def get_cov_test():
decay = 0.003
Coef = pd.read_csv(r'%s/Coef_%s_%s_%.4f.csv' % (DataFolder, START_TRAIN.date(), END_TRAIN.date(), decay))
Res = pd.read_csv(r'%s/Res_%s_%s_%.4f.csv' % (DataFolder, START_TRAIN.date(), END_TRAIN.date(), decay))
total_cov = functions.get_cov(wTickers, Coef, Res, CarhartDaily, START_TRAIN, END_TRAIN)
# plt.pcolor(total_cov)
# plt.show()
return total_cov
def pfOptimizer6(longTickers, shortTickersHigh, shortTickersLow,
Coef, Res, CarhartDaily, StockBeta,
BETA_BOUND, WEIGHT_BOUND, back_date, start_date):
shortTickers = shortTickersHigh.append(shortTickersLow).sort('ticker').reset_index(drop=True)
longTickers['bWeight'] = 1 # binary weights
shortTickers['bWeight'] = -1
shortTickersLow['bWeight'] = -1
pfTickers = pd.concat((shortTickers[['ticker']], longTickers[['ticker']]),
axis=0).sort('ticker').reset_index(drop=True)
sens = Coef[['ticker', 'Mkt-RF', 'SMB', 'HML', 'UMD']].merge(pfTickers)
mBeta = matrix(sens['Mkt-RF'])
mBeta_smb = matrix(sens['SMB'])
mBeta_hml = matrix(sens['HML'])
mBeta_umd = matrix(sens['UMD'])
mCqaBeta = matrix(StockBeta.merge(pfTickers)['cqaBeta'])
longIndex = matrix(pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = np.diag(pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = matrix(mLongIndex[np.logical_or.reduce([np.sum(mLongIndex, 1) > 0.5])]).trans()
shortIndex = -matrix(pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = -np.diag(pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = matrix(mShortIndex[np.logical_or.reduce([np.sum(mShortIndex, 1) > 0.5])]).trans()
shortLowIndex = -matrix(pfTickers.merge(shortTickersLow, how='left').fillna(0)['bWeight'])
N = pfTickers.shape[0]
id = spmatrix(1.0, range(N), range(N))
wBounds = matrix(np.ones((N, 1)) * WEIGHT_BOUND)
longBounds = matrix(np.zeros((shortTickers.shape[0], 1)))
shortBounds = matrix(np.zeros((longTickers.shape[0], 1)))
total_cov = matrix(functions.get_cov(pfTickers, Coef, Res, CarhartDaily, back_date, start_date))
q = matrix(np.zeros((pfTickers.shape[0], 1)))
G = matrix([[mBeta], [-mBeta],
# [mBeta_smb], [-mBeta_smb],
# [mBeta_hml], [-mBeta_hml],
# [mBeta_umd], [-mBeta_umd],
[mCqaBeta], [-mCqaBeta],
[longIndex], [-longIndex],
[shortIndex], [-shortIndex],
[-shortLowIndex],
[id], [-id],
[-mLongIndex], [mShortIndex]]).trans()
opt_comp = pd.DataFrame()
h = matrix([0.1, 0.2,
# 0.1, 0.1,
# 0.1, 0.1,
# 0.1, 0.1,
BETA_BOUND, BETA_BOUND,
1, -0.98,
-0.98, 1,
0.3,
wBounds, wBounds,
longBounds, shortBounds])
sol = solvers.qp(total_cov, q, G, h)
w_final = sol['x']
wTickers = pfTickers
wTickers['weight'] = w_final
return (opt_comp, wTickers)
def pfOptimizer5(longTickers, shortTickersHigh, shortTickersLow, Coef, Res,
CarhartDaily, StockBeta, BETA_BOUND, WEIGHT_BOUND, back_date,
start_date):
shortTickers = shortTickersHigh.append(shortTickersLow).sort(
'ticker').reset_index(drop=True)
longTickers['bWeight'] = 1 # binary weights
shortTickers['bWeight'] = -1
shortTickersLow['bWeight'] = -1
pfTickers = pd.concat((shortTickers[['ticker']], longTickers[['ticker']]),
axis=0).sort('ticker').reset_index(drop=True)
sens = Coef[['ticker', 'Mkt-RF', 'SMB', 'HML', 'UMD']].merge(pfTickers)
mBeta = matrix(sens['Mkt-RF'])
mBeta_smb = matrix(sens['SMB'])
mBeta_hml = matrix(sens['HML'])
mBeta_umd = matrix(sens['UMD'])
mCqaBeta = matrix(StockBeta.merge(pfTickers)['cqaBeta'])
longIndex = matrix(
pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = np.diag(
pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = matrix(mLongIndex[np.logical_or.reduce(
[np.sum(mLongIndex, 1) > 0.5])]).trans()
shortIndex = -matrix(
pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = -np.diag(
pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = matrix(mShortIndex[np.logical_or.reduce(
[np.sum(mShortIndex, 1) > 0.5])]).trans()
shortLowIndex = -matrix(
pfTickers.merge(shortTickersLow, how='left').fillna(0)['bWeight'])
N = pfTickers.shape[0]
id = spmatrix(1.0, range(N), range(N))
wBounds = matrix(np.ones((N, 1)) * WEIGHT_BOUND)
longBounds = matrix(np.zeros((shortTickers.shape[0], 1)))
shortBounds = matrix(np.zeros((longTickers.shape[0], 1)))
total_cov = matrix(
functions.get_cov(pfTickers, Coef, Res, CarhartDaily, back_date,
start_date))
q = matrix(np.zeros((pfTickers.shape[0], 1)))
G = matrix([[mBeta], [-mBeta], [mBeta_smb], [-mBeta_smb], [mBeta_hml],
[-mBeta_hml], [mBeta_umd], [-mBeta_umd], [mCqaBeta],
[-mCqaBeta], [longIndex], [-longIndex], [shortIndex],
[-shortIndex], [-shortLowIndex], [id], [-id], [-mLongIndex],
[mShortIndex]]).trans()
opt_comp = pd.DataFrame()
h = matrix([
0.1, 0.2, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, BETA_BOUND, BETA_BOUND, 1,
-0.98, -0.98, 1, 0.3, wBounds, wBounds, longBounds, shortBounds
])
sol = solvers.qp(total_cov, q, G, h)
w_final = sol['x']
wTickers = pfTickers
wTickers['weight'] = w_final
return (opt_comp, wTickers)
def get_cov_test():
decay = 0.003
Coef = pd.read_csv(
r'%s/Coef_%s_%s_%.4f.csv' %
(DataFolder, START_TRAIN.date(), END_TRAIN.date(), decay))
Res = pd.read_csv(
r'%s/Res_%s_%s_%.4f.csv' %
(DataFolder, START_TRAIN.date(), END_TRAIN.date(), decay))
total_cov = functions.get_cov(wTickers, Coef, Res, CarhartDaily,
START_TRAIN, END_TRAIN)
# plt.pcolor(total_cov)
# plt.show()
return total_cov
def pf_optimizer(long_tickers, short_tickers,
Coef, industry_data, CarhartDaily, StockBeta,
beta_bound, position_bound, sector_bound, three_factor_bound, trim,
back_date, start_date):
long_tickers['bWeight'] = 1 # binary weights
short_tickers['bWeight'] = -1
pf_tickers = pd.concat((short_tickers[['ticker']], long_tickers[['ticker']]),
axis=0).sort('ticker').reset_index(drop=True).merge(industry_data[['ticker', 'sector']])
sens = Coef[['ticker', 'Mkt-RF', 'SMB', 'HML', 'UMD']].merge(pf_tickers)
m_beta = matrix(sens['Mkt-RF'])
m_beta_smb = matrix(sens['SMB'])
m_beta_hml = matrix(sens['HML'])
m_beta_umd = matrix(sens['UMD'])
m_cqa_beta = matrix(StockBeta.merge(pf_tickers)['cqaBeta'])
longIndex = matrix(pf_tickers.merge(long_tickers, how='left').fillna(0)['bWeight'])
mLongIndex = np.diag(pf_tickers.merge(long_tickers, how='left').fillna(0)['bWeight'])
mLongIndex = matrix(mLongIndex[np.logical_or.reduce([np.sum(mLongIndex, 1) > 0.5])]).trans()
shortIndex = -matrix(pf_tickers.merge(short_tickers, how='left').fillna(0)['bWeight'])
mShortIndex = -np.diag(pf_tickers.merge(short_tickers, how='left').fillna(0)['bWeight'])
mShortIndex = matrix(mShortIndex[np.logical_or.reduce([np.sum(mShortIndex, 1) > 0.5])]).trans()
sector_index = pf_tickers[['ticker', 'sector']]
sector_list = pf_tickers['sector'].unique()
for sector in sector_list:
sector_index.loc[:, sector] = 0.0
sector_index.ix[sector_index['sector'] == sector, sector] = 1.0
mSector_index = matrix(sector_index.iloc[:, 2:].as_matrix())
N = pf_tickers.shape[0]
id = spmatrix(1.0, range(N), range(N))
wBounds = matrix(np.ones((N, 1)) * position_bound)
longBounds = matrix(np.zeros((short_tickers.shape[0], 1)))
shortBounds = matrix(np.zeros((long_tickers.shape[0], 1)))
total_cov = matrix(functions.get_cov(pf_tickers, Coef, Res, CarhartDaily, back_date, start_date))
q = matrix(np.zeros((pf_tickers.shape[0], 1)))
# three_factor_bound = 0.05
G = matrix([[mSector_index], [-mSector_index],
[m_beta], [-m_beta],
[m_beta_smb], [-m_beta_smb],
[m_beta_hml], [-m_beta_hml],
[m_beta_umd], [-m_beta_umd],
[m_cqa_beta], [-m_cqa_beta],
[longIndex], [-longIndex],
[shortIndex], [-shortIndex],
[id], [-id],
[-mLongIndex], [mShortIndex]]).trans()
h = matrix([sector_bound, sector_bound, sector_bound, sector_bound,
sector_bound, sector_bound, sector_bound, sector_bound,
sector_bound, sector_bound, sector_bound, sector_bound,
sector_bound, sector_bound, sector_bound, sector_bound,
0.2, 0.4,
three_factor_bound, three_factor_bound,
three_factor_bound, three_factor_bound,
three_factor_bound, three_factor_bound,
beta_bound, beta_bound,
1, -0.98,
-0.98, 1,
wBounds, wBounds,
longBounds, shortBounds])
sol = solvers.qp(total_cov, q, G, h)
w_final = sol['x']
wTickers = pf_tickers
wTickers['weight'] = w_final
wTickers = wTickers[np.abs(wTickers['weight']) > trim]
wTickers_properties = wTickers.merge(Coef).merge(StockBeta)
stats = pd.DataFrame({'beta': np.dot(wTickers_properties['weight'], wTickers_properties['Mkt-RF']),
'beta_smb': np.dot(wTickers_properties['weight'], wTickers_properties['SMB']),
'beta_hml': np.dot(wTickers_properties['weight'], wTickers_properties['HML']),
'beta_umd': np.dot(wTickers_properties['weight'], wTickers_properties['UMD']),
'beta_cqa': np.dot(wTickers_properties['weight'], wTickers_properties['cqaBeta']),
'long weight': wTickers[wTickers['weight'] > 0]['weight'].sum(),
'short weight': wTickers[wTickers['weight'] < 0]['weight'].sum()
}, index=[0])
for sector in sector_list:
stats[sector] = wTickers_properties[wTickers_properties['sector'] == sector]['weight'].sum()
stats = stats.transpose().reset_index()
stats.columns = ['statistics', 'value']
return (stats, wTickers)
def pfOptimizer3(longTickers, shortTickers, Coef, Res, CarhartDaily, StockBeta,
BETA_BOUND, WEIGHT_BOUND, back_date, start_date):
longTickers['bWeight'] = 1 # binary weights
shortTickers['bWeight'] = -1
pfTickers = pd.concat((shortTickers[['ticker']], longTickers[['ticker']]),
axis=0).sort('ticker').reset_index(drop=True)
sens = Coef[['ticker', 'Mkt-RF', 'SMB', 'HML', 'UMD']].merge(pfTickers)
mBeta = matrix(sens['Mkt-RF'])
# mBeta_smb = matrix(sens['SMB'])
# mBeta_hml = matrix(sens['HML'])
# mBeta_umd = matrix(sens['UMD'])
mCqaBeta = matrix(StockBeta.merge(pfTickers)['cqaBeta'])
longIndex = matrix(
pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = np.diag(
pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = matrix(mLongIndex[np.logical_or.reduce(
[np.sum(mLongIndex, 1) > 0.5])]).trans()
shortIndex = -matrix(
pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = -np.diag(
pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = matrix(mShortIndex[np.logical_or.reduce(
[np.sum(mShortIndex, 1) > 0.5])]).trans()
N = pfTickers.shape[0]
id = spmatrix(1.0, range(N), range(N))
wBounds = matrix(np.ones((N, 1)) * WEIGHT_BOUND)
longBounds = matrix(np.zeros((shortTickers.shape[0], 1)))
shortBounds = matrix(np.zeros((longTickers.shape[0], 1)))
total_cov = matrix(
functions.get_cov(pfTickers, Coef, Res, CarhartDaily, back_date,
start_date))
q = matrix(np.zeros((pfTickers.shape[0], 1)))
G = matrix([
[mBeta],
[-mBeta],
# [mBeta_smb], [-mBeta_smb],
# [mBeta_hml], [-mBeta_hml],
# [mBeta_umd], [-mBeta_umd],
[mCqaBeta],
[-mCqaBeta],
[longIndex],
[-longIndex],
[shortIndex],
[-shortIndex],
[id],
[-id],
[-mLongIndex],
[mShortIndex]
]).trans()
opt_comp = pd.DataFrame()
max_slope = 0
for k in range(11):
print 'k = %d' % k
h = matrix([
(k + 1) * 0.05,
-k * 0.05,
# 0.1, 0.1,
# 0.1, 0.1,
# 0.1, 0.1,
BETA_BOUND,
BETA_BOUND,
1,
-0.98,
-0.98,
1,
wBounds,
wBounds,
longBounds,
shortBounds
])
# sol = solvers.lp(-mBeta, A, b)
try:
sol = solvers.qp(total_cov, q, G, h)
except ValueError:
break
w_res = sol['x']
cov_res = sol['primal objective']
beta_res = np.float64(w_res.trans() * mBeta)[0, 0]
beta_cqa_res = np.float64(w_res.trans() * mCqaBeta)[0, 0]
# beta_smb_res = np.float64(w_res.trans() * mBeta_smb)[0,0]
# beta_hml_res = np.float64(w_res.trans() * mBeta_hml)[0,0]
# beta_umd_res = np.float64(w_res.trans() * mBeta_umd)[0,0]
opt_comp = opt_comp.append(
pd.DataFrame([{
'beta': beta_res,
'beta_cqa': beta_cqa_res,
# 'beta_smb': beta_smb_res,
# 'beta_hml': beta_hml_res,
# 'beta_umd': beta_umd_res,
'vol': math.sqrt(cov_res),
}]))
slope = beta_res / math.sqrt(cov_res)
if slope > max_slope:
w_final = w_res
wTickers = pfTickers
wTickers['weight'] = w_final
return (opt_comp, wTickers)
def pf_optimizer(long_tickers, short_tickers, Coef, industry_data,
CarhartDaily, StockBeta, beta_bound, position_bound,
sector_bound, three_factor_bound, trim, back_date,
start_date):
long_tickers['bWeight'] = 1 # binary weights
short_tickers['bWeight'] = -1
pf_tickers = pd.concat(
(short_tickers[['ticker']], long_tickers[['ticker']]),
axis=0).sort('ticker').reset_index(drop=True).merge(
industry_data[['ticker', 'sector']])
sens = Coef[['ticker', 'Mkt-RF', 'SMB', 'HML', 'UMD']].merge(pf_tickers)
m_beta = matrix(sens['Mkt-RF'])
m_beta_smb = matrix(sens['SMB'])
m_beta_hml = matrix(sens['HML'])
m_beta_umd = matrix(sens['UMD'])
m_cqa_beta = matrix(StockBeta.merge(pf_tickers)['cqaBeta'])
longIndex = matrix(
pf_tickers.merge(long_tickers, how='left').fillna(0)['bWeight'])
mLongIndex = np.diag(
pf_tickers.merge(long_tickers, how='left').fillna(0)['bWeight'])
mLongIndex = matrix(mLongIndex[np.logical_or.reduce(
[np.sum(mLongIndex, 1) > 0.5])]).trans()
shortIndex = -matrix(
pf_tickers.merge(short_tickers, how='left').fillna(0)['bWeight'])
mShortIndex = -np.diag(
pf_tickers.merge(short_tickers, how='left').fillna(0)['bWeight'])
mShortIndex = matrix(mShortIndex[np.logical_or.reduce(
[np.sum(mShortIndex, 1) > 0.5])]).trans()
sector_index = pf_tickers[['ticker', 'sector']]
sector_list = pf_tickers['sector'].unique()
for sector in sector_list:
sector_index.loc[:, sector] = 0.0
sector_index.ix[sector_index['sector'] == sector, sector] = 1.0
mSector_index = matrix(sector_index.iloc[:, 2:].as_matrix())
N = pf_tickers.shape[0]
id = spmatrix(1.0, range(N), range(N))
wBounds = matrix(np.ones((N, 1)) * position_bound)
longBounds = matrix(np.zeros((short_tickers.shape[0], 1)))
shortBounds = matrix(np.zeros((long_tickers.shape[0], 1)))
total_cov = matrix(
functions.get_cov(pf_tickers, Coef, Res, CarhartDaily, back_date,
start_date))
q = matrix(np.zeros((pf_tickers.shape[0], 1)))
# three_factor_bound = 0.05
G = matrix([[mSector_index], [-mSector_index], [m_beta], [-m_beta],
[m_beta_smb], [-m_beta_smb], [m_beta_hml], [-m_beta_hml],
[m_beta_umd], [-m_beta_umd], [m_cqa_beta], [-m_cqa_beta],
[longIndex], [-longIndex], [shortIndex], [-shortIndex], [id],
[-id], [-mLongIndex], [mShortIndex]]).trans()
h = matrix([
sector_bound, sector_bound, sector_bound, sector_bound, sector_bound,
sector_bound, sector_bound, sector_bound, sector_bound, sector_bound,
sector_bound, sector_bound, sector_bound, sector_bound, sector_bound,
sector_bound, 0.2, 0.4, three_factor_bound, three_factor_bound,
three_factor_bound, three_factor_bound, three_factor_bound,
three_factor_bound, beta_bound, beta_bound, 1, -0.98, -0.98, 1,
wBounds, wBounds, longBounds, shortBounds
])
sol = solvers.qp(total_cov, q, G, h)
w_final = sol['x']
wTickers = pf_tickers
wTickers['weight'] = w_final
wTickers = wTickers[np.abs(wTickers['weight']) > trim]
wTickers_properties = wTickers.merge(Coef).merge(StockBeta)
stats = pd.DataFrame(
{
'beta':
np.dot(wTickers_properties['weight'],
wTickers_properties['Mkt-RF']),
'beta_smb':
np.dot(wTickers_properties['weight'], wTickers_properties['SMB']),
'beta_hml':
np.dot(wTickers_properties['weight'], wTickers_properties['HML']),
'beta_umd':
np.dot(wTickers_properties['weight'], wTickers_properties['UMD']),
'beta_cqa':
np.dot(wTickers_properties['weight'],
wTickers_properties['cqaBeta']),
'long weight':
wTickers[wTickers['weight'] > 0]['weight'].sum(),
'short weight':
wTickers[wTickers['weight'] < 0]['weight'].sum()
},
index=[0])
for sector in sector_list:
stats[sector] = wTickers_properties[wTickers_properties['sector'] ==
sector]['weight'].sum()
stats = stats.transpose().reset_index()
stats.columns = ['statistics', 'value']
return (stats, wTickers)
def pfOptimizer3(longTickers, shortTickers, Coef, Res, CarhartDaily, StockBeta,
BETA_BOUND, WEIGHT_BOUND, back_date, start_date):
longTickers['bWeight'] = 1 # binary weights
shortTickers['bWeight'] = -1
pfTickers = pd.concat((shortTickers[['ticker']], longTickers[['ticker']]),
axis=0).sort('ticker').reset_index(drop=True)
sens = Coef[['ticker', 'Mkt-RF', 'SMB', 'HML', 'UMD']].merge(pfTickers)
mBeta = matrix(sens['Mkt-RF'])
# mBeta_smb = matrix(sens['SMB'])
# mBeta_hml = matrix(sens['HML'])
# mBeta_umd = matrix(sens['UMD'])
mCqaBeta = matrix(StockBeta.merge(pfTickers)['cqaBeta'])
longIndex = matrix(pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = np.diag(pfTickers.merge(longTickers, how='left').fillna(0)['bWeight'])
mLongIndex = matrix(mLongIndex[np.logical_or.reduce([np.sum(mLongIndex, 1) > 0.5])]).trans()
shortIndex = -matrix(pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = -np.diag(pfTickers.merge(shortTickers, how='left').fillna(0)['bWeight'])
mShortIndex = matrix(mShortIndex[np.logical_or.reduce([np.sum(mShortIndex, 1) > 0.5])]).trans()
N = pfTickers.shape[0]
id = spmatrix(1.0, range(N), range(N))
wBounds = matrix(np.ones((N, 1)) * WEIGHT_BOUND)
longBounds = matrix(np.zeros((shortTickers.shape[0], 1)))
shortBounds = matrix(np.zeros((longTickers.shape[0], 1)))
total_cov = matrix(functions.get_cov(pfTickers, Coef, Res, CarhartDaily, back_date, start_date))
q = matrix(np.zeros((pfTickers.shape[0], 1)))
G = matrix([[mBeta], [-mBeta],
# [mBeta_smb], [-mBeta_smb],
# [mBeta_hml], [-mBeta_hml],
# [mBeta_umd], [-mBeta_umd],
[mCqaBeta], [-mCqaBeta],
[longIndex], [-longIndex],
[shortIndex], [-shortIndex],
[id], [-id],
[-mLongIndex], [mShortIndex]]).trans()
opt_comp = pd.DataFrame()
max_slope = 0
for k in range(11):
print 'k = %d' % k
h = matrix([(k + 1) * 0.05, -k * 0.05,
# 0.1, 0.1,
# 0.1, 0.1,
# 0.1, 0.1,
BETA_BOUND, BETA_BOUND,
1, -0.98,
-0.98, 1,
wBounds, wBounds,
longBounds, shortBounds])
# sol = solvers.lp(-mBeta, A, b)
try:
sol = solvers.qp(total_cov, q, G, h)
except ValueError:
break
w_res = sol['x']
cov_res = sol['primal objective']
beta_res = np.float64(w_res.trans() * mBeta)[0, 0]
beta_cqa_res = np.float64(w_res.trans() * mCqaBeta)[0, 0]
# beta_smb_res = np.float64(w_res.trans() * mBeta_smb)[0,0]
# beta_hml_res = np.float64(w_res.trans() * mBeta_hml)[0,0]
# beta_umd_res = np.float64(w_res.trans() * mBeta_umd)[0,0]
opt_comp = opt_comp.append(pd.DataFrame([{'beta': beta_res,
'beta_cqa': beta_cqa_res,
# 'beta_smb': beta_smb_res,
# 'beta_hml': beta_hml_res,
# 'beta_umd': beta_umd_res,
'vol': math.sqrt(cov_res),
}]))
slope = beta_res / math.sqrt(cov_res)
if slope > max_slope:
w_final = w_res
wTickers = pfTickers
wTickers['weight'] = w_final
return (opt_comp, wTickers)