Tuesday, March 17, 2015

A Flash Boys Finance Problem

A Flash Boys Finance Problem

The new book by Michael Lewis “Flash Boys” discusses how Wall Street is now using a more direct cable between Chicago and New Jersey to trade faster.     A millisecond or two does not seem like much time but Wall Street firms can make a lot of money buying and selling quicker than the competition.

A previous post uses the issues raised in Flash Boys to motivate velocity and distance math problems.




This post considers the financial issues posed by Flash Boys.   Specifically, why should Wall Street firms pay millions of dollars up front in order to make trades a few milliseconds sooner.

This is a very entertaining book.  Here is its link to Amazon.


Here is its kindle link:



Question:   The contract between the people making the new line and the banks and investment firms using the new line specifies that any firm that buys access to the line could use it for its proprietary trading but could not use if for its customers.   Why would it be desirable for the firm creating the new line to include a clause stating that the line could be used exclusively for proprietary trading and not for customers?  (See page 19 of the hardcover on this issue.)

Answer:  Why would any firm pay money for a faster line that only benefits its customers?   The firm would not even gain more customers in the long run because other firms would be forced to follow suit.

Question:  On page 20 the founder of the new line a man named Spivey tells a brokerage firm that the cost of the line is $10.6 million plus costs if the firm paid up front or $20 million if the firm paid in installments.    The firm goes back to Spivey and asks him to double the price.   Why does this brokerage firm want Spivey to charge a higher price?

Answer:  At a higher price fewer firms will buy the line.   The advantages realized by the firms with the faster lines will be larger when the number of firms with the faster line is small.   There might be tremendous profits and great opportunities for market manipulation when only one firm has access to the high-speed line.


Comment:   The book does not contain detailed information on the contract banks signed to use the new line.    The book mentions a $300,000 per month fee but also mentions up front fees that lead to total payments of $10,000,000 to $14,000,000.    My net present value problem below assumes an annual fee for the use of line of $5.0 million.    I don’t have actual contractual information.


Question:   How much profit per day must be realized if the brokerage firm is to pay $5.0 million for the use of this line for one year?  Assume management requires the line purchase project to realize an IRR of 20%.  Fees for the use of the line are paid on the first day of the year.   Profits from the faster trades are received on the day the trades are made.

Answer:    The Net Present Value of daily profits must be compared to the initial upfront fee of $5.0 million.

The daily discount rate is 1/(1+(0.20/365))ed


Where ed is the number of elapsed days between the day of payment on the first day of the year and the current day.   Due to the time value of money, a day at the end of the year has a lower discount factor than the day at the beginning of the year.

There are no profits when the market is closed.    The chart on the bottom of this post lists the discount rates for each trading day during the year. 

I assume the same profit each day.  Under these circumstances, the sum of the discount factors times the daily profit is the net present value of the receipts from faster trading. 

The sum of the discount factors is 231.14.


The NPV of receipts plus upfront fee equals zero when NPV of receipts is $5.0 million.  The firm must get $21,632 ($5,000,000/231.14) per day to break even at a hurdle rate of 20%.  



Discount Factors on Future Trading Days in 2015
Days Elapsed Since Start of Year
1 if market open
Discount Factor
0
1-Jan-15
0
0.0000
1
2-Jan-15
1
0.9995
2
3-Jan-15
0
0.0000
3
4-Jan-15
0
0.0000
4
5-Jan-15
1
0.9978
5
6-Jan-15
1
0.9973
6
7-Jan-15
1
0.9967
7
8-Jan-15
1
0.9962
8
9-Jan-15
1
0.9956
9
10-Jan-15
0
0.0000
10
11-Jan-15
0
0.0000
11
12-Jan-15
1
0.9940
12
13-Jan-15
1
0.9934
13
14-Jan-15
1
0.9929
14
15-Jan-15
1
0.9924
15
16-Jan-15
1
0.9918
16
17-Jan-15
0
0.0000
17
18-Jan-15
0
0.0000
18
19-Jan-15
0
0.0000
19
20-Jan-15
1
0.9896
20
21-Jan-15
1
0.9891
21
22-Jan-15
1
0.9886
22
23-Jan-15
1
0.9880
23
24-Jan-15
0
0.0000
24
25-Jan-15
0
0.0000
25
26-Jan-15
1
0.9864
26
27-Jan-15
1
0.9859
27
28-Jan-15
1
0.9853
28
29-Jan-15
1
0.9848
29
30-Jan-15
1
0.9842
30
31-Jan-15
0
0.0000
31
1-Feb-15
0
0.0000
32
2-Feb-15
1
0.9826
33
3-Feb-15
1
0.9821
34
4-Feb-15
1
0.9815
35
5-Feb-15
1
0.9810
36
6-Feb-15
1
0.9805
37
7-Feb-15
0
0.0000
38
8-Feb-15
0
0.0000
39
9-Feb-15
1
0.9789
40
10-Feb-15
1
0.9783
41
11-Feb-15
1
0.9778
42
12-Feb-15
1
0.9773
43
13-Feb-15
1
0.9767
44
14-Feb-15
0
0.0000
45
15-Feb-15
0
0.0000
46
16-Feb-15
0
0.0000
47
17-Feb-15
1
0.9746
48
18-Feb-15
1
0.9740
49
19-Feb-15
1
0.9735
50
20-Feb-15
1
0.9730
51
21-Feb-15
0
0.0000
52
22-Feb-15
0
0.0000
53
23-Feb-15
1
0.9714
54
24-Feb-15
1
0.9709
55
25-Feb-15
1
0.9703
56
26-Feb-15
1
0.9698
57
27-Feb-15
1
0.9693
58
28-Feb-15
0
0.0000
59
1-Mar-15
1
0.9682
60
2-Mar-15
1
0.9677
61
3-Mar-15
1
0.9671
62
4-Mar-15
1
0.9666
63
5-Mar-15
1
0.9661
64
6-Mar-15
1
0.9655
65
7-Mar-15
0
0.0000
66
8-Mar-15
0
0.0000
67
9-Mar-15
1
0.9640
68
10-Mar-15
1
0.9634
69
11-Mar-15
1
0.9629
70
12-Mar-15
1
0.9624
71
13-Mar-15
1
0.9619
72
14-Mar-15
0
0.0000
73
15-Mar-15
0
0.0000
74
16-Mar-15
1
0.9603
75
17-Mar-15
1
0.9597
76
18-Mar-15
1
0.9592
77
19-Mar-15
1
0.9587
78
20-Mar-15
1
0.9582
79
21-Mar-15
0
0.0000
80
22-Mar-15
0
0.0000
81
23-Mar-15
1
0.9566
82
24-Mar-15
1
0.9561
83
25-Mar-15
1
0.9556
84
26-Mar-15
1
0.9550
85
27-Mar-15
1
0.9545
86
28-Mar-15
0
0.0000
87
29-Mar-15
0
0.0000
88
30-Mar-15
1
0.9529
89
31-Mar-15
1
0.9524
90
1-Apr-15
1
0.9519
91
2-Apr-15
1
0.9514
92
3-Apr-15
1
0.9509
93
4-Apr-15
0
0.0000
94
5-Apr-15
0
0.0000
95
6-Apr-15
1
0.9493
96
7-Apr-15
1
0.9488
97
8-Apr-15
1
0.9483
98
9-Apr-15
1
0.9477
99
10-Apr-15
1
0.9472
100
11-Apr-15
0
0.0000
101
12-Apr-15
0
0.0000
102
13-Apr-15
1
0.9457
103
14-Apr-15
1
0.9451
104
15-Apr-15
1
0.9446
105
16-Apr-15
1
0.9441
106
17-Apr-15
1
0.9436
107
18-Apr-15
0
0.0000
108
19-Apr-15
0
0.0000
109
20-Apr-15
1
0.9420
110
21-Apr-15
1
0.9415
111
22-Apr-15
1
0.9410
112
23-Apr-15
1
0.9405
113
24-Apr-15
1
0.9400
114
25-Apr-15
0
0.0000
115
26-Apr-15
0
0.0000
116
27-Apr-15
1
0.9384
117
28-Apr-15
1
0.9379
118
29-Apr-15
1
0.9374
119
30-Apr-15
1
0.9369
120
1-May-15
1
0.9364
121
2-May-15
0
0.0000
122
3-May-15
0
0.0000
123
4-May-15
1
0.9348
124
5-May-15
1
0.9343
125
6-May-15
1
0.9338
126
7-May-15
1
0.9333
127
8-May-15
1
0.9328
128
9-May-15
0
0.0000
129
10-May-15
0
0.0000
130
11-May-15
1
0.9313
131
12-May-15
1
0.9308
132
13-May-15
1
0.9302
133
14-May-15
1
0.9297
134
15-May-15
1
0.9292
135
16-May-15
0
0.0000
136
17-May-15
0
0.0000
137
18-May-15
1
0.9277
138
19-May-15
1
0.9272
139
20-May-15
1
0.9267
140
21-May-15
1
0.9262
141
22-May-15
1
0.9257
142
23-May-15
0
0.0000
143
24-May-15
0
0.0000
144
25-May-15
1
0.9241
145
26-May-15
1
0.9236
146
27-May-15
1
0.9231
147
28-May-15
1
0.9226
148
29-May-15
1
0.9221
149
30-May-15
0
0.0000
150
31-May-15
0
0.0000
151
1-Jun-15
1
0.9206
152
2-Jun-15
1
0.9201
153
3-Jun-15
1
0.9196
154
4-Jun-15
1
0.9191
155
5-Jun-15
1
0.9186
156
6-Jun-15
0
0.0000
157
7-Jun-15
0
0.0000
158
8-Jun-15
1
0.9171
159
9-Jun-15
1
0.9166
160
10-Jun-15
1
0.9161
161
11-Jun-15
1
0.9156
162
12-Jun-15
1
0.9151
163
13-Jun-15
0
0.0000
164
14-Jun-15
0
0.0000
165
15-Jun-15
1
0.9136
166
16-Jun-15
1
0.9131
167
17-Jun-15
1
0.9126
168
18-Jun-15
1
0.9121
169
19-Jun-15
1
0.9116
170
20-Jun-15
0
0.0000
171
21-Jun-15
0
0.0000
172
22-Jun-15
1
0.9101
173
23-Jun-15
1
0.9096
174
24-Jun-15
1
0.9091
175
25-Jun-15
1
0.9086
176
26-Jun-15
1
0.9081
177
27-Jun-15
0
0.0000
178
28-Jun-15
0
0.0000
179
29-Jun-15
1
0.9066
180
30-Jun-15
1
0.9061
181
1-Jul-15
1
0.9056
182
2-Jul-15
1
0.9051
183
3-Jul-15
0
0.0000
184
4-Jul-15
0
0.0000
185
5-Jul-15
0
0.0000
186
6-Jul-15
1
0.9031
187
7-Jul-15
1
0.9026
188
8-Jul-15
1
0.9021
189
9-Jul-15
1
0.9016
190
10-Jul-15
1
0.9012
191
11-Jul-15
0
0.0000
192
12-Jul-15
0
0.0000
193
13-Jul-15
1
0.8997
194
14-Jul-15
1
0.8992
195
15-Jul-15
1
0.8987
196
16-Jul-15
1
0.8982
197
17-Jul-15
1
0.8977
198
18-Jul-15
0
0.0000
199
19-Jul-15
0
0.0000
200
20-Jul-15
1
0.8962
201
21-Jul-15
1
0.8957
202
22-Jul-15
1
0.8952
203
23-Jul-15
1
0.8948
204
24-Jul-15
1
0.8943
205
25-Jul-15
0
0.0000
206
26-Jul-15
0
0.0000
207
27-Jul-15
1
0.8928
208
28-Jul-15
1
0.8923
209
29-Jul-15
1
0.8918
210
30-Jul-15
1
0.8913
211
31-Jul-15
1
0.8908
212
1-Aug-15
0
0.0000
213
2-Aug-15
0
0.0000
214
3-Aug-15
1
0.8894
215
4-Aug-15
1
0.8889
216
5-Aug-15
1
0.8884
217
6-Aug-15
1
0.8879
218
7-Aug-15
1
0.8874
219
8-Aug-15
0
0.0000
220
9-Aug-15
0
0.0000
221
10-Aug-15
1
0.8860
222
11-Aug-15
1
0.8855
223
12-Aug-15
1
0.8850
224
13-Aug-15
1
0.8845
225
14-Aug-15
1
0.8840
226
15-Aug-15
0
0.0000
227
16-Aug-15
0
0.0000
228
17-Aug-15
1
0.8826
229
18-Aug-15
1
0.8821
230
19-Aug-15
1
0.8816
231
20-Aug-15
1
0.8811
232
21-Aug-15
1
0.8807
233
22-Aug-15
0
0.0000
234
23-Aug-15
0
0.0000
235
24-Aug-15
1
0.8792
236
25-Aug-15
1
0.8787
237
26-Aug-15
1
0.8782
238
27-Aug-15
1
0.8778
239
28-Aug-15
1
0.8773
240
29-Aug-15
0
0.0000
241
30-Aug-15
0
0.0000
242
31-Aug-15
1
0.8758
243
1-Sep-15
1
0.8754
244
2-Sep-15
1
0.8749
245
3-Sep-15
1
0.8744
246
4-Sep-15
1
0.8739
247
5-Sep-15
0
0.0000
248
6-Sep-15
0
0.0000
249
7-Sep-15
1
0.8725
250
8-Sep-15
1
0.8720
251
9-Sep-15
1
0.8715
252
10-Sep-15
1
0.8711
253
11-Sep-15
1
0.8706
254
12-Sep-15
0
0.0000
255
13-Sep-15
0
0.0000
256
14-Sep-15
1
0.8692
257
15-Sep-15
1
0.8687
258
16-Sep-15
1
0.8682
259
17-Sep-15
1
0.8677
260
18-Sep-15
1
0.8673
261
19-Sep-15
0
0.0000
262
20-Sep-15
0
0.0000
263
21-Sep-15
1
0.8658
264
22-Sep-15
1
0.8654
265
23-Sep-15
1
0.8649
266
24-Sep-15
1
0.8644
267
25-Sep-15
1
0.8639
268
26-Sep-15
0
0.0000
269
27-Sep-15
0
0.0000
270
28-Sep-15
1
0.8625
271
29-Sep-15
1
0.8620
272
30-Sep-15
1
0.8616
273
1-Oct-15
1
0.8611
274
2-Oct-15
1
0.8606
275
3-Oct-15
0
0.0000
276
4-Oct-15
0
0.0000
277
5-Oct-15
1
0.8592
278
6-Oct-15
1
0.8587
279
7-Oct-15
1
0.8583
280
8-Oct-15
1
0.8578
281
9-Oct-15
1
0.8573
282
10-Oct-15
0
0.0000
283
11-Oct-15
0
0.0000
284
12-Oct-15
0
0.0000
285
13-Oct-15
1
0.8555
286
14-Oct-15
1
0.8550
287
15-Oct-15
1
0.8545
288
16-Oct-15
1
0.8541
289
17-Oct-15
0
0.0000
290
18-Oct-15
0
0.0000
291
19-Oct-15
1
0.8526
292
20-Oct-15
1
0.8522
293
21-Oct-15
1
0.8517
294
22-Oct-15
1
0.8512
295
23-Oct-15
1
0.8508
296
24-Oct-15
0
0.0000
297
25-Oct-15
0
0.0000
298
26-Oct-15
1
0.8494
299
27-Oct-15
1
0.8489
300
28-Oct-15
1
0.8485
301
29-Oct-15
1
0.8480
302
30-Oct-15
1
0.8475
303
31-Oct-15
0
0.0000
304
1-Nov-15
0
0.0000
305
2-Nov-15
1
0.8461
306
3-Nov-15
1
0.8457
307
4-Nov-15
1
0.8452
308
5-Nov-15
1
0.8447
309
6-Nov-15
1
0.8443
310
7-Nov-15
0
0.0000
311
8-Nov-15
0
0.0000
312
9-Nov-15
1
0.8429
313
10-Nov-15
1
0.8424
314
11-Nov-15
0
0.0000
315
12-Nov-15
1
0.8415
316
13-Nov-15
1
0.8411
317
14-Nov-15
0
0.0000
318
15-Nov-15
0
0.0000
319
16-Nov-15
1
0.8397
320
17-Nov-15
1
0.8392
321
18-Nov-15
1
0.8388
322
19-Nov-15
1
0.8383
323
20-Nov-15
1
0.8378
324
21-Nov-15
0
0.0000
325
22-Nov-15
0
0.0000
326
23-Nov-15
1
0.8365
327
24-Nov-15
1
0.8360
328
25-Nov-15
1
0.8355
329
26-Nov-15
0
0.0000
330
27-Nov-15
1
0.8346
331
28-Nov-15
0
0.0000
332
29-Nov-15
0
0.0000
333
30-Nov-15
1
0.8333
334
1-Dec-15
1
0.8328
335
2-Dec-15
1
0.8323
336
3-Dec-15
1
0.8319
337
4-Dec-15
1
0.8314
338
5-Dec-15
0
0.0000
339
6-Dec-15
0
0.0000
340
7-Dec-15
1
0.8301
341
8-Dec-15
1
0.8296
342
9-Dec-15
1
0.8292
343
10-Dec-15
1
0.8287
344
11-Dec-15
1
0.8282
345
12-Dec-15
0
0.0000
346
13-Dec-15
0
0.0000
347
14-Dec-15
1
0.8269
348
15-Dec-15
1
0.8264
349
16-Dec-15
1
0.8260
350
17-Dec-15
1
0.8255
351
18-Dec-15
1
0.8251
352
19-Dec-15
0
0.0000
353
20-Dec-15
0
0.0000
354
21-Dec-15
1
0.8237
355
22-Dec-15
1
0.8233
356
23-Dec-15
1
0.8228
357
24-Dec-15
1
0.8224
358
25-Dec-15
1
0.8219
359
26-Dec-15
0
0.0000
360
27-Dec-15
0
0.0000
361
28-Dec-15
1
0.8206
362
29-Dec-15
1
0.8201
363
30-Dec-15
1
0.8197
364
31-Dec-15
1
0.8192
231.1420




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