Been ranting a bit about math problems so its time for another 6am post - please excuse the occasional incoherence By math I mean what probabilities a strategy must hit to be profitable given the rules of the game.
Basic math to NASDAQ is as follows (in units of $0.0001 per share)
-30 remove liquidity
+21 add liquidity
-0.0000192 * dollar value of sold symbol
0 to -20 for commission
+ gross realized value of the trade
(its a variable commission as depending who you clear with, it could be 0 e.g. mega fund with its own clearing division, or say -20 for entry level algo brokers)
Lets simplify this somewhat and say, its a pair of buy/sell at different price but same qty, making the net realized gain
Net = Qty * (SellPrice - BuyPrice + Rebate + Commission + Tax)
First structure classification is what kind of entry/exit points you choose. Options are
Aggressive + Aggressive (AA) : -30 - 30 = -60
Aggressive + Passive (AP) : -30 + 21 = -9
Passive + Agressive (PA) : +21 - 30 = -9
Passive + Passive (PP) : +21 + 21 = +42
(Passive means your orders was visible on the book when it got executed)
(Aggressive means your order hit something that was visible on the book e.g. crossed the spread)
Simplify this a little into 3 classes
AA ( -60) AP (-9) PP(+42)
Note: AA your crossing the spread thus its really -160 but for back of the envelope purposes lets ignore that and enjoy Disney Land.
Let say our strategy has 2 discrete poles, +100 win and -100 loss, so 1 tick each side with no 0 draw result.
Below is a plot of the the trades winning probability (most left column) and the realized gain/loss for 1 share @ the specified probability for each entry/exit styles.
Rebate Only
0.000000 : AA: -160 AP: -109 PP: -58
0.040000 : AA: -152 AP: -101 PP: -50
0.080000 : AA: -144 AP: -93 PP: -42
0.120000 : AA: -136 AP: -85 PP: -34
0.160000 : AA: -128 AP: -77 PP: -26
0.200000 : AA: -120 AP: -69 PP: -18
0.240000 : AA: -112 AP: -61 PP: -10
0.280000 : AA: -104 AP: -53 PP: -2
0.320000 : AA: -96 AP: -45 PP: 6
0.360000 : AA: -88 AP: -37 PP: 14
0.400000 : AA: -80 AP: -29 PP: 22
0.440000 : AA: -72 AP: -21 PP: 29
0.480000 : AA: -64 AP: -13 PP: 38
0.520000 : AA: -56 AP: -5 PP: 46
0.560000 : AA: -47 AP: 3 PP: 54
0.600000 : AA: -40 AP: 11 PP: 62
0.640000 : AA: -32 AP: 19 PP: 70
0.680000 : AA: -24 AP: 27 PP: 78
0.720000 : AA: -16 AP: 35 PP: 86
0.760000 : AA: -8 AP: 43 PP: 94
0.800000 : AA: 0 AP: 51 PP: 102
0.840000 : AA: 8 AP: 59 PP: 110
0.880000 : AA: 16 AP: 67 PP: 118
0.920000 : AA: 24 AP: 75 PP: 126
0.960000 : AA: 32 AP: 83 PP: 134
1.000000 : AA: 40 AP: 91 PP: 142
Result here is, you need a strategy > 80% wins with an AA model > 56% wins for a AP model, and > 32% for a PP model.
That makes sense, so lets add the tax @ say a $20symbol
Rebate + Tax @ $20
0.000000 : AA: -163 AP: -112 PP: -61
0.040000 : AA: -155 AP: -104 PP: -53
0.080000 : AA: -147 AP: -96 PP: -45
0.120000 : AA: -139 AP: -88 PP: -37
0.160000 : AA: -131 AP: -80 PP: -29
0.200000 : AA: -123 AP: -72 PP: -21
0.240000 : AA: -115 AP: -64 PP: -13
0.280000 : AA: -107 AP: -56 PP: -5
0.320000 : AA: -99 AP: -48 PP: 2
0.360000 : AA: -91 AP: -40 PP: 10
0.400000 : AA: -83 AP: -32 PP: 18
0.440000 : AA: -75 AP: -24 PP: 26
0.480000 : AA: -67 AP: -16 PP: 34
0.520000 : AA: -59 AP: -8 PP: 42
0.560000 : AA: -51 AP: 0 PP: 50
0.600000 : AA: -43 AP: 7 PP: 58
0.640000 : AA: -35 AP: 15 PP: 66
0.680000 : AA: -27 AP: 23 PP: 74
0.720000 : AA: -19 AP: 31 PP: 82
0.760000 : AA: -11 AP: 39 PP: 90
0.800000 : AA: -3 AP: 47 PP: 98
0.840000 : AA: 4 AP: 55 PP: 106
0.880000 : AA: 12 AP: 63 PP: 114
0.920000 : AA: 20 AP: 71 PP: 122
0.960000 : AA: 28 AP: 79 PP: 130
1.000000 : AA: 36 AP: 87 PP: 138
Not a huge difference, yet even $20 in tax shifts everything by a few %, which could easily move your strategy into the red.
Lets up it a notch and say you want to trade SPY @ say $139 (2012/04/17)
Rebate + Tax @ $139
0.000000 : AA: -186 AP: -135 PP: -84
0.040000 : AA: -178 AP: -127 PP: -76
0.080000 : AA: -170 AP: -119 PP: -68
0.120000 : AA: -162 AP: -111 PP: -60
0.160000 : AA: -154 AP: -103 PP: -52
0.200000 : AA: -146 AP: -95 PP: -44
0.240000 : AA: -138 AP: -87 PP: -36
0.280000 : AA: -130 AP: -79 PP: -28
0.320000 : AA: -122 AP: -71 PP: -20
0.360000 : AA: -114 AP: -63 PP: -12
0.400000 : AA: -106 AP: -55 PP: -4
0.440000 : AA: -98 AP: -47 PP: 3
0.480000 : AA: -90 AP: -39 PP: 11
0.520000 : AA: -82 AP: -31 PP: 19
0.560000 : AA: -74 AP: -23 PP: 27
0.600000 : AA: -66 AP: -15 PP: 35
0.640000 : AA: -58 AP: -7 PP: 43
0.680000 : AA: -50 AP: 0 PP: 51
0.720000 : AA: -42 AP: 8 PP: 59
0.760000 : AA: -34 AP: 16 PP: 67
0.800000 : AA: -26 AP: 24 PP: 75
0.840000 : AA: -18 AP: 32 PP: 83
0.880000 : AA: -10 AP: 40 PP: 91
0.920000 : AA: -2 AP: 48 PP: 99
0.960000 : AA: 5 AP: 56 PP: 107
1.000000 : AA: 13 AP: 64 PP: 115
Things look a bit more "difficult", with an AA structure you need to hit >= 96% accuracy, PA >= 68% and PP >= 44%. Pretty clear AA for a +100/-100 trade is getting near impossible and if you consider the additional -100 spread cost... it is impossible.
The above has a commission of 0, so lets add say -5 commission on a $20 symbol
Rebate + Commission (-5) + Tax @ $20
0.000000 : AA: -173 AP: -122 PP: -71
0.040000 : AA: -165 AP: -114 PP: -63
0.080000 : AA: -157 AP: -106 PP: -55
0.120000 : AA: -149 AP: -98 PP: -47
0.160000 : AA: -141 AP: -90 PP: -39
0.200000 : AA: -133 AP: -82 PP: -31
0.240000 : AA: -125 AP: -74 PP: -23
0.280000 : AA: -117 AP: -66 PP: -15
0.320000 : AA: -109 AP: -58 PP: -7
0.360000 : AA: -101 AP: -50 PP: 0
0.400000 : AA: -93 AP: -42 PP: 8
0.440000 : AA: -85 AP: -34 PP: 16
0.480000 : AA: -77 AP: -26 PP: 24
0.520000 : AA: -69 AP: -18 PP: 32
0.560000 : AA: -61 AP: -10 PP: 40
0.600000 : AA: -53 AP: -2 PP: 48
0.640000 : AA: -45 AP: 5 PP: 56
0.680000 : AA: -37 AP: 13 PP: 64
0.720000 : AA: -29 AP: 21 PP: 72
0.760000 : AA: -21 AP: 29 PP: 80
0.800000 : AA: -13 AP: 37 PP: 88
0.840000 : AA: -5 AP: 45 PP: 96
0.880000 : AA: 2 AP: 53 PP: 104
0.920000 : AA: 10 AP: 61 PP: 112
0.960000 : AA: 18 AP: 69 PP: 120
1.000000 : AA: 26 AP: 77 PP: 128
At -5 / share (remember its on both sides) AA requires nearly 90% accuracy, that`s a tough number to hit.
Rebate + Commission @ -10 / shares + Tax @ $20
0.000000 : AA: -183 AP: -132 PP: -81
0.040000 : AA: -175 AP: -124 PP: -73
0.080000 : AA: -167 AP: -116 PP: -65
0.120000 : AA: -159 AP: -108 PP: -57
0.160000 : AA: -151 AP: -100 PP: -49
0.200000 : AA: -143 AP: -92 PP: -41
0.240000 : AA: -135 AP: -84 PP: -33
0.280000 : AA: -127 AP: -76 PP: -25
0.320000 : AA: -119 AP: -68 PP: -17
0.360000 : AA: -111 AP: -60 PP: -9
0.400000 : AA: -103 AP: -52 PP: -1
0.440000 : AA: -95 AP: -44 PP: 6
0.480000 : AA: -87 AP: -36 PP: 14
0.520000 : AA: -79 AP: -28 PP: 22
0.560000 : AA: -71 AP: -20 PP: 30
0.600000 : AA: -63 AP: -12 PP: 38
0.640000 : AA: -55 AP: -4 PP: 46
0.680000 : AA: -47 AP: 3 PP: 54
0.720000 : AA: -39 AP: 11 PP: 62
0.760000 : AA: -31 AP: 19 PP: 70
0.800000 : AA: -23 AP: 27 PP: 78
0.840000 : AA: -15 AP: 35 PP: 86
0.880000 : AA: -7 AP: 43 PP: 94
0.920000 : AA: 0 AP: 51 PP: 102
0.960000 : AA: 8 AP: 59 PP: 110
1.000000 : AA: 16 AP: 67 PP: 118
Commissions at -10/share with a +100/-100 2 pole result, AA nearing impossible requiring 95% accuracy for any return e.g. you need a time machine to make money with this structure.
Finally lets really push it to -20/share
0.000000 : AA: -203 AP: -152 PP: -101
0.040000 : AA: -195 AP: -144 PP: -93
0.080000 : AA: -187 AP: -136 PP: -85
0.120000 : AA: -179 AP: -128 PP: -77
0.160000 : AA: -171 AP: -120 PP: -69
0.200000 : AA: -163 AP: -112 PP: -61
0.240000 : AA: -155 AP: -104 PP: -53
0.280000 : AA: -147 AP: -96 PP: -45
0.320000 : AA: -139 AP: -88 PP: -37
0.360000 : AA: -131 AP: -80 PP: -29
0.400000 : AA: -123 AP: -72 PP: -21
0.440000 : AA: -115 AP: -64 PP: -13
0.480000 : AA: -107 AP: -56 PP: -5
0.520000 : AA: -99 AP: -48 PP: 2
0.560000 : AA: -91 AP: -40 PP: 10
0.600000 : AA: -83 AP: -32 PP: 18
0.640000 : AA: -75 AP: -24 PP: 26
0.680000 : AA: -67 AP: -16 PP: 34
0.720000 : AA: -59 AP: -8 PP: 42
0.760000 : AA: -51 AP: 0 PP: 50
0.800000 : AA: -43 AP: 7 PP: 58
0.840000 : AA: -35 AP: 15 PP: 66
0.880000 : AA: -27 AP: 23 PP: 74
0.920000 : AA: -19 AP: 31 PP: 82
0.960000 : AA: -11 AP: 39 PP: 90
1.000000 : AA: -3 AP: 47 PP: 98
At this point AA is theoretically impossible with PA needing 76% of trades to be correct just to break even.
Obviously its far more involved with a ton of subtle yet major pain-in-the-ass-problems but gives you an idea of the level of accuracy & commissions needed to play the sub-tick game.
Also this says nothing about what kind of latency/tech needed for passively executed orders... or how low the real-world probabilities are but that`s for some other time.... if only that order passively unwound at that price, there would be peace joy and happiness in the world :P
... the grind continues
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