Two-Way Cuts on Size and Residual Coverage
In Table 5, we disaggregate the analysis of Table 4 by size. The methodology is exactly the same except we look at four separate subsamples. The first includes all stocks between the 20th and 40th NYSE/AMEX percentiles, the second includes those between the 40th and 60th percentiles, and so forth. We have two motivations for doing this disaggregation. First, as a matter of economics, it seems reasonable to conjecture that the marginal importance of coverage will be greater in the smaller stocks, which have fewer analysts on average, and are probably less well-researched in other ways. Second, as a matter of methodology, this approach should give us better size matches across residual coverage classes, since we now will be running the analyst coverage regressions separately for each size-based subsample. Compared to our earlier approach, this is like allowing the analyst-size relationship to be piecewise linear.
|Residual Coverage||1:20,h-40lh Percentile||2: 40*h-60th Percentile||3: 60,h-80,h Percentile||4: 80,и-100№ Percentile|
|P3-P1=.01511 (6.46)||P3-P1=.01057 (4.49)||P3-P1=.00605 (3.11)||P3-P1 = 00092 (0.49)|
|Low:Sub1||Mean Size=63||Mean Size=199||Mean Size=653||Mean Size=5056|
|Median Size=59||Median Size-183||Median Size=592||Median Size=2363|
|Median Coverage=0.0||Median Coverage=0.6||Median Coverage=3.7||Median Coverages 1.1|
|P3-P1 =0.01389 (5.48)||P3-P1 =0.00975 (4.95)||P3-P1 =0.00316 (1.62)||P3-P1 =0.00009 (0.05)|
|Medium:Sub2||Mean Size=61||Mean Size=207||Mean Size=678||Mean Size=5163|
|Median Size=56||Median Size=193||Median Size=629||Median Size=2853|
|Median Coverage=0.9||Median Coverage=3.6||Median Coverage=9.0||Median Coverage=18.8|
|P3-P1=0.01147 (5.10)||P3-P1 =0.00730 (3.60)||P3-P1 =0.00424 (2.02)||P3-P1 =0.00070 (0.33)|
|High:Sub3||Mean Size=64||Mean Size=202||Mean Size=663||Mean Size=3650|
|Median Size=61||Median Size=188||Median Size=615||Median Size=2511|
|Median Coverage=3.1||Median Coverage=7.6||Median Coverage=14.7||Median Coverage=24.9|
|Sub1-Sub3||P3-P1 =0.00364 (2.13)||P3-P1=0.00327 (1.95)||P3-P1 =0.00180 (1.18)||P3-P1 =0.00023 (.14)|
As can be seen from the table, the size matching is now almost flawless, except for in the largest class of stocks. Consider first the results for the smallest size class, that corresponding to the 20th-40th percentile range. The mean size is $63 million in SUB1, vs. $64 million in SUB3. (The medians are $59 and $61 million respectively.) Yet we still have a good spread in coverage, with a mean of 0.0 analysts in SUB1 and 3.7 analysts in SUB3. And the basic results from Table 4 carry over. The P3-P1 momentum measure is 1.51% per month in SUB1, and 1.15% per month in SUB3. The difference of 0.36% is statistically significant, (t-stat of 2.13) even though the standard errors are quite a bit higher with the smaller sample.
As we move to progressively larger size classes, two things happen. First, the overall momentum effect shrinks, just as in Table 3. Second, the differential in momentum between SUB1 and SUB3 shrinks also, consistent with the hypothesis that the marginal importance of analysts should decline with size. In the next size class, covering the 40th-60th percentile range —in which stocks average around $200 million in market capitalization–the SUB3-SUB1 momentum differential is not much smaller, at 0.33% (t = 1.95). But by the time we get to the 60th-80th percentile range—with mean size of close to $700 million—the differential is down to 0.18% (t = 1.18). And it is essentially zero for the largest size class.