A B C D E F G H I J K L M N
1 Investment example
2
3 Initial cash $100,000
4
5 Probability distributions (lookup tables)
6 Lookup table following decrease Lookup table following increase Lookup table following no change
7 Cum prob Change Cum prob Change Cum prob Change
8 0.00 -2 0.00 -2 0.00 -2
9 0.20 -1 0.10 -1 0.15 -1
10 0.45 0 0.25 0 0.35 0
11 0.75 1 0.55 1 0.65 1
12 0.90 2 0.80 2 0.85 2
13
Current Previous Current Current
Previous Change in share shares Shares Shares shares Previous Change in Current worth of Cumulative Random
14 Day share price share price price owned sold purchased owned cash cash cash shares gain/loss number
15 1 $50 ($1) $49 0 0 500 500 ######## ($24,500) $75,500 $24,500 $0 0.295665
16 2 $49 ($1) $48 500 0 50 550 $75,500 ($2,400) $73,100 $26,400 ($500) 0.447913
17 3 $48 $1 $49 550 0 0 550 $73,100 $0 $73,100 $26,950 $50 0.836116
18 4 $49 $2 $51 550 55 0 495 $73,100 $2,805 $75,905 $25,245 $1,150 0.939342
19 5 $51 $2 $53 495 124 0 371 $75,905 $6,572 $82,477 $19,663 $2,140 0.958493
20 6 $53 $1 $54 371 93 0 278 $82,477 $5,022 $87,499 $15,012 $2,511 0.743007
21 7 $54 $0 $54 278 0 0 278 $87,499 $0 $87,499 $15,012 $2,511 0.295482
22 8 $54 $2 $56 278 0 0 278 $87,499 $0 $87,499 $15,568 $3,067 0.936117
23 9 $56 $1 $57 278 28 0 250 $87,499 $1,596 $89,095 $14,250 $3,345 0.618747
24 10 $57 $0 $57 250 0 0 250 $89,095 $0 $89,095 $14,250 $3,345 0.26106
25 11 $57 $2 $59 250 0 0 250 $89,095 $0 $89,095 $14,750 $3,845 0.952068
26 12 $59 $0 $59 250 0 0 250 $89,095 $0 $89,095 $14,750 $3,845 0.30923
27 13 $59 $2 $61 250 0 0 250 $89,095 $0 $89,095 $15,250 $4,345 0.981931
28 14 $61 $0 $61 250 0 0 250 $89,095 $0 $89,095 $15,250 $4,345 0.39265
29 15 $61 $0 $61 250 0 0 250 $89,095 $0 $89,095 $15,250 $4,345 0.499184
30 16 $61 $0 $61 250 0 0 250 $89,095 $0 $89,095 $15,250 $4,345 0.435649
31 17 $61 ($2) $59 250 0 0 250 $89,095 $0 $89,095 $14,750 $3,845 0.143737
32 18 $59 ($1) $58 250 0 25 275 $89,095 ($1,450) $87,645 $15,950 $3,595 0.28219
33 19 $58 ($1) $57 275 0 69 344 $87,645 ($3,933) $83,712 $19,608 $3,320 0.441452
34 20 $57 ($1) $56 344 0 86 430 $83,712 ($4,816) $78,896 $24,080 $2,976 0.282738
35 21 $56 $1 $57 430 0 0 430 $78,896 $0 $78,896 $24,510 $3,406 0.844039
36 22 $57 $0 $57 430 0 0 430 $78,896 $0 $78,896 $24,510 $3,406 0.308425
37 23 $57 $1 $58 430 0 0 430 $78,896 $0 $78,896 $24,940 $3,836 0.8359
38 24 $58 $1 $59 430 43 0 387 $78,896 $2,537 $81,433 $22,833 $4,266 0.693828
39 25 $59 ($2) $57 387 0 0 387 $81,433 $0 $81,433 $22,059 $3,492 0.074184
40 26 $57 $0 $57 387 0 0 387 $81,433 $0 $81,433 $22,059 $3,492 0.596865
41 27 $57 ($2) $55 387 0 0 387 $81,433 $0 $81,433 $21,285 $2,718 0.058696
42 28 $55 $1 $56 387 0 0 387 $81,433 $0 $81,433 $21,672 $3,105 0.856257
43 29 $56 ($1) $55 387 0 0 387 $81,433 $0 $81,433 $21,285 $2,718 0.168392
44 30 $55 ($2) $53 387 0 39 426 $81,433 ($2,067) $79,366 $22,578 $1,944 0.032677
45 31 $53 ($1) $52 426 0 107 533 $79,366 ($5,564) $73,802 $27,716 $1,518 0.351852
46 32 $52 $0 $52 533 0 0 533 $73,802 $0 $73,802 $27,716 $1,518 0.555496
47 33 $52 $1 $53 533 0 0 533 $73,802 $0 $73,802 $28,249 $2,051 0.725703
48 34 $53 ($2) $51 533 0 0 533 $73,802 $0 $73,802 $27,183 $985 0.010958
49 35 $51 ($1) $50 533 0 53 586 $73,802 ($2,650) $71,152 $29,300 $452 0.215836
50 36 $50 ($2) $48 586 0 147 733 $71,152 ($7,056) $64,096 $35,184 ($720) 0.113479
51 37 $48 ($2) $46 733 0 183 916 $64,096 ($8,418) $55,678 $42,136 ($2,186) 0.192113
52 38 $46 ($2) $44 916 0 229 1145 $55,678 ($10,076) $45,602 $50,380 ($4,018) 0.15966
53 39 $44 $1 $45 1145 0 0 1145 $45,602 $0 $45,602 $51,525 ($2,873) 0.885027
54 40 $45 $2 $47 1145 115 0 1030 $45,602 $5,405 $51,007 $48,410 ($583) 0.894322
55 41 $47 $1 $48 1030 258 0 772 $51,007 $12,384 $63,391 $37,056 $447 0.685802
56 42 $48 $0 $48 772 0 0 772 $63,391 $0 $63,391 $37,056 $447 0.457364
57 43 $48 ($1) $47 772 0 0 772 $63,391 $0 $63,391 $36,284 ($325) 0.298734
58 44 $47 ($2) $45 772 0 77 849 $63,391 ($3,465) $59,926 $38,205 ($1,869) 0.094938
59 45 $45 $0 $45 849 0 0 849 $59,926 $0 $59,926 $38,205 ($1,869) 0.672113
60 46 $45 $0 $45 849 0 0 849 $59,926 $0 $59,926 $38,205 ($1,869) 0.361101
61 47 $45 $0 $45 849 0 0 849 $59,926 $0 $59,926 $38,205 ($1,869) 0.36521
62 48 $45 $0 $45 849 0 0 849 $59,926 $0 $59,926 $38,205 ($1,869) 0.540239
63 49 $45 $0 $45 849 0 0 849 $59,926 $0 $59,926 $38,205 ($1,869) 0.539358
64 50 $45 $2 $47 849 0 0 849 $59,926 $0 $59,926 $39,903 ($171) 0.85528
65 51 $47 $2 $49 849 85 0 764 $59,926 $4,165 $64,091 $37,436 $1,527 0.995271
66 52 $49 $0 $49 764 0 0 764 $64,091 $0 $64,091 $37,436 $1,527 0.500433
67 53 $49 $0 $49 764 0 0 764 $64,091 $0 $64,091 $37,436 $1,527 0.534054
68 54 $49 ($2) $47 764 0 0 764 $64,091 $0 $64,091 $35,908 ($1) 0.026169
69 55 $47 $2 $49 764 0 0 764 $64,091 $0 $64,091 $37,436 $1,527 0.960474
70 56 $49 $1 $50 764 76 0 688 $64,091 $3,800 $67,891 $34,400 $2,291 0.767018
71 57 $50 $0 $50 688 0 0 688 $67,891 $0 $67,891 $34,400 $2,291 0.460534
72 58 $50 ($1) $49 688 0 0 688 $67,891 $0 $67,891 $33,712 $1,603 0.242858
73 59 $49 ($2) $47 688 0 69 757 $67,891 ($3,243) $64,648 $35,579 $227 0.124678
74 60 $47 ($2) $45 757 0 189 946 $64,648 ($8,505) $56,143 $42,570 ($1,287) 0.026532
75 61 $45 ($1) $44 946 0 237 1183 $56,143 ($10,428) $45,715 $52,052 ($2,233) 0.411713
76 62 $44 ($1) $43 1183 0 296 1479 $45,715 ($12,728) $32,987 $63,597 ($3,416) 0.36466
77 63 $43 ($2) $41 1479 0 370 1849 $32,987 ($15,170) $17,817 $75,809 ($6,374) 0.029239
78 64 $41 $0 $41 1849 0 0 1849 $17,817 $0 $17,817 $75,809 ($6,374) 0.748959
79 65 $41 $1 $42 1849 0 0 1849 $17,817 $0 $17,817 $77,658 ($4,525) 0.819633
80 66 $42 $0 $42 1849 0 0 1849 $17,817 $0 $17,817 $77,658 ($4,525) 0.444991
81 67 $42 $0 $42 1849 0 0 1849 $17,817 $0 $17,817 $77,658 ($4,525) 0.586849
82 68 $42 $2 $44 1849 0 0 1849 $17,817 $0 $17,817 $81,356 ($827) 0.864369
83 69 $44 $0 $44 1849 0 0 1849 $17,817 $0 $17,817 $81,356 ($827) 0.422939
84 70 $44 $1 $45 1849 0 0 1849 $17,817 $0 $17,817 $83,205 $1,022 0.758919
85 71 $45 $2 $47 1849 185 0 1664 $17,817 $8,695 $26,512 $78,208 $4,720 0.947805
86 72 $47 $2 $49 1664 416 0 1248 $26,512 $20,384 $46,896 $61,152 $8,048 0.920719
87 73 $49 $2 $51 1248 312 0 936 $46,896 $15,912 $62,808 $47,736 $10,544 0.923065
88 74 $51 $0 $51 936 0 0 936 $62,808 $0 $62,808 $47,736 $10,544 0.539055
89 75 $51 ($1) $50 936 0 0 936 $62,808 $0 $62,808 $46,800 $9,608 0.285704
90
91 Data table to replicate gain/loss over 75 days Frequency table
92 Replication Gain/loss Positive? Value Frequency
93 $9,608 ($10,000) 8
94 1 $10,007 1 ($7,500) 4
95 2 $5,256 1 ($5,000) 1
96 3 $1,232 1 ($2,500) 0
97 4 ($32,799) 0 $0 11
98 5 $846 1 $2,500 27
99 6 $7,399 1 $5,000 26
100 7 $3,353 1 $7,500 16
101 8 ($22,278) 0 $10,000 2
102 9 $5,719 1 5
103 10 $10,353 1
190 97 $3,815 1
191 98 $5,023 1
192 99 ($8,360) 0
193 100 $7,202 1
194 Average $785 % positive 76%
195 StDev $8,055
196 Minimum ($32,799)
197 Maximum $14,766
Cumulative gain/loss time series for 75 days
$12,000
$10,000
$8,000
$6,000
$4,000
Cum gain/loss
$2,000
$0
($2,000)
($4,000)
($6,000)
($8,000)
Day
30
25
20
Frequency
15
10
5
0
($10,000) ($7,500) ($5,000) ($2,500) $0 $2,500 $5,000 $7,500 $10,000
Cumulative gain/loss (upper limit of category)
A B C D E F G H I J K L M N
1 Investment example
2
3 Initial cash $100,000
4
5 Probability distributions (lookup tables)
6 Lookup table following decrease Lookup table following increase Lookup table following no change
7 Cum prob Change Cum prob Change Cum prob Change
8 0.00 -2 0.00 -2 0.00 -2
9 0.20 -1 0.10 -1 0.15 -1
10 0.45 0 0.25 0 0.35 0
11 0.75 1 0.55 1 0.65 1
12 0.90 2 0.80 2 0.85 2
13
Current Previous Current Current
Previous Change in share shares Shares Shares shares Previous Change in Current worth of Cumulative Random
14 Day share price share price price owned sold purchased owned cash cash cash shares gain/loss number
15 1 $50 ($2) $48 0 0 500 500 ######## ($24,000) $76,000 $24,000 $0 0.114837
16 2 $48 ($2) $46 500 0 50 550 $76,000 ($2,300) $73,700 $25,300 ($1,000) 0.028227
17 3 $46 ($1) $45 550 0 138 688 $73,700 ($6,210) $67,490 $30,960 ($1,550) 0.428447
18 4 $45 $2 $47 688 0 0 688 $67,490 $0 $67,490 $32,336 ($174) 0.991129
19 5 $47 ($2) $45 688 0 0 688 $67,490 $0 $67,490 $30,960 ($1,550) 0.090257
20 6 $45 $0 $45 688 0 0 688 $67,490 $0 $67,490 $30,960 ($1,550) 0.626621
21 7 $45 ($1) $44 688 0 0 688 $67,490 $0 $67,490 $30,272 ($2,238) 0.253885
22 8 $44 $0 $44 688 0 0 688 $67,490 $0 $67,490 $30,272 ($2,238) 0.619421
23 9 $44 $0 $44 688 0 0 688 $67,490 $0 $67,490 $30,272 ($2,238) 0.548954
24 10 $44 $0 $44 688 0 0 688 $67,490 $0 $67,490 $30,272 ($2,238) 0.48392
25 11 $44 $1 $45 688 0 0 688 $67,490 $0 $67,490 $30,960 ($1,550) 0.789099
26 12 $45 $2 $47 688 69 0 619 $67,490 $3,243 $70,733 $29,093 ($174) 0.951647
27 13 $47 $0 $47 619 0 0 619 $70,733 $0 $70,733 $29,093 ($174) 0.334811
28 14 $47 $0 $47 619 0 0 619 $70,733 $0 $70,733 $29,093 ($174) 0.388622
29 15 $47 $2 $49 619 0 0 619 $70,733 $0 $70,733 $30,331 $1,064 0.868324
30 16 $49 ($2) $47 619 0 0 619 $70,733 $0 $70,733 $29,093 ($174) 0.018564
31 17 $47 $0 $47 619 0 0 619 $70,733 $0 $70,733 $29,093 ($174) 0.527754
32 18 $47 ($1) $46 619 0 0 619 $70,733 $0 $70,733 $28,474 ($793) 0.278475
33 19 $46 ($2) $44 619 0 62 681 $70,733 ($2,728) $68,005 $29,964 ($2,031) 0.112955
34 20 $44 $0 $44 681 0 0 681 $68,005 $0 $68,005 $29,964 ($2,031) 0.545687
35 21 $44 $0 $44 681 0 0 681 $68,005 $0 $68,005 $29,964 ($2,031) 0.406403
36 22 $44 $0 $44 681 0 0 681 $68,005 $0 $68,005 $29,964 ($2,031) 0.495498
37 23 $44 $0 $44 681 0 0 681 $68,005 $0 $68,005 $29,964 ($2,031) 0.500234
38 24 $44 ($2) $42 681 0 0 681 $68,005 $0 $68,005 $28,602 ($3,393) 0.012596
39 25 $42 $2 $44 681 0 0 681 $68,005 $0 $68,005 $29,964 ($2,031) 0.915465
40 26 $44 $2 $46 681 68 0 613 $68,005 $3,128 $71,133 $28,198 ($669) 0.992102
41 27 $46 $1 $47 613 153 0 460 $71,133 $7,191 $78,324 $21,620 ($56) 0.64311
42 28 $47 ($1) $46 460 0 0 460 $78,324 $0 $78,324 $21,160 ($516) 0.194842
43 29 $46 $1 $47 460 0 0 460 $78,324 $0 $78,324 $21,620 ($56) 0.751817
44 30 $47 $2 $49 460 46 0 414 $78,324 $2,254 $80,578 $20,286 $864 0.802985
45 31 $49 $0 $49 414 0 0 414 $80,578 $0 $80,578 $20,286 $864 0.329589
46 32 $49 ($2) $47 414 0 0 414 $80,578 $0 $80,578 $19,458 $36 0.10111
47 33 $47 ($1) $46 414 0 41 455 $80,578 ($1,886) $78,692 $20,930 ($378) 0.212389
48 34 $46 ($2) $44 455 0 114 569 $78,692 ($5,016) $73,676 $25,036 ($1,288) 0.083121
49 35 $44 $0 $44 569 0 0 569 $73,676 $0 $73,676 $25,036 ($1,288) 0.545344
50 36 $44 ($2) $42 569 0 0 569 $73,676 $0 $73,676 $23,898 ($2,426) 0.030419
51 37 $42 $2 $44 569 0 0 569 $73,676 $0 $73,676 $25,036 ($1,288) 0.961052
52 38 $44 $1 $45 569 57 0 512 $73,676 $2,565 $76,241 $23,040 ($719) 0.706843
53 39 $45 ($1) $44 512 0 0 512 $76,241 $0 $76,241 $22,528 ($1,231) 0.119069
54 40 $44 $0 $44 512 0 0 512 $76,241 $0 $76,241 $22,528 ($1,231) 0.591332
55 41 $44 $1 $45 512 0 0 512 $76,241 $0 $76,241 $23,040 ($719) 0.686568
56 42 $45 $2 $47 512 51 0 461 $76,241 $2,397 $78,638 $21,667 $305 0.993065
57 43 $47 ($1) $46 461 0 0 461 $78,638 $0 $78,638 $21,206 ($156) 0.106723
58 44 $46 ($1) $45 461 0 46 507 $78,638 ($2,070) $76,568 $22,815 ($617) 0.338206
59 45 $45 $0 $45 507 0 0 507 $76,568 $0 $76,568 $22,815 ($617) 0.734044
60 46 $45 ($1) $44 507 0 0 507 $76,568 $0 $76,568 $22,308 ($1,124) 0.255585
61 47 $44 ($1) $43 507 0 51 558 $76,568 ($2,193) $74,375 $23,994 ($1,631) 0.313289
62 48 $43 ($2) $41 558 0 140 698 $74,375 ($5,740) $68,635 $28,618 ($2,747) 0.027427
63 49 $41 $0 $41 698 0 0 698 $68,635 $0 $68,635 $28,618 ($2,747) 0.568587
64 50 $41 ($1) $40 698 0 0 698 $68,635 $0 $68,635 $27,920 ($3,445) 0.308088
65 51 $40 $2 $42 698 0 0 698 $68,635 $0 $68,635 $29,316 ($2,049) 0.940386
66 52 $42 $1 $43 698 70 0 628 $68,635 $3,010 $71,645 $27,004 ($1,351) 0.739404
67 53 $43 $2 $45 628 157 0 471 $71,645 $7,065 $78,710 $21,195 ($95) 0.900413
68 54 $45 ($1) $44 471 0 0 471 $78,710 $0 $78,710 $20,724 ($566) 0.171577
69 55 $44 ($1) $43 471 0 47 518 $78,710 ($2,021) $76,689 $22,274 ($1,037) 0.272345
70 56 $43 $2 $45 518 0 0 518 $76,689 $0 $76,689 $23,310 ($1) 0.907106
71 57 $45 $2 $47 518 52 0 466 $76,689 $2,444 $79,133 $21,902 $1,035 0.90287
72 58 $47 $0 $47 466 0 0 466 $79,133 $0 $79,133 $21,902 $1,035 0.296047
73 59 $47 $1 $48 466 0 0 466 $79,133 $0 $79,133 $22,368 $1,501 0.684561
74 60 $48 $0 $48 466 0 0 466 $79,133 $0 $79,133 $22,368 $1,501 0.287944
75 61 $48 ($2) $46 466 0 0 466 $79,133 $0 $79,133 $21,436 $569 0.110682
76 62 $46 ($1) $45 466 0 47 513 $79,133 ($2,115) $77,018 $23,085 $103 0.21463
77 63 $45 ($2) $43 513 0 128 641 $77,018 ($5,504) $71,514 $27,563 ($923) 0.095924
78 64 $43 ($1) $42 641 0 160 801 $71,514 ($6,720) $64,794 $33,642 ($1,564) 0.280178
79 65 $42 $1 $43 801 0 0 801 $64,794 $0 $64,794 $34,443 ($763) 0.836697
80 66 $43 $0 $43 801 0 0 801 $64,794 $0 $64,794 $34,443 ($763) 0.416499
81 67 $43 $0 $43 801 0 0 801 $64,794 $0 $64,794 $34,443 ($763) 0.649598
82 68 $43 $2 $45 801 0 0 801 $64,794 $0 $64,794 $36,045 $839 0.914189
83 69 $45 $0 $45 801 0 0 801 $64,794 $0 $64,794 $36,045 $839 0.46461
84 70 $45 ($2) $43 801 0 0 801 $64,794 $0 $64,794 $34,443 ($763) 0.148656
85 71 $43 ($2) $41 801 0 80 881 $64,794 ($3,280) $61,514 $36,121 ($2,365) 0.163828
86 72 $41 ($2) $39 881 0 220 1101 $61,514 ($8,580) $52,934 $42,939 ($4,127) 0.166172
87 73 $39 ($2) $37 1101 0 275 1376 $52,934 ($10,175) $42,759 $50,912 ($6,329) 0.18472
88 74 $37 ($1) $36 1376 0 344 1720 $42,759 ($12,384) $30,375 $61,920 ($7,705) 0.35089
89 75 $36 ($1) $35 1720 0 430 2150 $30,375 ($15,050) $15,325 $75,250 ($9,425) 0.297319
90
91 Data table to replicate gain/loss over 75 days Frequency table
92 Replication Gain/loss Positive? Value Frequency
93 ($9,425) ($10,000) 8
94 1 $10,007 1 ($7,500) 4
95 2 $5,256 1 ($5,000) 1
96 3 $1,232 1 ($2,500) 0
97 4 ($32,799) 0 $0 11
98 5 $846 1 $2,500 27
99 6 $7,399 1 $5,000 26
100 7 $3,353 1 $7,500 16
101 8 ($22,278) 0 $10,000 2
102 9 $5,719 1 5
103 10 $10,353 1
190 97 $3,815 1
191 98 $5,023 1
192 99 ($8,360) 0
193 100 $7,202 1
194 Average $785 % positive 76%
195 StDev $8,055
196 Minimum ($32,799)
197 Maximum $14,766