Optimalf 141
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
2.00 1.82 1.67 1.54 1.43 1.33 1.25 1.18 1.11 1.05 1.00
7.00 6.82 6.67 6.54 6.43 6.33 6.25 6.18 6.11 6.05 6.00
3.50 3.07 2.67 2.29 1.93 1.59 1.25 0.93 0.61 0.30 0.00
12.25 11.51 10.67 9.73 8.68 7.52 6.25 4.86 3.36 1.74 0.00
21.446.13 19.425.18 17.074.27 14.473.40 11.722.60 8.931.88 6.251.25 0.733.83 0.341.85 0.090.50 0.000.00
10.72 8.74 6.83 5.06 3.51 2.23 1.25 0.57 0.18 0.03 0.00
37.52 32.76 27.31 21.52 15.82 10.61 6.25 3.02 1.02 0.14 0.00
65.6518.76 14.7455.29 43.6910.92 32.017.53 21.354.75 12.592.65 6.251.25 0.452.38 0.100.56 0.010.04 0.000.00
32.83 24.88 17.48 11.20 6.41 3.15 1.25 0.36 0.06 .00 0.00
114.89 93.30 69.91 47.62 28.83 14.96 6.25 1.87 0.31 0.01 0.00
57.45 41.99 27.96 16.67 8.65 3.74 1.25 0.28 0.03 .00 0.00
100.53201.06 157.4570.85 111.8544.74 70.8324.79 11.6738.92 17.764.44 6.251.25 1.470.22 0.170.02 .00.00 0.000.00
351.86 265.69 178.96 105.36 52.54 21.09 6.25 1.16 0.09 .00 0.00
175.93 119.56 71.58 36.88 15.76 5.27 1.25 0.17 0.01 .00 0.00
307.87615.75 448.35201.76 114.53286.33 156.7254.85 21.2870.92 25.046.26 1.256.25 0.910.14 0.050.01 .00.00 0.000.00
1077.56 756.59 458.13 233.12 95.75 29.74 6.25 0.72 0.03 .00 0.00
538.78 340.47 183.25 81.59 28.72 7.43 1.25 0.11 .00 .00 0.00
1885.73 1276.75 733.01 346.77 129.26 35.32 6.25 0.57 0.02 .00 0.00
3300.02942.86 2154.52574.54 1172.81293.20 121.37515.82 174.5038.78 41.948.83 6.251.25 0.080.45 0.01.00 .00.00 0.000.00
1650.01 969.53 469.12 180.54 52.35 10.48 1.25 0.07 .00 .00 0.00
5775.04 3635.75 1876.50 767.29 235.57 49.80 6.25 0.35 .00 .00 0.00
10106.312887.52 6135.331636.09 3002.40750.60 1141.34268.55 318.0270.67 59.1412.45 6.251.25 0.050.28 .00.00 .00.00 0.000.00
5053.16 2760.90 1200.96 399.47 95.41 14.78 1.25 0.04 .00 .00 0.00
17686.04 10353.36 4803.84 1697.75 429.33 70.23 6.25 0.22 .00 .00 0.00
8843.02 4659.01 1921.54 594.21 128.80 17.56 1.25 0.03 .00 .00 0.00
15475.2930950.58 17471.307862.09 3074.467686.14 2525.40883.89 173.88579.59 20.8583.39 1.256.25 0.170.03 .00.00 .00.00 0.000.00
54163.51 29482.82 12297.83 3756.53 782.45 99.03 6.25 0.14 .00 .00 0.00
27081.76 13267.27 4919.13 1314.79 234.73 24.76 1.25 0.02 .00 .00 0.00
47393.0794786.15 49752.2722388.52 19676.537870.61 5587.841955.74 1056.30316.89 117.6029.40 6.251.25 0.110.02 .00.00 .00.00 0.000.00
165875.76 83956.95 31482.44 8311.92 1426.01 139.65 6.25 0.08 .00 .00 0.00
82937.88 37780.63 12592.98 2909.17 427.80 34.91 1.25 0.01 .00 .00 0.00
290282.57 141677.35 50371.91 12363.97 1925.11 165.83 6.25 0.07 .00 .00 0.00
145141.29 63754.81 20148.76 4327.39 577.53 41.46 1.25 0.01 .00 .00 0.00
72570.64 35065.14 12089.26 2812.80 404.27 31.09 1.00 0.01 .00 .00 0.00
Drawdown and Largest Loss withf
First, if you havef=1.00, then as soon as the biggest loss is encountered,
you would be tapped out. This is as it should be. You wantfto be bounded
at 0 (nothing at stake) and 1 (the lowest amount at stake where you would
lose 100%).
Second, in an independent trials process the sequence of trades that
results in the drawdown is, in effect, arbitrary (as a result of the indepen-
dence). Suppose we toss a coin six times, and we get heads three times and
tails three times. Suppose that we win $1 every time heads comes up and
lose $1 every time tails comes up. Considering all possible sequences here
our drawdown could be $1, $2, or $3, the extreme case where all losses
bunch together. If we went through this exercise once and came up with
a $2 drawdown, it wouldn’t mean anything. Since drawdown is anextreme
case situation, and we are speaking of exact sequences of trades that are
independent, we have to assume that the extreme case can be all losses
bunching together in a row (the extreme worst case in the sample space).