Python：「破産の確率」の計算とグラフ化（コピペするだけ！）

import numpy as np

win_pct     = 0.38     # 勝率
risk_reward = 2.09     # リスクリワード比率
risk_rate   = 0.05     # 1回のトレードで取るリスク率

class ruin_fixed_amonunt():

    def __init__( self ,win_pct ,risk_reward ,risk_rate ):
        self.win_pct     = win_pct
        self.risk_reward = risk_reward
        self.risk_rate   = risk_rate
        if self.is_error() : raise

    def is_error( self ) :
        if self.win_pct     == 0 \
        or self.risk_reward == 0 \
        or self.risk_rate   == 0 :
            return True
        elif not 0 <= self.win_pct <= 1   \
        or   not 0 <  self.risk_reward    \
        or   not 0 <= self.risk_rate <= 1 :
            return True
        else :
            return False

    def equation( self ,x ,P ,R ) :
        return P * x**( R + 1 ) + ( 1 - P ) - x

    def solve_equation( self ) :
        S ,P ,R = 0 ,self.win_pct ,self.risk_reward
        while self.equation( S ,P ,R ) > 0:
            S += 1e-4
        if S >= 1 : S = 1
        return S

    def calc( self ) :
        S = self.solve_equation()
        return S ** ( 1 / self.risk_rate )    



if __name__=='__main__' :
    ruin_rate = ruin_fixed_amonunt( win_pct ,risk_reward ,risk_rate ).calc()
    print( f"破産確率（定額）は{ ruin_rate :.2%}です" )

破産確率（定額）は3.87%です

import numpy as np

win_pct     = 0.38     # 勝率
risk_reward = 2.09     # 損益レシオ
risk_rate   = 0.05     # 1回のトレードで取るリスク率
funds       = 1000000  # 初期資金
ruin_line   = 200000   # 撤退ライン（破産）

class ruin_fixed_rate():

    def __init__( self ,win_pct ,risk_reward ,risk_rate ,funds ,ruin_line ):
        self.win_pct     = win_pct
        self.risk_reward = risk_reward
        self.risk_rate   = risk_rate
        self.funds       = funds
        self.ruin_line   = ruin_line
        if self.is_error() : raise

    def is_error( self ) :
        if self.win_pct     == 0 \
        or self.risk_reward == 0 \
        or self.risk_rate   == 0 \
        or self.ruin_line   == 0 :
            return True
        elif not 0 <= self.win_pct <= 1   \
        or   not 0 <  self.risk_reward    \
        or   not 0 <= self.risk_rate <= 1 \
        or self.funds < 0                 \
        or self.ruin_line < 0             \
        or self.ruin_line > self.funds :
            return True
        else :
            return False

    def equation( self ,x ,P ,R ) :
        return P * x**( R + 1 ) + ( 1 - P ) - x

    def solve_equation( self ,win_pct ,R ) :
        S ,P = 0 ,win_pct
        while self.equation( S ,P ,R ) > 0:
            S += 1e-4
        if S >= 1 : S = 1
        return S

    def calc( self ) :
        a = np.log( 1 + self.risk_reward * self.risk_rate )
        b = abs( np.log( 1 - self.risk_rate ) )
        n = np.log( self.funds / self.ruin_line )
        R = a / b
        S = self.solve_equation( self.win_pct ,R )
        return S ** ( n / b )



if __name__=='__main__' :
    ruin_rate = ruin_fixed_rate( win_pct ,risk_reward ,risk_rate ,funds ,ruin_line ).calc()
    print( f"破産確率（定率）は{ ruin_rate :.2%}です" )

破産確率（定率）は2.46%です

# Plotly のインストール
!pip install plotly --upgrade

import pandas as pd
import plotly
import plotly.graph_objs as go
import plotly.figure_factory as ff
plotly.offline.init_notebook_mode( connected=True )

# google colabでplotlyを表示するにはこれが必要。
# グラフを書き出すセルごとに使用する
def enable_plotly_in_cell():
    import IPython
    from plotly.offline import init_notebook_mode
    display(IPython.core.display.HTML('''
            <script src="/static/components/requirejs/require.js"></script>
    '''))
    init_notebook_mode( connected=False )

win_range = np.arange(0.3 ,0.62 ,0.005)
rr_range  = np.arange(0.4 ,3.1 ,0.025)
risk_rate = 0.02
funds     = 1000000
ruin_line = 200000

df_ruin = pd.DataFrame()
for win in win_range :
    for rr in rr_range :
        ruin_rate = ruin_fixed_rate( win ,rr ,risk_rate ,funds ,ruin_line ).calc()
        df_ruin.loc[ rr ,win ] = ruin_rate

df_ruin

layout = go.Layout( title         = f'定率、損失の許容：{risk_rate}、元金{funds/10000:.0f}万円、破産の基準：{ruin_line/10000:.0f}万円'
                  , autosize      = False
                  , paper_bgcolor = "#000"
                  , width         = 1000
                  , height        = 800
                  , scene = dict(
                          aspectmode  = "manual"
                        , aspectratio = dict(x=1 ,y=1 ,z=0.5)
                        , xaxis = dict(color="#fff" ,linecolor="#fff" ,gridcolor="#eee" ,title="勝率")
                        , yaxis = dict(color="#fff" ,linecolor="#fff" ,gridcolor="#eee" ,title="リスクリワード比率")
                        , zaxis = dict(color="#fff" ,linecolor="#fff" ,gridcolor="#eee" ,title="破産の確率")
                        , camera = dict(eye=dict(x=2 ,y=1.25 ,z=1.5)) )
                  , font = dict(color="#fff") )

z1 = df_ruin

data = [ go.Surface( z = z1.T
                   , y = z1.index
                   , x = z1.columns
                   , cmin=0 ,cmax=1
                   , colorscale = "Jet"
                   , colorbar   = dict(lenmode='fraction', len=0.5)
                   , contours   = dict(x=dict(color="#fff") ,y=dict(color="#fff") ,z=dict(color="#fff")) ) ]

enable_plotly_in_cell()
plotly.offline.iplot( go.Figure( data=data ,layout=layout ) )