momentum profits and macroeconomic risk1 · momentum profits and macroeconomic risk1 susan ji2, ......
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Momentum Profits and Macroeconomic Risk1
Susan Ji2, J. Spencer Martin
3, Chelsea Yao
4
Abstract
We propose that measurement problems are responsible for existing findings associating
macroeconomic risk with stock price momentum. For instance, Liu and Zhang (2008) find that
the growth rate of industrial production “plays an important role in driving momentum profits.”
In contrast, we show that winners and losers only differ in factor exposure during January when
losers massively outperform winners. During months where momentum exists, winner and loser
exposures offset nearly completely. Similar findings apply to other macroeconomic risk factor
variables. Furthermore, the magnitude of macroeconomic risk premia appear to seasonally vary
contra momentum.
JEL Classification: G12, E44
Keywords: Momentum, Macroeconomy, January
1 We appreciate the comments from Werner De Bondt, William Goetzmann, John Griffin, Bruce Grundy, Narasimhan Jegadeesh,
Laura Xiaolei Liu, Terry Walter (PhD Conference discussant), and seminar participants at Lancaster University, Melbourne
University, New York University, Sydney University, the 25th PhD Conference in Economics and Business (Perth), and Midwest
Finance Association annual meeting 2013 (Chicago). All remaining errors are ours.
2 Susan Ji, Associate Professor of Finance, College of Business and Public Administration, Governors State University,
University Park, IL 60484. Email: [email protected]; Tel: +1 708 235 7642. 3 J. Spencer Martin, Professor of Finance, Faculty of Business and Economics, University of Melbourne, Level 12, 198 Berkeley
Street, Parkville, Victoria 3010, Australia. Email: [email protected]; Tel: +61 3 83446466. 4 Yaqiong (Chelsea) Yao, Assistant Professor of Finance, Department of Accounting and Finance, Lancaster University
Management School, Lancaster LA1 4YX, United Kingdom. Email: [email protected]; Tel: +44 1524 510731.
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1. Introduction
A momentum strategy, buying recent winners and shorting recent losers, generates considerable
profits (Jegadeesh and Titman, 1993). This cross-sectional predictability has prevailed geographically and
temporally. Among others, Rouwenhorst (1998), Griffin, Ji and Martin (2005) and Asness, Moskowitz
and Pedersen (2013) document the popularity of momentum in the US, the UK, many European and some
Asian equity markets. Such evidence largely eliminates the possibility that momentum is due to data
mining. An extensive body of recent literature has attempted to account for momentum.
Behavioral patterns have been put forward to explain the momentum effect and various anomalies.
Barberis, Shleifer and Vishny (1998), Daniel, Hirshleifer and Subrahmanyam (1998), and Hong and
Stein’s (1999) provide unified accounts of intermediate-term momentum and long-term reversal. Hong,
Lim and Stein (2000) find that momentum is more pronounced for small firms than large firms, as
predicted by Hong and Stein’s gradual-information-diffusion model. In marked contrast, Sagi and
Seasholes (2007) and Israel and Moskowitz (2013) suggest that momentum profits exhibit no reliable
relation with size, and attribute Hong, Lim and Stein’s results to sample specificity. Grinblatt and
Moskowitz (2004) and Yao (2012) argue that momentum and reversal evolve independently: long-term
reversal exists only in January and momentum appears outside of January.
Another main strand of literature focuses on risk-based explanations. Neither the capital asset pricing
model nor the Fama–French three factors model can account for momentum profits (Jegadeesh and
Titman, 1993; Fama and French, 1996; Grundy and Martin, 2001). Macroeconomic risk, which affects
firm’s investment cycles and growth rates, continues to be proposed as the source of momentum profits.
Chordia and Shivakumar (2002) argue that the conditional macroeconomic risk-factor model including a
set of lagged macroeconomic variables can capture momentum phenomenon. In sharp contrast, Griffin, Ji
and Martin (2003) document that neither the unconditional nor the conditional macroeconomic risk-factor
model can explain momentum profits. More importantly, they show that Chen, Roll and Ross’s (1986)
five-factor model cannot subsume momentum. Liu and Zhang (2008) revive this issue by asserting that
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the growth rate of industrial production (MP) in a set of macroeconomic variables can account for more
than half of momentum profits. They argue that it is due to the fact that winners have higher return
sensitivities to MP than losers do.
One way to investigate the source of momentum profits is to examine the 11 months of a year when
momentum does exist. Only a few previous studies have pursued this path. The literature shows that
momentum strategies lose considerably in January and return continuation exists only outside of January
(Jegadeesh and Titman, 1993; Grundy and Martin, 2001). Grundy and Martin demonstrate that the
massive January loss is due to betting against the classic January size effect through the short sell of
losers, which tend to be extremely small firms.
In this paper, we explore whether macroeconomic risk is the underlying risk for momentum profits
outside of January. Most relevant to our study, Liu and Zhang (2008) claim that the MP loadings for
momentum ten deciles increase from the loser portfolio to the winner portfolio, which can be attributed to
the momentum effect. We use an empirical framework similar to Liu and Zhang (2008) except that we
estimate momentum portfolios’ sensitivity to MP outside of January, when winners do outperform losers.
Our main results are the following. Outside of January, the MP loadings for momentum ten deciles
are U-shaped: the MP loadings for the winner and loser portfolios are 0.59 and 0.62, respectively. Thus,
the winner–loser portfolios have essentially a net zero MP loading outside of January. In addition, the
loadings for winner and loser portfolios are only significantly different in January, when winners
substantially underperform losers.
We find that, in various empirical specifications, the MP risk-premium estimates range from −0.34%
per month to 1.19% per month, all of which (with one exception) are insignificant outside of January.
Such results indicate that there is no significant cross-sectional relation between non-January stock
returns and the MP. This finding is robust to a variety of base assets including industry portfolios.
More importantly, we provide direct evidence of momentum profits not being the reward for the
exposure to macroeconomic risk. The incremental contribution of MP is 5% to 66% of the observed
momentum return year round and 0% to 18% in non-January months when momentum is present. The
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latter numbers decrease to a maximum of 7% when industry portfolios are used. Depending on empirical
specifications, the Chen, Roll and Ross five-factor model predicts 44% to 88% of observed momentum
return year round; with one exception, all the differences between observed and expected momentum
returns are significant. The results are similar for non-January months. This indicates that momentum
profits cannot be attributed to macroeconomic risk, the MP factor in particular.
The remainder of this article proceeds as follows. Section 2 describes data and momentum portfolio
formation, and also analyzes the seasonal patterns of momentum trading strategies. Section 3 presents the
evidence that winners and losers have nearly identical MP loadings outside of January when momentum
does exist. Section 4 shows that neither the complete macroeconomic risk-factor models nor the MP risk
factor itself can capture momentum profits. Section 5 addresses the influence of so-called momentum
“crashes”. Section 6 concludes.
2. Data and Definitions
Our sample is constructed from all stocks traded on the New York Stock Exchange (NYSE), the
American Stock Exchange (Amex) and Nasdaq on the monthly files of the Center for Research in
Security Prices (CRSP). Closed-end funds, real estate investment trusts, American depository receipts,
and foreign stocks are excluded. The sample period runs from March 1947 to November 2009 to match
the data availability of macroeconomic variables we use in this study.
2.1. Portfolio Definitions
At each month, all of NYSE, Amex and Nasdaq stocks in the sample are ranked on the basis of
cumulative returns in month t - 7 to t - 2, and accordingly are assigned into ten deciles.5 Stocks with the
highest returns in the preceding two-to-seven months are defined as winners (P10), whereas stocks with
5 The original study on momentum by Jegadeesh and Titman (1993) examines momentum trading strategies by analyzing a
sample portfolio of NYSE and Amex stocks; they exclude Nasdaq stocks in order to avoid the results being driven by small and
illiquid stocks or the mechanical bid–ask bias. Nevertheless, both Jegadeesh and Titman (2001) and Liu and Zhang (2008) add
Nasdaq stocks to the sample to construct momentum portfolios. They argue that the addition of Nasdaq stocks has very little
impact on the profitability of momentum strategies, but it may increase the January losses noticeably. To demonstrate the
robustness of our findings, we analyze the NYSE and Amex stock sample in addition to the sample NYSE, Amex and Nasdaq
stocks. The results show that our findings remain hold.
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the lowest returns during the same period are defined as losers (P1). The momentum strategy buys prior
winners (P10) and sells prior losers (P1). Zero-investment winner–loser portfolios (P10–P1) are
rebalanced each month, and held for six months from month t + 1 to t + 6. There is a one-month gap
between portfolio formation and portfolio investing, in order to circumvent the mechanical bid–ask bias.6
We investigate both equal- and value-weighted portfolio returns. Not only does this practice prevent our
results being driven by small or even tiny stocks of extreme size deciles, but the value-weighted returns
allow for precisely reflecting the investors’ total wealth effect.7
2.2. Summary Statistics
Table 1 reports average monthly returns on winner–loser portfolios formed on the basis of the past
two-to-seven months’ returns. Table 1 distinguishes between January and other months. Panel A of Table
1 reports the profitability of the momentum strategy without a $5 minimum stock price screen. Between
March 1947 and November 2009, the equal-weighted monthly return to the momentum strategy is 0.67%
per month (t-statistic=3.44) and the value-weighted monthly return is 1.20% per month (t-statistics=5.51).
The equal-weighted return is substantially smaller than the value-weighted one. This finding holds
regardless different subsample periods.
The average return is decreased by large losses in Januaries (see also for Jegadeesh and Titman, 1993;
Grundy and Martin, 2001; Asness, Moskowitz and Pedersen, 2013). Prior winners underperform prior
losers by 5.69% in Januaries for equal weighting and 2.30% in Januaries for value weighting.
Neither the Capital Asset Pricing Model (CAPM) nor the Fama–French (1993) three-factor model can
capture the momentum portfolio returns obtained from long–short positions in the extreme deciles.
However, note that the Fama–French (1996) three-factor model can capture momentum losses in January
6 Strong winners are likely to have close prices at the ask than at the bid, and strong losers are likely to have close prices at the
bid than at the ask. 7 In the literature, there is mixed practice for two weighting methods, equal and value weighting, respectively. Many momentum
studies examine equal-weighted returns (e.g., Jegadeesh and Timan, 1993, 2001; Hong, Lim and Stein, 2000; Chordia and
Shivakumar, 2002; Liu and Zhang, 2008). Notwithstanding, value weighting has gained ground recently (e.g., Fama and French,
2008; Heston and Sadka, 2008; Israel and Moskowitz, 2013).
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to some degree. Controlling for the market, size and value factor results in the Fama-French alpha for the
momentum return being smaller than the raw losses.8
Panel B of Table 1 reports the profitability of the momentum strategy after the low-price screen. The
screen of low-priced stocks lessens the strategy’s often disastrous bet against the January effect. Over the
full 1947–2009 period, the strategy produces the equal-weighted monthly return of –1.72% and the value-
weighted monthly return of –1.49% in Januaries. The associated t-statistics of –1.85 and –1.49 are easy to
dismiss. This finding suggests that the low priced stocks—which are likely to be extremely small
stocks—are largely responsible for the January losses to the momentum strategy.
2.3. Macroeconomic Variables
For macroeconomic variables, the Chen, Roll and Ross (1986) five factors—unexpected inflation
(UI), change in expected inflation (DEI), term spread (UTS), default spread (UPR) and changes in
industrial production (MP)—are constructed by using monthly data from various sources. Unexpected
inflation is defined as [ | ] and change of expected inflation as [ | ]
[ | ] . The inflation rate is designated as , where is the
seasonally adjusted consumer price index (CUSR0000SA0 series) from Bureau of Labor Statistics. The
expected inflation rate is [ | ] [ | ], where is the one-month Treasury bill rate
from the CRSP monthly file, and is the ex post real one-month Treasury bill rate. In line
with Fama and Gibbons (1984), we measure the ex ante real rate, [ | ]. The difference between
and is modeled as . Accordingly it arrives at [ |
] . Term spread (UTS) is defined as the yield difference between 20- and
1-year Treasury bonds, and default spread (UPR) is the yield difference between BAA- and AAA-rated
corporate bonds, with data being obtained from the FRED database at Federal Reserve Bank of St. Louis.
The growth rate of industrial production for month t is defined as , where is
8 Our findings are consistent with Grundy and Martin (2001) who state that the momentum losses in January are due to betting
against the classic size effect in January, through buying small firms and selling extremely small firms. We also find that the
value-weighted raw returns in January (−2.30% per month, with an associated t-statistic of −2.16) turn out to be insignificant
(−0.53% per month, with an associated t-statistic of −0.45).
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the industry production index (INDPRO series) in month t from the FRED database at Federal Reserve
Bank of St. Louis. Note that MP is led by one month to match the timing with financial variables since
INDPRO series is recorded as of the beginning of a month whereas stock returns are recorded as of the
end of a month.
3. Momentum Loadings on Macroeconomic Risk
Many studies have documented the fact that momentum strategies are profitable outside of January,
whereas they suffer substantial losses in January (Jegadeesh and Titman, 1993; Grundy and Martin, 2001).
If the momentum phenomenon is really driven by winners having higher MP sensitivities than losers (as
argued by Liu and Zhang (2008)), then this prediction should be particularly true outside of January,
when momentum profits are actually present. If not, then it suggests that Liu and Zhang (2008)’s findings
are due entirely to the January influence. This paper utilizes four different factor-model specifications: the
one-factor MP model (MP), the Fama-French three-factor model augmented by MP (FF+MP), the Chen,
Roll and Ross (1986) model without default premium (CRR4) and the full-fledged CRR model (CRR5).
This section provides direct evidence that winners and losers have almost identical loadings on MP in the
11 months of a year when momentum does exist. As a result, there is essentially a net zero MP loading
outside of January—and a difference only in January, when losers substantially outperform winners.
Section 3.1 shows that MP loadings of winners and losers exhibit unnoticeable differences outside of
January. Section 3.2 provides further confirmatory evidence, and it also suggests no converging
tendencies of MP loadings for winners and losers one year after portfolio formation. In marked contrast
with Liu and Zhang (2008), both of the two pieces of evidence demonstrate that winners have similar MP
loadings with losers outside of January, while winners outperform losers considerably. In addition, the
findings reflect the fact that Liu and Zhang (2008)’s results are driven entirely by the behavior of the
January returns.
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3.1. MP Loadings for Momentum Portfolios
Figure 1 presents MP loadings for equal-weighted ten decile momentum portfolios. Table 1 of Liu
and Zhang (2008) asserts that using all observations (i.e., from January through December), the MP
loadings for momentum ten deciles rise gradually from L (the loser portfolio), P2… P9 to W (the winner
decile). Panel A presents the MP loadings for the equal-weighted ten decile momentum portfolios across
the year. Simple regression produces the wide MP-loading spread between the loser and winner portfolios
(0.32 and 0.61, respectively). Consistent with Liu and Zhang (2008), with respect to the one-factor MP
model, there is negligible difference in MP loadings from the loser portfolio up to decile six—but from
that point the MP loadings rise monotonically from 0.29 to 0.61 for the winner portfolio. Controlling for
the Fama–French three factors does not materially affect these asymmetric patterns. The wide MP-loading
spread between winners and losers remains present in that the loser portfolio has the MP loading of −0.10,
and the winner portfolio has the MP loading of 0.28. Similarly, the CRR5 model yields an MP loading for
the loser portfolio (0.37) that is lower than the corresponding loading for the winner portfolio (0.56).
Panel B displays the MP loadings for ten equal-weighted decile momentum portfolios from time-
series regressions using non-January observations. The MP loadings are U-shaped for the ten decile
momentum portfolios outside of January. The U-shape implies that extreme deciles load relatively heavily
on MP, while the middle deciles load relatively weakly on MP. More importantly, in a sharp contrast with
Panel A, we show that the broad spread of MP loadings between winners and losers virtually disappears
outside of January, when winners outperform losers. It can be inferred from Panel B that winners and
losers have almost identical MP loadings outside of January.
All of the evidence suggests that extreme decile momentum portfolios have very similar sensitivities
to the growth rate of industrial production outside of January. This highlights the fact that there is
essentially a net zero MP factor loading in the 11 months of a year when momentum does exist—and a
difference only in January, when losers massively outperform winners. In contrast, Liu and Zhang (2008)
point to the asymmetric pattern in loadings: high MP loadings for the winner portfolio, and low MP
loadings for the loser portfolio. Their results are driven by overlooking that momentum trading strategies
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are profitable outside of January but fail substantially in January. In addition, the U-shaped pattern
implies that extreme momentum portfolios have slightly high exposure to MP relative to other momentum
portfolios. This is consistent with conventional wisdom, since the two extreme deciles generally consist
of small firms (Grundy and Martin, 2001), which tend to be more sensitive to macroeconomic business
cycle factors (Fama and French, 1993; Balvers and Huang, 2007).
Figure 2 depicts MP loadings for ten value-weighted decile momentum portfolios. As Section 2.2
shows, equal- and value-weighted momentum portfolios exhibit very distinct features in terms of the
overall and non-January profitability. Specifically speaking, equal weighting produces non-January
momentum returns that are noticeably higher than the overall returns, whereas value weighting does not.
Panel A presents the MP loadings for value-weighted momentum portfolios across the year. In
comparison with the results of its equal-weighted counterpart in Panel A of Figure 1, the MP loadings for
ten value-weighted momentum decile portfolios are relatively small. This indicates that value-weighted
momentum portfolios bear only a weak link with industrial production risk, relative to equal-weighted
momentum portfolios. Nonetheless, wide MP-loading variations between the loser and winner portfolios
are still present. The one-factor MP model yields MP loadings for losers and winners of 0.14 and 0.47,
respectively. The slopes of the MP loadings from the one-factor model basically flatten out from the loser
portfolio (0.14) until the turning point of decile six (0.13), at which point they increase steadily to the
winner portfolio (0.47).
Panel B shows the sensitivities of ten value-weighted momentum decile portfolios to MP from
February through December, when the momentum phenomenon is present. In stark contrast with an
increasing trend of MP loadings in Panel A, Panel B depicts the U-shaped pattern of MP loadings for
value-weighted ten decile momentum portfolios outside of January, besides the FF three-factor model
augmented by MP. The important implication of the U-shaped results is that extreme decile momentum
portfolio returns have nearly identical sensitivities to MP. The results not only suggest that there is
essentially a net zero factor loading in the 11 months of a year when momentum is indeed present, but
also imply that all of the difference that is measured by Liu and Zhang (2008) appears only in January,
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when losers massively outperform winners. This raises some doubt that MP is the main driving force for
the momentum phenomenon.
3.2. Time-series Evolution of MP Loadings
As an extension of the findings in Section 3.1, this section examines the evolution of MP loadings for
winners and losers after portfolio formation due to the following three considerations. First, since ten
decile momentum portfolios have a six-month holding period, the MP loadings estimated from calendar-
based time-series regressions are in fact averaged over the six months. It is worth examining the evolution
of MP loadings month by month after portfolio formation using pooled time-series regressions. Second,
the evolution of MP loadings for winners and losers makes it possible to examine whether the wide
spread in MP loadings for the winner and loser portfolios is temporary. In other words, we can investigate
whether the large gap converges gradually after portfolio formation as momentum profits dissipate
gradually. Third, if we extend the event window to two years after portfolio formation, the evolution
allows us to examine whether there is a reversal in MP loadings beyond one year to two years, given the
well-documented return reversal (e.g., De Bondt and Thaler, 1986). Consistent with our findings in
Section 3.1, the results confirm that the MP-loading dispersion between winners and losers is
economically unimportant outside of January, when momentum exists—and further, that there is no clear
trend of convergence/reversal in the MP loadings between winners and losers.
We estimate the MP loadings from pooled time-series factor regressions (Ball and Kothari, 1989).
Our event months t + m (where m=0, 1, …, 24) commence from the month right after portfolio formation
to the twenty-fourth month. For each event month t + m, we pool together across the calendar month the
observations of returns to winners and losers, the Fama–French three factors, and the Chen, Roll and Ross
five factors. We perform pooled time-series factor regressions to estimate MP factor loadings for winners
and losers.
Figure 3 displays the MP loadings of the winner and loser portfolios estimated from pooled time-
series factor regressions for each of the event months during the twenty-four-month event-window period
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after portfolio formation. In line with Liu and Zhang(2008), we find that all standard asset-pricing models
produce the MP loadings for winners to be reliably higher than those for losers in the first few months
after portfolio formation. The one-factor MP model gives rise to the enormous dispersion in MP loadings
between the winner and loser portfolios: 0.86 in month t, 0.58 in month t + 1 and 0.54 in month t + 2. The
spread between winners and losers converges in the eighth month, and the magnitudes of the gaps
between extreme deciles are subsequently relatively small. De Bondt and Thaler (1986) document that
recent past winners underperform recent past losers beyond the one-year holding period. We do not
observe this reversal effect in MP loadings of the winner and loser portfolios.
Controlling for the Fama–French three factors produces broad spreads in MP loadings between
winners and losers: 1.00 in month t, 0.67 in month t + 1 and 0.61 in month t + 2. Controlling for the other
three macroeconomic factors from the CRR4 model also produces broad spreads in MP loadings between
winners and losers: 0.89 in month t, 0.60 in month t + 1 and 0.56 in month t + 2. From the eighth month
onward, not only do the spreads between winners and losers reverse, but also the magnitudes of the
spreads between extreme deciles become noticeably small. Similarly, the CRR5 model indicates the
spread in the MP loadings between winners and losers to be 0.59 in the first month after portfolio
formation (i.e., month t) and 0.38 in the first holding-period month (i.e., month t + 1). The wide spreads
gradually converge around month seven after portfolio formation.
Using February-to-December observations instead of all observations reduces substantially the
spreads in MP loadings between the winner and loser portfolios. Only the month right after portfolio
formation reports winners having slightly higher MP loadings than losers. After that, winners have even
lower MP loadings than losers, despite the magnitudes of the MP-loading dispersion between winners and
losers being unnoticeably small. The one-factor MP model reveals the MP-loading variation between
winners and losers to be 0.27 in month t, 0.09 in month t + 1 and 0.05 in month t + 2, which are only 31%,
15% and 9% of the corresponding MP-loading average spreads across the year. Similarly, the CRR4
model reports the MP-loading dispersion to be 0.30 in month t, 0.11 in month t + 1 and 0.08 in month t +
2, which are only 33%, 18% and 14% of the corresponding MP-loading average spreads across the year.
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Interestingly, the CRR5 model shows that the MP loadings of the winner portfolios are generally
smaller than those of the loser portfolios (in the month subsequent to portfolio formation), although the
spreads are inconsiderable. All of the evidence points to the fact that there is no asymmetric pattern of MP
loadings between winners and losers outside of January; in fact, the MP-loading variation between the
winner and loser portfolios is economically insignificant in the 11 months of a year when momentum
exists. The stochastic growth rate model of Johnson (2002) suggests that momentum profits are the
reward for the time-varying exposure to macroeconomic risk, which means that the exposure increases
gradually in portfolio formation and eventually dissipates afterwards. Sagi and Seasholes (2007) and Liu
and Zhang (2008) provide empirical results to support Johnson’s (2002) model. In contrast, we find little
evidence that the exposure of momentum trading to the growth rate of industrial production is temporary
outside of January (when momentum is present).
4. Momentum Profits and Macroeconomic Risk
Thus far, we have shown that winner and loser portfolios have very similar MP loadings outside of
January, despite the fact that winners outperform losers considerably. This section addresses directly the
central question of this study: are momentum profits the rewards for the exposure to macroeconomic risk
(especially the growth rate of industrial production, MP)? Section 4.1. estimates macroeconomic risk
premiums from two-stage Fama–MacBeth (1973) cross-sectional regressions. Because our economic
question seeks to trace the source of momentum profits that exist only outside of January, we are most
interested in examining whether MP can account for the cross-sectional variations in non-January stock
returns. Intuitively, if MP plays an important role in explaining momentum profits, then the MP risk-
premium estimates are very likely to be economically and statistically significant outside of January and
vice versa. Several of our tests confirm the conjecture by showing that MP cannot capture the cross-
sectional dispersions of non-January stock returns. Section 4.2. uses the risk premium estimates to
calculate expected momentum returns implied by macroeconomic risk. Our analysis shows that expected
momentum returns turn out to be far smaller than the observed average returns outside of January. Our
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analysis thus suggests that macroeconomic risk cannot be the source of momentum profits. Finally,
Section 4.3. demonstrates the robustness of our conclusion.
4.1. Estimating Macroeconomic Risk Premium
We estimate the macroeconomic risk premiums by using the two-stage Fama–MacBeth (1973) cross-
sectional regressions. The first-stage time-series regression involves regressing the returns of the base
portfolios on the Fama–French three factors and/or CRR five factors in order to estimate factor loadings.
We use the full sample, extended- and rolling windows in the first-stage time-series regressions.9 Note
that the extended window requires at least two-years of monthly observations to run the first-stage
regressions.
The second-stage cross-sectional regression regresses the returns of the base portfolios excess of the
risk-free rate on factor loadings obtained from the first-stage regressions in order to estimate risk
premiums. Using the full sample, we regress portfolios’ excess returns in month t on factor loadings
estimated from the first-stage time-series regression of the full sample. Using the extended window, we
regress portfolios’ excess returns in month t on factor loadings estimated from the first-stage regression in
month t – x to t –t0 (where t0 is the first observation and x ranges from the 24th observation). Using the
sixty-month rolling window, we regress portfolios’ excess returns in month t on factor loadings estimated
from the first-stage regressions in month t – 60 to t – 1. The risk premiums—the time-series averages of
the estimated slopes—will be used for calculating expected momentum return in order to test its
significance relative to the observed momentum return, which will be discussed in detail in Section 4.2.
9 Liu and Zhang (2008, Tables 5 and 6) show that the results, from both full-sample and extended-window regressions, suggest
that the MP premium is economically and statistically significant, and also that the growth rate of industrial production can
account for momentum profits. Their results from rolling-window regressions, however, provide the opposite findings. Factor
loadings are estimated more precisely from full-sample and extended-window regressions than from rolling regressions. Thus the
focus of our discussions is on the result from the full-sample and extended-window regressions—unless mentioned otherwise.
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For test assets, we first use thirty base portfolios—ten size-, ten value- and ten momentum portfolios
(Banz, 1981; Rosenberg, Reid and Lanstein, 1985; Jegadeesh and Titman, 1993)—in two-stage Fama–
MacBeth cross-sectional regressions. For robustness, our tests also add industry-sorted portfolios to the
existing thirty. Moreover, because Section 2.2 shows that equal- and value-weighted momentum
portfolios have different characteristics, we utilize both sets of ten momentum portfolios. Panel A of
Table 2 reports the estimates of risk premiums using ten equal-weighted momentum-, ten size-, and ten
value portfolios. Depending on empirical specifications, the MP premium estimates range from 0.76% per
month to 1.07% per month—all of which are significant. The MKT, SMB, HML premium estimates are
small (and mostly insignificant). In contrast to Liu and Zhang (2008), our sample period of 03/1947–
11/2009 reports the UTS premium as −1.22% per month (with an associated t-statistic of −2.57).
The foremost issue of our paper is to investigate whether the MP risk premium continues to exist in
the 11 months of a year when momentum is present. With the objective to rationalize momentum profits,
it is important to understand whether stock returns are cross-sectionally related to macroeconomic risk
exposure in those months when momentum exists.
Accordingly, we estimate risk premiums for the Chen, Roll and Ross (1986) five factors, and Fama
and French (1996) three factors by using February-to-December observations. If momentum profits are
the reward for the MP exposure, then MP would play a role in accounting for the cross-sectional
dispersions of non-January stock returns, and vice versa (Johnson, 2002).
Use of February-to-December observations (instead of all observations) results in very different
inferences about the role of the MP risk factor in explaining cross-sectional returns. Depending on
empirical specifications, the MP risk-premium estimates vary from −0.34% per month (t-statistic=−1.04)
to 0.16% per month (t-statistic=0.43). This finding reveals that the growth rate of industrial production is
not a priced risk factor outside of January. More importantly, Section 4.2 highlights the fact that the
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growth rate of industrial production cannot explain momentum profits outside of January, which we will
discuss in detail later.
Another dramatic change is that both the economic and statistical significance of the MKT and UTS
risk premiums become strong outside of January relative to across the year. Depending on empirical
specifications, the MKT risk-premium estimates range from −0.84% per month (t-statistic=−2.82) to -
0.81% per month (t-statistic=-2.72). The negative market risk premiums are consistent with the
counterpart results of Chen, Roll and Ross (1986), and Liu and Zhang (2008). Similar with the two
aforementioned papers, the UTS risk-premium estimate is −2.34% per month (t-statistic=−5.72). It
indicates that stock returns are inversely related to increases in long-term government bond rates over
short-term government bond rates.
Panel B of Table 2 presents risk-premium estimates using value-weighted momentum-, size- and
value portfolios as the base portfolios. Outside of January there are dramatic changes for the MP risk-
premium estimates as compared to Panel A. The MP risk-premium estimates range from −0.19% per
month (t-statistic=−0.56) to 1.19% per month (t-statistic=2.01), which are mostly insignificant and even
negative at times. The results of Table 2, taken together, indicate that the growth rate of industrial
production is not priced outside of January.
4.1.1. Additional Base Assets
Considering the significance of the industry characteristics in cross-sectional stock returns, we
estimate risk premiums for the Chen, Roll and Ross (1986) five factors and Fama and French (1996) three
factors by adding ten industry portfolios to the existing thirty base portfolios. If the growth rate of
industrial production is really a priced risk factor, then this change should not quantitatively affect the MP
premium estimates. If the growth rate of industrial production is not a priced risk factor, then this change
of research design might materially affect the MP premium estimates.
Table 3 shows that adding ten industry-sorted portfolios into the base portfolios does quantitatively
weaken the MP risk-premium estimates—although a majority of cases still produce statistically
15
significant MP risk-premium estimates. Panel A presents the risk-premium estimates of the forty base
portfolios (ten equal-weighted momentum-, ten size-, ten value- and ten industry portfolios). The one-
factor MP model reports the MP risk-premium estimate to be 0.49% per month (t-statistic=2.31) in the
sample of March 1943 to November 2009. It is less than half of its corresponding estimates from the
thirty base portfolios in Table 2, 1.07% per month (t-statistic=3.67). Despite the marked change of the
MP risk-premium estimates, adding industry portfolios to the existing base portfolios does not change
other risk-premium estimates substantially.
Outside of January, depending on model specifications, the MP risk premium ranges from −0.22%
per month (t-statistic=−1.00) to 0.53% per month (t-statistic=2.35). This finding is mostly consistent with
the estimates from using non-January observations of the thirty base portfolios in Table 2. It further
confirms the fact that the growth rate of industrial production might not be a priced risk factor outside of
January. All of the estimates of other risk-factor premiums are very similar to the corresponding estimates
from using non-January observations of the thirty base portfolios in Table 3 (with one exception, the
MKT risk premium).
To summarize, all of the evidence in this section confirms that the growth rate of industrial
production is not a priced risk factor in standard asset-pricing tests, which refutes the claims by Liu and
Zhang (2008). Further, this finding weakens fundamentally the foundation of the stochastic growth-rate
model by Johnson (2002) because his model hinges on growth-rate risk being priced. Johnson suggests
that firms with high prior realized returns are likely to have had high growth rates. As growth risk
increases with the growth rate, stocks with high prior realized returns earn high future expected returns.
Our use of the growth rate of industrial production to study growth-related risk provides no evidence that
growth risk is priced outside of January, when momentum is present.
4.2. Expected Momentum Profits
The factor loadings of momentum trading in Section 2.3 and risk premiums in Section 4.1. provide
some basic clues for the role of macroeconomic risk in rationalizing momentum profits. This section
16
predicts expected momentum returns on the basis of these findings. We analyze the significance of
expected momentum returns relative to observed momentum returns. If the complete macroeconomic
factor models can capture momentum returns, then expected momentum returns implied from the models
should not differ significantly from the observed momentum returns, and vice versa. Similarly, we
conjecture that if the growth rate of industrial production can account for momentum returns, then the
incremental contribution of the MP risk factor should also not differ significantly from the observed
momentum returns. Our analysis, however, provides no evidence that an explanation for momentum
profits lies in macroeconomic risk.
Specifically, we estimate factor loadings of a momentum strategy on the Chen, Roll and Ross (1986)
five factors.
The incremental contribution of MP, measured by [ ], is estimated as the product of the MP
factor loading ( ) from Equation (3) and the MP risk-premium estimate ( ) from Equation (2).
Expected momentum returns, [ ], are estimated as the product of the Chen, Roll and Ross (1986)
factor loading of a momentum strategy (i.e., betas) from Equation (3) and risk-premium estimates from
two-stage Fama–MacBeth cross-sectional regressions (i.e., gammas) from Equation (2). Note that our
discussions concentrate on the results from the full samples and extended windows, since the estimates
from the full samples and extended windows are more precise than those obtained from the rolling
regressions.
[ ]
[ ]
17
The analysis of the exposures of momentum portfolios demonstrates the predominant role of January
in examining the relation between momentum profits and macroeconomic risk. This section examines the
significance of expected momentum returns relative to observed momentum returns across the year (in the
left blocks of Tables 4 to 7) and outside of January (in the right blocks of Tables 4 to 7) separately. Our
tests not only allow us to disentangle any contamination effect associated with the month of January from
the rest of a year, but also enable us to directly address the issue of whether macroeconomic risk can
rationalize momentum profits that exists only outside of January.
4.2.1. Observed vs Expected Momentum Profits
Panel A of Table 4 reports the expected momentum returns implied by macroeconomic risk as well as
the t-statistics for the difference tests between the observed equal-weighted WML returns and expected
WML returns. In estimating risk premiums for computing expected WML returns, we use thirty base
portfolios—ten equal-weighted momentum-, ten size- and ten value portfolios. Regarding whether the
growth rate of industrial production can rationalize the momentum effect, the full sample yields
conflicting findings for different model specifications.
The single-factor MP model estimates [ ] to be 0.31% per month (or 49% of the observed
equal-weighted returns), with the other 51% being insignificant. Controlling for the Fama–French three
factors does not have a material impact on the ability of the MP risk factor to capture momentum returns.
The FF+MP model determines the MP incremental distribution to be 0.42% (or 66% of the observed
equal-weighted returns), with the remaining 34% being insignificant. The findings suggest that industrial
production risk can explain roughly half of momentum profits. Conversely, the Chen, Roll and Ross
(1986) five-factors (CRR5) model produces an MP incremental contribution of 0.14% per month, or 23%
of the observed equal-weighted returns. The remaining 77% percent is significant (t-statistic=2.55). It
indicates that industrial production risk can hardly subsume the momentum effect. As to the issue whether
macroeconomic risk factors taken together can capture the momentum effect, the full sample again
produces inconsistent results for different model specifications. The FF+MP model finds the expected
18
WML return, E[WML], to be 0.36% per month (or 56% of the observed equal-weighted WML return),
which is significant from the observed average return. In contrast, the CRR5 model generates the
expected WML returns to be 0.56% per month (or 88% of the observed equal-weighted WML returns),
with the remaining 12% being insignificant.
4.2.2. Change in Estimation Window, Change in Results
Differing from the full-sample findings, the extended window unanimously shows that neither the MP
risk factor nor the multi-factor models can account for momentum returns. For instance, the single-factor
MP model predicts the expected return, [ ], to be 0.14% (or 22% of the observed WML return),
with the remaining 78% being significant (t-statistic=2.30). The CRR5 model determines the incremental
contribution of MP, [ ], to be 0.03% or 5% of the observed WML return, and the difference
between them is significant (t-statistic=3.10). What follows is our analysis of the role of macroeconomic
risk factors combined together in rationalizing momentum profits. The CRR5 model generates the
expected WML return to be 0.43% per month, or 69% of the observed equal-weighted return, with the
remaining 31% being significant (t-statistic=3.30). Since the MP risk factor captures only 5% out of 69%
being explained by the combined CRR5 model, this finding reflects that the MP risk factor is the least
important source among the CRR five factors.10
Our analysis of the momentum effect all year round appears to suggest that MP can rationalize
momentum profits—but we need to exercise caution in offering any conclusive statements for the time
being, due to the complexity associated with the month of January. We now address the concerns
associated with the month of January: (a) massive momentum losses in January and (b) the exclusive
presence in January of the relation between momentum returns and the MP factor. Excluding January is
the most direct way to tackle the above-mentioned concerns.
4.2.3 Pivotal Role of January in Measuring Macroeconomic Risk Effects
10 Like the extended-window findings, the rolling-window results simultaneously suggest that macroeconomic risk cannot
rationalize momentum returns—regardless of which model specification is used.
19
Excluding the month of January leads to quite remarkable changes. Both the MP risk factor itself and
the complete standard asset-pricing models can barely capture the observed equal-weighted profits
outside of January.11
Standing in sharp contrast with the findings of averaging across the year, with the
extended window, the one-factor MP model reports expected WML return, [ ], as 0.03% per
month (or 3% of the observed equal-weighted WML return), with the remaining 97% being significant (t-
statistic=7.05). Controlling for the Fama–French three factors or the Chen, Roll and Ross (1986) five
factors does not qualitatively affect the finding. For example, with the extended window, the FF+MP
model yields the incremental contribution of MP to be 0.10% per month or 9% of the observed equal-
weighted WML profit. And the remaining 91% is significant (t-statistic=6.92).
Further, we find that the macroeconomic factors together cannot rationalize momentum profits
outside of January. With the full sample, the CRR5 model generates the expected WML returns, E[WML],
as 1.05% per month or 88% of the observed equal-weighted WML returns outside of January. Although
the Chen, Roll and Ross (1986) five-factor model can capture more than half of momentum profits, a
difference test rejects the null of no difference between the observed and expected WML returns (t-
statistic=2.97). Similarly, with the extended window, the CRR5 model produces the expected WML
return of 0.72% per month (or 60% of the observed equal-weighted WML profit) outside of January, and
the remaining 40% is significant (t-statistic=6.67).
Excluding the month of January alters the results tremendously by providing further supportive
evidence that macroeconomic risk is not the main driving force of momentum profits. For the best
scenario of all of the cases examined, the MP risk factor can capture 18% of the observed value-weighted
WML profits outside of January, which are overwhelmingly smaller than the corresponding ones of
averaging across the year. For example, the one-factor MP model produces only 1% of the value-
weighted momentum profits outside of January, whereas it explains 34% of the profits on average across
11 We replicate Liu and Zhang (2008, Table 6, Panel B) using the same sample in their period of 1960–2004. Consistent with Liu
and Zhang, we find that the growth rate of industrial production can explain momentum returns across the entire year.
Interestingly, when concentrating purely on momentum profits outside of January, we find that Liu and Zhang’s claims barely
hold. The results are available on request.
20
the year. By contrast, excluding January has no material impact on the role of macroeconomic risk
together in capturing momentum profits outside of January (with one exception, the FF+MP model).
4.2.4 Addition of Industry Base Portfolios
Focusing on the discussion about equal-weighted momentum trading strategies, Panel A of Table 5
reports the expected momentum returns as well as the t-statistics for the difference tests between the
observed and expected WML returns. With the full samples, the one-factor MP model reports expected
WML return, [ ], as 0.14% per month (or 22% of the observed equal-weighted WML return).
And the remaining 78% is significant (t-statistic=2.21). The MP incremental contribution of 0.14% per
month is considerably smaller than the corresponding value of 0.31% per month using the thirty base
portfolios (excluding ten industry portfolios). More importantly, it leads to the opposite inference—the
growth rate of industrial production plays a negligible role in rationalizing momentum profits.
With the control for the Fama–French (1996) three factors or the Chen, Roll and Ross (1986) five
factors, the MP incremental contributions range from 0.04% per month to 0.19% per month (or 6% to 30%
of the observed equal-weighted WML returns). And the remaining differences are all significant. To sum
up, our analysis of momentum returns all year round appears to unanimously suggest that MP cannot
account for momentum profits.
The central thrust of our analysis is to understand the source of momentum profits that exists only
outside of January. Using non-January observations, the incremental contribution of MP, [ ],
ranges from ‘none’ to a maximum of 6% of the observed WML return. For example, with the extended
windows, the CRR5 model yields the incremental contribution of MP to be 0.05% per month (or 4% of
the observed equal-weighted WML return). Regarding the complete macroeconomic factor models, none
of them are able to explain non-January momentum profits. For instance, with the full samples, the CRR5
model yields an expected WML return of 0.87% per month, or 73% of the observed equal-weighted
WML return, but the remaining 27% is significant (t-statistic=3.38). And the MP risk factor accounts for
none of the observed equal-weighted profits, which implies that MP plays only a negligible role in
21
explaining momentum profits.12
With the extended windows, the Chen, Roll and Ross five factors taken
together capture 42% of the observed equal-weighted WML profits outside of January, with the
remaining 58% being significant (t-statistic=5.80). Again, the MP risk factor contributes little (4%) to the
observed equal-weighted profits. These findings reveal that the MP risk factor among other factors is
generally the least important source of momentum profits. All of these findings highlight yet again that
macroeconomic risk, particularly the growth rate of industrial production, cannot account for momentum
profits.
Panel B of Table 5 focuses on the discussion about value-weighted momentum trading strategies. The
results resemble strongly the equal-weighted findings of their counterpart in Panel A. Our analysis of the
momentum effect all year round suggests that momentum profits cannot be attributed to the exposure to
macroeconomic risk. For example, with the full sample, the single-factor MP model produces expected
momentum returns of 0.16% per month (or 14% of the value-weighted WML profit). With the extended
windows, the complete CRR5 model produces an expected momentum profit, E[WML], of 0.44% per
month (or 37% of the observed value-weighted momentum profit), with the remaining 63% being
significant (t-statistic=5.04).
Consistent with the findings in Table 4, averaging across February to December provides further
confirmatory evidence that macroeconomic risk is not the main driving force of momentum profits. Even
taken together, macroeconomic risk factors can hardly rationalize momentum profits. With the full
sample, the CRR5 model produces expected WML returns, E[WML], of 0.89% per month (or 59% of the
value-weighted WML return); however, the remaining 41% is significant (t-statistic=4.64). With the
extended windows, the CRR5 model generates expected WML returns of 0.28% per month (or 19% of the
value-weighted WML return), with the remaining 81% being significant (t-statistic=7.25).
This section shows that the momentum effect is not a manifestation of recent winners having
temporarily higher loadings than recent losers on the growth rate of industrial production. Our
conclusions rest on three pieces of evidence. Firstly, outside of January, there are no significant
12 For rolling windows, the elimination of January observations does not weaken substantially the explanatory power of MP.
Nevertheless, the expected momentum profits by MP, [ ], are significantly different from the observed momentum
profits.
22
differences—between either the observed and expected momentum returns, or between the observed
momentum return and the incremental contribution of MP. It is obvious that excluding January
observations in a variety of our tests is the most direct way to allow for a focus on the 11 months of a year
when momentum is indeed present. Secondly, the MP risk factor plays a negligible role in explaining
value-weighted momentum profits relative to equal-weighted momentum profits. Using value-weighted
momentum returns instead of equal-weighted returns alleviates moderately the contamination of
momentum losses in January, because winners underperform losers to a lesser degree for value-weighted
than for equal-weighted momentum strategies in January. Thirdly, including industry portfolios in
addition to size-, value- and momentum portfolios in the base portfolios also undermines Liu and Zhang’s
(2008) arguments. Adding industry portfolios has a diluting effect on the possible January influence on
our test, due to the fact that all of the other base portfolios (instead of industry portfolios) are associated
with the classic January size effect. These three pieces of evidence point out the fact that momentum
profits are not the reward for exposure to macroeconomic risk.
4.3. Robustness Checks
This section performs several robustness checks to enrich the discussions about our main conclusions
drawn from the results of the preceding section. Section 4.2 uses ten industry portfolios—which are one
set of industry-sorted portfolios provided on Kenneth French’s website—in addition to the other thirty
base portfolios.13
The French website also provides seventeen industry portfolios, thirty industry
portfolios, and so forth, which are formed by different industry specifications. To address the concerns
about the robustness of our findings, we replicate the tests by including different sets of industry-sorted
portfolios. Further, another potential concern has to do with the extent to which our results may be due to
many tiny and illiquid stocks traded in Nasdaq. To avoid this problem, we use NYSE and Amex stocks
13 Please refer to Kenneth French’s website, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#Research.
23
(excluding Nasdaq stocks) to construct ten decile momentum portfolios, which are utilized as base
portfolios to replicate all tests performed in Section 4.2.14
Panel A of Table 6 replaces ten industry-sorted portfolios with seventeen industry-sorted portfolios in
the base portfolios. In other words, when estimating risk premiums that are used for computing expected
momentum returns, we use thirty-seven base portfolios—ten size-, ten value-, ten momentum- and
seventeen industry portfolios. Regardless of empirical specification, expected momentum returns implied
by macroeconomic variable(s) are significantly different from observed momentum profit. For instance,
with the full sample, the one-factor MP factor produces an expected momentum return, [ ], of
0.11% per month (or 17% of the observed WML return), with the remaining 83% being significant. With
the full samples, the complete CRR5 model indicates that the expected WML return is 0.24% per month
(or 37% of the observed WML return). And, more importantly, the remaining 63% is significant at the 1%
level. 15
The MP risk factor itself yields the incremental of 0.04% per month (or 6% of the observe WML
return), meaning that MP plays only a negligible role in capturing the momentum effect. The results
provide further supportive evidence that macroeconomic risk—in particular, the growth rate of industrial
production—cannot subsume momentum. Moreover, our main conclusion continues to hold even if we
use other sets of Kenneth French industry-sorted portfolios (for example, his thirty industry-sorted
portfolios).16
Controlling for the month of January (when momentum is nonexistent) does have a material impact
on our major findings. The role of industrial production risk in explaining momentum profits seems to be
weakening outside of January, relative to all year round. For instance, with the full sample, the one-factor
MP model produces the MP incremental contribution of 0.11% per month (or 17% of the observed WML
return) all year round, whereas it indicates the MP incremental contribution of −0.01% per month (or 0%
of the observed WML return) outside of January. Our analysis presents no evidence of the growth-related
14 For the sake of brevity in this section we report the results from using equal-weighted momentum portfolios. The basic
inferences remain the same if we replace equal- with value-weighted momentum portfolios in the test. 15 The only two insignificant cases appear when the CRR4 and CRR5 models use the rolling windows in the first-stage
regressions in 1947–2009. Rolling regressions provide less-precise estimates than full-sample and extended-window regressions
(Liu and Zhang, 2008). 16 The results are available upon request.
24
risk being a reward for momentum profits outside of January. For the best scenario of all of the cases
examined, the incremental contribution of MP, [ ], is 0.05% per month (or 4% of the observed
WML return), averaging from February to December. Regarding the role of macroeconomic risk factors
taken together in explaining the momentum effect, we find little evidence that explanations of momentum
profits lie in macroeconomic risk. For example, with the extended windows, the CRR5 model provides an
expected WML return of 0.40% per month (or 34% of the observed return)—and the difference between
the observed and expected returns is significant at the 1% level (with an associated t-statistic of 5.84).
Panel B of Table 6 estimates risk premiums by using ten industry-sorted portfolios alone as the base
portfolios.17
Using industry portfolios alone leads to the incremental contribution of MP being extremely
small or nonexistent. The results are rather striking, which is in stark contrast to the corresponding results
from using size-, value- and momentum portfolios as base portfolios (in Table 4). For instance, with the
full samples, the one-factor MP model produces an expected WML return of 0.01% per month (or 1% of
the observed WML return). Further, the complete macroeconomic factor models not only produce meager
expected momentum returns, but even generate negative expected returns occasionally. With the full
samples, the CRR5 model produces an expected momentum return of 0.06% per month (or 10% of the
observed WML return). And the associated t-statistic of 1.66 rejects marginally the null hypothesis of no
difference between the observed and expected returns. With the extended windows, the CRR5 model has
an expected WML return of 0.28% per month (or 45% of the observed returns); there is an insignificant
difference between the observed and expected WML returns (t-statistic=1.12). So far, we find mixed
evidence about whether the complete macroeconomic risk model can capture momentum profits.
Nevertheless, using only industry-sorted portfolios as base portfolios provides strong confirmatory
evidence that the growth rate of industrial production is not the main driving force of momentum profits.
The literature provides scant documented evidence of the classic January effects on industry-sorted
portfolios, whereas many previous studies have shown that the January effects are embedded in size-,
17
For robustness, we also utilize seventeen industry-sorted portfolios and thirty industry-sorted portfolios, respectively, as the
base portfolios. The basic inferences remain robust.
25
value- and momentum portfolios (Daniel and Titman, 1997; Daniel, Titman and Wei, 2001; Grundy and
Martin, 2001; Keim, 2008). Despite the fact that there is no documented evidence of the January effects
embedded in industry-sorted portfolios, we shall still treat the assumption made in the last section with
some caution.
Excluding the month of January leads to strong and consistent evidence that macroeconomic risk—
both the complete macroeconomic risk-factor models and the MP itself—cannot rationalize momentum
profits. The one-factor MP model can hardly predict momentum profits in the 11 months of a year when
momentum strategies generate profits. Depending on empirical specifications, the incremental
contribution of MP, [ ], ranges from ‘none’ to the maximum of 4% of the observed WML return
outside of January. Contrary to the findings of averaging across the year, none of the complete
macroeconomic risk-factor models can capture momentum profits outside of January. With the full
samples, the complete CRR5 model yields an expected WML return of 0.43% per month, or 36% of the
observed WML profit outside of January, with the remaining 64% being significant (t-statistic=3.04).
And the MP risk factor subsumes none of the observed profit. The results confirm that our findings
remain robust to different empirical designs.
Another potential concern is the impact of small and illiquid firms traded on the Nasdaq Stock
Exchange on our tests. To address this concern, we use momentum portfolios formed in the sample of
NYSE and Amex stocks excluding Nasdaq stocks, referring to them as NYSE−Amex momentum
portfolios. The previous momentum portfolios formed on NYSE, Amex and Nasdaq stocks are denoted as
NYSE−Amex−Nasdaq momentum portfolios. Now the base portfolios utilized in two-stage
Fama−MacBeth cross-sectional regressions consist of ten size-, ten value- and ten NYSE−Amex
momentum portfolios. This change might result in a particularly pronounced impact on equal-weighted
rather than value-weighted portfolio returns.
Panel A of Table 7 reports the results for equal-weighted NYSE−Amex momentum portfolios. With
respect to the economic significance of the incremental contribution of MP, the results are very similar
(although there are also slightly dissimilar findings) to those of the counterpart for NYSE−Amex−Nasdaq
26
momentum strategies. With the full samples, the one-factor MP model generates the incremental
contribution of MP of 0.38% per month, (or 48% of the observed WML return), which is significantly
different from the observed WML return (t-statistic=2.18). We also note that the complete
macroeconomic factor models cannot account for momentum profits, which is consistent with the
corresponding findings for NYSE−Amex−Nasdaq momentum strategies. For example, with the extended
windows, the CRR5 model produces an expected WML return of 0.49% per month (or 62% of the
observed WML return). And the difference between the observed and expected WML returns is
significant (t-statistic=4.3).
Consistent with most of the evidence above, outside of January, neither the complete macroeconomic
factor models nor the MP risk factor itself can subsume momentum. For example, the CRR5 model, with
extended windows, produces an expected WML return of 0.74% per month (or 58% of the observed
equal-weighted WML return). And the remaining 42% is significant. Moreover, the incremental
contribution of MP, [ ], is 0.09% per month (or 7% of the equal-weighted observed WML
return), which is also significantly different from the expected WML return (t-statistic=7.17). Panel B
presents the results for value-weighted NYSE−Amex momentum strategies, which shows that our main
conclusions remain robust. Taken together, all of our robustness tests provide further supportive evidence
that momentum profits are not the reward for the exposure to macroeconomic risk, particularly industrial
production risk.
5. Extreme Momentum Payoffs
Most recent studies by Daniel, Jagannathan and Kim (2012), Daniel and Moskowitz (2013) point out
that the momentum strategy experiences infrequent but severe losses. They show that 13 out of 978
months from 1929 to 2010 in the United States market, momentum losses exceed 20 percent per month,
which often occurs in the economic downturn. Daniel, Jagannathan and Kim (2012), Daniel and
Moskowitz (2013) focus on the downside of momentum trading—momentum crashes. It is equal
importance of analyzing the upside of momentum trading—when the momentum strategy produces
27
considerably large profits. We find that the best monthly returns to the momentum strategy is 35.84% in
February 2000 followed by the second best monthly return of 25.15% in June 2000.
Do extreme momentum returns arise principally from extreme macroeconomic states? In the spirit of
Grundy and Martin (2001), our analysis compares the performance of a total return momentum strategy to
the performance of two alternative momentum strategies—the factor-related return momentum strategy
and the stock-specific return momentum strategy. Each momentum strategy assigns winners and losers as
the top and bottom deciles of stocks by a ranking criterion. The ranking period is six months and the
holding period is six months, with one-month gap between ranking and holding. The factor-related return
momentum strategy ranks stocks according to an estimate of the factor component of their ranking period
returns. The stock-specific return momentum strategy ranks stocks according to an estimate of their
component of their ranking period returns that is unrelated to macroeconomic risk factors.
To distinguish the factor-related and stock-specific components of their ranking period returns, we
first estimate the parameters of the Chen, Roll and Ross five-factor model.18
At each month, the following
regression was undertaken for all of NYSE, Amex and Nasdaq stocks i with minimum 36-month returns
on the CRSP tapes, month t - 37 to t – 2: for max [t – 61], …, t – 2,
where the dummy of Dis equal to 1 if month is one of six ranking months; otherwise Dis equal to
0.
The stock-specific return momentum strategy ranks stocks by estimated i. The factor-related return
momentum strategy ranks stocks based on∑
.
Figure 4 plots the worst and best value-weighted monthly returns to the total return momentum
strategy as well as the matching returns to two alternative momentum strategies. The largest loss to the
18 Our findings are robust to other macroeconomic factor models examined in this paper. Results are available on request.
28
total return momentum strategy is 37.18% in April 2009.19
The total return strategy experiences severe
losses in its preceding month (e.g., March 2009) and its following month (e.g., May 2009). In the other
words, the momentum crash periods are clustered. In panel A, averaging across the ten worst returns of
the total return momentum strategy produces the average monthly loss of 21.88%, compared to the
corresponding monthly loss of 3.62% for the factor-related return strategy and 7.19% for the stock-
specific return strategy. It is clear from Panel A that the factor-related return strategy can hardly generate
the similar magnitudes of losses as does the total return strategy, although the stock-specific return
strategy produces a closer, less volatile losses relative to the total return strategy.20
Excluding January in
parameter estimation leads to similar results as shown in Panel B.
Turning to extreme momentum profits in Panel C and D, we see that the total return momentum
strategy earned the largest profit of 35.84% in February 2000. Between 1999 and 2000, the momentum
strategy earned handsome profits, being (far) more than 12% per month in October 1999 and December
1999, June 2000 and December 2000. The profitability of the factor-related return strategy is markedly
smaller than the total return strategy; however, the profitability of the stock-specific return strategy is
relatively close to the total return strategy.
We have shown that the profitability of the factor-related return strategy is considerably smaller than
the total return strategy. This finding suggests that extreme momentum returns cannot be explained by
macroeconomic risk.
6. Conclusion
We study the role of macroeconomic risk in explaining momentum profits. Our analysis presents
three major findings. First, the winner and loser portfolios have almost identical loadings on the growth
rate of industrial production outside of January, when momentum is present. Thus, there is essentially a
19
Our worst momentum returns are smaller in absolute terms than those ones in Daniel and Moskowitz (2013). The differences
come from the fact that at a given month, we hold six winner-loser portfolios formed on six different ranking periods, whereas
Daniel and Moskowitz (2013) hold one winner-loser portfolio formed on unique ranking period. In the other words, our average
monthly return is the average of the six portfolios, which reduces the magnitudes of the worst momentum returns. 20 In estimation of parameters in Equation (6), our analysis carries on the tests in two ways—including January observations and
excluding January observations, to avoid the influences of the January seasonality, and find the similar results for both cases.
29
zero MP loading on the winner–loser portfolio; the difference in loadings mainly occurs in January when
winners underperform losers massively. Second, the MP risk-premium estimates are statistically and
economically insignificant outside of January, meaning that the growth rate of industrial production is not
a priced risk factor and cannot capture cross-sectional variations of non-January stock returns. Third,
macroeconomic risk-premium estimates together with the corresponding factor loadings cannot generate
the observed momentum return. In all, we conclude that macroeconomic risk is not the main driving force
of momentum profits.
Our empirical analysis has implications for the existing literature on investigating the source of
momentum profits. Most of the existing studies do not concentrate on the 11 months of a year when the
momentum effect is really present. As this may lead to illusory conclusions about what drives momentum,
it behoves us to be wary of the substantial January contamination when we investigate the cause of
momentum profits.
Our empirical results also raise some questions for future study. For example, would the growth rate
of industrial production account for the fact that winners underperform losers in January? Despite having
shown that the existence of return reversal in extremely small stocks is largely responsible for the January
losses to the momentum strategy, we do not provide full explanations for the January losses. Since this
question is beyond the scope of our study, it might be worth investigating in depth in future research why
momentum strategies fail in January. This would help to understand long-term reversal, which has been
demonstrated to be present only in January. These issues are left for future research.
30
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32
Table 1
Momentum Strategy Payoffs
All NYSE, Amex and Nasdaq stocks on the monthly file of CRSP are ranked on the basis of cumulative
returns in months t - 7 to t - 2 and assigned to ten deciles. The momentum strategy buys prior winners
(P10) and sells prior losers (P1). Zero-investment winner–loser portfolios (WML) are reconstructed at the
start of each month t, and held for six months t to t + 5. The table reports average monthly returns of the
winner–loser portfolios (WML); the associated t statistics are in parentheses. In Panel B, we screen out
stocks under $5 at the beginning of the investment period to avoid return reversals in those extremely
small stocks.
EW VW
Overall January Non-Jan Overall January Non-Jan
Panel A: without a screen on stock price
All investment periods 3/47–11/09
Mean profits 0.67 -5.69 1.24 1.20 -2.30 1.51
(t-statistic) (3.44) (-4.59) (7.56) (5.51) (-2.16) (7.09)
CAPM alpha 0.66 -5.37 1.26 1.24 -2.05 1.55
(t-statistic) (3.38) (-4.26) (7.66) (5.64) (-1.88) (7.26)
Fama–French alpha 0.69 -4.51 1.35 1.43 -0.53 1.70
(t-statistic) (3.45) (-3.44) (8.19) (6.47) (-0.43) (8.00)
3/47–1/68
Mean profits 0.97 -3.85 1.40 1.15 -2.14 1.45
(t-statistic) (4.73) (-3.74) (7.96) (5.04) (-2.23) (6.49)
2/68–12/88
Mean profits 0.89 -4.45 1.38 1.23 -2.47 1.56
(t-statistic) (3.27) (-2.89) (5.80) (3.85) (-1.60) (5.05)
1/89–11/09
Mean profits 0.15 -8.35 0.92 1.19 -2.42 1.52
(t-statistic) (0.31) (-2.66) (2.36) (2.28) (-0.92) (2.96)
Panel B: with the screen eliminating stocks priced below $5
All investment periods 3/47–11/09
Mean profits 1.35 -1.72 1.63 1.28 -1.49 1.53
(t-statistic) (7.58) (-1.85) (9.67) (6.08) (-1.49) (7.32)
CAPM alpha 1.34 -1.45 1.66 1.33 -1.29 1.57
(t-statistic) (7.79) (-1.58) (9.58) (6.28) (-1.27) (7.44)
Fama–French alpha 1.55 -0.34 1.78 1.50 0.14 1.70
(t-statistic) (8.63) (-0.31) (10.40) (7.03) (0.12) (8.15)
3/47–1/68
Mean profits 1.12 -3.09 1.50 1.17 -2.04 1.46
(t-statistic) (5.75) (-3.35) (8.02) (5.09) (-2.11) (6.48)
2/68–12/88
Mean profits 1.47 -1.40 1.73 1.22 -1.50 1.47
(t-statistic) (5.84) (-1.13) (7.07) (3.87) (-1.05) (4.66)
1/89–11/09
Mean profits 1.47 -0.60 1.64 1.43 -1.11 1.66
(t-statistic) (3.42) (-0.26) (3.96) (2.87) (-0.45) (3.36)
33
Table 2
Risk-premium estimates from two-stage Fama-MacBeth (1973) cross-sectional regressions: using
ten size-, ten value- and ten momentum portfolios as the base portfolios.
This table reports risk premiums of Chen, Roll and Ross (1986) five factors and Fama and French (1993)
three factors, including the growth rate of industrial production (MP), unexpected inflation (UI), change
in expected inflation (DEI), term premium (UTS), and default premium (UPR), market premium (MKT),
size premium (SMB) and value premium (HML) from two-stage Fama-MacBeth (1973) cross-sectional
regressions. The Fama-MacBeth t-statistics are calculated from the Shanken (1992) method and are
reported in parentheses, and the average cross-sectional are also reported. We use thirty base portfolios
that consist of decile one-sorted portfolios formed on size (market capitalization), value (book-to-market
equity) and momentum (past two-to-seven months’ returns). Note that the difference in the base portfolios
between Panels A and B is that Panel A includes ten equal-weighted decile momentum portfolios,
whereas Panel B consists of ten value-weighted decile momentum portfolios. In the first-stage time-series
regressions, for each test portfolio, we estimate factor loadings using the full samples, the extended
window and sixty-month rolling window regressions. In the second-stage cross-sectional regressions, we
estimate risk premiums by regressing base portfolios’ excess returns on factor loadings estimated from the
first-stage time-series regressions. We start the second-stage cross-sectional regressions from March 1949
in the entire sample of March 1947–November 2009, in order to ensure that there are at least two years of
monthly observations in the first-stage extended- and rolling-window time-series regressions. For the
extended-window case, the first-stage time-series regressions start from the first month to month t and the
second-stage cross-sectional regressions regress base portfolios’ excess returns in month t + 1 on factor
loadings using information up to month t. The table only reports the results based on the full samples in
the first-stage time-series regressions, and the extended-window regressions generate quantitatively
similar results. Panel A: Equal-Weighted Momentum Decile Portfolios
Overall
MP 0.45 1.07 12%
(2.83) (3.67)
FF 0.90 -0.25 0.17 0.17 43%
(3.44) (-0.83) (1.40) (1.58)
FF+MP 0.93 -0.22 0.09 0.21 1.07 49%
(3.53) (-0.74) (0.69) (1.95) (3.43)
CRR5 0.78 0.23 0.09 -1.22 0.25 0.76 46%
(4.48) (1.31) (0.50) (-2.57) (1.93) (2.68)
Non-January
MP 0.71 -0.34 20%
(4.38) (-1.04)
FF 1.42 -0.81 -0.11 0.04 42%
(5.73) (-2.72) (-0.82) (0.37)
FF+MP 1.45 -0.84 -0.13 0.05 0.16 45%
(5.95) (-2.82) (-0.99) (0.38) (0.43)
CRR5 1.20 0.35 0.10 -2.34 0.34 -0.03 46%
(6.56) (1.22) (0.29) (-5.72) (2.23) (-0.12)
Panel B: Value-Weighted Momentum Decile Portfolios
Overall
34
MP 0.35 1.24 12%
(2.05) (4.73)
FF 1.77 -1.13 0.19 0.13 39%
(5.32) (-2.96) (1.52) (1.02)
FF+MP 1.35 -0.62 0.02 0.21 1.41 49%
(4.59) (-1.89) (0.18) (1.81) (3.25)
CRR5 0.97 0.32 0.11 -1.83 0.22 0.80 41%
(5.52) (1.15) (0.36) (-3.05) (1.73) (2.88)
Non-January
MP 0.49 0.17 13%
(2.88) (0.62)
FF 2.03 -1.44 0.05 -0.02 38%
(6.29) (-3.75) (0.32) (-0.17)
FF+MP 1.94 -1.28 -0.07 -0.01 1.19 44%
(6.19) (-3.49) (-0.53) (-0.06) (2.01)
CRR5 1.34 0.44 0.12 -2.30 0.16 -0.19 39%
(7.40) (1.08) (0.26) (-5.68) (1.10) (-0.56)
35
Table 3
Risk-premium estimates from two-stage Fama–MacBeth (1973) cross-sectional regressions: using
10 size, 10 value, 10 momentum, and 10 industry portfolios as base portfolios
This table reports risk premiums of Chen, Roll, and Ross (1986) five factors and Fama and French (1993)
three factors, including the growth rate of industrial production (MP), unexpected inflation (UI), change
in expected inflation (DEI), term premium (UTS), and default premium (UPR), market premium (MKT),
size premium (SMB), and value premium (HML) estimated from two-stage Fama–MacBeth (1973) cross-
sectional regressions. The Fama–MacBeth t-statistics are calculated from the Shanken (1992) method and
are reported in parentheses and the average cross-sectional are also reported. We use forty base
portfolios that consist of ten size-, ten value-, ten momentum- and ten industry portfolios. Note that the
difference in the base portfolios between Panels A and B is that Panel A includes ten equal-weighted
decile momentum portfolios, whereas Panel B consists of ten value-weighted decile momentum portfolios.
In the first-stage time-series regressions, for each test portfolio, we estimate factor loadings using the full
samples, the extended window, and sixty-month rolling window regressions. In the second-stage cross-
sectional regressions, we estimate risk premiums by regressing base portfolios’ excess returns on factor
loadings estimated from the first-stage time-series regressions. We start the second-stage cross-sectional
regressions from March 1949 in the whole sample of March 1947–November 2009, in order to ensure that
there are at least two years of monthly observations in the first-stage extended-window time-series
regressions. For the extended-window case, the first-stage time-series regressions start from the first
month to month t and the second-stage cross-sectional regressions regress base portfolios’ excess returns
in month t + 1 on factor loadings using information from the first month to month t. The table only
reports the results based on the full samples in the first-stage time-series regressions, and the extended-
window regressions generate quantitatively similar results. Panel A: Equal-Weighted Momentum Decile Portfolios
Overall
MP 0.61 0.49 11%
(4.20) (2.31)
FF 0.66 0.00 0.17 0.09 38%
(3.43) (0.02) (1.46) (0.79)
FF+MP 0.99 -0.30 0.14 0.10 0.48 42%
(4.76) (-1.14) (1.16) (0.83) (2.28)
CRR5 0.79 0.18 0.08 -0.75 0.12 0.42 38%
(5.71) (0.86) (0.46) (-2.18) (1.23) (1.86)
Non-January
MP 0.66 -0.22 14%
(4.49) (-1.00)
FF 0.76 -0.16 -0.11 0.00 37%
(3.98) (-0.62) (-0.89) (0.01)
FF+MP 0.73 -0.13 -0.10 0.00 -0.05 40%
(3.99) (-0.52) (-0.86) (0.01) (-0.26)
CRR5 0.90 0.10 0.04 -1.75 0.02 0.53 38%
(6.14) (0.45) (0.18) (-5.73) (0.20) (2.35)
Panel B: Value-Weighted Momentum Decile Portfolios
Overall
36
MP 0.55 0.50 9%
(3.63) (2.72)
FF 1.04 -0.41 0.17 0.08 32%
(4.93) (-1.53) (1.45) (0.66)
FF+MP 1.42 -0.72 0.10 0.09 0.79 38%
(5.92) (-2.47) (0.83) (0.71) (2.76)
CRR5 0.86 0.19 0.08 -1.24 0.08 0.66 31%
(6.35) (0.81) (0.37) (-3.08) (0.83) (2.82)
Non-January
MP 0.58 -0.06 10%
(3.88) (-0.30)
FF 1.18 -0.61 0.02 -0.02 31%
(5.54) (-2.21) (0.18) (-0.19)
FF+MP 1.41 -0.80 -0.01 -0.04 0.44 36%
(6.19) (-2.78) (-0.11) (-0.28) (1.60)
CRR5 0.95 0.18 0.05 -1.53 -0.12 0.41 31%
(6.56) (0.73) (0.22) (-4.91) (-1.42) (1.84) (6.56)
37
Table 4
Expected momentum profits versus observed momentum profits (base portfolios: ten size-, value- and momentum portfolios)
This table reports estimated momentum profits based on four different factor models, including the one-factor MP model (MP), the Fama-French
(1993) model augmented with MP (FF+MP), the Chen, Roll and Ross (1986) model without the default premium (CRR4) and the Chen, Roll and
Ross (1986) model (CRR5). We calculate expected momentum profits as the sum of the products of factor sensitivities and estimated risk
premium: [ ] . Factor sensitivities ( ) are estimated from
. Risk premiums ( ) are estimated from two-stage Fama-MacBeth (1973) cross-sectional regressions using ten
size-, ten value- and ten momentum portfolios as base portfolios.21
In the first-stage time-series regressions, for each of thirty base portfolios, we
estimate factor sensitivities by regressing base portfolios’ returns on factors, using the full-sample, extended windows and rolling windows:
. In the second-stage cross-sectional regressions, we regress thirty base
portfolios’ excess returns on the estimated factor sensitivities from the first-stage time-series regressions for each month:
. This table also presents the t-statistics (e.g., t(diff1)) testing the null that the
difference between the observed momentum return and the incremental contribution of MP ( [ ]) is zero and the t-statistics (e.g., t(diff2))
testing the null that the difference between observed and expected momentum returns is zero.
[
]
[ ]
t(diff1) [ ] [ ]
t(diff2) [
]
[ ]
t(diff1) [ ] [ ]
t(diff2)
Panel A: equal-weighted momentum
Overall Non-January
Full-sample window in the first-stage regressions
MP 0.31 49% 1.44 0.31 49% 1.44 MP -0.01 — 7.12 -0.01 — 7.12
FF+MP 0.42 66% 1.69 0.36 56% 2.93 FF+MP 0.02 1% 7.15 0.08 7% 7.50
CRR4 0.24 39% 2.03 0.48 76% 2.81 CRR4 0.00 0% 7.13 0.95 80% 3.73
CRR5 0.14 23% 2.55 0.56 88% 1.84 CRR5 0.00 0% 7.14 1.05 88% 2.97
Extended window in the first-stage regressions
MP 0.14 22% 2.30 0.14 22% 2.30 MP 0.03 3% 7.05 0.03 3% 7.05
FF+MP 0.28 45% 2.19 0.20 31% 3.25 FF+MP 0.10 9% 6.92 0.20 17% 6.76
CRR4 0.08 13% 2.95 0.38 61% 3.27 CRR4 0.11 9% 6.90 0.60 50% 6.33
CRR5 0.03 5% 3.10 0.43 69% 3.30 CRR5 0.10 8% 6.91 0.72 60% 6.67
Rolling windows in the first-stage regressions
MP 0.08 13% 3.08 0.08 13% 3.08 MP 0.34 28% 5.39 0.34 28% 5.39
FF+MP 0.23 36% 2.89 0.17 27% 4.30 FF+MP 0.36 30% 5.88 0.48 40% 6.43
CRR4 0.12 19% 2.67 0.29 46% 3.30 CRR4 0.28 24% 5.66 0.58 49% 5.60
CRR5 0.09 14% 3.01 0.28 44% 3.92 CRR5 0.20 17% 6.21 0.64 53% 5.75
21 Please note that momentum portfolios used in Table 4–6 are constructed based on the sample of NYSE, AMEX and Nasdaq stocks on the CRSP monthly files. Momentum
portfolios utilized in Table 7 are constructed on the basis of the sample of NYSE and AMEX stocks on the CRSP monthly file as robustness check.
38
[
]
[ ]
t(diff1) [ ] [ ]
t(diff2) [
]
[ ]
t(diff1) [ ] [ ]
t(diff2)
Panel B: value-weighted momentum
Overall Non-January
Full-sample window in the first-stage regressions MP 0.41 34% 4.02 0.41 34% 4.02 MP 0.02 1% 6.86 0.02 1% 6.86
FF+MP 0.65 54% 4.43 0.67 55% 6.23 FF+MP 0.27 18% 7.07 0.49 32% 8.09
CRR4 0.21 18% 4.36 0.85 71% 4.51 CRR4 -0.02 — 6.74 1.13 75% 4.38
CRR5 0.15 13% 4.73 0.85 70% 4.55 CRR5 0.00 0% 6.87 1.14 76% 4.28
Extended window in the first-stage regressions
MP 0.18 15% 4.77 0.18 15% 4.77 MP 0.02 1% 6.76 0.02 1% 6.76
FF+MP 0.43 36% 4.98 0.42 35% 6.10 FF+MP 0.07 5% 6.85 0.17 11% 7.09
CRR4 0.24 20% 4.39 0.49 40% 5.89 CRR4 0.09 6% 6.65 0.39 26% 7.73
CRR5 0.16 13% 4.74 0.53 44% 5.74 CRR5 0.07 5% 6.76 0.47 31% 7.54
Rolling windows in the first-stage regressions
MP 0.18 15% 5.07 0.18 15% 5.07 MP 0.30 20% 6.26 0.30 20% 6.26
FF+MP 0.27 23% 5.23 0.39 32% 7.15 FF+MP 0.34 23% 6.00 0.61 40% 7.29
CRR4 0.21 18% 4.57 0.64 53% 5.06 CRR4 0.23 16% 6.37 0.77 51% 6.33
CRR5 0.13 11% 5.04 0.67 55% 5.61 CRR5 0.16 10% 6.79 0.88 58% 6.36
39
Table 5
Expected momentum profits versus observed momentum profits(base portfolios: ten size-, value-, momentum- and industry portfolios)
This table reports expected momentum returns based on four different factor models, including the one-factor MP model (MP), the Fama–French
(1993) model augmented with MP (FF+MP), the Chen Roll, and Ross (1986) model without default premium (CRR4) and the Chen, Roll, and
Ross (1986) model (CRR5). We calculate expected momentum returns as the sum of the products of factor sensitivities and estimated risk
premiums: [ ]
. Factor sensitivities ( ) are estimated from
. Risk premiums ( ) are estimated from two-stage Fama–MacBeth (1973) cross-sectional regressions, using ten
size-, ten value-, ten momentum- and ten industry portfolios as base portfolios. In the first-stage time-series regressions, for each of forty base
portfolios, we estimate factor sensitivities by regressing base portfolios’ returns on factors, using the full-sample, extended windows and rolling
windows:
. In the second-stage cross-sectional regressions, we regress
forty base portfolios’ excess returns on the estimated factor sensitivities from the first-stage time-series regressions for each month
. This table also presents the t-statistics (e.g., t(diff1)) testing the null that
the difference between the observed momentum return and the incremental contribution of MP ( [
]) is zero and the t-statistics (e.g., t(diff2))
testing the null that the difference between observed and expected momentum returns is zero.
[
]
[ ]
t(diff1) [ ] [ ]
t(diff2) [
]
[ ]
t(diff1) [ ] [ ]
t(diff2)
Panel A: equal-weighted momentum Overall Non-January
Full-sample window in the first-stage regressions MP 0.14 22% 2.21 0.14 22% 2.21 MP 0.00 0% 7.13 0.00 0% 7.13
FF+MP 0.19 30% 2.60 0.15 24% 3.24 FF+MP -0.01 0% 7.15 0.01 1% 7.48
CRR4 0.07 12% 2.96 0.35 56% 2.71 CRR4 0.01 1% 7.11 0.81 67% 3.43
CRR5 0.08 13% 2.93 0.43 68% 2.46 CRR5 -0.03 — 7.18 0.87 73% 3.38
Extended window in the first-stage regressions
MP 0.08 12% 2.63 0.08 12% 2.63 MP 0.03 3% 7.03 0.03 3% 7.03
FF+MP 0.04 7% 2.98 -0.04 — 3.75 FF+MP 0.05 4% 6.96 0.11 9% 6.75
CRR4 0.05 8% 2.98 0.36 56% 2.26 CRR4 0.06 5% 6.95 0.43 36% 5.72
CRR5 0.04 6% 3.11 0.40 63% 2.36 CRR5 0.05 4% 6.93 0.50 42% 5.80
Rolling window in the first-stage regressions
MP 0.01 2% 3.22 0.01 2% 3.22 MP 0.26 22% 5.71 0.26 22% 5.71
FF+MP 0.11 17% 3.31 0.05 7% 4.26 FF+MP 0.24 20% 6.17 0.32 27% 6.41
CRR4 0.07 11% 2.86 0.28 44% 2.41 CRR4 0.25 21% 5.77 0.51 43% 4.93
CRR5 0.08 13% 2.88 0.32 51% 2.26 CRR5 0.22 18% 6.10 0.57 48% 4.98
40
[ ] [ ]
t(diff1) [
] [ ]
t(diff2) [ ]
[ ]
t(diff1) [
] [ ]
t(diff2)
Panel B: value-weighted momentum Overall Non-January
Full-sample window in the first-stage regressions MP 0.16 14% 4.66 0.16 14% 4.66 MP -0.01 0% 6.84 -0.01 0% 6.84
FF+MP 0.37 30% 4.93 0.45 37% 5.74 FF+MP 0.10 7% 6.91 0.25 17% 7.66
CRR4 0.13 11% 4.89 0.69 58% 4.35 CRR4 0.03 2% 6.73 0.89 59% 4.60
CRR5 0.12 10% 4.99 0.71 59% 4.30 CRR5 -0.01 — 6.87 0.89 59% 4.64
Extended window in the first-stage regressions
MP 0.08 7% 4.96 0.08 7% 4.96 MP 0.02 1% 6.75 0.02 1% 6.75
FF+MP 0.14 11% 5.29 0.11 9% 5.88 FF+MP 0.01 1% 6.86 0.06 4% 6.89
CRR4 0.17 14% 4.59 0.39 32% 5.00 CRR4 0.05 3% 6.76 0.24 16% 7.18
CRR5 0.13 11% 4.85 0.44 37% 5.04 CRR5 0.03 2% 6.88 0.28 19% 7.25
Rolling window in the first-stage regressions
MP 0.10 8% 5.17 0.10 8% 5.17 MP 0.19 13% 6.4 0.19 13% 6.40
FF+MP 0.14 12% 5.52 0.20 17% 6.66 FF+MP 0.20 14% 6.36 0.39 26% 7.07
CRR4 0.17 14% 4.77 0.50 42% 4.76 CRR4 0.19 13% 6.35 0.62 41% 5.78
CRR5 0.11 9% 5.14 0.57 47% 4.88 CRR5 0.11 8% 6.76 0.71 47% 5.89
41
Table 6
Expected momentum returns versus observed momentum returns: using different industry portfolios as base portfolios
This table reports expected momentum returns based on four different factor models, including the one-factor MP model (MP), the Fama–French
(1993) model augmented with MP (FF+MP), the Chen, Roll and Ross (1986) model without the default premium (CRR4) and the Chen, Roll, and
Ross (1986) model (CRR5). We calculate expected momentum returns as the sum of the products of factor sensitivities and estimated risk
premiums: [ ]
. Factor sensitivities ( ) are estimated from
. Risk premiums ( ) are estimated from two-stage Fama–MacBeth (1973) cross-sectional regressions, using
different sets of base portfolios. In the first-stage time-series regressions, for each of the base portfolios, we estimate factor sensitivities by
regressing base portfolios’ returns on factors, using the full-sample, extended windows and rolling
windows:
. In the second-stage cross-sectional regressions, we regress the
base portfolios’ excess returns on the estimated factor sensitivities from the first-stage time-series regressions for each month
. This table also presents the t-statistics (e.g., t(diff1)) testing the null that the
difference between the observed momentum return and the incremental contribution of MP ( [
]) is zero and the t-statistics (e.g., t(diff2))
testing the null that the difference between observed and expected momentum returns is zero.
[
] [ ]
t(diff1) [ ]
[ ]
t(diff2) [
] [ ]
t(diff1) [ ]
[ ]
t(diff2)
Panel A: 10 size, 10 value, 10 momentum, and 17 industry portfolios as base portfolios
Overall Non-January
Full sample in the first-stage regressions
MP 0.11 17% 2.41 0.11 17% 2.41 MP -0.01 0% 7.14 -0.01 0% 7.14
FF+MP 0.16 25% 2.61 0.14 22% 3.07 FF+MP 0.00 0% 7.11 0.04 4% 7.22
CRR4 0.03 5% 3.01 0.20 32% 3.81 CRR4 0.00 0% 7.12 0.60 50% 4.64
CRR5 0.04 6% 3.04 0.24 37% 3.90 CRR5 -0.01 — 7.17 0.62 52% 4.75
Extended window in the first-stage regressions
MP 0.05 9% 2.75 0.05 9% 2.75 MP 0.03 2% 7.03 0.03 2% 7.03
FF+MP 0.04 6% 3.02 -0.06 — 3.80 FF+MP 0.03 2% 7.08 0.07 6% 6.90
CRR4 0.01 1% 3.13 0.21 33% 3.04 CRR4 0.05 4% 7.02 0.35 29% 5.94
CRR5 0.00 0% 3.21 0.26 42% 2.93 CRR5 0.05 4% 7.00 0.40 34% 5.84
Rolling window in the first-stage regressions
MP 0.14 22% 2.27 0.14 22% 2.27 MP 0.21 18% 5.95 0.21 18% 5.95
FF+MP 0.10 16% 2.47 0.04 6% 2.64 FF+MP 0.14 12% 6.54 0.22 18% 6.77
CRR4 0.14 21% 2.33 0.31 49% 1.33 CRR4 0.21 17% 6.05 0.47 39% 5.07
CRR5 0.15 23% 2.25 0.39 61% 1.01 CRR5 0.19 16% 6.17 0.52 44% 5.07
Panel B: 10 industry portfolios as base portfolios
42
Overall Non-January
Full sample in the first-stage regressions
MP 0.01 1% 2.85 0.01 1% 2.85 MP 0.00 0% 7.13 0.00 0% 7.13
FF+MP -0.05 — 2.82 0.05 8% 2.39 FF+MP -0.04 — 7.13 -0.07 — 7.19
CRR4 -0.09 — 3.09 0.12 19% 1.56 CRR4 -0.02 — 7.18 -0.10 — 3.98
CRR5 -0.07 — 3.14 0.06 10% 1.66 CRR5 0.05 4% 6.95 -0.19 — 4.23
Extended window in the first-stage regressions
MP 0.00 — 3.04 0.00 — 3.04 MP 0.03 2% 7.02 0.03 2% 7.02
FF+MP -0.04 — 3.01 -0.02 — 2.95 FF+MP 0.04 3% 6.94 0.01 1% 6.76
CRR4 0.00 0% 2.87 0.42 66% 0.81 CRR4 0.05 4% 6.82 0.26 22% 4.25
CRR5 -0.06 — 3.07 0.28 45% 1.12 CRR5 0.00 0% 7.04 0.43 36% 3.04
Rolling window in the first-stage regressions
MP -0.02 — 2.91 -0.02 — 2.91 MP 0.17 14% 5.70 0.17 14% 5.70
FF+MP 0.09 14% 2.38 0.07 12% 2.11 FF+MP 0.13 11% 5.68 0.16 13% 4.52
CRR4 0.00 — 2.56 0.05 7% 1.47 CRR4 0.14 12% 5.51 0.49 41% 2.59
CRR5 0.01 1% 2.50 0.25 40% 0.86 CRR5 0.15 13% 5.51 0.60 50% 2.04
43
Table 7
Expected momentum profits versus observed NYSE-Amex momentum profits: using ten size-, ten value- and ten NYSE-Amex momentum
portfolios as base portfolios
This table reports expected momentum returns based on four different factor models, including the one-factor MP model (MP), the Fama–French
(1993) model augmented with MP (FF+MP), the Chen, Roll and Ross (1986) model without the default premium (CRR4) and the Chen, Roll, and
Ross (1986) model (CRR5). We calculate expected momentum returns as the sum of the products of factor sensitivities and estimated risk
premiums: [ ] . Factor sensitivities ( ) are estimated from
. Risk premiums ( ) are estimated from two-stage Fama–MacBeth (1973) cross-sectional
regressions, for the sample using ten size-, ten value- and ten NYSE–Amex momentum portfolios as base portfolios. In the first-stage time-series
regressions, for each of the thirty base portfolios, we estimate factor sensitivities by regressing base portfolios’ returns on factors, using the full-
sample and extended windows: . In the second-stage cross-sectional
regressions, we regress the thirty base portfolios’ excess returns on the estimated factor sensitivities from the first-stage time-series regressions
for each month: . This table also presents the t-statistics (e.g.,
t(diff1)) testing the null that the difference between the observed momentum return and the incremental contribution of MP ( [ ]) is zero
and the t-statistics (e.g., t(diff2)) testing the null that the difference between observed and expected momentum returns is zero.
[
]
[ ]
t(diff1) [ ] [ ]
t(diff2) [
]
[ ]
t(diff1) [ ] [ ]
t(diff2)
Panel A: equal-weighted momentum Overall Non-January
Full sample in the first-stage regressions
MP 0.38 48% 2.18 0.38 48% 2.18 MP 0.00 0% 7.07 0.00 0% 7.07
FF+MP 0.41 52% 3.23 0.31 40% 5.65 FF+MP 0.27 21% 7.74 0.38 30% 8.44
CRR4 0.19 24% 3.10 0.47 60% 4.69 CRR4 -0.01 -1% 7.45 0.95 74% 4.60
CRR5 0.17 22% 3.30 0.60 76% 3.46 CRR5 0.00 0% 7.48 1.09 85% 3.37
Extended window in the first-stage regressions
MP 0.12 15% 3.39 0.12 15% 3.39 MP 0.02 2% 7.23 0.02 2% 7.23
FF+MP 0.24 30% 4.00 0.13 17% 5.66 FF+MP 0.03 3% 7.67 0.10 8% 7.70
CRR4 0.07 9% 3.94 0.37 47% 4.75 CRR4 0.09 7% 7.06 0.58 46% 7.35
CRR5 0.02 3% 4.17 0.49 62% 4.30 CRR5 0.09 7% 7.17 0.74 58% 7.03
Rolling window in the first-stage regressions
MP 0.01 1% 4.74 0.01 1% 4.74 MP 0.20 16% 6.97 0.20 16% 6.97
FF+MP 0.24 30% 3.86 0.18 23% 5.75 FF+MP 0.24 19% 7.19 0.41 33% 7.49
CRR4 0.07 9% 3.93 0.37 47% 3.73 CRR4 0.16 12% 6.90 0.60 47% 6.19
CRR5 0.08 10% 3.91 0.36 46% 4.27 CRR5 0.13 10% 6.99 0.69 54% 6.10
Panel B: value-weighted momentum
44
Overall Non-January
Full sample in the first-stage regressions
MP 0.36 36% 3.57 0.36 36% 3.57 MP 0.02 2% 6.21 0.02 2% 6.21
FF+MP 0.51 51% 4.54 0.50 50% 6.03 FF+MP 0.23 18% 6.64 0.32 26% 7.33
CRR4 0.20 20% 3.94 0.61 61% 4.59 CRR4 -0.02 -2% 6.07 0.82 66% 4.69
CRR5 0.14 14% 4.36 0.59 59% 4.65 CRR5 0.00 0% 6.21 0.83 67% 4.62
Extended window in the first-stage regressions
MP 0.17 17% 4.39 0.17 17% 4.39 MP 0.02 1% 6.10 0.02 1% 6.10
FF+MP 0.35 35% 4.91 0.34 34% 5.96 FF+MP 0.05 4% 6.31 0.16 13% 6.17
CRR4 0.23 23% 4.04 0.48 48% 5.02 CRR4 0.07 6% 5.88 0.40 32% 6.03
CRR5 0.16 16% 4.45 0.51 51% 4.75 CRR5 0.06 5% 6.00 0.49 39% 5.74
Rolling window in the first-stage regressions
MP 0.16 16% 4.78 0.16 16% 4.78 MP 0.20 16% 5.90 0.20 16% 5.90
FF+MP 0.27 27% 4.50 0.33 33% 5.90 FF+MP 0.23 18% 5.81 0.48 39% 6.11
CRR4 0.18 18% 4.35 0.52 51% 4.57 CRR4 0.14 11% 6.04 0.65 52% 5.31
CRR5 0.14 14% 4.57 0.53 53% 5.01 CRR5 0.08 6% 6.30 0.71 57% 5.46
45
Figure 1 MP factor loadings of equal-weighted momentum portfolio returns
This figure presents the results from calendar-based time-series regressions on the growth rate of
industrial production (MP) using returns of ten equal-weighted momentum decile portfolios, L, P2,…,
P9,W, where L stands for losers and W denotes winners. The table below shows the MP loadings for ten
equal-weighted momentum deciles. The figure reports the MP factor loadings based on four different
factor models, including the one-factor MP model (MP), the Fama–French three-factor (1993) model
augmented with MP (FF+MP), the Chen, Roll and Ross (1986) model without default premium (CRR4)
and the Chen, Roll, and Ross (1986) model (CRR5). The Fama and French (1993) three factors consist of
the market factor (MKT), the value factor (HML) and the size factor (SMB). The Chen, Roll, and Ross
(1986) five factors include MP(the growth rate of industry production), UI (unexpected inflation), DEI
(change in expected inflation), UTS (term premium) and UPR (default premium).
Panel A:Overall
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP 0.32 0.30 0.29 0.25 0.26 0.29 0.32 0.39 0.46 0.61
FF+MP -0.10 -0.09 -0.08 -0.10 -0.09 -0.04 -0.01 0.06 0.14 0.28
CRR4 0.23 0.25 0.25 0.22 0.22 0.26 0.28 0.34 0.40 0.52
CRR5 0.37 0.36 0.36 0.31 0.31 0.34 0.36 0.41 0.46 0.56
Panel B: Non-January
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP 0.59 0.51 0.47 0.40 0.38 0.40 0.41 0.46 0.51 0.62
FF+MP 0.71 0.60 0.56 0.48 0.46 0.47 0.47 0.51 0.56 0.65
CRR4 0.68 0.56 0.51 0.44 0.42 0.44 0.45 0.50 0.57 0.70
CRR5 0.10 0.04 0.03 -0.03 -0.04 -0.01 0.00 0.05 0.10 0.20
-0.3-0.2-0.1
00.10.20.30.40.50.60.70.80.9
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP
Lo
adin
gs
Panel A: Overall
MP FF+MP CRR4 CRR5
-0.3-0.2-0.1
00.10.20.30.40.50.60.70.80.9
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP
Lo
adin
gs
Panel B: Non-January
MP FF+MP CRR4 CRR5
46
Figure 2
MP factor loadings of value-weighted momentum portfolio returns
This figure presents the results from calendar-based time-series regressions on the growth rate of
industrial production (MP) using returns of ten value-weighted momentum decile portfolios, L, P2,…,
P9,W, where L stands for losers and W denotes winners. The table below shows the MP loadings for ten
value-weighted momentum deciles. The figure reports the MP factor loadings based on four different
factor models, including the one-factor MP model (MP), the Fama–French three-factor (1993) model
augmented with MP (FF+MP), the Chen, Roll and Ross (1986) model without the default premium
(CRR4) and the Chen, Roll, and Ross (1986) model (CRR5). The Fama and French (1993) three factors
consist of the market factor (MKT), the value factor (HML) and the size factor (SMB). The Chen, Roll,
and Ross (1986) five factors include MP(the growth rate of industrial production), UI (unexpected
inflation), DEI (change in expected inflation), UTS (term premium) and UPR (default premium).
Panel A: Overall
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP 0.14 0.13 0.13 0.10 0.09 0.13 0.21 0.30 0.36 0.47
FF+MP -0.25 -0.20 -0.18 -0.19 -0.19 -0.14 -0.06 0.04 0.11 0.21
CRR4 0.13 0.13 0.14 0.11 0.10 0.13 0.20 0.29 0.34 0.42
CRR5 0.23 0.20 0.21 0.17 0.15 0.18 0.24 0.32 0.35 0.42
Panel B: Non-January
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP 0.40 0.21 0.23 0.05 0.02 0.02 0.13 0.22 0.24 0.42
FF+MP 0.06 -0.06 -0.01 -0.17 -0.20 -0.20 -0.09 -0.01 -0.02 0.12
CRR4 0.30 0.16 0.20 0.03 0.00 0.01 0.09 0.17 0.16 0.31
CRR5 0.44 0.30 0.36 0.16 0.11 0.13 0.20 0.29 0.28 0.41
-0.3-0.2-0.1
00.10.20.30.40.50.60.70.80.9
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP
Lo
adin
gs
Panel A: Overall
MP FF+MP CRR4 CRR5
-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.9
L P2 P3 P4 P5 P6 P7 P8 P9 W
MP
Lo
adin
gs
Panel B: Non-January
MP FF+MP CRR4 CRR5
47
Figure 3
Event-time MP factor loadings on winners and losers
This figure presents the results from pooled time-series factor regressions on MP using returns of winners (W) and losers (L). For the all-month
regressions, the event month t + m (where m=0,1,…, 24) starts the month right after portfolio formation to the twenty-fourth month. For the non-
January regressions, the event month t + m (where m=0,1,…, 24) starts the month right after portfolio formation to the twenty-four month. For
each event month, we pool together across calendar month the observations of returns to winners and losers, the FF three factors (the market factor,
MKT; the value factor, HML; the size factor, SMB), and the CRR five factors (the growth rate of industrial production, MP; unexpected inflation,
UI; change in expected inflation, DEI; term premium, UTS; default premium, UPR) for each of event month t + m. We perform pooled time-series
factor regressions to estimate MP factor loadings for winners (solid line) and losers (broken line).
-0.5
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-0.3
-0.2
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FF+MP:Non-January
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Lo
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Event Month
CRR4:Non-January
48
Panel A: Overall
Winner 0 1 2 3 4 5 6 7 8 9 10 11 12
MP 0.79 0.76 0.81 0.81 0.78 0.69 0.59 0.58 0.51 0.41 0.37 0.34 0.33
FF+MP 0.57 0.51 0.54 0.55 0.52 0.44 0.34 0.34 0.26 0.16 0.12 0.11 0.12
CRR4 0.65 0.62 0.66 0.68 0.65 0.56 0.46 0.46 0.39 0.30 0.27 0.24 0.23
CRR5 0.69 0.67 0.72 0.76 0.71 0.63 0.57 0.57 0.50 0.42 0.4 0.35 0.33
Loser 0 1 2 3 4 5 6 7 8 9 10 11 12
MP -0.07 0.18 0.27 0.29 0.40 0.42 0.47 0.48 0.50 0.51 0.49 0.52 0.58
FF+MP -0.43 -0.16 -0.07 -0.03 0.07 0.11 0.19 0.18 0.20 0.23 0.18 0.20 0.26
CRR4 -0.24 0.02 0.10 0.10 0.2 0.23 0.31 0.31 0.33 0.34 0.31 0.33 0.39
CRR5 0.10 0.29 0.36 0.33 0.43 0.43 0.46 0.47 0.52 0.54 0.52 0.51 0.60
Panel B: Non-January
Winner 0 1 2 3 4 5 6 7 8 9 10 11 12
MP 0.82 0.83 0.87 0.90 0.91 0.86 0.86 0.82 0.76 0.7 0.66 0.65 0.67
FF+MP 0.35 0.32 0.34 0.39 0.41 0.38 0.38 0.35 0.29 0.23 0.17 0.17 0.21
CRR4 0.69 0.69 0.73 0.77 0.79 0.74 0.73 0.7 0.64 0.58 0.54 0.54 0.56
CRR5 0.73 0.76 0.80 0.86 0.84 0.81 0.84 0.83 0.77 0.74 0.7 0.67 0.69
Loser 0 1 2 3 4 5 6 7 8 9 10 11 12
MP 0.55 0.74 0.82 0.85 0.90 0.90 0.92 0.93 0.88 0.88 0.80 0.84 0.95
FF+MP -0.03 0.16 0.24 0.29 0.32 0.34 0.37 0.36 0.33 0.34 0.24 0.27 0.39
CRR4 0.39 0.58 0.65 0.65 0.71 0.72 0.76 0.76 0.72 0.72 0.64 0.67 0.78
CRR5 0.73 0.85 0.90 0.88 0.95 0.92 0.92 0.91 0.88 0.87 0.81 0.82 0.95
49
Figure 4
The profitability of momentum strategies with respect to the Chen, Roll and Ross five-factor model
This table reports the value-weighted monthly returns to a total return momentum strategy (star ) as well as two alternative momentum strategies—
the factor-related return momentum strategy (solid line) and the stock-specific return momentum strategy(broken line). Each momentum strategy
assigns winners and losers as the top and bottom deciles of stocks by a ranking criterion. The ranking period is six months and the holding period
is six months, with one-month gap between ranking and holding. The factor-related return momentum strategy ranks stocks according to an
estimate of the factor component of their ranking period returns. The stock-specific return momentum strategy ranks stocks according to an
estimate of their component of their ranking period returns that is unrelated to macroeconomic risk factors. o distinguish the factor-related and
stock-specific components of their ranking period returns, We estimate the parameters of the Chen, Roll and Ross five-factor model for all of
NYSE, Amex and Nasdaq stocks i with minimum 36-month returns on the CRSP tapes, month t - 37 to t – 2: for max [t – 61], …, t – 2,
where the dummy of Dis equal to 1 if month is one of six ranking months; otherwise Dis equal to 0.
The stock-specific return momentum strategy ranks stocks by estimated i. The factor-related return momentum strategy ranks stocks based
on∑
. The total return momentum strategy and two alternative momentum
strategies are implemented in a comparable sample.
50
-37.18
-15.19
-40
-30
-20
-10
0
10
04/09 01/01 11/02 05/00 03/09 01/08 01/74 04/99 05/09 01/75
Pane A: Worst Monthly Momentum Returns
Overall
Stock-specific Factor-related Total
-37.18
-14.01
-40
-30
-20
-10
0
10
04/09 11/02 05/00 03/09 04/99 05/09 10/02 02/91 09/70 07/73
Panel B: Worst Monthly Momentum Returns
Non-January
Stock-specific Factor-related Total
12.85
35.84
-10
0
10
20
30
40
12/00 11/66 07/74 04/68 11/73 06/08 10/99 12/99 06/00 02/00
Panel C: Best Monthly Momentum Returns
Overall
Stock-specific Factor-related Total
12.85
35.84
-10
0
10
20
30
40
12/00 11/66 07/74 04/68 11/73 06/08 10/99 12/99 06/00 02/00
Panel D: Best Monthly Momentum Returns
Non-January
Stock-specific Factor-related Total