#Normalize returns--Nat Log -- Technically, it uses log returns, but the difference is immaterial.

#log_ret = np.log(ret/ret.shift(1)) #Calc for log returns, if official is important (This is instead of pct_change())

log_ret = pct

ret = log_ret

#Create Temporary (Random) weights

weights = np.array(np.random.random(15)) #USE NUM SECURITIESS 

​

#Rebalance w/ constraints (CANNOT BE > 1)

weights = weights/np.sum(weights)

print(weights)

​

#DEFINE ARRAYS FOR STORING METRICS 

num_runs = 1000    #Kick this number up 10k-100k for better results

all_weights = np.zeros((num_runs,len(ret.columns)))

ret_arr = np.zeros(num_runs)

vol_arr = np.zeros(num_runs)

sharpe_arr = np.zeros(num_runs)

​

#Begin MC Loop

for run in range(num_runs):

    #Weights

    weights = np.array(np.random.random(15))  #CHG to number securities *** THIS is the key to MC, this random value creation for weights

    #If you're looking for a challenge, try using a poisson, gamma or Student T dist!

    weights = weights/np.sum(weights)

    #Save weights (For reference Later)

    all_weights[run,:] = weights

    #Expected Ret (Record each runs return in ret_arr)

    exp_ret = np.sum((log_ret.mean() * weights) * 252)

    ret_arr[run] = np.sum( (log_ret.mean() * weights) * 252) #Time =  year

    #Exp Vol: (Lets attempt some linear algebra w/out runtime error!)

    exp_vol = np.sum((log_ret.std() * weights) * 252)

    # Sqrt of dot product of Transposed weights X Cov of Log returns & weights--whew.

    vol_arr[run] = np.sqrt(np.dot(weights.T,np.dot(log_ret.cov()*252,weights)))

    #Sharpe

    SR = exp_ret/exp_vol

sharpe_arr[run] = ret_arr[run]/vol_arr[run]

%matplotlib inline

import numpy as np

import matplotlib.pyplot as plt

import math

n_sim = 1000

angle_means = np.zeros(n_sim)

distance_means = np.zeros(n_sim)

for i in range(0 ,  n_sim):

    angle = np.random.uniform(low=0, high= (np.pi/2.0), size=(i+1,))

    distance = np.tan(angle)

    angle_means[i] = np.mean(angle)

    distance_means[i] = np.mean(distance)

plt1 = plt.plot(angle_means)

plt.title("Mean of Angles as a Function of n")

plt.xlabel("n")

plt.ylabel("Mean of Angle")

plt.grid()

plt.savefig("angle_means.png", bbox_inches='tight')

plt.show()

plt1 = plt.plot(distance_means)

plt.title("Mean of Distances as a Function of n")

plt.ylabel("Mean of Distances")

plt.xlabel("n")

plt.yscale('log')

plt.grid()

plt.savefig("distance_means.png", bbox_inches='tight')

plt.show()