Optimalf 143
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
1.00 0.82 0.67 0.54 0.43 0.33 0.25 0.18 0.11 0.05 0.00
0.50 0.37 0.27 0.19 0.13 0.08 0.05 0.03 0.01 .00 0.00
0.25 0.17 0.11 0.07 0.04 0.02 0.01 .00 .00 .00 0.00
0.060.13 0.070.03 0.020.04 0.020.01 0.01.00 0.01.00 .00.00 .00.00 .00.00 .00.00 0.000.00
0.03 0.02 0.01 .00 .00 .00 .00 .00 .00 .00 0.00
0.02 0.01 .00 .00 .00 .00 .00 .00 .00 .00 0.00
0.01.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 0.000.00
.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 0.00
.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 0.00
.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 0.00
0.010.01 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 0.000.00
0.01 0.01 .00 .00 .00 .00 .00 .00 .00 .00 0.00
0.02 0.01 .00 .00 .00 .00 .00 .00 .00 .00 0.00
0.050.03 0.020.01 0.01.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 .00.00 0.000.00
0.08 0.03 0.01 .00 .00 .00 .00 .00 .00 .00 0.00
0.11 0.05 0.02 0.01 .00 .00 .00 .00 .00 .00 0.00
0.17 0.08 0.03 0.01 .00 .00 .00 .00 .00 .00 0.00
0.380.25 0.180.12 0.080.05 0.030.02 0.01.00 .00.00 .00.00 .00.00 .00.00 .00.00 0.000.00
0.57 0.29 0.13 0.05 0.01 .00 .00 .00 .00 .00 0.00
0.86 0.44 0.20 0.08 0.02 0.01 .00 .00 .00 .00 0.00
1.921.28 1.070.69 0.520.32 0.210.13 0.070.04 0.020.01 .00.00 .00.00 .00.00 .00.00 0.000.00
2.89 1.65 0.83 0.35 0.12 0.03 0.01 .00 .00 .00 0.00
4.33 2.56 1.32 0.58 0.20 0.05 0.01 .00 .00 .00 0.00
6.49 3.97 2.11 0.95 0.34 0.09 0.02 .00 .00 .00 0.00
14.619.74 9.536.15 5.413.38 2.581.57 0.990.58 0.280.16 0.050.03 0.01.00 .00.00 .00.00 0.000.00
21.92 14.77 8.65 4.26 1.68 0.49 0.10 0.01 .00 .00 0.00
32.88 22.89 13.85 7.04 2.86 0.87 0.17 0.02 .00 .00 0.00
73.9849.32 55.0035.49 35.4522.15 19.1611.61 8.284.87 2.651.51 0.568.31 0.030.06 .00.00 .00.00 0.000.00
110.97 85.25 56.71 31.61 14.07 4.64 1.00 0.11 .00 .00 0.00
166.45 132.14 90.74 52.16 23.92 8.12 1.80 0.21 0.01 .00 0.00
249.68 204.82 145.19 86.06 40.66 14.21 3.24 0.38 0.01 .00 0.00
374.51 317.48 232.30 142.00 69.12 24.86 5.83 0.70 0.03 .00 0.00
187.26 174.61 139.38 92.30 48.38 18.64 4.66 0.60 0.02 .00 0.00
Just because we experienced one exact sequence of six coin flips wherein
the drawdown was $2 doesn’t mean we can use that as any kind of a mean-
ingful benchmark, since the next exact sequence is equally likely to be any
other possible sequence as it is to be the sequence we are basing this draw-
down figure on.
Return to the coin toss, whereby if we win, we win $1, and if we lose,
we lose $1. Suppose 20 tosses have gone by and you have experienced a
drawdown of $5 at one point. What does this mean? Does this mean that we
can expect “about” a $5 drawdown on the next 20 tosses? Since coin tossing
is an independent trials process (as trading is for the most part), the answer
to all of these questions is no. The only estimating we can perform here is
one based on the losing streaks involved. With a 20-coin toss we can figure
probabilities of getting 20 tosses against us, 19 tosses, and so on. But what
we are talking about with drawdown is absolute worst case—an extreme.
What we are looking for is an answer to the question, “How far out on the
tails of the distribution, to the adverse side, is the limit?” The answer is that
there is no limit—all future coin tosses, the next 20 tosses and all sequences
of 20 tosses, could go against us. It’s highly unlikely, but it could happen. To