-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathex2.py
388 lines (334 loc) · 12.2 KB
/
ex2.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
import fix_yahoo_finance as yf
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import datetime
start= '2006-01-01'
end= '2018-01-01'
tickers=['GS','JPM','C','BAC','MS']
data=yf.download(tickers, start, end)
mo=data['Adj Close'].resample('M').last() #monthly obs
#read in the market excess return from the FAMA French Liquidity Factor in WRDS
rf= pd.read_csv(r'C:\Users\Alvi Mahmud\Desktop\QFA\ff.csv', parse_dates=['dateff'], index_col=['dateff']).fillna(value = 0)
mat=np.matrix(pd.concat([mo.GS, mo.JPM, mo.C, mo.BAC, mo.MS], axis=1))
rfr= np.matrix([rf.rf]).T
mktrf= np.matrix([rf.mktrf]).T
M=mat.shape[0] #Number of rows in rmat
N=mat.shape[1] #number of columns (assets) in rmat
import statsmodels.api as sm
#OLS
GS= mo['GS'].pct_change(1).fillna(0)
JPM=mo['JPM'].pct_change(1).fillna(0)
C= mo['C'].pct_change(1).fillna(0)
BAC=mo['BAC'].pct_change(1).fillna(0)
MS=mo['MS'].pct_change(1).fillna(0)
mkr=np.matrix(rf.mktrf.fillna(0)).T
Ygs=np.matrix(GS).T
Yjp=np.matrix(JPM).T
Yc=np.matrix(C).T
Ybac=np.matrix(BAC).T
Yms=np.matrix(MS).T
X = (sm.add_constant(mkr))
[a,b]= (X.T*X)**(-1)*X.T*Ygs
[c,d]= (X.T*X)**(-1)*X.T*Yjp
[e,f]= (X.T*X)**(-1)*X.T*Yc
[g,h]= (X.T*X)**(-1)*X.T*Ybac
[i,j]= (X.T*X)**(-1)*X.T*Yms
# LAD
dt_gs= pd.concat([rf.mktrf, GS], axis=1).fillna(method='ffill')
dt_jp= pd.concat([rf.mktrf, JPM], axis=1).fillna(method='ffill')
dt_c= pd.concat([rf.mktrf, C], axis=1).fillna(method='ffill')
dt_bac= pd.concat([rf.mktrf, BAC], axis=1).fillna(method='ffill')
dt_ms= pd.concat([rf.mktrf, MS], axis=1).fillna(method='ffill')
from statsmodels.regression.quantile_regression import QuantReg
import statsmodels.formula.api as smf
mod_gs = smf.quantreg('mktrf~ GS', dt_gs)
res_gs = mod_gs.fit(q=.5)
print(res_gs.summary())
mod_jp = smf.quantreg('mktrf~ JPM', dt_jp)
res_jp = mod_jp.fit(q=.5)
print(res_jp.summary())
mod_c = smf.quantreg('mktrf~ C', dt_c)
res_c = mod_c.fit(q=.5)
print(res_c.summary())
mod_bac = smf.quantreg('mktrf~ BAC', dt_bac)
res_bac = mod_bac.fit(q=.5)
print(res_bac.summary())
mod_ms = smf.quantreg('mktrf~ MS', dt_ms)
res_ms = mod_ms.fit(q=.5)
print(res_ms.summary())
#Shrinkage
from sklearn.linear_model import Lasso
lassoReg = Lasso(alpha=-0.002,fit_intercept= True, normalize=True)
lassoReg.fit(mkr,Ygs)
print(lassoReg.coef_)
print(lassoReg.intercept_)
lassoReg = Lasso(alpha=0.0031176,fit_intercept= True, normalize=True)
lassoReg.fit(mkr,Yjp)
print(lassoReg.coef_)
print(lassoReg.intercept_)
lassoReg = Lasso(alpha=-0.018568,fit_intercept= True, normalize=True)
lassoReg.fit(mkr,Yc)
print(lassoReg.coef_)
print(lassoReg.intercept_)
lassoReg = Lasso(alpha=0.02,fit_intercept= True, normalize=True)
lassoReg.fit(mkr,Ybac)
print(lassoReg.coef_)
print(lassoReg.intercept_)
lassoReg = Lasso(alpha=-0.00476,fit_intercept= True, normalize=True)
lassoReg.fit(mkr,Yms)
print(lassoReg.coef_)
print(lassoReg.intercept_)
#Bayesian Estimator
import pymc3 as pm
# Context for the model
with pm.Model() as normal_model:
# The prior for the data likelihood is assumed a Normal Distribution
prior = pm.glm.families.Normal()
# Creating the model requires a formula and data (and optionally a family)
pm.GLM.from_formula('mktrf~GS', data = dt_gs, family = prior)
# Perform Markov Chain Monte Carlo sampling letting PyMC3 choose the algorithm
normal_trace = pm.sample(draws=2000, chains = 2, tune = 750, njobs=-1)
print(pm.summary(normal_trace))
pm.plot_posterior(normal_trace)
with pm.Model() as normal_model:
# The prior for the data likelihood is assumed a Normal Distribution
prior = pm.glm.families.Normal()
pm.GLM.from_formula('mktrf~JPM', data = dt_jp, family = prior)
normal_trace = pm.sample(draws=2000, chains = 2, tune = 750, njobs=-1)
pm.plot_posterior(normal_trace)
with pm.Model() as normal_model:
prior = pm.glm.families.Normal()
pm.GLM.from_formula('mktrf~C', data = dt_c, family = prior)
normal_trace = pm.sample(draws=2000, chains = 2, tune = 750, njobs=-1)
pm.plot_posterior(normal_trace)
with pm.Model() as normal_model:
prior = pm.glm.families.Normal()
pm.GLM.from_formula('mktrf~BAC', data = dt_bac, family = prior)
normal_trace = pm.sample(draws=2000, chains = 2, tune = 750, njobs=-1)
pm.plot_posterior(normal_trace)
with pm.Model() as normal_model:
prior = pm.glm.families.Normal()
pm.GLM.from_formula('mktrf~BAC', data = dt_bac, family = prior)
normal_trace = pm.sample(draws=2000, chains = 2, tune = 750, njobs=-1)
pm.plot_posterior(normal_trace)
#t-test
model= sm.OLS(Ygs,X)
print(model.fit().summary())
model= sm.OLS(Yjp,X)
print(model.fit().summary())
model= sm.OLS(Yc,X)
print(model.fit().summary())
model= sm.OLS(Ybac,X)
print(model.fit().summary())
model= sm.OLS(Yms,X)
print(model.fit().summary())
#Rolling Estimation 60 month
from pyfinance import ols
rolling = ols.PandasRollingOLS(y= GS, x=rf.mktrf, window=60)
roll= pd.concat([rolling.alpha, rolling.beta, rf.mktrf], axis=1)
pred=roll.intercept + roll.feature1*roll.mktrf #feature1 is the Beta
roll['pred']=pred.shift()
roll['GS']=GS
roll_60=roll.reset_index()
from sklearn.metrics import mean_squared_error
from math import sqrt
def rmse(predictions, targets):
return np.sqrt(((predictions - targets) ** 2).mean())
rmse_gs= rmse(roll.pred,roll.GS)
print(rmse_gs*100)
x=roll.intercept
plt.plot(roll.index,x, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
y=roll.feature1
plt.plot(roll.index,y, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingJPM = ols.PandasRollingOLS(y= JPM, x=rf.mktrf, window=60)
roll_JPM= pd.concat([rollingJPM.alpha, rollingJPM.beta, rf.mktrf], axis=1)
pred_JPM=roll_JPM.intercept + roll_JPM.feature1*roll_JPM.mktrf
roll_JPM['pred']=pred_JPM.shift()
roll_JPM['JPM']=JPM
roll_60=roll_JPM.reset_index()
rmse_JPM= rmse(roll_JPM.pred,roll_JPM.JPM)
print(rmse_JPM*100)
x=roll.intercept
plt.plot(roll.index,x, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
y=roll.feature1
plt.plot(roll.index,y, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingC = ols.PandasRollingOLS(y= C, x=rf.mktrf, window=60)
roll_C= pd.concat([rollingC.alpha, rollingC.beta, rf.mktrf], axis=1)
pred_C=roll_C.intercept + roll_C.feature1*roll_C.mktrf
roll_C['pred']=pred_C.shift()
roll_C['C']=C
roll_60=roll_C.reset_index()
rmse_C= rmse(roll_C.pred,roll_C.C)
print(rmse_C*100)
x=roll.intercept
plt.plot(roll.index,x, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
y=roll.feature1
plt.plot(roll.index,y, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingBAC = ols.PandasRollingOLS(y= BAC, x=rf.mktrf, window=60)
roll_BAC= pd.concat([rollingBAC.alpha, rollingBAC.beta, rf.mktrf], axis=1)
pred_BAC=roll_BAC.intercept + roll_BAC.feature1*roll_BAC.mktrf
roll_BAC['pred']=pred_BAC.shift()
roll_BAC['BAC']=BAC
roll_60=roll_BAC.reset_index()
rmse_BAC= rmse(roll_BAC.pred,roll_BAC.BAC)
print(rmse_BAC*100)
xx=roll.intercept
plt.plot(roll.index,xx, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yy=roll.feature1
plt.plot(roll.index,yy, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingMS = ols.PandasRollingOLS(y= MS, x=rf.mktrf, window=60)
roll_MS= pd.concat([rollingMS.alpha, rollingMS.beta, rf.mktrf], axis=1)
pred_MS=roll_MS.intercept + roll_MS.feature1*roll_MS.mktrf
roll_MS['pred']=pred_MS.shift()
roll_MS['MS']=MS
roll_60=roll_MS.reset_index()
rmse_MS= rmse(roll_MS.pred,roll_MS.MS)
print(rmse_MS*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
#Rolling estimation cumulative
rolling = ols.PandasRollingOLS(y= GS, x=rf.mktrf, window=2)
roll= pd.concat([rolling.alpha, rolling.beta, rf.mktrf], axis=1)
pred=roll.intercept + roll.feature1*roll.mktrf #feature1 is the Beta
roll['pred']=pred.shift()
roll['GS']=GS
roll_60=roll.reset_index()
from sklearn.metrics import mean_squared_error
from math import sqrt
def rmse(predictions, targets):
return np.sqrt(((predictions - targets) ** 2).mean())
rmse_gs= rmse(roll.pred,roll.GS)
print(rmse_gs*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingJPM = ols.PandasRollingOLS(y= JPM, x=rf.mktrf, window=2)
roll_JPM= pd.concat([rollingJPM.alpha, rollingJPM.beta, rf.mktrf], axis=1)
pred_JPM=roll_JPM.intercept + roll_JPM.feature1*roll_JPM.mktrf
roll_JPM['pred']=pred_JPM.shift()
roll_JPM['JPM']=JPM
roll_60=roll_JPM.reset_index()
rmse_JPM= rmse(roll_JPM.pred,roll_JPM.JPM)
print(rmse_JPM*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingC = ols.PandasRollingOLS(y= C, x=rf.mktrf, window=2)
roll_C= pd.concat([rollingC.alpha, rollingC.beta, rf.mktrf], axis=1)
pred_C=roll_C.intercept + roll_C.feature1*roll_C.mktrf
roll_C['pred']=pred_C.shift()
roll_C['C']=C
roll_60=roll_C.reset_index()
rmse_C= rmse(roll_C.pred,roll_C.C)
print(rmse_C*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingBAC = ols.PandasRollingOLS(y= BAC, x=rf.mktrf, window=2)
roll_BAC= pd.concat([rollingBAC.alpha, rollingBAC.beta, rf.mktrf], axis=1)
pred_BAC=roll_BAC.intercept + roll_BAC.feature1*roll_BAC.mktrf
roll_BAC['pred']=pred_BAC.shift()
roll_BAC['BAC']=BAC
roll_60=roll_BAC.reset_index()
rmse_BAC= rmse(roll_BAC.pred,roll_BAC.BAC)
print(rmse_BAC*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingMS = ols.PandasRollingOLS(y= MS, x=rf.mktrf, window=60)
roll_MS= pd.concat([rollingMS.alpha, rollingMS.beta, rf.mktrf], axis=1)
pred_MS=roll_MS.intercept + roll_MS.feature1*roll_MS.mktrf
roll_MS['pred']=pred_MS.shift()
roll_MS['MS']=MS
roll_60=roll_MS.reset_index()
rmse_MS= rmse(roll_MS.pred,roll_MS.MS)
print(rmse_MS*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()
rollingMS = ols.PandasRollingOLS(y= MS, x=rf.mktrf, window=2)
roll_MS= pd.concat([rollingMS.alpha, rollingMS.beta, rf.mktrf], axis=1)
pred_MS=roll_MS.intercept + roll_MS.feature1*roll_MS.mktrf
roll_MS['pred']=pred_MS.shift()
roll_MS['MS']=MS
roll_60=roll_MS.reset_index()
rmse_MS= rmse(roll_MS.pred,roll_MS.MS)
print(rmse_MS*100)
xms=roll.intercept
plt.plot(roll.index,xms, color='blue', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('alpha')
plt.show()
yms=roll.feature1
plt.plot(roll.index,yms, color='green', marker='o',linewidth=2, markersize=4)
plt.xlabel('Date')
plt.ylabel('beta')
plt.show()