorted into decile portfolios based on adjusted 52-week high price measure. Momentum is defined
as a zero-cost portfolio that long-buy top winner portfolio and short-sell loser portfolio. The
adjusted 52-week high price measure is defined as: MGH = GH + RR – ID, where GH denotes the ratio
of current price to 52-week high price, RR (Recency ratio), is defined as 1 – number of days since
52-week high price/364, and ID (information discreteness) is defined as sgn(PRET) × [%neg
−%pos ] where PRET is the cumulative return during the formation period. sgn(PRET) is denoted as
the sign of PRET. sgn(PRET) = 1 if PRET > 0 and sgn(PRET) = -1 if PRET < 0. %neg and %pos are the
percentage of days during the formation period with positive and negative returns. The monthly
average raw returns and Fama and French (1993)’s alpha of each momentum portfolio during
all periods are provided Panels A and B. Panel C provides the Fama and French (1993)’s alpha
excluding January. t-statistics are in parentheses.
Loser 2 3 4 5 6 7 8 9 Winner WML
Panel A: All periods
Raw returns 0.247 0.650 0.806 0.893 0.981 1.153 1.245 1.376 1.567 1.988 1.741
(0.88) (2.65) (3.51) (4.09) (4.67) (5.64) (6.24) (6.90) (7.96) (10.00) (11.03)
FF3 alpha -1.054 -0.582 -0.392 -0.259 -0.146 0.055 0.165 0.309 0.542 0.992 2.045
(-10.11) (-7.60) (-6.91) (-5.67) (-3.44) (1.37) (4.13) (7.58) (11.22) (16.70) (14.51)
Panel B: January
Raw returns 3.136 2.931 2.533 2.191 1.980 1.956 1.817 1.913 1.995 2.474 -0.662
(2.60) (2.73) (2.61) (2.38) (2.29) (2.31) (2.21) (2.24) (2.54) (3.07) (-0.87)
FF3 alpha -0.261 -0.246 -0.415 -0.557 -0.568 -0.467 -0.452 -0.374 -0.021 0.526 0.787
(-0.49) (-0.59) (-1.43) (-2.08) (-2.68) (-2.54) (-2.54) (-2.10) (-0.11) (2.21) (1.11)
Panel C: Excluding January
Raw returns -0.015 0.443 0.649 0.775 0.890 1.080 1.193 1.327 1.529 1.944 1.959
(-0.05) (1.78) (2.78) (3.49) (4.14) (5.16) (5.83) (6.52) (7.54) (9.52) (12.65)
FF3 alpha -1.152 -0.640 -0.411 -0.250 -0.121 0.092 0.217 0.370 0.602 1.040 2.192
(-11.30) (-8.66) (-7.40) (-5.74) (-2.92) (2.30) (5.45) (9.08) (12.30) (17.03) (15.81)
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Table 6 Fama-MacBeth cross-sectional regression For each month from January 1965 to December 2017, the following cross-sectional regression is
estimated. Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtJTHi,t−j+b4.jtJTLi,t−j+b5.jtRRHi,t−j+b6.jtRRLi,t−j+b7.jtGHHi,t−j+
b8.jtGHLi,t−j +b8.jtMGHHi,t−j+b9.jtMGHLi,t−j++eit, Average parameter values are the time series averages
from the cross-sectional estimates of stock variables, and t-statistics are the time-series averages divided
by the time-series standard errors. Ri,t-1 and Sizei;t are the return and log (market capitalization) of
stock i in month t-1. JTH (JTL) is a dummy variable that equals 1 for 30% of the stocks with
largest (smallest) 12-month cumulative returns at the end of month t- j, and is 0 otherwise, RRH
(RRL) is a dummy variable that equals 1 if the stock belongs to top (bottom) 30% of the stocks
based on their recency ratio at the end of month t - j, and is 0 otherwise, GHH (GHL) is a
dummy variables that equals 1 for 30% of the stocks with largest (smallest) GH measure at the
end of month t - j, and is 0 otherwise, and MGHH (MGHL) is a dummy variables that equals 1
for 30% of the stocks with largest (smallest) MGH measure at the end of month t - j, and is 0
otherwise
Panel A: All periods Panel B: January excluded
Model1 Model2 Model3 Model4 Model1 Model2 Model3 Model4
1 Intercept 2.168 3.030 2.183 2.995 1.669 2.526 1.594 2.481
(4.31) (5.77) (3.82) (5.48) (3.33) (4.80) (2.78) (4.50)
2 Rt-1 -0.025 -0.028 -0.024 -0.025 -0.019 -0.023 -0.019 -0.020
(-6.66) (-7.03) (-6.08) (-6.18) (-5.00) (-5.51) (-4.54) (-4.70)
3 MV -0.074 -0.147 -0.086 -0.146 -0.036 -0.109 -0.047 -0.108
(-2.39) (-4.65) (-2.57) (-4.50) (-1.18) (-3.46) (-1.39) (-3.33)
4 JTH 0.030 0.030
(1.27) (1.18)
5 JTL -0.074 -0.100
(-3.53) (-4.66)
6 GHH 0.107 0.105
(12.91) (12.29)
7 GHL -0.117 -0.140
(-6.01) (-7.00)
8 RRH 0.070 0.090
(3.32) (4.17)
9 RRL -0.044 -0.055
(-2.61) (-3.16)
10 MGHH 0.108 0.109
(11.99) (11.91)
11 MGHL -0.109 -0.130
(-6.86) (-7.98)
12=4-5 JT 0.104 0.129
(3.63) (4.36)
13=6-7 GH 0.224 0.245
(11.13) (11.97)
14=8-9 RR 0.114 0.145
(4.37) (5.38)
15=10-11 MGH 0.218 0.238
(11.48) (12.35)
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Table 7 Fama-MacBeth cross-sectional regression: Momentum profits
conditional on recency ratio For each month from January 1965 to December 2017, the following cross-sectional regression is
estimated. Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtGHHi,t−j+b4.jtGHLi,t−j+b5.jtRRHi,t−j+b6.jtRRLi,t−j+b7.jtRRHi,t−j
*GHHi,t−j+b8.jtRRHi,t−j*GHLi,t−j+b9.jtRRLi,t−j*GHHi,t−j+b10.jtRRLi,t−j*GHLi,t−j+eit, Average parameter
values are the time series averages from the cross-sectional estimates of stock variables, and t-statistics
are the time-series averages divided by the time-series standard errors. Ri,t-1 and Sizei;t are the return
and log (market capitalization) of stock i in month t-1. JTH (JTL) is a dummy variable that
equals 1 for 30% of the stocks with largest (smallest) 12-month cumulative returns at the end
of month t- j, and is 0 otherwise, RRH (RRL) is a dummy variable that equals 1 if the stock
belongs to top (bottom) 30% of the stocks based on their recency ratio at the end of month t - j,
and is 0 otherwise, and GHH (GHL) is a dummy variables that equals 1 for 30% of the stocks
with largest (smallest) GH measure at the end of month t - j, and is 0 otherwise.
All No Jan.
1 Intercept 3.278 2.787
(6.30) (5.31)
2 Rt-1 -0.031 -0.026
(-8.34) (-6.75)
3 MV -0.157 -0.121
(-5.00) (-3.84)
4 GHH 0.059 0.054
(5.17) (4.53)
5 GHL -0.108 -0.130
(-4.48) (-5.31)
6 RRH -0.051 -0.037
(-2.50) (-1.80)
7 RRL -0.015 -0.026
(-0.87) (-1.52)
8 GHH*RRH 0.136 0.136
(6.53) (6.25)
9 GHH*RRL 0.030 0.035
(1.72) (1.96)
10 GHL*RRH -0.009 0.007
(-0.31) (0.23)
11 GHL*RRL -0.012 -0.008
(-0.56) (-0.35)
12 = 9-11 GHRRL 0.042 0.043
(1.96) (1.96)
13 = 8-10 GHRRH 0.146 0.129
(5.02) (4.35)
14 = 13-12 GHRR 0.104 0.086
(4.31) (3.51)
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Table 8 Fama-MacBeth cross-sectional regression: Momentum profits
conditional on information discreteness For each month from January 1965 to December 2017, the following cross-sectional regression is
estimated. Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtGHHi,t−j+b4.jtGHLi,t−j+b5.jtIDHi,t−j+b6.jtIDLi,t−j+b7.jtIDHi,t−j*
GHHi,t−j+b8.jtIDHi,t−j*GHLi,t−j+b9.jtIDLi,t−j*GHHi,t−j+b10.jtIDLi,t−j*GHLi,t−j+eit, Average parameter values
are the time series averages from the cross-sectional estimates of stock variables, and t-statistics are the
time-series averages divided by the time-series standard errors. Ri,t-1 and Sizei;t are the return and log
(market capitalization) of stock i in month t-1. JTH (JTL) is a dummy variable that equals 1 for
30% of the stocks with largest (smallest) 12-month cumulative returns at the end of month t- j,
and is 0 otherwise, IDH (IDL) is a dummy variable that equals 1 if the stock belongs to top
(bottom) 30% of the stocks based on their information discreteness at the end of month t - j,
and is 0 otherwise, and GHH (GHL) is a dummy variables that equals 1 for 30% of the stocks
with largest (smallest) GH measure at the end of month t - j, and is 0 otherwise.
All No Jan.
1 Intercept 3.105 2.568
(6.00) (4.96)
2 Rt-1 -0.029 -0.024
(-7.50) (-5.96)
3 MV -0.151 -0.114
(-4.86) (-3.67)
4 GHH 0.099 0.106
(6.97) (7.19)
5 GHL -0.063 -0.078
(-2.78) (-3.30)
6 IDH -0.010 -0.000
(-0.56) (-0.02)
7 IDL 0.000 0.008
(0.00) (0.43)
8 GHH*IDH -0.009 -0.025
(-0.40) (-1.09)
9 GHH*IDL 0.039 0.028
(1.85) (1.28)
10 GHL*IDH -0.056 -0.054
(-2.08) (-1.97)
11 GHL*IDL -0.109 -0.125
(-3.91) (-4.38)
12 = 9-11 GHIDL 0.148 0.154
(5.12) (5.02)
13 = 8-10 GHIDH 0.047 0.029
(1.62) (0.99)
14 = 12-13 GHID 0.101 0.124
(2.64) (3.14)
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Table 9 Fama-MacBeth cross-sectional regression: Momentum profits
conditional on information discreteness and recency ratio For each month from January 1965 to December 2017, the following cross-sectional regression is
estimated.Rit=b0.jt+b1.jtRi,t−1+b2.jtSIZEi,t−1+b3.jtGHHi,t−j+b4.jtGHLi,t−j+b5.jtRRHi,t−j+b6.jtRRLi,t−j+b7.jtIDHi,t−j
+b8.jtIDLi,t−j+b9.jtIDHi,t−j*RRHi,t−j*GHHi,t−j+b10.jtIDHi,t−j*RRHi,t−j*GHLi,t−j+b11.jtIDHi,t−j*RRLi,t−j*GHHi,t−j
+b12.jtIDHi,t−j*RRLi,t−j*GHLi,t−j+b13.jtIDLi,t−j*RRHi,t−j*GHHi,t−j+b14.jtIDLi,t−j*RRHi,t−j*GHLi,t−j+b15.jtIDLi,t
−j*RRLi,t−j*GHHi,t−j+b16.jtIDLi,t−j *RRLi,t−j* GHLi,t−j +eit. Average parameter values are the time series
averages from the cross-sectional estimates of stock variables, and t-statistics are the time-series averages
divided by the time-series standard errors. Ri,t-1 and Sizei;t are the return and log (market
capitalization) of stock i in month t-1. JTH (JTL) is a dummy variable that equals 1 for 30% of
the stocks with largest (smallest) 12-month cumulative returns at the end of month t- j, and is 0
otherwise, RRH (RRL) is a dummy variable that equals 1 if the stock belongs to top (bottom)
30% of the stocks based on their recency ratio at the end of month t - j, and is 0 otherwise, and
GHH (GHL) is a dummy variables that equals 1 for 30% of the stocks with largest (smallest)
GH measure at the end of month t - j, and is 0 otherwise.
Coefficients All No Jan.
1 GHH*IDH*RRH 0.061 0.042
(2.33) (1.54)
2 GHL*IDH*RRH -0.094 -0.089
(-2.15) (-1.94)
3 GHH*IDL*RRH 0.144 0.146
(6.07) (5.84)
4 GHL*IDL*RRH 0.014 0.033
(0.33) (0.75)
5 GHH*IDH*RRL -0.006 -0.003
(-0.25) (-0.13)
6 GHL*IDH*RRL -0.022 -0.010
(-0.74) (-0.33)
7 GHH*IDL*RRL 0.001 -0.005
(0.04) (-0.17)
8 GHL*IDL*RRL -0.079 -0.090
(-2.92) (-3.23)
9 = 1-2 GHIDHRRH 0.155 0.131
(3.23) (2.59)
10 = 3-4 GHIDLRRH 0.130 0.113
(2.92) (2.44)
11= 5-6 GHIDHRRL 0.016 0.007
(0.50) (0.21)
12 = 7-8 GHIDLRRL 0.080 0.085
(2.32) (2.37)
13 = 9-11 GHIDHRR 0.139 0.124
(2.77) (2.36)
14 = 10-12 GHIDLRR 0.050 0.028
(0.97) (0.52)
15 = 10-9 GHIDRRH -0.025 -0.018
(-0.39) (-0.26)
16 = 12-11 GHIDRRL 0.064 0.078
(1.38) (1.65)
17 = 10-11 GHIDRR 0.114 0.106
(2.27) (2.05)
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