"""
Name : c9_52_impacto_of_correlation_on_efficient_frontier.py
Book : Python for Finance (2nd ed.)
Publisher: Packt Publishing Ltd.
Author : Yuxing Yan
Date : 6/6/2017
email : yany@canisius.edu
paulyxy@hotmail.com
"""
from matplotlib.finance import quotes_historical_yahoo_ochl as getData
import matplotlib.pyplot as plt
import numpy as np, pandas as pd, scipy as sp
from numpy.linalg import inv, pinv
begYear,endYear = 2012,2016
stocks=['IBM','WMT']
def ret_monthly(ticker): # function 1
x = getData(ticker,(begYear,1,1),(endYear,12,31),asobject=True,adjusted=True)
logret=np.log(x.aclose[1:]/x.aclose[:-1])
date=[]
d0=x.date
for i in range(0,np.size(logret)):
date.append(''.join([d0[i].strftime("%Y"),d0[i].strftime("%m")]))
y=pd.DataFrame(logret,date,columns=[ticker])
return y.groupby(y.index).sum()
def std_f(ticker):
x=ret_monthly(ticker)
return sp.std(x)
def objFunction(W, R, target_ret):
stock_mean=np.mean(R,axis=0)
port_mean=np.dot(W,stock_mean) # portfolio mean
#cov=np.cov(R.T) # var-cov matrix
cov=cov0
port_var=np.dot(np.dot(W,cov),W.T) # portfolio variance
penalty = 2000*abs(port_mean-target_ret)# penalty 4 deviation
return np.sqrt(port_var) + penalty # objective function
R0=ret_monthly(stocks[0]) # starting from 1st stock
n_stock=len(stocks) # number of stocks
std1=std_f(stocks[0])
std2=std_f(stocks[1])
for jj in sp.arange(1):
k=0.1*std1*std2
#cov0=sp.array([[0.00266285,0.00037303],[0.00037303,0.0021296]])
#cov0=sp.array([[std1**2,k],[k,std2**2]])
cov0=sp.array([[std1**2,0.00037303],[0.00037303,std2**2]])
for i in xrange(1,n_stock): # merge with other stocks
x=ret_monthly(stocks[i])
R0=pd.merge(R0,x,left_index=True,right_index=True)
R=np.array(R0)
out_mean,out_std,out_weight=[],[],[]
stockMean=np.mean(R,axis=0)
for r in np.linspace(np.min(stockMean),np.max(stockMean),num=100):
W = np.ones([n_stock])/n_stock # starting from equal weights
b_ = [(0,1)
for i in range(n_stock)] # bounds, here no short
c_ = ({'type':'eq', 'fun': lambda W: sum(W)-1. })#constraint
result=sp.optimize.minimize(objFunction,W,(R,r),method='SLSQP',constraints=c_, bounds=b_)
if not result.success: # handle error raise
BaseException(result.message)
out_mean.append(round(r,4)) # 4 decimal places
std_=round(np.std(np.sum(R*result.x,axis=1)),6)
out_std.append(std_)
out_weight.append(result.x)
plt.title('Efficient Frontier')
plt.xlabel('Standard Deviation of the porfolio (Risk))')
plt.ylabel('Return of the portfolio')
plt.figtext(0.5,0.75,str(n_stock)+' stock are used: ')
plt.figtext(0.5,0.7,' '+str(stocks))
plt.figtext(0.5,0.65,'Time period: '+str(begYear)+' ------ '+str(endYear))
plt.plot(out_std,out_mean,'--')
plt.show()
