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I performed a simulation on Bob Fulks's problem and confirmed my
previous statement.
First, let me say that I am NOT attempting to refute the math shown by
both Bob and Mark Johnson - my point is that one must be very cautious
in attributing significance to such purely mathematical results when the
mathematical model contains one or more crucial simplifying
assumptions. Sometimes such assumptions will be essentially harmless,
but at other times they could be fatal.
The model I used is certainly far from being a perfect model of reality,
but I feel it more closely represents real trading than the assumptions
of the simple math model. Following is my model:
The numbers of wins and losses are APPROXIMATELY equal: For each
"trade" I generated a random win probability uniformly distributed in
the interval 25% to 75%. I then generated another random number
uniformly distributed in the interval 0 to 99; the "trade" was a win if
the latter number was <= (less than or equal to) the generated
probability, otherwise it was a loss.
Similarly, the win factors were generated as random values uniformly
distributed in the interval 1.019 to 1.021 and loss factors in the
interval 0.985 to 0.995 resulting in average gains of 2% and average
losses of 1%. Note that the min gain is 1.9%, the max gain 2.1%, and
the min and max losses 0.5% and 1.5% respectively with average gain of
2% and average loss of 1%.
The attached file shows how variable the results can be with even such
tight constraints on the parameters. Also, note that with longer runs,
the results DIverge, they do not CONverge as one might expect from
"averaging".
Regards - Carroll S.Each following line represents a run of 100 trades:
53 wins, 47 losses. 0.02000 ave win; -0.00939 ave loss. Final equity: 1.833
54 wins, 46 losses. 0.02009 ave win; -0.01018 ave loss. Final equity: 1.828
57 wins, 43 losses. 0.02013 ave win; -0.00916 ave loss. Final equity: 2.097
54 wins, 46 losses. 0.01999 ave win; -0.01038 ave loss. Final equity: 1.802
46 wins, 54 losses. 0.01999 ave win; -0.00998 ave loss. Final equity: 1.446
46 wins, 54 losses. 0.01996 ave win; -0.00902 ave loss. Final equity: 1.521
47 wins, 53 losses. 0.01989 ave win; -0.00917 ave loss. Final equity: 1.549
53 wins, 47 losses. 0.01983 ave win; -0.00975 ave loss. Final equity: 1.785
54 wins, 46 losses. 0.01996 ave win; -0.00987 ave loss. Final equity: 1.841
43 wins, 57 losses. 0.01987 ave win; -0.00989 ave loss. Final equity: 1.322
49 wins, 51 losses. 0.02002 ave win; -0.01075 ave loss. Final equity: 1.522
57 wins, 43 losses. 0.01999 ave win; -0.01045 ave loss. Final equity: 1.967
60 wins, 40 losses. 0.01995 ave win; -0.00966 ave loss. Final equity: 2.218
61 wins, 39 losses. 0.02003 ave win; -0.01063 ave loss. Final equity: 2.210
48 wins, 52 losses. 0.02014 ave win; -0.00997 ave loss. Final equity: 1.546
49 wins, 51 losses. 0.01996 ave win; -0.01041 ave loss. Final equity: 1.544
44 wins, 56 losses. 0.02012 ave win; -0.01048 ave loss. Final equity: 1.332
53 wins, 47 losses. 0.02002 ave win; -0.01103 ave loss. Final equity: 1.698
55 wins, 45 losses. 0.02005 ave win; -0.00975 ave loss. Final equity: 1.917
43 wins, 57 losses. 0.02002 ave win; -0.01034 ave loss. Final equity: 1.296
Final equity ranges from low of 1.296 to high of 2.218 (high/low ratio of 1.71).
Each following line represents a run of 1000 trades:
510 wins, 490 losses. 0.02002 ave win; -0.00986 ave loss. Final equity: 190.824
515 wins, 485 losses. 0.02001 ave win; -0.00985 ave loss. Final equity: 221.673
510 wins, 490 losses. 0.01998 ave win; -0.00982 ave loss. Final equity: 191.567
500 wins, 500 losses. 0.02000 ave win; -0.01000 ave loss. Final equity: 130.954
526 wins, 474 losses. 0.02001 ave win; -0.01008 ave loss. Final equity: 274.120
517 wins, 483 losses. 0.02000 ave win; -0.00982 ave loss. Final equity: 237.786
496 wins, 504 losses. 0.01998 ave win; -0.00973 ave loss. Final equity: 131.742
512 wins, 488 losses. 0.01999 ave win; -0.00991 ave loss. Final equity: 194.504
506 wins, 494 losses. 0.02002 ave win; -0.01006 ave loss. Final equity: 153.380
506 wins, 494 losses. 0.01999 ave win; -0.01008 ave loss. Final equity: 149.552
486 wins, 514 losses. 0.02002 ave win; -0.00992 ave loss. Final equity: 90.897
504 wins, 496 losses. 0.01998 ave win; -0.00976 ave loss. Final equity: 164.895
521 wins, 479 losses. 0.02001 ave win; -0.01009 ave loss. Final equity: 235.222
537 wins, 463 losses. 0.01996 ave win; -0.01008 ave loss. Final equity: 371.493
475 wins, 525 losses. 0.02003 ave win; -0.01012 ave loss. Final equity: 59.157
482 wins, 518 losses. 0.01999 ave win; -0.01007 ave loss. Final equity: 73.285
509 wins, 491 losses. 0.02002 ave win; -0.01007 ave loss. Final equity: 167.058
539 wins, 461 losses. 0.01999 ave win; -0.01012 ave loss. Final equity: 393.623
511 wins, 489 losses. 0.01997 ave win; -0.01012 ave loss. Final equity: 168.686
495 wins, 505 losses. 0.01999 ave win; -0.01016 ave loss. Final equity: 103.392
Final equity ranges from low of 59.157 to high of 393.6 (high/low ratio of 6.65).
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