Table IⅡ Momentum Strategies,1/1980-12/1996,Using Raw Returns and Sorting by Size This table includes all stocks.The relative momentum portfolios are formed based on six-month lagged raw returns and held for six months.The stocks are ranked in ascending order on the basis of six-month lagged returns.Portfolio Pl is an equally weighted portfolio of stocks in the worst-performing 30 percent,portfolio P2 includes the middle 40 percent,and portfolio P3 includes the best-performing 30 percent.This table reports the average monthly returns of these portfolios and portfolios formed using size-based subsamples of stocks.Using NYSE/AMEX decile breakpoints,the smallest firms are in size class 1.the next in 2,and the largest are in 10.Mean (median)size is in millions.t-statistics are in parentheses. Size Class (NYSE/AMEX Decile Breakpoints) All Past Stocks 2 3 4 5 6 7 9 10 P1 0.01043 0.02106 0.00653 0.00231 0.00194 0.00469 0.00573 0.00606 0.01010 0.00922 0.01258 (2.44) (4.44) (1.37） (0.52) (0.43) (1.05 (1.32) (1.43) 2.51) (2.25) 3.37) Coverage, P2 0.01378 0.01662 0.01290 0.01280 0.01244 0.01395 0.01374 0.01375 0.01393 0.01401 0.01355 (4.48) (4.97) (3.84) (3.88) (3.75) (4.18) (4.14) (4.27) (4.40) (4.43) (4.50) P3 0.01570 0.01733 0.01507 0.01664 0.01570 0.01655 0.01608 0.01491 0.01436 0.01363 0.01278 (4.35) (4.40) (3.89) (4.35) (4.05】 (4.26) (4.26) (4.13) (4.04) (3.96) (3.84) P3-P1 0.00527 -0.00374 0.00854 0.01433 0.01376 0.01187 0.01035 0.00885 0.00425 0.00441 0.00021 (2.61) (-1.77 (3.60) (6.66) (6.10) (6.32) (4.80) (3.72) (1.90) (1.73) (0.08) P2-P1 0.746 0.732 0.763 0.780 0.774 0.869 0.901 1.086 P3-P1 Profitability Mean size > 21 44 79 138 242 437 806 1658 7290 Median size 7 21 43 78 136 237 430 786 1612 4504 Mean analyst 0.1 0.5 1.1 2.0 3.2 5.0 7.3 10.6 15.3 21.4 Median analyst 0.0 0.0 0.7 1.3 2.5 4.4 6.9 10.5 15.7 22.4
Table III Momentum Strategies, 1/1980–12/1996, Using Raw Returns and Sorting by Size This table includes all stocks. The relative momentum portfolios are formed based on six-month lagged raw returns and held for six months. The stocks are ranked in ascending order on the basis of six-month lagged returns. Portfolio P1 is an equally weighted portfolio of stocks in the worst-performing 30 percent, portfolio P2 includes the middle 40 percent, and portfolio P3 includes the best-performing 30 percent. This table reports the average monthly returns of these portfolios and portfolios formed using size-based subsamples of stocks. Using NYSE0AMEX decile breakpoints, the smallest firms are in size class 1, the next in 2, and the largest are in 10. Mean ~median! size is in millions. t-statistics are in parentheses. Size Class ~NYSE0AMEX Decile Breakpoints! Past All Stocks 1 2 3 4 5 6 7 8 9 10 P1 0.01043 0.02106 0.00653 0.00231 0.00194 0.00469 0.00573 0.00606 0.01010 0.00922 0.01258 ~2.44! ~4.44! ~1.37! ~0.52! ~0.43! ~1.05! ~1.32! ~1.43! ~2.51! ~2.25! ~3.37! P2 0.01378 0.01662 0.01290 0.01280 0.01244 0.01395 0.01374 0.01375 0.01393 0.01401 0.01355 ~4.48! ~4.97! ~3.84! ~3.88! ~3.75! ~4.18! ~4.14! ~4.27! ~4.40! ~4.43! ~4.50! P3 0.01570 0.01733 0.01507 0.01664 0.01570 0.01655 0.01608 0.01491 0.01436 0.01363 0.01278 ~4.35! ~4.40! ~3.89! ~4.35! ~4.05! ~4.26! ~4.26! ~4.13! ~4.04! ~3.96! ~3.84! P3 2 P1 0.00527 20.00374 0.00854 0.01433 0.01376 0.01187 0.01035 0.00885 0.00425 0.00441 0.00021 ~2.61! ~21.77! ~3.60! ~6.66! ~6.10! ~5.32! ~4.80! ~3.72! ~1.90! ~1.73! ~0.08! P22P1 P32P1 — 0.746 0.732 0.763 0.780 0.774 0.869 0.901 1.086 — Mean size 7 21 44 79 138 242 437 806 1658 7290 Median size 7 21 43 78 136 237 430 786 1612 4504 Mean analyst 0.1 0.5 1.1 2.0 3.2 5.0 7.3 10.6 15.3 21.4 Median analyst 0.0 0.0 0.7 1.3 2.5 4.4 6.9 10.5 15.7 22.4 Size, Analyst Coverage, and Profitability 275
276 The Journal of Finance 0.016 0.014 +-P3P1 0.012 0.01 0.006 0.006 0.004 0.002 0 0.002 0.004 0.006 1 2 3 4 5 6 7 8 9 10 NYSE AMEX-based Size Deciles Figure 1.Momentum profits and firm size.Momentum profits(P3-P1)plotted against NYSE/AMEX-based size deciles,1(smallest)to 10(largest). up chopping the universe of stocks into 120 portfolios,and we would reach a point where some of the individual portfolios are quite undiversified,thereby creating larger standard errors in our test statistics.12 The first column in Table III confirms that there is significant momentum in the full sample:The baseline strategy that buys top-30 percent(P3)win- ners and shorts bottom-30 percent (P1)losers generates 0.53 percent per month (t-statistic =2.61).13 The next columns break the momentum effect down by size(measured six months before the start of the ranking period). We use an independent sort to generate 10 subsamples,with the break- points determined by NYSE/AMEX deciles.Figure 1 illustrates the results, plotting the relationship between size and the magnitude of the momentum effect.As can be seen,there is a pronounced,inverted U-shape.In the very smallest stocks (which are tiny,with a mean market capitalization of $7 million)momentum is actually negative.By the second size decile,momen- 12 In fact,we have redone all our key tests,using the Jegadeesh and Titman(1993)P10-P1 momentum measure in place of our P3-P1 measure.As might be expected,the point estimates of interest-that is,the differences in momentum between low-and high-coverage firms-are typically larger in absolute value.However,the standard errors are also larger,so in many cases the t-statistics turn out to be smaller.This confirms the notion that our P3-P1 measure has better signal-to-noise properties for the particular type of tests we focus on. 13 This is lower than the Jegadeesh-Titman(1993)figure of 0.95 percent per month.The difference arises for two distinct reasons noted above.First,our strategy invests in stocks with less-extreme past performance.And second,it turns out that including the smaller Nasdag firms substantially damps the results since,as can be seen from Table III,the momentum measure is actually negative for the very smallest firms.The different sample period is not responsible for the difference in results because when we use an NYSE/AMEX sample and a P10-P1 momentum measure over our sample period we obtain numbers almost identical to Jegadeesh and Titman
up chopping the universe of stocks into 120 portfolios, and we would reach a point where some of the individual portfolios are quite undiversified, thereby creating larger standard errors in our test statistics.12 The first column in Table III confirms that there is significant momentum in the full sample: The baseline strategy that buys top-30 percent ~P3! winners and shorts bottom-30 percent ~P1! losers generates 0.53 percent per month ~t-statistic 5 2.61!. 13 The next columns break the momentum effect down by size ~measured six months before the start of the ranking period!. We use an independent sort to generate 10 subsamples, with the breakpoints determined by NYSE0AMEX deciles. Figure 1 illustrates the results, plotting the relationship between size and the magnitude of the momentum effect. As can be seen, there is a pronounced, inverted U-shape. In the very smallest stocks ~which are tiny, with a mean market capitalization of $7 million! momentum is actually negative. By the second size decile, momen- 12 In fact, we have redone all our key tests, using the Jegadeesh and Titman ~1993! P10 2 P1 momentum measure in place of our P3 2 P1 measure. As might be expected, the point estimates of interest—that is, the differences in momentum between low- and high-coverage firms—are typically larger in absolute value. However, the standard errors are also larger, so in many cases the t-statistics turn out to be smaller. This confirms the notion that our P3 2 P1 measure has better signal-to-noise properties for the particular type of tests we focus on. 13 This is lower than the Jegadeesh–Titman ~1993! figure of 0.95 percent per month. The difference arises for two distinct reasons noted above. First, our strategy invests in stocks with less-extreme past performance. And second, it turns out that including the smaller Nasdaq firms substantially damps the results since, as can be seen from Table III, the momentum measure is actually negative for the very smallest firms. The different sample period is not responsible for the difference in results because when we use an NYSE0AMEX sample and a P10 2 P1 momentum measure over our sample period we obtain numbers almost identical to Jegadeesh and Titman. Figure 1. Momentum profits and firm size. Momentum profits ~P3 2 P1! plotted against NYSE0AMEX-based size deciles, 1 ~smallest! to 10 ~largest!. 276 The Journal of Finance