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Introduction

In this article, we present a mechanical trading system that is a generalization of a dual moving average cross over system with a fixed time period for exits.

Array Of Dual Moving Averages

In canonical dual moving average (DMA) systems, a long entry signal occurs when a small moving average (MA) goes from less than to greater than a large moving average. When the opposite occurs, this indicates going flat (from an existing long trade) or going short. While there are other types of exits that are frequently used, the cross over event is the entry signal.

In our system, we generalized this concept with a small MA and multiple large MAs. If the small MA is above one of the large MAs it is assigned the letter A, if it is below or equal it is assigned the letter B. These letters are then merged into a word, in which the length is equal to the number of large moving averages.

Specifically, we use 10 days as the small MA. We use two different large moving average arrays: 63, 126, 189, 252 days (4 trading quarters) and 21, 42, …, 252 days (12 trading months). The first yields an array of length 4 and is merged to become a word of the same length (i.e. ABBA). There are 2**4 = 16 possible words. The second yields an array of length 12 and is merged to become a word of the same length. There are 2**12 = 4096 possible words.

We define any cross over as an event in which the word at the end of the current day is different than that of the previous day.

Fixed Time Period For Exits

In DMA systems, a cross over event can also indicate an exit. For long-short systems, the trade direction is reversed. For long only systems, the cross over results in exiting the trade. Of course there are many other exit criteria used. Here, we use a simple time exit of 21, 42, or 63 days, representing 1, 2, and 3 trading months.

Particulars Of The Backtest

• The trade period is from 2000 to 2021 (the last data date is 20210908).
• We only use stocks.
• Only long trades are permitted.
• Trade initiation is determined at the end of the trading day, as described above, and new positions occur at the open price of the following day.
• Exits occur at the close price.
• A minimum average volume filter, that is a function of the data year, is applied to remove thinly traded stocks.

Results

All results are contained in csv files and can be downloaded here: DMA Array Time Exits Results

Below are the summary results for all years. For the 4 quarters MAs, all possible results are included. While for the 12 months MAs, only those that passed the minimum average volume filter are included.

DMA 4 Quarters All Years

dma word 4 quartersEntry Exit TypeAnnualized Expectancy50 Pctl % ReturnTradesWinsLossesWin %Median WinMedian LossExpectancyMedian Win - abs(Median Loss)
bbba4_quarters_entry_21_day_exit13.9231.48331435179821345357.2046.103-5.4461.1600.657
baab4_quarters_entry_21_day_exit12.5081.25083374586375155.0087.388-6.7161.0420.672
baab4_quarters_entry_63_day_exit12.0033.40383374822351557.83914.128-12.2643.0011.864
baab4_quarters_entry_42_day_exit11.9282.45383374698363956.35111.321-10.0611.9881.260
abab4_quarters_entry_42_day_exit11.6552.34924911407108456.48310.233-8.8191.9431.415
baaa4_quarters_entry_21_day_exit11.4741.22962246350412720556.2945.763-5.2350.9560.528
baba4_quarters_entry_21_day_exit11.3111.41629011634126756.3255.953-5.5190.9430.434
abab4_quarters_entry_63_day_exit11.3003.33324911417107456.88513.863-11.7372.8252.125
bbaa4_quarters_entry_21_day_exit11.1501.26340525226931783255.9985.942-5.4500.9290.492
baba4_quarters_entry_42_day_exit10.9802.06329011652124956.9469.158-7.8621.8301.296
bbba4_quarters_entry_63_day_exit10.9753.41531435186401279559.29711.058-9.3682.7441.690
bbba4_quarters_entry_42_day_exit10.8682.33031435182601317558.0888.711-7.7521.8110.959
babb4_quarters_entry_63_day_exit10.7303.313125837219536457.37113.873-12.3772.6821.495
abaa4_quarters_entry_42_day_exit10.6962.313158919284660758.4238.151-7.1661.7830.985
bbaa4_quarters_entry_63_day_exit10.5063.09740525237871673858.69710.950-9.2022.6261.748
babb4_quarters_entry_42_day_exit10.4451.964125836944563955.18611.120-9.8091.7411.311
bbbb4_quarters_entry_63_day_exit10.3513.45151447297542169357.83413.088-11.8142.5881.274
abaa4_quarters_entry_63_day_exit10.2543.239158919396649559.12810.526-8.9562.5631.570
abaa4_quarters_entry_21_day_exit10.2031.158158918879701255.8745.531-5.0760.8500.454
bbaa4_quarters_entry_42_day_exit9.9962.00540525230981742756.9978.592-7.5131.6661.078
baaa4_quarters_entry_42_day_exit9.9312.06862246356792656757.3198.414-7.4211.6550.992
aaaa4_quarters_entry_42_day_exit9.8042.06065627377192790857.4758.222-7.2701.6340.952
aaaa4_quarters_entry_63_day_exit9.7923.14765627386432698458.88310.491-9.0702.4481.421
baaa4_quarters_entry_63_day_exit9.7512.92262246363462590058.39110.647-9.0822.4381.565
abba4_quarters_entry_42_day_exit9.5792.057109206327459357.9407.891-7.0741.5970.817
baba4_quarters_entry_63_day_exit9.5533.49929011711119058.98011.525-10.7492.3880.776
abba4_quarters_entry_21_day_exit9.5481.162109206122479856.0625.480-5.1820.7960.299
aaab4_quarters_entry_63_day_exit9.4993.3162347013504996657.53712.916-11.9092.3751.007
bbbb4_quarters_entry_21_day_exit9.4701.07851447279932345454.4117.081-6.7200.7890.361
abbb4_quarters_entry_21_day_exit9.2371.03142772232321954054.3167.116-6.7750.7700.340
abba4_quarters_entry_63_day_exit9.1582.900109206387453358.48910.315-9.0192.2891.296
bbbb4_quarters_entry_42_day_exit9.0252.13151447287422270555.86710.266-9.5881.5040.679
aaaa4_quarters_entry_21_day_exit8.9111.07665627364882913955.5995.443-5.1440.7430.300
aaba4_quarters_entry_42_day_exit8.8391.86780064553345356.8707.987-7.1161.4730.871
abab4_quarters_entry_21_day_exit8.8070.84024911359113254.5566.520-6.2130.7340.307
aaab4_quarters_entry_42_day_exit8.6442.07623470130911037955.77810.000-9.3551.4410.645
aaab4_quarters_entry_21_day_exit8.3431.10023470128511061954.7556.588-6.4360.6950.152
aabb4_quarters_entry_63_day_exit8.1302.83429201165551264656.69312.673-11.8982.0320.776
aaba4_quarters_entry_63_day_exit8.1142.89280064673333358.36910.126-9.3252.0280.801
abbb4_quarters_entry_63_day_exit8.0732.86442772241461862656.45312.778-11.9302.0180.848
abbb4_quarters_entry_42_day_exit7.7791.76842772235141925854.97510.216-9.5941.2960.622
babb4_quarters_entry_21_day_exit7.6230.809125836687589653.1437.276-6.8970.6350.380
aabb4_quarters_entry_21_day_exit7.4670.98529201158421335954.2526.684-6.5660.6220.118
aabb4_quarters_entry_42_day_exit7.3641.91029201161931300855.4549.910-9.5821.2270.329
aaba4_quarters_entry_21_day_exit6.4580.87580064405360155.0215.127-5.0750.5380.052
bbab4_quarters_entry_63_day_exit6.2672.95163633609275456.71912.311-12.5131.567-0.202
bbab4_quarters_entry_42_day_exit5.1521.24063633411295253.6079.736-9.3990.8590.337
bbab4_quarters_entry_21_day_exit0.7570.39363633279308451.5326.389-6.6630.063-0.274

DMA 12 Months All Years

dma word 12 monthsEntry Exit TypeAnnualized Expectancy50 Pctl % ReturnTradesWinsLossesWin %Median WinMedian LossExpectancyMedian Win - abs(Median Loss)
bbbaaaaaabbb12_months_entry_21_day_exit20.5791.268170694875855.5698.593-6.8881.7151.706
bbbbaaaaaabb12_months_entry_21_day_exit18.1531.094124167256954.1508.601-6.8591.5131.742
bbbbaaaabbbb12_months_entry_42_day_exit17.5133.541157092464658.85411.939-9.9832.9191.956
bbbbbaabbbbb12_months_entry_42_day_exit17.2852.745172898274656.82912.340-9.5712.8812.769
bbbbbbabbbbb12_months_entry_42_day_exit17.0292.581139979260756.61212.116-9.2672.8382.849
abaaabbbbbbb12_months_entry_21_day_exit16.9691.967169297471857.5657.652-7.0481.4140.604
bbbbbbbbbbba12_months_entry_21_day_exit16.2191.622166829635704757.7576.208-5.2881.3520.920
bbbbaabbbbbb12_months_entry_63_day_exit16.0494.7192156126988758.85915.381-12.2524.0123.129
bbbbbbbbbaaa12_months_entry_21_day_exit15.9521.6771892210982794058.0386.252-5.4791.3290.773
bbaabbbbbbbb12_months_entry_42_day_exit15.7283.08150872937215057.73511.530-9.5482.6211.982
bbbabbbbbbbb12_months_entry_21_day_exit15.6811.68239562240171656.6237.463-6.7301.3070.734
bbbbbaaabbbb12_months_entry_42_day_exit15.4352.626137478858657.35112.039-10.1572.5721.882
bbbbbbbbbbaa12_months_entry_21_day_exit15.2091.5711769010166752457.4676.171-5.3581.2670.813
abaaaabbbbbb12_months_entry_21_day_exit15.1101.223126969157854.4527.818-6.5821.2591.236
bbbbaaabbbbb12_months_entry_42_day_exit15.0852.7031882108779557.75811.315-9.5192.5141.796
bbbaaaaaaabb12_months_entry_21_day_exit15.0461.493154285668655.5127.765-6.8701.2540.894
babbbbbbbbbb12_months_entry_21_day_exit15.0351.413148618195666655.1448.187-7.2721.2530.915
bbbbaaaaabbb12_months_entry_63_day_exit14.9754.190138682456259.45215.101-12.9083.7442.193
bbbaaaaaabbb12_months_entry_63_day_exit14.8683.747170699171558.08915.227-12.2353.7172.991
baaaaaaaaabb12_months_entry_21_day_exit14.7931.52633381862147655.7827.600-6.8001.2330.800
bbbbbbbbaaaa12_months_entry_21_day_exit14.6501.5382074811965878357.6686.108-5.4371.2210.671
abaaabbbbbbb12_months_entry_63_day_exit14.5524.6571692102167160.34314.329-12.6303.6381.699
bbaaabbbbbbb12_months_entry_21_day_exit14.4651.42641302289184155.4247.566-6.7031.2050.863
baabbaaaaaaa12_months_entry_21_day_exit14.0841.375122667954755.3836.486-5.4201.1741.066
aaaabbbbbaaa12_months_entry_21_day_exit14.0391.3181848104979956.7645.620-4.6721.1700.948
bbbbaaabbbbb12_months_entry_63_day_exit13.9323.9631882110877458.87414.676-12.5403.4832.136
bbbbaaaaabbb12_months_entry_42_day_exit13.8623.480138680358357.93712.126-11.2092.3100.917
aabbbbbbbbbb12_months_entry_21_day_exit13.6131.41338417213321708555.5287.540-6.8631.1340.677
bbaaaaaaaabb12_months_entry_42_day_exit13.5572.3892061115490755.99212.508-10.7802.2591.728
bbbbbaaaaaaa12_months_entry_21_day_exit13.2911.48229994171701282457.2455.925-5.3431.1080.582
bbbbbbabbbbb12_months_entry_63_day_exit13.2653.730139979660356.89816.005-13.4343.3162.571
bbbbbaabbbbb12_months_entry_21_day_exit13.2541.073172893779154.2257.521-6.4971.1051.025
abaaabbbbbbb12_months_entry_42_day_exit13.2453.079169296273056.85611.385-9.8862.2081.498
bbaaabbbbbbb12_months_entry_42_day_exit13.2372.42841302317181356.10211.578-9.7712.2061.807
bbbbbbbaaaaa12_months_entry_21_day_exit13.1681.4042315013222992857.1146.005-5.4391.0970.566
bbbaaaaaabbb12_months_entry_42_day_exit13.1642.800170697673057.21012.173-11.1472.1941.025
bbbaabbbbbbb12_months_entry_21_day_exit13.1360.77231671667150052.6377.974-6.5501.0951.423
bbbaaaaaaaab12_months_entry_63_day_exit12.9923.754145784061757.65314.967-12.7063.2482.261
abbabbbbbbbb12_months_entry_42_day_exit12.9752.205137277260056.26810.386-8.4182.1631.968
bbbbaabbbbbb12_months_entry_42_day_exit12.9462.7752156123492257.23611.390-10.1992.1581.191
bbbbbaaabbbb12_months_entry_21_day_exit12.9141.288137475362154.8037.407-6.6011.0760.806
baabaaaaaaaa12_months_entry_42_day_exit12.8911.948166796070757.5888.819-6.9092.1491.910
abaaaabbbbbb12_months_entry_63_day_exit12.8694.147126974852158.94413.409-11.4163.2171.994
abaabbbbbbbb12_months_entry_42_day_exit12.8672.4501881105882356.24711.310-9.6392.1441.672
bbbaaaaabbbb12_months_entry_63_day_exit12.8563.4881873106381056.75414.690-11.8473.2142.843
abaabbbbbbbb12_months_entry_63_day_exit12.8114.0611881111276959.11713.480-11.6593.2031.821
bbbbaaabbbbb12_months_entry_21_day_exit12.7530.690188298889452.4977.615-6.1781.0631.437
abbbbbbbbbbb12_months_entry_42_day_exit12.7422.62962775358672690857.13611.074-9.8062.1241.267
baaaaaaaaabb12_months_entry_63_day_exit12.7214.08933381944139458.23814.726-12.9213.1801.805
bbbbaaaaaaaa12_months_entry_21_day_exit12.7081.34035257200931516456.9905.856-5.2981.0590.559
bbbaaaaaaabb12_months_entry_63_day_exit12.7043.903154289864458.23614.872-13.1333.1761.739
bbbaaaaaaaaa12_months_entry_21_day_exit12.6511.28743009243741863556.6725.803-5.1561.0540.646
bbbbaaaabbbb12_months_entry_21_day_exit12.5851.178157085771354.5867.590-6.8141.0490.776
bbaaaaaaaaaa12_months_entry_21_day_exit12.5811.31658175330712510456.8475.725-5.1121.0480.613
bbbbbaabbbbb12_months_entry_63_day_exit12.5453.103172897075856.13415.749-13.0043.1362.745
baabbaaaaaaa12_months_entry_42_day_exit12.5362.601122671750958.4838.605-7.0882.0891.516
aaaabbbbbbba12_months_entry_21_day_exit12.4811.380152788664158.0225.305-4.8551.0400.450
baaaaaaaaaab12_months_entry_63_day_exit12.4703.74831571831132657.99814.060-11.9923.1172.068
baabbaaaaaaa12_months_entry_63_day_exit12.4363.498122673748960.11410.811-8.4993.1092.312
bbbaaaaabbbb12_months_entry_42_day_exit12.4161.7851873102584854.72511.559-9.4022.0692.158
baaaaaaaaabb12_months_entry_42_day_exit12.3882.40433381882145656.38111.146-9.6742.0651.472
abbabbbbbbbb12_months_entry_63_day_exit12.3153.719137281256059.18412.663-10.8193.0791.845
bbaabbbbbbbb12_months_entry_63_day_exit12.2703.81950872958212958.14813.720-11.7333.0681.987
bbbbaaaabbbb12_months_entry_63_day_exit12.2693.644157090966157.89814.584-12.7713.0671.813
bbbbbbbbbaaa12_months_entry_42_day_exit12.2492.5031892211055786758.4248.968-7.6922.0421.276
bbabaaaaaaaa12_months_entry_42_day_exit12.2022.706125776149660.5418.406-7.7442.0340.663
bbbbbbaaaaaa12_months_entry_21_day_exit12.1141.31626038146541138456.2796.001-5.4161.0090.585
aabbbbbbbaaa12_months_entry_63_day_exit12.0743.41831091861124859.85810.605-8.2943.0192.311
baaaaaaabbbb12_months_entry_63_day_exit12.0593.24140302289174156.79914.841-12.5343.0152.307
aaabbbbbbbba12_months_entry_42_day_exit12.0182.2311903111478958.5398.391-7.0172.0031.374
babbbbbbbbbb12_months_entry_42_day_exit11.9032.421148618388647356.44311.355-10.1601.9841.195
bbaaaaaaaabb12_months_entry_63_day_exit11.8933.5172061119786458.07915.027-13.7262.9731.301
bbbbaaaaaabb12_months_entry_63_day_exit11.8102.814124169354855.84214.278-11.3692.9522.908
abbbbbbbbbbb12_months_entry_21_day_exit11.7901.34062775346822809355.2487.421-6.9660.9830.455
aaaabbaaaaaa12_months_entry_42_day_exit11.7442.67628241691113359.8808.408-7.6711.9570.738
bbaaaaaabbbb12_months_entry_63_day_exit11.7433.28225411436110556.51315.217-13.0242.9362.193
aaaaaaaaaaab12_months_entry_63_day_exit11.7383.435128267442538458.02313.123-11.1492.9341.974
aaaabaaaaaaa12_months_entry_63_day_exit11.6453.23430801827125359.31810.928-8.7782.9112.150
baaaaaaaaaaa12_months_entry_21_day_exit11.6301.21599108558734323556.3765.581-4.9900.9690.590
baaaaaaaaaab12_months_entry_42_day_exit11.5712.38831571795136256.85810.728-9.6691.9281.059
bbbbaaaaaabb12_months_entry_42_day_exit11.5512.440124170853357.05110.945-10.0561.9250.889
aaaabbaaaaaa12_months_entry_63_day_exit11.5283.57128241674115059.27811.295-9.3652.8821.930
bbbabbbbbbbb12_months_entry_42_day_exit11.5232.10239562183177355.18211.217-9.5261.9201.691
aaaabbbaaaaa12_months_entry_21_day_exit11.4701.49823781374100457.7805.197-4.8490.9560.349
bbbaaaaaaaab12_months_entry_21_day_exit11.4540.742145776868952.7118.017-6.9180.9551.099
baaaaaaaaaaa12_months_entry_42_day_exit11.4442.22299108576464146258.1658.366-7.0721.9071.294
bbbbbbbbbbaa12_months_entry_63_day_exit11.4273.4781769010494719659.32211.360-9.5432.8571.817
bbbbbbbbbbba12_months_entry_63_day_exit11.4223.524166829936674659.56111.313-9.6022.8551.711
abaaaaaaaaaa12_months_entry_42_day_exit11.2332.0562289213179971357.5708.505-7.1271.8721.378
bbbbbbbbbaaa12_months_entry_63_day_exit11.2143.3891892211253766959.47011.099-9.3682.8041.730
abaaaaaaaaaa12_months_entry_21_day_exit11.2101.17322892128331005956.0595.615-5.0380.9340.577
bbabaaaaaaaa12_months_entry_21_day_exit11.1941.426125771454356.8025.668-5.2940.9330.374
bbaaaaaaaaaa12_months_entry_42_day_exit11.1362.10258175335932458257.7458.491-7.2101.8561.280
aaaaabaaaaaa12_months_entry_42_day_exit11.1162.4752249133891159.4938.076-7.2881.8530.788
aaaabaaaaaaa12_months_entry_42_day_exit11.1042.08730801795128558.2798.221-7.0481.8511.173
bbbbbbbbbbba12_months_entry_42_day_exit11.0572.483166829722696058.2788.863-7.9631.8430.900
bbbabbbbbbbb12_months_entry_63_day_exit11.0493.79039562308164858.34213.248-11.9232.7621.325
bbaaabbbbbbb12_months_entry_63_day_exit11.0453.49541302363176757.21513.486-11.5822.7611.905
aaabbbbbbbba12_months_entry_63_day_exit10.9913.2631903113576859.64310.734-9.0552.7481.679
aaabbbaaaaaa12_months_entry_63_day_exit10.9903.53535072113139460.25110.646-9.2252.7471.421
bbbbaaaaabbb12_months_entry_21_day_exit10.9851.139138675463254.4017.682-7.1580.9150.525
bbaaaaaaabbb12_months_entry_63_day_exit10.9423.4922230127195956.99614.991-13.5062.7361.484
aaabbbbaaaaa12_months_entry_63_day_exit10.9403.41829331754117959.80210.574-8.9272.7351.647
babbbbbbbbbb12_months_entry_63_day_exit10.8883.823148618605625657.90313.898-12.6512.7221.247
abbaabbbbbbb12_months_entry_63_day_exit10.8753.435121570351257.86012.838-11.1752.7191.662
aaabbbbaaaaa12_months_entry_42_day_exit10.8482.36829331728120558.9167.964-7.0201.8080.944
bbbbbaaabbbb12_months_entry_63_day_exit10.8193.720137478658857.20514.905-13.6042.7051.301
bbbbaaaaaaaa12_months_entry_42_day_exit10.8152.16235257203081494957.6008.502-7.2981.8031.204
bbbbbbbbbbaa12_months_entry_42_day_exit10.7832.2851769010258743257.9888.881-7.9801.7970.901
abaaaabbbbbb12_months_entry_42_day_exit10.7622.262126971155856.02810.932-9.8501.7941.082
aaaaabaaaaaa12_months_entry_63_day_exit10.7213.4362249134290759.67110.568-8.9902.6801.578
aabbbbbaaaaa12_months_entry_63_day_exit10.7203.67838432327151660.55210.311-9.0342.6801.277
bbbbbbbbaaaa12_months_entry_42_day_exit10.7172.3822074812065868358.1508.678-7.7901.7860.888
aaaaabbaaaaa12_months_entry_42_day_exit10.7111.9541998114785157.4078.014-6.6101.7851.404
aabbbbaaaaaa12_months_entry_63_day_exit10.6803.25246842778190659.30810.519-8.7712.6701.749
bbbbbbbbaaaa12_months_entry_63_day_exit10.6793.3252074812298845059.27310.981-9.4272.6701.555
baaaaaabbbbb12_months_entry_63_day_exit10.6733.19644712559191257.23614.154-12.7042.6681.450
aaaaaaaaaabb12_months_entry_63_day_exit10.6543.596133777795558258.27213.069-11.8672.6631.201
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aaaaabbbbbaa12_months_entry_63_day_exit6.6462.557151087363757.8159.669-9.3131.6620.356
aabbbaaaaaaa12_months_entry_42_day_exit6.6401.33956063057254954.5318.062-7.2351.1070.827
baaaaabbbbbb12_months_entry_42_day_exit6.6381.40553032878242554.27110.636-10.2041.1060.432
aabbaaaaaaaa12_months_entry_42_day_exit6.6091.26870133829318454.5998.102-7.3171.1020.785
aaaaabbbbbba12_months_entry_42_day_exit6.5891.617132874758156.2507.459-7.0791.0980.379
abbbbbbaaaaa12_months_entry_21_day_exit6.5260.87265733609296454.9065.456-5.4380.5440.019
abaabbbbbbbb12_months_entry_21_day_exit6.5141.1861881102985254.7056.870-7.0990.543-0.229
aaaaabbbbaaa12_months_entry_21_day_exit6.4420.733164087976153.5985.198-4.8480.5370.351
aaaabaaaaaaa12_months_entry_21_day_exit6.4130.81130801677140354.4485.467-5.3610.5340.105
aaaaaaabbbbb12_months_entry_42_day_exit6.3621.634164818973750854.4459.973-9.5911.0600.382
aaabbbbbbbbb12_months_entry_42_day_exit6.3431.54129240159281331254.47310.144-9.8161.0570.329
baaaaabbbbbb12_months_entry_21_day_exit6.3420.72853032798250552.7637.021-6.7240.5290.298
aaaabbbbbbaa12_months_entry_21_day_exit6.3411.303166094571556.9285.282-5.7550.528-0.472
aaaaaabbbbaa12_months_entry_42_day_exit6.3411.450134774859955.5317.620-7.1401.0570.481
baaabbbbbbbb12_months_entry_21_day_exit6.3310.87476544095355953.5016.859-6.7580.5280.102
aaaaabbbbbaa12_months_entry_21_day_exit6.3080.951151084966156.2254.712-4.8510.526-0.139
bbbbbabbbbbb12_months_entry_21_day_exit6.2780.9631925105287354.6496.893-7.1520.523-0.260
aaaaaabbaaaa12_months_entry_21_day_exit6.2330.831148381566854.9565.258-5.2620.519-0.004
aabbbbbbbbba12_months_entry_21_day_exit6.2271.05326511443120854.4325.660-5.6220.5190.038
abbbbbbbbaaa12_months_entry_21_day_exit6.1390.83851362773236353.9915.335-5.1490.5120.186
aaabaaaaaaaa12_months_entry_21_day_exit6.1300.85148402620222054.1325.445-5.3130.5110.133
aabaaaaaaaaa12_months_entry_21_day_exit6.1030.73493074980432753.5085.527-5.2680.5090.260
bbaaaaaaabbb12_months_entry_21_day_exit6.0580.83422301193103753.4987.507-7.5510.505-0.044
aaaabbbbbbbb12_months_entry_63_day_exit6.0302.19124064132081085654.88712.502-11.8691.5070.633
baabaaaaaaaa12_months_entry_21_day_exit5.9981.027166792374455.3695.516-5.7240.500-0.207
aaabbbaaaaaa12_months_entry_21_day_exit5.9890.84935071910159754.4635.461-5.4350.4990.026
bbaaaaabbbbb12_months_entry_42_day_exit5.9821.65828441544130054.29010.983-10.8630.9970.120
aaaabbbbbbaa12_months_entry_42_day_exit5.9731.995166095970157.7717.386-7.7470.996-0.361
aaaaabbbbbbb12_months_entry_63_day_exit5.9192.1972064011316932454.82612.509-11.9051.4800.604
aabbbbbbaaaa12_months_entry_21_day_exit5.7560.70535291908162154.0665.371-5.2780.4800.093
bbbaaabbbbbb12_months_entry_21_day_exit5.6610.19625291282124750.6927.801-7.0630.4720.738
abbaabbbbbbb12_months_entry_42_day_exit5.5901.147121565356253.74510.067-9.6830.9320.384
aaaaaabaaaaa12_months_entry_21_day_exit5.5560.724166088977153.5545.391-5.2190.4630.172
abbaabbbbbbb12_months_entry_21_day_exit5.5350.954121565056553.4987.160-7.2450.461-0.085
baaaaaaabbbb12_months_entry_21_day_exit5.4040.69640302133189752.9287.042-6.9620.4500.081
aaabbbbbaaaa12_months_entry_21_day_exit5.2890.76125651369119653.3725.389-5.2240.4410.166
aaaaaabbbbbb12_months_entry_42_day_exit5.2171.467183259936838954.2219.780-9.6840.8700.096
aaaaabbbbbbb12_months_entry_42_day_exit5.2161.3072064011109953153.8239.768-9.5020.8690.265
aaaaaabbbbbb12_months_entry_21_day_exit5.1780.762183259748857753.1956.735-6.7320.4320.002
bbaaaaaabbbb12_months_entry_21_day_exit5.1190.38225411305123651.3587.319-6.8510.4270.468
baabbbbbbbbb12_months_entry_42_day_exit5.1161.41697625227453553.54410.794-10.6060.8530.188
aaaaaabaaaaa12_months_entry_42_day_exit5.1061.328166092573555.7237.473-7.4830.851-0.010
ababbbbbbbbb12_months_entry_21_day_exit5.0741.12425971409118854.2557.287-7.7190.423-0.431
aaaaabbbbaaa12_months_entry_42_day_exit4.8371.113164090173954.9397.394-7.2250.8060.168
bbbbabbbbbbb12_months_entry_21_day_exit4.7750.43525161307120951.9487.680-7.4740.3980.206
aaaaaabaaaaa12_months_entry_63_day_exit4.4311.941166092273855.5429.723-9.6551.1080.068
babbbaaaaaaa12_months_entry_21_day_exit4.2690.9401934104988554.2405.709-5.9900.356-0.281
aaaabbbbbbbb12_months_entry_42_day_exit4.1171.11724064128731119153.4959.714-9.6990.6860.015
aaaaabbbbbbb12_months_entry_21_day_exit3.7250.4712064010695994551.8176.768-6.6340.3100.134
bbaaaabbbbbb12_months_entry_21_day_exit3.6490.28532361658157851.2367.231-6.9740.3040.257
aabbbaaaaaaa12_months_entry_21_day_exit3.6470.64256062975263153.0685.495-5.5660.304-0.071
aaabbaaaaaaa12_months_entry_21_day_exit3.6160.58140082118189052.8445.357-5.3640.301-0.007
aabbbbaaaaaa12_months_entry_21_day_exit3.2810.65446842504218053.4595.337-5.5420.273-0.206
aabbbbbaaaaa12_months_entry_21_day_exit3.0800.73338432066177753.7605.284-5.5880.257-0.304
baaaaaabbbbb12_months_entry_21_day_exit2.6260.50344712327214452.0476.797-6.9210.219-0.124
baaaaaaaabbb12_months_entry_21_day_exit2.0030.61136071896171152.5647.119-7.5370.167-0.418
aaaabbbbbbbb12_months_entry_21_day_exit1.9240.42024064123851167951.4676.803-6.8840.160-0.081
aaaaaabbbaaa12_months_entry_21_day_exit1.8740.772143979264755.0384.515-5.1790.156-0.665
baabbbbbbbbb12_months_entry_21_day_exit1.6170.46397625053470951.7627.176-7.4210.135-0.245
aaaaaabbbbaa12_months_entry_21_day_exit1.0970.137134768466350.7805.002-4.9740.0910.027
bbbaaaabbbbb12_months_entry_21_day_exit0.3380.27021311079105250.6347.353-7.4850.028-0.132
bbabbbbbbbbb12_months_entry_21_day_exit-0.6250.29562793209307051.1077.048-7.473-0.052-0.426
bbaaaaabbbbb12_months_entry_21_day_exit-1.6130.18028441437140750.5276.970-7.390-0.134-0.420

The percent returns were divided into deciles, so that the 50th percentile is the median percent return. Expectancy is defined as (positive % returns)*win_fraction + (negative % returns)*(1 – win_fraction). Annualized expectancy is a simple linear scaling from that of the exit days to a full trading year of 252 days (it is not compounded).

Remarks

The results presented here are for long positions in stocks only. In order to incorporate ETFs, a curated list should be created to avoid redundant ETFs. Also, inverse ETFs would be interesting to examine as a means of taking short positions.