Minimization of variance problem

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#packages
from IPython import get_ipython
get_ipython().magic('reset -sf')
import numpy as np
import pandas as pd
import datetime as dt
import matplotlib as mpl
import matplotlib.pyplot as plt
get_ipython().magic('matplotlib inline')

import pandas_datareader.data as web
from pandas_datareader.famafrench import get_available_datasets
import quandl

import statsmodels.formula.api as smf
import statsmodels.api as sm
from scipy.optimize import minimize

from datetime import datetime
from zipline.api import order, symbol, record, order_target
from zipline.utils.factory import load_bars_from_yahoo
from zipline.algorithm import TradingAlgorithm
from zipline.data.bundles import register, yahoo_equities
from zipline.api import symbol, order, record, history
import zipline
import pytz
from collections import OrderedDict

#%%
#Fetching and cleaning data, compute returns

myassets = 'AAPL GOOG'
#type(myassets)
myassets = myassets.split()
#define beginning date and time
start_date = '2014-01-01'
end_date = '2015-12-31'
#extract data from yahoo
data = web.DataReader(myassets, 'yahoo', start_date, end_date)
data.items
#data.items = [x.lower() for x in data.items] 
data.items=['open', 'high', 'low', 'close', 'volume', 'adjclose'] #changing to lower case and adjclose together
prices=pd.DataFrame(data.adjclose, index=data.major_axis, columns=data.minor_axis)
returns=(prices/prices.shift(1))-1


#%%
#Download Fama French factors

ff  = web.DataReader("F-F_Research_Data_Factors_daily", "famafrench",start=start_date, end=end_date)

ff = pd.DataFrame(ff[0]/100) #tranform the % values of factors to decimals
ff.columns = (['mktrf', 'smb', 'hml', 'rf']) #change to lower case, and prettier look :)
#join returns of assets and risk free
return_rf = returns.join(ff.rf, how='inner') #inner=intersection, and outer=union
#join returns of assets and all factors
return_all = returns.join(ff, how='inner')

#return_3 = returns.join([ff.rf, ff.smb], how='inner') #only two factors

#%%
#Regressions
betas = []

for id in return_all.columns:
    formula = id + '~mktrf'
    res = smf.ols(formula = formula, data = return_all).fit()
    betas.append(res.params[1])
betas = (betas)

betas = pd.DataFrame([betas], columns=return_all.columns)

#%%
#Minimizations
#Minimize variance of portfolio and beta below 2,5

def PtfVar(w,b,vcv):
    temp = w.dot(vcv).dot(w.T)
    return temp
    
w = pd.DataFrame([],index=data.major_axis, columns=data.minor_axis)

for id in data.major_axis[::]:
    b = np.matrix(betas)
    #b = np.matrix(betas.iloc[-1,:])
    vcv = np.array(return_all.loc[:,:].cov())
    #vcv = np.array(return_all.loc[t-pd.DateOffset(days = 365):t,:].cov())
    
    cons = ({'type': 'ineq',
    'fun' : lambda x,b: 0.2-abs(x.dot(b.T)),
    'args': (b,)},
    {'type':'eq',
     'fun': lambda x: x.sum()-1})     


res = minimize(PtfVar, np.ones((1,6))/6 , args=(b,vcv,),constraints=cons,options={'disp': True,'ftol':1e-12}, method='SLSQP')#, jac=func_deriv,  options={'disp': True})
w.loc[t,:]=res.x