def get_johansen(y, p):
"""
Get the cointegration vectors at 95% level of significance
given by the trace statistic test.
"""
N, l = y.shape
jres = coint_johansen(y, 0, p)
trstat = jres.lr1 # trace statistic
tsignf = jres.cvt # critical values
for i in range(l):
if trstat[i] > tsignf[i, 1]: # 0: 90% 1:95% 2: 99%
r = i + 1
jres.r = r
jres.evecr = jres.evec[:, :r]
return jres
if __name__ == '__main__':
#Use in-sample data to calculate the Eigen Vector
symbols = ['FED/RXI_N_B_JA', 'LBMA/GOLD']
num_assets = len(symbols)
FX_data = quandl_stocks(symbols, [1, 2], (2010, 6, 10), (2015, 6, 9))
FX_data.fillna(method='ffill', inplace=True)
FX_data.iloc[:, 0] = 1 / FX_data.iloc[:, 0]
FX_log_data = pd.DataFrame(index=FX_data.index.copy())
FX_log_data = np.log(FX_data)
FX_log_ret_data = pd.DataFrame(index=FX_data.index.copy())
jres = coint_johansen(FX_log_data, 0,
1) # The inputs are log price levels.
weights = jres.evec[0, :] / jres.evec[0,
0] # The Eigen Vector is calculated.
#Use out-of-sample data to calculate the stationary series to generate trading signals.
FX_data = quandl_stocks(symbols, [1, 2], (2015, 6, 10), (2018, 6, 10))
FX_data.fillna(method='ffill', inplace=True)
FX_data.iloc[:, 0] = 1 / FX_data.iloc[:, 0]
FX_log_data = np.log(FX_data)
coint_series = np.matmul(FX_log_data, weights.reshape(2, 1))
coint_series_data = pd.DataFrame(index=FX_data.index.copy())
coint_series_data['value'] = coint_series
coint_series_data.plot()
z = zscore(coint_series_data, 26)
z.fillna(0, inplace=True)
def main():
###########################################################################
# import data from CSV file
###########################################################################
path = my_path('PC')
data = pd.read_csv(path + 'CAD_AUD.csv', index_col='Date')
CAD = 1 / pd.DataFrame(data['USDCAD'])
AUD = pd.DataFrame(data['AUDUSD'], index=data.index)
y = AUD.join(CAD)
# strategy parameters
lookback = 20
trainlen = 250
hedgeratio = pd.DataFrame(np.zeros([len(data), 2]),
columns=y.columns,
index=y.index)
numunits = pd.DataFrame(np.zeros([len(data), 1]),
columns=['numunits'],
index=y.index)
for t in range(trainlen + 1, len(data)):
results = coint_johansen(log(data[t - trainlen:t]),
0,
1,
print_on_console=False)
hedgeratio.iloc[t] = results.evec[0, 0], results.evec[1, 0]
# we apply the t+0 hedgeratio to all the data in the lookback period
# for calculation of the yport
yport = np.sum(y[t - lookback:t] *
repmat(hedgeratio.iloc[t], lookback, 1),
axis=1)
ma = np.mean(yport)
std = np.std(yport)
numunits.iloc[t] = -(yport[-1] - ma) / std
positions = repmat(numunits, 1, 2) * hedgeratio * y
pnl = np.sum(positions.shift(1) * y.pct_change(1), axis=1)
rtn = pnl / np.sum(np.abs(positions.shift(1)), axis=1)
rtn = rtn[trainlen + 2:]
#rtn.to_csv(path+'rtn.csv')
cumret = pd.DataFrame(np.cumprod((1 + rtn)) - 1, index=rtn.index)
#print(rtn.head())
print(cumret.head())
print(cumret.tail())
#cumret = cumret.fillna(method='pad')
# compute performance statistics
sharpe = (np.sqrt(252) * np.mean(rtn)) / np.std(rtn)
APR = np.prod(1 + rtn)**(252 / len(rtn)) - 1
##################################################
# print the results
##################################################
print('Sharpe: {:.4}'.format(sharpe))
print('APR: {:.4%}'.format(APR))
###########################################################################
# plotting the chart
###########################################################################
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(cumret)
ax.set_title('C')
ax.set_xlabel('Data points')
ax.set_ylabel('acumm rtn')
ax.text(1000, -0.05, 'Sharpe: {:.4}'.format(sharpe))
ax.text(1000, 0, 'APR: {:.4%}'.format(APR))
plt.show()
def main():
###########################################################################
# import data from CSV file
###########################################################################
path = my_path('PC')
data = pd.read_csv(path + 'CAD_AUD.csv' , index_col='Date')
CAD = 1 / pd.DataFrame(data['USDCAD'])
AUD = pd.DataFrame(data['AUDUSD'], index=data.index)
y = AUD.join(CAD)
# strategy parameters
lookback = 20
trainlen = 250
hedgeratio = pd.DataFrame(np.zeros([len(data),2]), columns=y.columns, index=y.index)
numunits = pd.DataFrame(np.zeros([len(data),1]), columns=['numunits'], index=y.index)
for t in range(trainlen+1,len(data)):
results = coint_johansen(log(data[t-trainlen:t]), 0, 1 , print_on_console=False)
hedgeratio.iloc[t] = results.evec[0,0], results.evec[1,0]
# we apply the t+0 hedgeratio to all the data in the lookback period
# for calculation of the yport
yport = np.sum(y[t-lookback:t] * repmat(hedgeratio.iloc[t], lookback, 1), axis=1)
ma = np.mean(yport)
std = np.std(yport)
numunits.iloc[t] = -(yport[-1] - ma) / std
positions = repmat(numunits, 1, 2) * hedgeratio * y
pnl = np.sum(positions.shift(1) * y.pct_change(1), axis=1)
rtn = pnl / np.sum(np.abs(positions.shift(1)), axis=1)
rtn= rtn[trainlen+2:]
#rtn.to_csv(path+'rtn.csv')
cumret = pd.DataFrame(np.cumprod((1+rtn))-1, index=rtn.index)
#print(rtn.head())
print(cumret.head())
print(cumret.tail())
#cumret = cumret.fillna(method='pad')
# compute performance statistics
sharpe = (np.sqrt(252)*np.mean(rtn)) / np.std(rtn)
APR = np.prod(1+rtn)**(252/len(rtn))-1
##################################################
# print the results
##################################################
print('Sharpe: {:.4}'.format(sharpe))
print('APR: {:.4%}'.format(APR))
###########################################################################
# plotting the chart
###########################################################################
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(cumret)
ax.set_title('C')
ax.set_xlabel('Data points')
ax.set_ylabel('acumm rtn')
ax.text(1000, -0.05, 'Sharpe: {:.4}'.format(sharpe))
ax.text(1000, 0, 'APR: {:.4%}'.format(APR))
plt.show()
# MAC: '/Users/Javi/Documents/MarketData/'
# WIN: 'C:/Users/javgar119/Documents/Python/Data'
filename = 'GLD_SLV_daily.csv'
full_path = root_path + filename
data = pd.read_csv(full_path, index_col='Date')
#create a series with the data range asked
#start_date = '2010-01-13'
#end_date = '2014-05-13'
#data = subset_dataframe(data, start_date, end_date)
#print('data import is {} lines'.format(str(len(data))))
#print(data.head(10))
#print(data.tail(5))
#johansen test with non-zero offset but zero drift, and with the lag k=1.
results = coint_johansen(data, 0, 1)
# those are the weigths of the portfolio
# the first eigenvector because it shows the strongest cointegration relationship
w = results.evec[:, 0]
print('Best eigenvector is: {}.'.format(str(w)))
# (net) market value of portfolio
# this is the syntetic asset we are going to trade. A freshly
# new mean reverting serie compose of the three assets in
# proportions given by the eigenvector
yport = pd.DataFrame.sum(w*data, axis=1)
#print('yport')
#print(yport.tail(10))
stks_list = list(stks.columns)
isCoint = pd.DataFrame(np.zeros([1,len(stks_list)], dtype=bool),
columns=stks_list, index=['isCoint'])
# set the confidence level
confidence = 0.90
if confidence==0.95: X=1
elif confidence==0.99:x=2
else: x=0
for col in isCoint:
# join the SPY to each of the stocks members in a Nx2 dataframe
# clean for missing values
y2 = etf_train.join(stks_train[col]).dropna()
# run johansen test for each of the N stocks vs SPY.
if len(y2) > 250:
results = coint_johansen(y2, 0, 1, print_on_console=False)
if results.lr1[0] > results.cvt[0,x]:
isCoint[col] = True
print('Johansen Test results for each stock vs SPY')
print('--------------------------------------------------')
print('Universe is {} stocks in the index'.format(len(stks_list)))
print('Johansen Test over {} data points'.format(len(stks_train)))
print('There are {} stocks that cointegrate with {:.2%} confidence'.
format(np.count_nonzero(isCoint), confidence))
print('--------------------------------------------------')
print()
print()
# capital allocation
isCoint = pd.DataFrame(np.zeros([1, len(stks_list)], dtype=bool),
columns=stks_list,
index=['isCoint'])
# set the confidence level
confidence = 0.90
if confidence == 0.95: X = 1
elif confidence == 0.99: x = 2
else: x = 0
for col in isCoint:
# join the SPY to each of the stocks members in a Nx2 dataframe
# clean for missing values
y2 = etf_train.join(stks_train[col]).dropna()
# run johansen test for each of the N stocks vs SPY.
if len(y2) > 250:
results = coint_johansen(y2, 0, 1, print_on_console=False)
if results.lr1[0] > results.cvt[0, x]:
isCoint[col] = True
print('Johansen Test results for each stock vs SPY')
print('--------------------------------------------------')
print('Universe is {} stocks in the index'.format(len(stks_list)))
print('Johansen Test over {} data points'.format(len(stks_train)))
print('There are {} stocks that cointegrate with {:.2%} confidence'.format(
np.count_nonzero(isCoint), confidence))
print('--------------------------------------------------')
print()
print()
# capital allocation
yN = repmat(isCoint, len(stks_train), 1) * stks_train
def get_johansen(y, p):
"""
Get the cointegration vectors at 95% level of significance
given by the trace statistic test.
"""
N, l = y.shape
jres = coint_johansen(y, 0, p)
trstat = jres.lr1 # trace statistic
tsignf = jres.cvt # critical values
for i in range(l):
if trstat[i] > tsignf[i, 1]: # 0: 90% 1:95% 2: 99%
r = i + 1
jres.r = r
jres.evecr = jres.evec[:, :r]
return jres
