Momentum Profits and Macroeconomic Risk 1

Transcription

1 Momentum Profits and Macroeconomic Risk 1 Susan Ji 2, 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 25 th 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 sji@govst.edu; Tel: J. Spencer Martin, Professor of Finance, Faculty of Business and Economics, University of Melbourne, Level 12, 198 Berkeley Street, Parkville, Victoria 3010, Australia. martis@unimelb.edu.au; Tel: Yaqiong (Chelsea) Yao, Assistant Professor of Finance, Department of Accounting and Finance, Lancaster University Management School, Lancaster LA1 4YX, United Kingdom. yaqiong.yao@lancaster.ac.uk; Tel:

2 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 1

3 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 2

4 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 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. 3

5 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 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). 4

6 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 period, the strategy produces the equal-weighted monthly return of 1.72% and the valueweighted 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 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). 5

7 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. 6

8 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 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 timeseries 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 7

9 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, 8

10 when losers massively outperform winners. This raises some doubt that MP is the main driving force for the momentum phenomenon 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 calendarbased 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 timeseries factor regressions for each of the event months during the twenty-four-month event-window period 9

11 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. 10

12 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 riskpremium 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 crosssectional 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 11

13 analysis thus suggests that macroeconomic risk cannot be the source of momentum profits. Finally, Section 4.3. demonstrates the robustness of our conclusion Estimating Macroeconomic Risk Premium We estimate the macroeconomic risk premiums by using the two-stage Fama MacBeth (1973) crosssectional 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 t 0 (where t 0 is the first observation and x ranges from the 24 th 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 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. 12

14 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/ /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 13

15 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 % 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 riskpremium 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 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 14

16 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 onefactor 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 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 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 15

17 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. [ ] [ ] 16

18 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 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 17

19 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 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 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. 18

20 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 (tstatistic=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 equalweighted 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 (tstatistic=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 valueweighted 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 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. 19

21 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) 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 20

22 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. 21