最近讀到股市投資 "超級績效" 系列, 裡面有一段關於勝率與獲利/虧損組合的計算, 提到虧損造成的傷害具有幾何累績性, 其實獲利也是幾何累積的, 為釐清其中的比例關係, 確定作者的觀點是如何計算出來的, 因此寫了一段程式來驗證看看.

def stockgain(win_gain, lost_gain, win_count, lost_count):

    #totalcount = wincount + lostcount

    gain = 1

    for i in range(win_count):

        gain = gain * (1+win_gain)

    for i in range(lost_count):

        gain = gain * (1-lost_gain)

    return gain-1

 

print("win_gain lost_gain   win:20%   win:30%   win:40%   win:50%   win:60%    win:70%")

print("-------- ---------   -------   -------   -------   -------   -------    -------")

 

for gain in range(4, 101, 2):

    win_gain = gain/100

    lost_gain = win_gain/2

    g2 = stockgain(win_gain, lost_gain, 2, 8)*100

    g3 = stockgain(win_gain, lost_gain, 3, 7)*100

    g4 = stockgain(win_gain, lost_gain, 4, 6)*100

    g5 = stockgain(win_gain, lost_gain, 5, 5)*100

    g6 = stockgain(win_gain, lost_gain, 6, 4)*100

    g7 = stockgain(win_gain, lost_gain, 7, 3)*100

    print("{:6.2f}%  {:6.2f}%    {:7.2f}%  {:7.2f}%  {:7.2f}%  {:7.2f}%  {:7.2f}%   {:7.2f}%".format(win_gain*100, lost_gain*100, g2, g3, g4, g5, g6, g7))

 結果如下:

 

win_gain lost_gain   win:20%   win:30%   win:40%   win:50%   win:60%    win:70%

-------- ---------   -------   -------   -------   -------   -------    -------

  4.00%    2.00%      -7.98%    -2.35%     3.63%     9.98%    16.71%     23.85%

  6.00%    3.00%     -11.94%    -3.77%     5.16%    14.92%    25.58%     37.23%

  8.00%    4.00%     -15.86%    -5.34%     6.49%    19.80%    34.78%     51.63%

 10.00%    5.00%     -19.73%    -7.05%     7.62%    24.62%    44.29%     67.08%

 12.00%    6.00%     -23.54%    -8.89%     8.55%    29.34%    54.11%     83.62%

 14.00%    7.00%     -27.28%   -10.86%     9.27%    33.95%    64.20%    101.27%

 16.00%    8.00%     -30.94%   -12.93%     9.79%    38.43%    74.54%    120.07%

 18.00%    9.00%     -34.52%   -15.09%    10.10%    42.76%    85.12%    140.05%

 20.00%   10.00%     -38.01%   -17.35%    10.20%    46.93%    95.91%    161.21%

 22.00%   11.00%     -41.41%   -19.68%    10.10%    50.92%   106.88%    183.59%

 24.00%   12.00%     -44.70%   -22.08%     9.80%    54.71%   118.00%    207.18%

 26.00%   13.00%     -47.89%   -24.53%     9.29%    58.29%   129.25%    232.01%

 28.00%   14.00%     -50.98%   -27.03%     8.60%    61.64%   140.58%    258.07%

 30.00%   15.00%     -53.95%   -29.57%     7.72%    64.74%   151.96%    285.35%

 32.00%   16.00%     -56.81%   -32.13%     6.65%    67.60%   163.37%    313.86%

 34.00%   17.00%     -59.56%   -34.71%     5.41%    70.18%   174.75%    343.58%

 36.00%   18.00%     -62.19%   -37.29%     4.00%    72.49%   186.08%    374.48%

 38.00%   19.00%     -64.71%   -39.88%     2.43%    74.51%   197.31%    406.53%

 40.00%   20.00%     -67.12%   -42.45%     0.71%    76.23%   208.41%    439.72%

 42.00%   21.00%     -69.41%   -45.01%    -1.16%    77.65%   219.33%    473.98%

 44.00%   22.00%     -71.59%   -47.55%    -3.17%    78.77%   230.03%    509.29%

 46.00%   23.00%     -73.66%   -50.05%    -5.30%    79.56%   240.47%    545.57%

 48.00%   24.00%     -75.62%   -52.52%    -7.55%    80.04%   250.61%    582.77%

 50.00%   25.00%     -77.47%   -54.95%    -9.90%    80.20%   260.41%    620.81%

 52.00%   26.00%     -79.23%   -57.33%   -12.35%    80.04%   269.82%    659.63%

 54.00%   27.00%     -80.87%   -59.65%   -14.88%    79.56%   278.81%    699.12%

 56.00%   28.00%     -82.42%   -61.92%   -17.49%    78.77%   287.33%    739.21%

 58.00%   29.00%     -83.88%   -64.13%   -20.17%    77.65%   295.34%    779.78%

 60.00%   30.00%     -85.24%   -66.27%   -22.90%    76.23%   302.82%    820.73%

 62.00%   31.00%     -86.52%   -68.34%   -25.67%    74.51%   309.72%    861.95%

 64.00%   32.00%     -87.70%   -70.35%   -28.48%    72.49%   316.01%    903.31%

 66.00%   33.00%     -88.81%   -72.28%   -31.31%    70.18%   321.65%    944.67%

 68.00%   34.00%     -89.84%   -74.13%   -34.16%    67.60%   326.61%    985.92%

 70.00%   35.00%     -90.79%   -75.92%   -37.01%    64.74%   330.87%   1026.89%

 72.00%   36.00%     -91.67%   -77.62%   -39.86%    61.64%   334.40%   1067.45%

 74.00%   37.00%     -92.49%   -79.25%   -42.69%    58.29%   337.18%   1107.44%

 76.00%   38.00%     -93.24%   -80.80%   -45.50%    54.71%   339.18%   1146.71%

 78.00%   39.00%     -93.93%   -82.28%   -48.28%    50.92%   340.39%   1185.08%

 80.00%   40.00%     -94.56%   -83.67%   -51.02%    46.93%   340.80%   1222.40%

 82.00%   41.00%     -95.14%   -85.00%   -53.72%    42.76%   340.39%   1258.49%

 84.00%   42.00%     -95.66%   -86.25%   -56.36%    38.43%   339.16%   1293.18%

 86.00%   43.00%     -96.14%   -87.42%   -58.95%    33.95%   337.10%   1326.31%

 88.00%   44.00%     -96.58%   -88.52%   -61.47%    29.34%   334.21%   1357.70%

 90.00%   45.00%     -96.98%   -89.56%   -63.93%    24.62%   330.50%   1387.18%

 92.00%   46.00%     -97.33%   -90.52%   -66.30%    19.80%   325.97%   1414.57%

 94.00%   47.00%     -97.66%   -91.42%   -68.60%    14.92%   320.64%   1439.71%

 96.00%   48.00%     -97.95%   -92.26%   -70.82%     9.98%   314.52%   1462.44%

 98.00%   49.00%     -98.21%   -93.03%   -72.96%     5.00%   307.64%   1482.58%

100.00%   50.00%     -98.44%   -93.75%   -75.00%     0.00%   300.00%   1500.00%

 

 

 

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