Trade parameters : win rate, take profit, stop loss, fees and leverage

In [1]:

# The trade parameters
win_rate = 0.55 # just above 0.5
take_profit = 0.10
stop_loss = 0.02
fee_rate = 0.002
leverage = 2

Simulation parameters : number of simulation and number of trade

In [2]:

# The simulations parameters
n_simus = 1000
n_trades = 300

In [3]:

import numpy as np
import matplotlib.pyplot as plt

In [4]:

# Win rate probability law
X = lambda : 1 if np.random.rand() <= win_rate else 0

# Return on Investment law
def s(x):
    """Return the PNl of a trade (fees included)"""
    if x == 1:
        return leverage * ((1-fee_rate)*take_profit - fee_rate - (1-fee_rate)*(1+take_profit)*fee_rate)
    else:
        return - leverage * ((1-fee_rate)*stop_loss + fee_rate + (1-fee_rate)*(1-stop_loss)*fee_rate)

# Define the array to store the simulations
MC = np.zeros(shape=(n_trades, n_simus))
for i in range(n_trades):
    for j in range(n_simus):
        MC[i,j] = s(X())

# Now, compute the cumulative sum, count the simulations that fail (reach 0)
# And plot each simulation
fig = plt.figure(figsize=(15, 10))
n_null = 0
for j in range(n_simus):
    MC[:,j] = 1 + MC[:,j].cumsum()
    plt.plot(MC[:,j], linewidth=0.6, color='darkblue')
    if False in np.where(MC[:,j] >= 0, True, False):
        n_null += 1
        
# Plot all the simulations
plt.plot([0]*n_trades, linewidth=0.8, color='red')
plt.xlabel("Number of trades", fontsize=16)
plt.ylabel("Performance", fontsize=16)
plt.title(f"Leverage:{leverage} ; Winning rate:{win_rate} ; Take profit: {take_profit} ; Stop loss: {stop_loss} ; Fees rate: {fee_rate}", fontsize=18)
plt.show() 


# Compute a few statistics
expectancy = win_rate * ((1-fee_rate)*take_profit - fee_rate - (1-fee_rate)*(1+take_profit)*fee_rate)
expectancy -= (1 - win_rate) * ((1-fee_rate)*stop_loss + fee_rate + (1-fee_rate)*(1-stop_loss)*fee_rate)
print('\n+++++++++++++++++++++++++\n')
print(f"Trade PNL expectancy (without any leverage): {round(100*expectancy, 2)}%")
print(f"Number of simulations that reached 0: {n_null}")
print(f"Minimal portfolio value encountered: {round(np.min(MC), 4)}")
print(f"Average final portfolio value: {round(np.mean(MC[-1,:]), 2)}")
print(f"Minimal final portfolio value: {round(np.min(MC[-1,:]), 2)}")
print('\n+++++++++++++++++++++++++\n')

+++++++++++++++++++++++++

Trade PNL expectancy (without any leverage): 4.18%
Number of simulations that reached 0: 0
Minimal portfolio value encountered: 0.6173
Average final portfolio value: 26.19
Minimal final portfolio value: 20.36

+++++++++++++++++++++++++

In [5]:

class PreDataFrame:
    """
    init with columns : \n
    x = PreDataFrame("ticker", "exchange")\n
    dataF = pd.DataFrame(x.__dict__)\n
    add function if necessary (every function name should start with "func*") : \n
    x = PreDataFrame("ticker", "exchange", "func0"=toto, "func1"=tata...)
    """
    def __init__(self, *args, **kwargs):  
        for x in args:
            self.__dict__.update({x:[]})
        self.__dict__.update(kwargs)

    def result(self):
        res={} 
        for key, val in self.__dict__.items():
            if not key.startswith("func"):
                res[key]=val
        return res

    def display(self):
        res={} 
        for key, val in self.__dict__.items():
            if not key.startswith("func") and key!= "Datas":
                res[key]=val
        return res

In [6]:

import pandas as pd

# simulation parameters
n_simus = 1000
n_trades = 300

# fix fees rate for Demo (Forex like on major currencies), fixed stop_loss (Forex context)
fee_rate = 0.002
stop_loss = 0.02

formate = PreDataFrame('Average_performance', 'Forecast_precision', 'Out_of_money_risk','Leverage'
                             ,'Take_profit', 'Fee_rate', 'Stop_loss','Datas')
final_result = pd.DataFrame(formate.result())

In [7]:

### Overview of different simulations, example with different leverages...

def loope(win_rate, take_profit, leverage, fee_rate, stop_loss, res_lists, n_simus, n_trades):
    
    stop_loss = 0.02
    fee_rate = 0.002

    # Win rate probability law
    X = lambda : 1 if np.random.rand() <= win_rate else 0

    # Return on Investment law
    def s(x):
        """Return the PNl of a trade (fees included)"""
        if x == 1:
            return leverage * ((1-fee_rate)*take_profit - fee_rate - (1-fee_rate)*(1+take_profit)*fee_rate)
        else:
            return - leverage * ((1-fee_rate)*stop_loss + fee_rate + (1-fee_rate)*(1-stop_loss)*fee_rate)

        
    # Define the array to store the simulations
    MC = np.zeros(shape=(n_trades, n_simus))
    for i in range(n_trades):
        for j in range(n_simus):
            MC[i,j] = s(X())
        
        
    # Now, compute the cumulative sum, count the simulations that fail (reach 0)
    # And plot each simulation
    n_null = 0
    for j in range(n_simus):
        MC[:,j] = 1 + MC[:,j].cumsum()
        #plt.plot(MC[:,j], linewidth=0.6, color='darkblue')
        if False in np.where(MC[:,j] >= 0, True, False):
            n_null += 1
    
    #return win_rate, round(np.mean(MC[-1,:]), 2), n_null/n_simus, leverage, take_profit, fee_rate, stop_loss, MC
    res_lists.Forecast_precision.append(win_rate)
    res_lists.Average_performance.append(round(np.mean(MC[-1,:]), 2))
    res_lists.Out_of_money_risk.append(n_null/n_simus)
    res_lists.Leverage.append(leverage)
    res_lists.Take_profit.append(take_profit)
    res_lists.Fee_rate.append(fee_rate)
    res_lists.Stop_loss.append(stop_loss)
    res_lists.Datas.append(MC)

    
for leverage in range(1, 10, 1):
    
    
    # win_rate, performance and risk main loop
    res_lists = PreDataFrame('Average_performance','Forecast_precision','Out_of_money_risk','Leverage'
                             ,'Take_profit','Fee_rate', 'Stop_loss','Datas')
    for win_rate in np.arange (0.1, 1, 0.1):
        for take_profit in np.arange (0.1, 1, 0.1):
            loope(win_rate, take_profit, leverage, fee_rate, stop_loss, res_lists, n_simus, n_trades)

    result = pd.DataFrame(res_lists.display())           
    display(result)
    final_result = pd.concat([final_result, pd.DataFrame(res_lists.result())])
    res_lists = None
    result = None
    

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-2.60	0.1	1.000	1	0.1	0.002	0.02
1	0.42	0.1	0.538	1	0.2	0.002	0.02
2	3.41	0.1	0.110	1	0.3	0.002	0.02
3	6.44	0.1	0.046	1	0.4	0.002	0.02
4	9.32	0.1	0.020	1	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	133.81	0.9	0.000	1	0.5	0.002	0.02
77	160.38	0.9	0.000	1	0.6	0.002	0.02
78	187.13	0.9	0.000	1	0.7	0.002	0.02
79	214.06	0.9	0.000	1	0.8	0.002	0.02
80	241.31	0.9	0.000	1	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-6.19	0.1	1.000	2	0.1	0.002	0.02
1	-0.29	0.1	0.821	2	0.2	0.002	0.02
2	5.72	0.1	0.329	2	0.3	0.002	0.02
3	11.62	0.1	0.211	2	0.4	0.002	0.02
4	17.86	0.1	0.146	2	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	266.26	0.9	0.000	2	0.5	0.002	0.02
77	319.83	0.9	0.000	2	0.6	0.002	0.02
78	374.16	0.9	0.000	2	0.7	0.002	0.02
79	427.40	0.9	0.000	2	0.8	0.002	0.02
80	481.52	0.9	0.000	2	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-9.80	0.1	1.000	3	0.1	0.002	0.02
1	-0.91	0.1	0.890	3	0.2	0.002	0.02
2	8.12	0.1	0.474	3	0.3	0.002	0.02
3	17.38	0.1	0.346	3	0.4	0.002	0.02
4	26.31	0.1	0.285	3	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	398.90	0.9	0.000	3	0.5	0.002	0.02
77	479.72	0.9	0.000	3	0.6	0.002	0.02
78	559.93	0.9	0.000	3	0.7	0.002	0.02
79	641.31	0.9	0.000	3	0.8	0.002	0.02
80	720.97	0.9	0.000	3	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-13.42	0.1	1.000	4	0.1	0.002	0.02
1	-1.26	0.1	0.911	4	0.2	0.002	0.02
2	10.53	0.1	0.590	4	0.3	0.002	0.02
3	22.82	0.1	0.460	4	0.4	0.002	0.02
4	34.80	0.1	0.368	4	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	531.73	0.9	0.000	4	0.5	0.002	0.02
77	639.45	0.9	0.000	4	0.6	0.002	0.02
78	746.24	0.9	0.000	4	0.7	0.002	0.02
79	853.91	0.9	0.000	4	0.8	0.002	0.02
80	962.02	0.9	0.000	4	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-16.97	0.1	1.000	5	0.1	0.002	0.02
1	-1.99	0.1	0.932	5	0.2	0.002	0.02
2	12.87	0.1	0.645	5	0.3	0.002	0.02
3	27.91	0.1	0.502	5	0.4	0.002	0.02
4	42.02	0.1	0.487	5	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	663.88	0.9	0.000	5	0.5	0.002	0.02
77	799.45	0.9	0.000	5	0.6	0.002	0.02
78	933.35	0.9	0.000	5	0.7	0.002	0.02
79	1069.09	0.9	0.000	5	0.8	0.002	0.02
80	1200.89	0.9	0.000	5	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-20.60	0.1	1.000	6	0.1	0.002	0.02
1	-2.29	0.1	0.933	6	0.2	0.002	0.02
2	15.13	0.1	0.697	6	0.3	0.002	0.02
3	32.86	0.1	0.602	6	0.4	0.002	0.02
4	51.59	0.1	0.526	6	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	796.98	0.9	0.000	6	0.5	0.002	0.02
77	957.95	0.9	0.000	6	0.6	0.002	0.02
78	1119.37	0.9	0.000	6	0.7	0.002	0.02
79	1282.46	0.9	0.000	6	0.8	0.002	0.02
80	1441.53	0.9	0.000	6	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-23.92	0.1	1.000	7	0.1	0.002	0.02
1	-3.12	0.1	0.939	7	0.2	0.002	0.02
2	18.01	0.1	0.713	7	0.3	0.002	0.02
3	39.17	0.1	0.635	7	0.4	0.002	0.02
4	59.96	0.1	0.574	7	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	929.74	0.9	0.000	7	0.5	0.002	0.02
77	1118.41	0.9	0.000	7	0.6	0.002	0.02
78	1306.60	0.9	0.000	7	0.7	0.002	0.02
79	1492.73	0.9	0.000	7	0.8	0.002	0.02
80	1681.60	0.9	0.000	7	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-28.03	0.1	1.000	8	0.1	0.002	0.02
1	-3.43	0.1	0.957	8	0.2	0.002	0.02
2	19.96	0.1	0.749	8	0.3	0.002	0.02
3	44.95	0.1	0.635	8	0.4	0.002	0.02
4	68.67	0.1	0.563	8	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	1062.14	0.9	0.000	8	0.5	0.002	0.02
77	1277.81	0.9	0.000	8	0.6	0.002	0.02
78	1491.95	0.9	0.000	8	0.7	0.002	0.02
79	1707.11	0.9	0.000	8	0.8	0.002	0.02
80	1923.21	0.9	0.000	8	0.9	0.002	0.02

81 rows × 7 columns

	Average_performance	Forecast_precision	Out_of_money_risk	Leverage	Take_profit	Fee_rate	Stop_loss
0	-31.16	0.1	1.000	9	0.1	0.002	0.02
1	-3.99	0.1	0.954	9	0.2	0.002	0.02
2	22.63	0.1	0.780	9	0.3	0.002	0.02
3	48.73	0.1	0.671	9	0.4	0.002	0.02
4	75.30	0.1	0.664	9	0.5	0.002	0.02
...	...	...	...	...	...	...	...
76	1195.21	0.9	0.000	9	0.5	0.002	0.02
77	1438.16	0.9	0.000	9	0.6	0.002	0.02
78	1679.40	0.9	0.000	9	0.7	0.002	0.02
79	1920.69	0.9	0.000	9	0.8	0.002	0.02
80	2163.77	0.9	0.000	9	0.9	0.002	0.02

81 rows × 7 columns

What matters ? and improvable factors...¶

1 - the forecast precision is the most important of all factors
2 - if the stop loss is greater than the take profit, bankrupt occurs easely
3 - leverage have a big impact on the bankrupt risk, but not that much I was expected...
(more like a systemic risk => low probability and high impact)

fees are also an important part of the performance but I have no action on it...
the take profit parameter have also an impact, as the time is also a key factor ; but "time impact" regarding the take profit is not an "easy mesurable factor" (needs analysis on volatility and time)

Running factor analysis on data¶

In [8]:

# Import required libraries
import pandas as pd
import sklearn.datasets
from factor_analyzer import FactorAnalyzer
import matplotlib.pyplot as plt

In [9]:

# nomralizing data func
# https://www.statology.org/normalize-data-between-0-and-100/
def prepare_data_for_factor_analysis(dframe):
    for col in dframe.columns:
        maxi = dframe[col].max()
        mini = dframe[col].min()
        coef = (maxi-mini) * 100
        dframe[col] = (dframe[col] - mini) / coef

In [13]:

# Duplicate data frame 
df_factors = final_result.copy()

# Dropping unnecessary columns
df_factors.drop(['Datas', 'Fee_rate', 'Stop_loss'],axis=1,inplace=True)

prepare_data_for_factor_analysis(df_factors)

In [14]:

pd.Index(['Average_performance','Forecast_precision','Out_of_money_risk','Leverage','Take_profit'],
      dtype='object')

from factor_analyzer.factor_analyzer import calculate_kmo

kmo_all,kmo_model=calculate_kmo(df_factors)
kmo_model

Out[14]:

0.3578953834486614

In [15]:

import seaborn as sns
df_factors = final_result.copy()
# Dropping unnecessary columns
df_factors.drop(['Datas', 'Fee_rate', 'Stop_loss'],axis=1,inplace=True)

corr = df_factors.corr()
ax = sns.heatmap(
corr,
vmin=-1, vmax=1, center=0,
cmap=sns.diverging_palette(150, 275, s=80, l=55, n=9),
square=True
)
ax.set_xticklabels(
ax.get_xticklabels(),
rotation=45,
horizontalalignment='right'
);

In [ ]:

Monte Carlo

What matters ? and improvable factors...¶

Running factor analysis on data¶