The liquidity risk factor (LIQ) is worked out separately for the 192701-196306 period and the period from 196307 onwards. For the period 192701-196306, the sample contains NYSE ordinary common stocks only. From 196307 onwards, the sample contains all NYSE/Amex/Nasdaq/Arca ordinary common stocks. Basically, LIQ is constructed as the long-short monthly profits over a 6-month holding period from buying $1 of an equally-weighted low-liquidity portfolio (LL) and selling $1 of an equally-weighted high-liquidity portfolio (HL).
------
For the 192701-196306 period, the NYSE sample is divided into TWO groups:
Group 1: (named as 'complete-volume sample') includes stocks that have daily trading volumes available without any missing over the 12-month period prior to portfolio formation;
Group 2: (named as 'incomplete-volume sample') contains stocks that have at least one MISSING daily trading volume in the 12-month period prior to portfolio formation and that have at least 80% of NON-MISSING daily trading volumes available in the 12-month period prior to portfolioformation.
LL is formed by 30% of the least-liquid stocks from Group 1 (i.e., 30% of the highest-LM12 stocks identified within Group 1) plus 30% of the least-liquid stocks from Group 2 (i.e., 30% of the highest-LM12 stocks identified within
Group 2).
HL is formed by choosing stocks from Group 1 only. Specifically, HL contains 35% of the most-liquid stocks (i.e., 35% of the lowest-LM12 stocks) from Group 1.
------
For the period from 196307 onwards, the construction of LL and HL requires that daily trading volumes must be available without any missing during the 12 months prior to portfolio formation. The LL and HL are formed by sorting LM12 using
NYSE and NASDAQ stocks, respectively.
(1) NYSE stocks are sorted in ascending order at the end of each month from 196306 to 201406 based on their liquidity measures (i.e., LM12, the standardized turnover-adjusted number of zero daily trading volumes over the prior 12 months).
(2) Separately, NASDAQ stocks are sorted in ascending order at the end of each month based on their LM12 measures. Based on the two separate sorts, two portfolios are formed at the end of each month. One is the low-liquidity (i.e., high-LM12) portfolio (LL), the other one is the high-liquidity (i.e., low-LM12) portfolio (HL).
LL contains lowest-liquid NYSE/Amex/Arca stocks based on a 15% NYSE breakpoint, plus 35% lowest-liquid NASDAQ stocks identified with NASDAQ stocks.
HL contains highest-liquid NYSE/Amex/Arca stocks using a 35% NYSE breakpoint, plus 15% highest-liquid NASDAQ stocks identified with NASDAQ stocks.
------
The two portfolios (LL and HL) are held for 6 months after portfolio formation.
Monthly portfolio returns of LL and HL over the six-month holding interval are worked out based on Equation (3) of Liu and Strong (2008, Review of Financial
Studies 21, No. 5, 2243-2274).
The mimicking liquidity risk factor (LIQ) is constructed as the monthly profits of buying one dollar of LL and selling one dollar of HL. The long-short profits
(i.e., the profits of longing LL and shorting HL) over the six-month holding period are calculated using Equation (11) of Liu and Strong (2008).
------
Note that this construction is based on the overlapping ranking period as well as overlapping holding period (on the monthly basis). However, the monthly values of the liquidity factor (and the monthly returns of LL and HL) over the whole sample period are worked out using Jegadeesh and Titman's (Journal of Finance 45, 1993, 65--91) technique, so that the monthly series of LIQ over the full sample period are non-overlapping. Suppose we start to form LL and HL at the end of December 2014. Then, the LIQ value for 6/2015 is the average of the six 6/2015 long-short profits, which are related to portfolios formed at the end of 12/2014, 1/2015. 2/2015, 3/2015, 4/2015, and 5/2015.
------
Also, when constructing the liquidity factor (LIQ), stocks must have one monthly CRSP return data available prior to portfolio formation plus one CRSP monthly return available in the first holding-period month. The requirement on the one return after portfolio formation ensures that each stock can be held for at least a day in the 6-month holding period. If a stock is delisted during a holding period, its post-delisting returns over the remaining holding-period months are set to zero.
------
Note:
NYSE Amex Equities (i.e., former AMEX) stocks are included from July 1963 onwards since daily trading volume data for AMEX stocks are only available from the beginning of July 1962.
NYSE Arca stocks are included from April 2007 onwards because daily trading volume data for Arca stocks are only available from March 8, 2006.
NASDAQ stocks are included from November 1983 onwards because daily trading volume data for NASDAQ stocks become commonly available only from the beginning of November 1982.
------
YEARMM LIQ
192701 0.00203401
192702 -0.03280870
192703 0.03522482
192704 0.00899847
192705 0.01970237
192706 0.03481247
192707 -0.01543169
192708 0.01886347
192709 -0.02962923
192710 0.03720860
192711 0.00692619
192712 -0.01040344
192801 0.08436421
192802 0.01216712
192803 -0.05489536
192804 0.08425047
192805 0.06449042
192806 -0.00832166
192807 -0.02051012
192808 -0.06090072
192809 -0.00495107
192810 0.00745068
192811 -0.05174776
192812 -0.02430999
192901 -0.02190305
192902 0.00734869
192903 -0.00590179
192904 0.00936887
192905 0.00893490
192906 -0.03837176
192907 0.00550304
192908 -0.02492042
192909 0.03947032
192910 0.07102975
192911 0.01598054
192912 -0.00946172
193001 0.00929766
193002 0.01085281
193003 -0.02305528
193004 -0.02996528
193005 -0.00235046
193006 0.08429222
193007 -0.05119319
193008 0.00425676
193009 0.06741871
193010 0.04709265
193011 -0.02560113
193012 -0.02689376
193101 0.01822645
193102 -0.06320344
193103 0.04756174
193104 -0.00362399
193105 0.05754264
193106 -0.07585973
193107 0.03553074
193108 -0.06293112
193109 0.11592952
193110 -0.07613568
193111 0.03033486
193112 -0.02224268
193201 0.02999769
193202 -0.06384937
193203 0.05172522
193204 0.05368405
193205 0.08758824
193206 -0.04134708
193207 -0.10987628
193208 0.17884086
193209 -0.12930812
193210 0.03003259
193211 -0.02530721
193212 -0.15019599
193301 -0.00639965
193302 0.07516796
193303 0.02463656
193304 -0.06652340
193305 0.64671621
193306 0.29977133
193307 -0.00930488
193308 -0.14823709
193309 -0.06648123
193310 0.00042035
193311 -0.07977327
193312 -0.00123942
193401 0.17037085
193402 0.10598462
193403 0.00754436
193404 0.09066188
193405 -0.05469494
193406 -0.02163155
193407 -0.02472234
193408 -0.00555595
193409 -0.01384427
193410 0.01640939
193411 0.02413594
193412 -0.01322613
193501 0.04097271
193502 0.00728741
193503 -0.01436363
193504 -0.00862289
193505 -0.00253644
193506 -0.06435885
193507 -0.01728211
193508 0.02841490
193509 -0.00769629
193510 -0.04189651
193511 0.14643758
193512 -0.03556378
193601 0.16094633
193602 0.03535420
193603 -0.02083461
193604 -0.01565922
193605 -0.01423167
193606 -0.01590294
193607 -0.00261424
193608 0.00279522
193609 0.03923196
193610 0.01197048
193611 0.06225063
193612 -0.01373912
193701 -0.00134130
193702 0.00241322
193703 -0.00831282
193704 -0.00984242
193705 0.00554838
193706 -0.01371367
193707 -0.04100865
193708 0.02633614
193709 0.00936419
193710 0.00748111
193711 -0.00745095
193712 0.00857181
193801 0.01976066
193802 -0.03268906
193803 0.06120919
193804 -0.03664237
193805 0.01570453
193806 -0.07603333
193807 -0.00857262
193808 -0.02502827
193809 -0.04123293
193810 -0.03250931
193811 -0.00367828
193812 -0.06914563
193901 0.04889655
193902 -0.00851195
193903 0.08830986
193904 -0.01025331
193905 -0.01522965
193906 0.04326895
193907 -0.05389718
193908 0.02909994
193909 0.10904874
193910 -0.01759028
193911 -0.01634552
193912 -0.03696194
194001 0.01866365
194002 0.02022128
194003 0.00390700
194004 0.01495710
194005 0.00144869
194006 -0.01924334
194007 0.00227799
194008 -0.01315334
194009 0.00719009
194010 -0.03287273
194011 0.03139986
194012 -0.02975626
194101 0.07648185
194102 -0.00248993
194103 0.01797008
194104 0.02727687
194105 -0.02538935
194106 0.00113970
194107 0.02247837
194108 -0.00385564
194109 0.01151966
194110 0.02224401
194111 -0.00601190
194112 -0.02482262
194201 0.06752397
194202 0.00602395
194203 0.01271776
194204 0.00601820
194205 -0.01381076
194206 0.01231446
194207 -0.00360781
194208 0.01228718
194209 0.02163837
194210 -0.03177217
194211 0.01345812
194212 -0.04900335
194301 0.04522127
194302 0.02625711
194303 0.00894605
194304 0.02659033
194305 0.00054481
194306 0.01094662
194307 0.04785372
194308 -0.03291025
194309 0.01445549
194310 0.01247397
194311 0.02920123
194312 -0.01924611
194401 0.01420233
194402 0.00115251
194403 -0.00455712
194404 0.01202954
194405 -0.00640884
194406 -0.02421025
194407 0.02462240
194408 -0.00843318
194409 -0.00425459
194410 0.02219366
194411 0.00640434
194412 -0.02519635
194501 -0.00686179
194502 -0.00483159
194503 0.01739233
194504 -0.04525939
194505 0.01283309
194506 -0.03221272
194507 0.01914018
194508 -0.00776699
194509 0.00154442
194510 0.02402838
194511 0.00127285
194512 0.01078688
194601 -0.02904130
194602 0.02274356
194603 0.03776313
194604 0.05569138
194605 -0.00339258
194606 0.00450590
194607 0.00777273
194608 0.01417100
194609 0.01329538
194610 0.00006775
194611 0.02540211
194612 0.00522317
194701 -0.00411798
194702 0.00559541
194703 0.00484926
194704 0.00087599
194705 0.00028285
194706 0.00779025
194707 -0.00286699
194708 0.00458181
194709 0.00455986
194710 0.01337084
194711 0.01855437
194712 -0.02186733
194801 0.00320089
194802 0.01055627
194803 -0.04072465
194804 -0.00189967
194805 -0.01913162
194806 -0.01117049
194807 0.01523141
194808 0.00049064
194809 0.01066431
194810 -0.01507040
194811 0.04256522
194812 -0.03180745
194901 0.01618416
194902 -0.00088811
194903 -0.01063090
194904 0.01457789
194905 0.01455652
194906 -0.00882228
194907 -0.00488952
194908 0.00460957
194909 -0.01364086
194910 0.01107465
194911 -0.00165313
194912 -0.00483054
195001 -0.00699740
195002 0.01002489
195003 -0.00733156
195004 -0.04697752
195005 0.01658882
195006 0.01200203
195007 -0.01036227
195008 0.02676579
195009 -0.01004209
195010 0.01804569
195011 -0.00774606
195012 -0.01450939
195101 0.00006479
195102 0.00709169
195103 0.00135293
195104 -0.01690364
195105 0.01536208
195106 0.02128124
195107 -0.03412117
195108 -0.01130345
195109 -0.01684419
195110 0.01104516
195111 -0.01045633
195112 -0.01398779
195201 -0.00013286
195202 0.00886770
195203 -0.02260884
195204 0.01668649
195205 -0.00740557
195206 -0.01531133
195207 0.00402564
195208 0.01220919
195209 0.01255424
195210 -0.00396265
195211 -0.02131655
195212 -0.01396778
195301 0.01845469
195302 0.00886314
195303 0.01218213
195304 0.00539888
195305 0.00323144
195306 0.00298410
195307 -0.00182933
195308 0.02170226
195309 -0.01268518
195310 -0.02030590
195311 -0.01112401
195312 -0.00001978
195401 -0.00758929
195402 -0.00447746
195403 -0.01912048
195404 0.00102723
195405 -0.01092396
195406 0.00661684
195407 -0.00184889
195408 0.01881662
195409 -0.01284443
195410 0.00978344
195411 -0.03375472
195412 -0.00960732
195501 0.00689079
195502 -0.00245324
195503 0.00415382
195504 0.00842589
195505 0.00108857
195506 -0.00678207
195507 0.01538013
195508 -0.00816500
195509 0.01603570
195510 0.00681449
195511 -0.02328002
195512 -0.01244759
195601 0.01544180
195602 -0.00634710
195603 -0.00356178
195604 0.00296406
195605 0.02023443
195606 -0.00885856
195607 -0.01415907
195608 0.00713134
195609 0.01375655
195610 0.00817043
195611 -0.00531038
195612 -0.01528625
195701 0.02132499
195702 0.00926596
195703 -0.00392177
195704 -0.00056737
195705 -0.01379212
195706 0.01669852
195707 0.00583041
195708 0.02227609
195709 0.02179630
195710 0.00354285
195711 -0.01566062
195712 0.02092120
195801 -0.00545966
195802 0.00827942
195803 -0.00552939
195804 0.00183785
195805 -0.01297258
195806 -0.00386321
195807 -0.01041849
195808 -0.00564642
195809 -0.01126385
195810 -0.01011507
195811 -0.00273302
195812 -0.00981270
195901 0.02800397
195902 0.00260157
195903 0.00608188
195904 -0.00391483
195905 -0.00214837
195906 -0.00663610
195907 0.00755793
195908 0.02839245
195909 0.02173520
195910 -0.01348453
195911 -0.01838056
195912 -0.00097546
196001 0.03214253
196002 -0.01795201
196003 0.03023172
196004 0.01451226
196005 -0.02960063
196006 0.01266462
196007 0.01827692
196008 0.00244132
196009 0.01997153
196010 0.02289776
196011 -0.02177640
196012 -0.01249980
196101 -0.01340973
196102 -0.01721950
196103 0.00373550
196104 0.00702339
196105 -0.01564161
196106 0.02074023
196107 -0.01201384
196108 0.00831718
196109 0.03443147
196110 0.02198790
196111 -0.00172845
196112 -0.01364788
196201 0.01154230
196202 0.01395034
196203 0.02247238
196204 0.03540642
196205 0.00336480
196206 0.01847463
196207 -0.02016864
196208 -0.01226565
196209 0.03681271
196210 0.00833626
196211 -0.03866756
196212 0.02731469
196301 -0.01095963
196302 0.02566669
196303 0.00317048
196304 -0.01238481
196305 -0.01301440
196306 0.00832303
196307 0.01473607
196308 -0.03994459
196309 0.04667317
196310 -0.02170764
196311 -0.00883336
196312 -0.00813793
196401 0.02710131
196402 -0.01455365
196403 -0.01567507
196404 0.02474495
196405 -0.00549962
196406 -0.01158907
196407 0.01631884
196408 0.01300309
196409 -0.01432017
196410 -0.00104992
196411 0.01624052
196412 -0.00889120
196501 0.00012827
196502 -0.00191963
196503 0.01240289
196504 0.00613876
196505 0.00666068
196506 0.01409396
196507 -0.01140159
196508 -0.03194015
196509 -0.02413049
196510 -0.00786668
196511 0.00155070
196512 -0.00616368
196601 0.02074936
196602 0.00230508
196603 0.02867244
196604 -0.00493719
196605 0.01723247
196606 -0.02039877
196607 0.00381145
196608 -0.00019560
196609 0.00892196
196610 0.01564706
196611 -0.06226182
196612 0.00706190
196701 -0.04997756
196702 0.02178974
196703 -0.01096972
196704 0.00776912
196705 0.03612010
196706 -0.01044591
196707 0.01281710
196708 0.02554407
196709 0.04651888
196710 0.03003953
196711 -0.01143451
196712 -0.00492277
196801 0.08600094
196802 0.02644799
196803 -0.00341204
196804 -0.00827154
196805 0.02172314
196806 0.04649578
196807 0.03941339
196808 0.01359971
196809 -0.00363301
196810 0.04714716
196811 -0.01511494
196812 0.00164230
196901 -0.00021592
196902 0.04090991
196903 -0.00974373
196904 -0.00305647
196905 0.01301146
196906 0.04082846
196907 0.02289629
196908 -0.01879983
196909 0.02182979
196910 -0.02921537
196911 0.02541600
196912 0.02226186
197001 0.04486949
197002 -0.01524678
197003 0.02696100
197004 0.05341897
197005 -0.01385999
197006 0.04566626
197007 -0.01404138
197008 -0.03088341
197009 -0.03270149
197010 0.04832740
197011 -0.03524774
197012 0.02383942
197101 0.04456287
197102 0.04260448
197103 -0.00422938
197104 -0.01985370
197105 0.01350928
197106 -0.01434068
197107 0.03263949
197108 -0.01973538
197109 0.01509238
197110 0.01968679
197111 -0.01540617
197112 -0.01662847
197201 0.01565313
197202 0.01941319
197203 0.00876918
197204 0.00712687
197205 -0.00517760
197206 0.01473293
197207 0.02602832
197208 -0.01055751
197209 0.00901805
197210 -0.00043095
197211 -0.02842768
197212 0.01400409
197301 0.06243130
197302 0.02917829
197303 0.00282141
197304 0.03293496
197305 -0.00037141
197306 0.00479729
197307 -0.03086968
197308 -0.00905262
197309 -0.05839690
197310 0.03314184
197311 0.01814051
197312 -0.04804355
197401 0.03864784
197402 -0.00613216
197403 0.04833781
197404 0.00938389
197405 0.00998498
197406 0.01380524
197407 0.00646630
197408 0.00288720
197409 0.03252353
197410 -0.06926305
197411 -0.03035710
197412 -0.03215134
197501 0.04172844
197502 -0.02165385
197503 0.01361739
197504 -0.03931314
197505 -0.00735858
197506 -0.00227638
197507 0.09349683
197508 -0.02521868
197509 0.01834376
197510 -0.02260036
197511 0.00855440
197512 -0.02333313
197601 0.03439956
197602 0.11753979
197603 -0.02504342
197604 0.00473868
197605 -0.02604817
197606 -0.05289797
197607 0.02279904
197608 0.01369456
197609 -0.00679142
197610 0.00979369
197611 -0.01869532
197612 0.00978887
197701 0.05220591
197702 0.01855872
197703 0.00091539
197704 -0.00294027
197705 0.01451966
197706 -0.01383709
197707 0.02539367
197708 0.00509674
197709 -0.00326095
197710 0.01549137
197711 -0.00604893
197712 0.00331677
197801 0.03932865
197802 0.01848335
197803 0.00785251
197804 -0.00218071
197805 0.01481952
197806 0.02324381
197807 -0.03337979
197808 0.03665691
197809 0.01762238
197810 0.00153800
197811 -0.01696126
197812 -0.02154106
197901 0.01914471
197902 0.01548481
197903 -0.03027318
197904 0.01301208
197905 0.01410296
197906 -0.01456733
197907 -0.01575600
197908 -0.01303934
197909 0.00344179
197910 0.00775167
197911 -0.04412427
197912 -0.01655706
198001 0.00844968
198002 -0.01886884
198003 0.02344036
198004 0.00424714
198005 -0.01196781
198006 0.00688358
198007 -0.03466613
198008 0.00376013
198009 -0.00508602
198010 0.00677840
198011 -0.08954294
198012 0.01372005
198101 0.07644088
198102 0.00800322
198103 0.00107800
198104 0.03595008
198105 -0.00370837
198106 0.06629466
198107 -0.00467745
198108 0.02009487
198109 0.01481578
198110 -0.02562508
198111 0.01725553
198112 0.01015108
198201 0.01715269
198202 0.02911781
198203 0.02174458
198204 -0.01164730
198205 0.03180230
198206 0.01240305
198207 0.01880478
198208 -0.04615991
198209 0.02571905
198210 -0.04242945
198211 0.03350626
198212 0.01676339
198301 0.03592863
198302 0.03933522
198303 0.04672111
198304 0.03530178
198305 0.04565022
198306 -0.01252337
198307 0.04778671
198308 -0.02325792
198309 0.01149337
198310 0.02853982
198311 -0.00604727
198312 0.03044389
198401 0.04844220
198402 0.02653395
198403 0.01256730
198404 0.01190273
198405 0.04876479
198406 -0.01324075
198407 0.03594085
198408 -0.06786157
198409 0.03277856
198410 0.01149109
198411 0.01740001
198412 -0.01413829
198501 -0.05811366
198502 0.03133442
198503 0.02795141
198504 0.01446466
198505 -0.02769374
198506 -0.00091616
198507 0.00563538
198508 0.01345047
198509 0.03531390
198510 -0.02585702
198511 -0.02657587
198512 -0.01256502
198601 0.01108893
198602 -0.02298134
198603 -0.00347520
198604 0.01969260
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