In [1]:
import pandas as pd
import numpy as np
In [2]:
data = pd.read_csv('3-B_EXAM4.csv', encoding='GB2312')
data
Out[2]:
日期 市场指数 组合1 组合2 组合3 组合4 组合5 无风险利率 市场溢酬因子 市值因子 账面市值比因子
0 20090109 1904.86 1727.01 1281.30 1591.43 2469.13 1822.58 0.000043 0.0204 0.0083 0.0010
1 20090112 1900.35 1715.86 1300.27 1590.85 2488.00 1829.90 0.000042 0.0044 0.0102 -0.0021
2 20090113 1863.37 1667.97 1273.80 1551.21 2407.01 1774.56 0.000041 -0.0249 -0.0019 0.0074
3 20090114 1928.87 1750.08 1329.63 1607.21 2463.77 1817.24 0.000041 0.0427 0.0029 -0.0022
4 20090115 1920.21 1739.64 1334.24 1614.49 2456.65 1814.10 0.000040 0.0033 0.0079 -0.0031
... ... ... ... ... ... ... ... ... ... ... ...
2422 20181224 2527.01 1289.12 1634.66 1869.08 7276.91 5275.89 0.000088 0.0056 -0.0008 -0.0045
2423 20181225 2504.82 1259.94 1605.20 1846.48 7256.91 5251.07 0.000090 -0.0088 -0.0034 -0.0057
2424 20181226 2498.29 1250.42 1598.94 1843.40 7216.06 5193.21 0.000091 -0.0030 0.0048 0.0030
2425 20181227 2483.09 1236.36 1587.71 1831.41 7233.59 5144.72 0.000091 -0.0080 -0.0095 0.0024
2426 20181228 2493.90 1225.71 1592.22 1848.19 7349.07 5177.93 0.000092 0.0039 -0.0031 -0.0009

2427 rows × 11 columns

In [3]:
p1 = data.iloc[:, 2].values
p2 = data.iloc[:, 3].values
p3 = data.iloc[:, 4].values
p4 = data.iloc[:, 5].values
p5 = data.iloc[:, 6].values
rf = data.iloc[:, 7].values
mkt = data.iloc[:, 8].values
p1
Out[3]:
array([1727.01, 1715.86, 1667.97, ..., 1250.42, 1236.36, 1225.71])
In [4]:
r1 = np.log(p1[1:]) - np.log(p1[:-1])
r2 = np.log(p2[1:]) - np.log(p2[:-1])
r3 = np.log(p3[1:]) - np.log(p3[:-1])
r4 = np.log(p4[1:]) - np.log(p4[:-1])
r5 = np.log(p5[1:]) - np.log(p5[:-1])
r1
Out[4]:
array([-0.00647718, -0.02830709,  0.04805418, ..., -0.00758461,
       -0.01130792, -0.00865131])
In [5]:
rexc1 = r1 - rf[1:]
rexc2 = r2 - rf[1:]
rexc3 = r3 - rf[1:]
rexc4 = r4 - rf[1:]
rexc5 = r5 - rf[1:]
rexc1
Out[5]:
array([-0.00651918, -0.02834809,  0.04801318, ..., -0.00767561,
       -0.01139892, -0.00874331])
In [6]:
R = np.concatenate([rexc1[:, None], 
                    rexc2[:, None],
                    rexc3[:, None], 
                    rexc4[:, None],
                    rexc5[:, None]], 
                   axis=1)
R
Out[6]:
array([[-0.00651918,  0.01465475, -0.00040652,  0.00757131,  0.00396624],
       [-0.02834809, -0.02060838, -0.02527419, -0.03313486, -0.03074982],
       [ 0.04801318,  0.04285515,  0.03542348,  0.02326638,  0.02372536],
       ...,
       [-0.00767561, -0.00399845, -0.00176043, -0.00573602, -0.01117086],
       [-0.01139892, -0.00713918, -0.00661653,  0.00233536, -0.00947206],
       [-0.00874331,  0.00274454,  0.00902862,  0.01574632,  0.00634242]])
In [7]:
Cov_Sample = np.mat(np.cov(R, rowvar=False))
Cov_Sample
Out[7]:
matrix([[0.00036161, 0.00031648, 0.00026988, 0.00021371, 0.00019017],
        [0.00031648, 0.00036965, 0.00028689, 0.00024158, 0.00022704],
        [0.00026988, 0.00028689, 0.00029853, 0.00021888, 0.00020663],
        [0.00021371, 0.00024158, 0.00021888, 0.00026741, 0.0002325 ],
        [0.00019017, 0.00022704, 0.00020663, 0.0002325 , 0.0002925 ]])
In [10]:
X = np.mat(np.concatenate([np.ones((len(mkt)-1, 1)), mkt[1:, None]], axis=1))
X
Out[10]:
matrix([[ 1.    ,  0.0044],
        [ 1.    , -0.0249],
        [ 1.    ,  0.0427],
        ...,
        [ 1.    , -0.003 ],
        [ 1.    , -0.008 ],
        [ 1.    ,  0.0039]])
In [13]:
Y = np.mat(R)
AB_hat = (X.T*X).I*(X.T*Y)
ALPHA = AB_hat[0]
BETA = AB_hat[1]
RESD = Y - X*AB_hat
covfactor = np.cov(mkt[1:])
covresidual = np.diag(np.diag(np.cov(RESD, rowvar=False)))
Cov_Factor = BETA.T*covfactor*BETA + covresidual
Cov_Factor
Out[13]:
matrix([[0.00036161, 0.00028866, 0.00026249, 0.00022798, 0.00022049],
        [0.00028866, 0.00036965, 0.00027923, 0.00024251, 0.00023454],
        [0.00026249, 0.00027923, 0.00029853, 0.00022053, 0.00021329],
        [0.00022798, 0.00024251, 0.00022053, 0.00026741, 0.00018524],
        [0.00022049, 0.00023454, 0.00021329, 0.00018524, 0.0002925 ]])
In [14]:
c = 0.5
Cov_Shrink = c*Cov_Sample + (1-c)*Cov_Factor
Cov_Shrink
Out[14]:
matrix([[0.00036161, 0.00030257, 0.00026619, 0.00022084, 0.00020533],
        [0.00030257, 0.00036965, 0.00028306, 0.00024205, 0.00023079],
        [0.00026619, 0.00028306, 0.00029853, 0.0002197 , 0.00020996],
        [0.00022084, 0.00024205, 0.0002197 , 0.00026741, 0.00020887],
        [0.00020533, 0.00023079, 0.00020996, 0.00020887, 0.0002925 ]])
In [17]:
uhat = np.mean(R, axis=0)
A = np.mat(np.concatenate([uhat[:, None], np.ones((len(uhat), 1))], axis=1)).T
up = np.mean(uhat)
b = np.mat(np.array([up, 1])[:, None])

omega_Shrink = Cov_Shrink.I*A.T*(A*Cov_Shrink.I*A.T).I*b
print(omega_Shrink)
omega_Sample = Cov_Sample.I*A.T*(A*Cov_Sample.I*A.T).I*b
print()
print(omega_Sample)

[[ 0.32532288]
 [-0.21248216]
 [ 0.38898507]
 [ 0.23881412]
 [ 0.25936009]]

[[ 0.39904587]
 [-0.32861957]
 [ 0.38202395]
 [ 0.23869463]
 [ 0.30885513]]