Date
Apple
Samsung
BMW
Lufthansa
PetroChina
12/15/2014
105.31
1062.40
90.02
13.54
0.88
12/22/2014
107.39
1081.60
90.55
13.86
0.91
12/29/2014
103.00
1064.00
87.84
14.04
0.92
1/5/2015
105.52
1051.20
88.60
14.06
0.95
1/12/2015
99.85
1052.80
93.61
14.25
0.99
1/20/2015
106.44
1045.60
98.80
14.39
0.96
1/26/2015
110.38
1092.00
103.60
15.06
0.95
2/2/2015
112.04
1097.60
105.90
13.87
0.98
2/9/2015
119.72
1088.80
107.39
13.47
0.99
2/17/2015
122.00
1086.60
110.56
13.20
1.00
2/23/2015
121.02
1085.60
112.85
13.10
1.05
3/2/2015
119.27
1153.60
115.15
13.09
1.00
3/9/2015
116.43
1165.60
120.00
13.04
1.00
3/16/2015
118.61
1171.20
116.85
13.97
0.99
3/23/2015
116.11
1136.80
116.17
13.05
1.00
3/30/2015
118.06
1147.20
115.21
12.72
1.04
4/6/2015
119.74
1192.00
117.50
12.96
1.22
4/13/2015
117.53
1160.00
110.29
12.20
1.21
4/20/2015
122.74
1128.00
110.29
12.28
1.19
4/27/2015
121.48
1128.00
105.69
12.40
1.15
5/4/2015
120.23
1070.40
109.44
13.24
1.11
5/11/2015
121.31
1060.80
102.50
13.79
1.07
5/18/2015
124.87
1080.00
104.80
13.33
1.12
5/26/2015
122.74
1078.20
100.26
12.98
1.06
6/1/2015
121.20
1072.80
99.55
12.37
1.02
6/8/2015
119.81
1021.60
100.00
12.20
1.03
6/15/2015
119.27
1012.80
97.33
11.62
0.99
6/22/2015
119.41
1022.40
103.54
11.84
1.02
6/29/2015
119.12
1014.40
99.37
11.61
1.02
7/6/2015
116.14
1007.20
95.65
12.27
0.93
7/13/2015
122.11
1044.00
95.77
12.82
0.95
7/20/2015
117.29
983.20
91.00
12.77
0.94
7/27/2015
114.28
948.00
91.50
12.35
0.91
8/3/2015
108.83
908.80
92.67
12.14
0.88
8/10/2015
109.25
912.00
86.74
11.85
0.85
8/17/2015
99.64
880.80
80.11
10.85
0.77
8/24/2015
106.73
864.80
83.18
11.03
0.75
8/31/2015
102.94
903.20
79.90
11.46
0.67
9/8/2015
107.60
930.20
82.40
11.50
0.66
9/14/2015
106.88
952.00
85.97
11.75
0.67
9/21/2015
108.07
889.60
79.07
11.83
0.66
9/28/2015
103.99
895.20
78.71
12.68
0.63
10/5/2015
105.63
1016.00
88.02
13.45
0.72
10/12/2015
10/19/2015
10/26/2015
11/2/2015
11/9/2015
11/16/2015
11/23/2015
11/30/2015
12/7/2015
12/14/2015
12/21/2015
12/28/2015
1/4/2016
1/11/2016
1/19/2016
1/25/2016
2/1/2016
2/8/2016
2/16/2016
2/22/2016
2/29/2016
3/7/2016
3/14/2016
3/21/2016
3/28/2016
4/4/2016
4/11/2016
4/18/2016
4/25/2016
5/2/2016
5/9/2016
5/16/2016
5/23/2016
5/31/2016
6/6/2016
6/13/2016
6/20/2016
6/27/2016
7/5/2016
7/11/2016
7/18/2016
7/25/2016
8/1/2016
8/8/2016
8/15/2016
104.61
112.19
112.58
114.05
105.84
112.39
110.99
112.14
106.63
99.89
101.78
99.17
91.35
91.51
95.55
91.70
88.58
88.55
90.48
91.30
97.05
96.34
99.79
99.55
103.62
102.37
103.49
99.56
88.31
87.35
85.28
89.71
94.54
92.25
93.11
89.81
87.99
90.34
91.08
93.06
92.95
98.18
101.26
101.92
103.03
1012.00
1031.20
1097.60
1070.40
1040.00
1028.00
1061.60
1015.20
1027.20
1022.40
1028.00
1008.00
936.80
905.60
910.00
920.00
931.20
904.00
925.65
937.60
972.00
999.20
1018.40
1030.40
1023.20
996.80
1040.00
1024.00
996.00
1032.00
1002.40
1015.20
1025.60
1105.50
1124.80
1140.80
1120.00
1172.80
1194.50
1214.40
1212.80
1231.20
1248.80
1236.00
1340.00
87.15
93.30
93.26
96.00
94.81
99.30
101.40
99.18
93.81
96.46
98.44
98.12
83.51
77.27
77.15
77.05
72.84
70.09
72.70
73.71
82.84
78.85
81.38
80.00
78.50
74.57
78.18
82.89
81.10
76.08
73.39
71.52
74.97
72.40
70.70
69.34
68.42
67.96
72.50
74.48
75.35
76.86
77.50
79.57
77.13
13.61
13.92
13.43
13.95
13.36
13.74
13.38
13.86
13.33
14.11
14.48
14.57
14.92
13.61
13.50
13.47
12.88
12.40
12.98
13.65
14.49
14.98
14.52
14.02
14.05
13.85
14.20
13.94
13.56
12.47
12.34
12.35
12.66
12.09
11.33
11.25
10.96
10.91
11.20
11.40
10.31
10.63
10.48
11.03
10.40
0.74
0.73
0.71
0.71
0.67
0.67
0.67
0.64
0.59
0.62
0.63
0.61
0.57
0.51
0.52
0.54
0.54
0.53
0.59
0.62
0.66
0.59
0.63
0.61
0.58
0.56
0.61
0.64
0.64
0.60
0.61
0.58
0.61
0.62
0.64
0.63
0.60
0.58
0.61
0.63
0.62
0.61
0.61
0.61
0.60
8/22/2016
8/29/2016
9/6/2016
9/12/2016
9/19/2016
9/26/2016
10/3/2016
10/10/2016
10/17/2016
10/24/2016
10/31/2016
11/7/2016
11/14/2016
11/21/2016
11/28/2016
12/5/2016
12/12/2016
100.75
101.49
97.16
108.27
106.18
106.50
107.46
110.82
109.85
107.14
102.54
102.15
103.69
105.32
103.54
107.35
106.74
1289.60
1277.60
1260.40
1221.60
1256.80
1278.40
1364.80
1261.60
1271.20
1291.20
1301.60
1278.40
1268.80
1320.00
1381.60
1424.00
1401.60
76.04
78.38
75.72
73.60
75.40
74.85
77.45
77.03
78.83
79.77
75.64
79.96
80.85
82.61
79.62
89.39
87.57
10.39
10.72
10.65
10.46
10.49
9.91
9.30
10.24
11.29
11.71
11.69
12.76
12.88
12.62
12.14
12.73
12.50
0.61
0.61
0.58
0.57
0.59
0.60
0.63
0.62
0.65
0.63
0.61
0.60
0.62
0.65
0.66
0.66
0.67
BritishTobacco
Gold
Returns
102.92
63.62 Apple
Samsung BMW
Lufthansa PetroChina
104.06
62.42 0.0198
0.0181 0.0060
0.0236
0.0330
99.98
64.97 -0.0409
-0.0163 -0.0300
0.0130
0.0121
99.20
70.57 0.0245
-0.0120 0.0087
0.0018
0.0359
102.47
76.22 -0.0537
0.0015 0.0565
0.0132
0.0346
106.74
75.97 0.0659
-0.0068 0.0555
0.0102
-0.0264
106.13
80.32 0.0370
0.0444 0.0486
0.0462
-0.0104
104.47
76.48 0.0151
0.0051 0.0222
-0.0790
0.0263
104.70
73.77 0.0685
-0.0080 0.0141
-0.0285
0.0133
106.88
71.70 0.0190
-0.0020 0.0295
-0.0200
0.0121
109.73
74.60 -0.0080
-0.0009 0.0207
-0.0076
0.0450
107.98
65.24 -0.0145
0.0626 0.0203
-0.0011
-0.0421
101.59
64.34 -0.0238
0.0104 0.0421
-0.0034
-0.0020
102.59
68.00 0.0187
0.0048 -0.0263
0.0713
-0.0070
99.92
66.85 -0.0210
-0.0294 -0.0057
-0.0659
0.0030
100.18
66.82 0.0168
0.0091 -0.0083
-0.0257
0.0442
102.38
67.07 0.0142
0.0391 0.0199
0.0189
0.1694
105.19
70.33 -0.0185
-0.0268 -0.0614
-0.0583
-0.0008
106.69
70.23 0.0443
-0.0276 0.0000
0.0066
-0.0231
104.78
71.40 -0.0102
0.0000 -0.0417
0.0098
-0.0312
105.76
69.10 -0.0103
-0.0511 0.0354
0.0673
-0.0339
107.23
71.76 0.0090
-0.0090 -0.0633
0.0416
-0.0351
105.68
69.31 0.0293
0.0181 0.0224
-0.0334
0.0448
104.31
68.05 -0.0171
-0.0017 -0.0433
-0.0259
-0.0527
98.64
65.84 -0.0125
-0.0050 -0.0071
-0.0474
-0.0406
100.39
67.33 -0.0115
-0.0477 0.0046
-0.0137
0.0147
105.97
66.25 -0.0045
-0.0086 -0.0268
-0.0472
-0.0368
105.57
64.92 0.0012
0.0095 0.0638
0.0185
0.0292
103.10
62.70 -0.0024
-0.0078 -0.0402
-0.0194
0.0010
106.01
60.45 -0.0250
-0.0071 -0.0374
0.0573
-0.0908
107.90
58.30 0.0514
0.0365 0.0013
0.0448
0.0204
103.95
56.95 -0.0395
-0.0582 -0.0498
-0.0039
-0.0158
112.11
56.87 -0.0257
-0.0358 0.0055
-0.0329
-0.0235
111.29
56.77 -0.0477
-0.0414 0.0128
-0.0170
-0.0340
110.01
58.43 0.0038
0.0035 -0.0640
-0.0239
-0.0363
102.40
61.94 -0.0880
-0.0342 -0.0765
-0.0848
-0.0894
101.01
57.69 0.0712
-0.0182 0.0383
0.0171
-0.0310
96.88
53.84 -0.0355
0.0444 -0.0394
0.0390
-0.1067
99.80
54.49 0.0452
0.0299 0.0313
0.0035
-0.0149
104.13
56.94 -0.0067
0.0234 0.0434
0.0213
0.0182
103.03
56.14 0.0111
-0.0655 -0.0803
0.0072
-0.0208
105.68
59.68 -0.0377
0.0063 -0.0045
0.0714
-0.0426
108.65
63.93 0.0158
0.1349 0.1183
0.0607
0.1397
111.57
111.20
111.26
108.19
105.95
110.09
110.35
108.65
102.71
102.59
105.29
104.05
98.61
96.00
97.87
104.58
102.04
102.62
103.56
102.20
108.34
110.32
108.16
106.79
109.59
111.04
113.36
112.78
115.08
114.75
113.59
113.28
115.82
115.65
113.57
112.02
112.74
121.96
119.82
120.34
119.25
120.30
118.75
120.93
120.16
65.28
67.07
63.00
56.28
56.60
56.36
56.70
61.41
58.79
56.07
59.52
58.34
60.09
58.52
61.87
66.63
73.77
85.05
85.59
84.20
85.74
84.91
88.05
84.88
85.30
88.62
89.06
87.87
94.68
84.27
83.23
84.15
78.67
86.69
89.25
89.38
95.31
110.80
115.24
110.32
109.16
110.80
103.15
102.79
102.31
-0.0096
0.0724
0.0035
0.0131
-0.0720
0.0620
-0.0125
0.0104
-0.0491
-0.0632
0.0189
-0.0256
-0.0789
0.0018
0.0442
-0.0402
-0.0341
-0.0003
0.0218
0.0091
0.0629
-0.0073
0.0358
-0.0024
0.0409
-0.0121
0.0110
-0.0380
-0.1130
-0.0109
-0.0237
0.0519
0.0539
-0.0242
0.0093
-0.0354
-0.0202
0.0267
0.0082
0.0217
-0.0012
0.0563
0.0314
0.0065
0.0109
-0.0039
0.0190
0.0644
-0.0248
-0.0284
-0.0115
0.0327
-0.0437
0.0118
-0.0047
0.0055
-0.0195
-0.0706
-0.0333
0.0049
0.0110
0.0122
-0.0292
0.0239
0.0129
0.0367
0.0280
0.0192
0.0118
-0.0070
-0.0258
0.0433
-0.0154
-0.0273
0.0361
-0.0287
0.0128
0.0102
0.0779
0.0175
0.0142
-0.0182
0.0471
0.0185
0.0167
-0.0013
0.0152
0.0143
-0.0102
0.0841
-0.0098
0.0706
-0.0005
0.0294
-0.0124
0.0474
0.0212
-0.0219
-0.0541
0.0282
0.0206
-0.0033
-0.1490
-0.0747
-0.0015
-0.0013
-0.0547
-0.0378
0.0373
0.0139
0.1238
-0.0481
0.0321
-0.0169
-0.0187
-0.0501
0.0484
0.0603
-0.0216
-0.0619
-0.0354
-0.0254
0.0483
-0.0343
-0.0235
-0.0192
-0.0133
-0.0067
0.0668
0.0272
0.0117
0.0200
0.0083
0.0267
-0.0307
0.0123
0.0224
-0.0349
0.0387
-0.0427
0.0285
-0.0262
0.0359
-0.0383
0.0585
0.0266
0.0059
0.0244
-0.0878
-0.0081
-0.0026
-0.0434
-0.0377
0.0472
0.0516
0.0615
0.0338
-0.0307
-0.0348
0.0025
-0.0142
0.0249
-0.0180
-0.0273
-0.0804
-0.0108
0.0012
0.0251
-0.0450
-0.0629
-0.0071
-0.0262
-0.0046
0.0271
0.0179
-0.0956
0.0310
-0.0141
0.0525
-0.0571
0.0292
-0.0149
-0.0247
0.0028
-0.0590
0.0045
-0.0045
-0.0507
-0.0676
0.0422
0.0113
-0.0240
-0.0721
-0.0936
0.0136
0.0462
-0.0074
-0.0278
0.1238
0.0492
0.0662
-0.1091
0.0731
-0.0380
-0.0478
-0.0329
0.0823
0.0512
0.0047
-0.0610
0.0133
-0.0395
0.0445
0.0164
0.0387
-0.0171
-0.0521
-0.0333
0.0517
0.0328
-0.0159
-0.0226
0.0132
-0.0081
-0.0115
118.64
121.71
116.28
116.07
120.52
120.26
114.49
112.50
106.79
107.48
105.95
101.97
101.10
103.57
103.85
104.57
104.25
93.35
94.04
92.08
90.89
95.24
94.28
83.14
78.23
81.91
80.88
80.92
69.40
68.01
66.97
69.49
68.89
68.63
-0.0221
0.0074
-0.0427
0.1143
-0.0192
0.0030
0.0089
0.0313
-0.0088
-0.0247
-0.0429
-0.0038
0.0150
0.0157
-0.0169
0.0369
-0.0057
-0.0376
-0.0093
-0.0135
-0.0308
0.0288
0.0172
0.0676
-0.0756
0.0076
0.0157
0.0081
-0.0178
-0.0075
0.0404
0.0467
0.0307
-0.0157
-0.0141
0.0307
-0.0339
-0.0280
0.0245
-0.0073
0.0348
-0.0054
0.0233
0.0120
-0.0518
0.0571
0.0111
0.0217
-0.0361
0.1227
-0.0203
-0.0014
0.0323
-0.0065
-0.0178
0.0024
-0.0553
-0.0611
0.1005
0.1031
0.0368
-0.0017
0.0916
0.0098
-0.0202
-0.0384
0.0490
-0.0185
0.0050
0.0083
-0.0492
-0.0172
0.0281
0.0222
0.0451
-0.0096
0.0435
-0.0201
-0.0410
-0.0082
0.0348
0.0353
0.0279
0.0000
0.0090
BritishTobacco Gold
0.0112 -0.0188
-0.0393 0.0407
-0.0077 0.0863
0.0330 0.0800
0.0416 -0.0032
-0.0057 0.0573
-0.0156 -0.0479
0.0022 -0.0355
0.0209 -0.0280
0.0266 0.0405
-0.0159 -0.1255
-0.0592 -0.0139
0.0098 0.0570
-0.0260 -0.0169
0.0026 -0.0004
0.0219 0.0037
0.0274 0.0486
0.0143 -0.0013
-0.0179 0.0166
0.0094 -0.0322
0.0139 0.0384
-0.0144 -0.0341
-0.0130 -0.0182
-0.0544 -0.0324
0.0178 0.0226
0.0556 -0.0161
-0.0037 -0.0201
-0.0234 -0.0342
0.0281 -0.0359
0.0179 -0.0355
-0.0366 -0.0231
0.0785 -0.0013
-0.0073 -0.0018
-0.0115 0.0292
-0.0692 0.0601
-0.0135 -0.0686
-0.0409 -0.0668
0.0301 0.0121
0.0434 0.0450
-0.0106 -0.0141
0.0257 0.0631
0.0282 0.0712
Apple
MEAN
VARIANCE
STD. DEV.
X_i
R_p
Samsung
0.000801
0.003208
0.001353
0.001106
0.036779
0.033261
0.13068238
1.60698851
0.008001
X_i
Name
0.1306824 Apple
1.6069885 Samsung
0.3683463 BMW
-0.0279453 Lufthansa
-1.1128895 PetroChina
-0.4313183 BritishTobacco
0.4661358 Gold
0.13068238
Apple
0.0013397
0.0002495
0.0006567
0.0002954
0.0004076
0.0002873
-0.0002332
2.28786E-005
5.23925E-005
3.16112E-005
-1.07887E-006
-5.92743E-005
-1.61944E-005
-1.42065E-005
Sigma^2p
var_p
sigma_p
Without shortsale
PetroChina
Samsung
-0.001551
0.003208
0.004760
max
min
distance
MVP
0.00130443 R_p
0.01999192 Sigma_p
-0.001551
0.0464603808
0.004000
0.003000
0.0269
-0.0034
0.0006
-0.0276
-0.0207
0.0391
0.0023
-0.0154
-0.0547
-0.0011
0.0263
-0.0117
-0.0523
-0.0265
0.0194
0.0686
-0.0243
0.0057
0.0091
-0.0131
0.0601
0.0183
-0.0196
-0.0127
0.0262
0.0132
0.0210
-0.0052
0.0204
-0.0029
-0.0101
-0.0027
0.0225
-0.0015
-0.0180
-0.0137
0.0065
0.0818
-0.0176
0.0044
-0.0091
0.0088
-0.0128
0.0183
-0.0063
0.0211
0.0274
-0.0607
-0.1066
0.0057
-0.0043
0.0060
0.0831
-0.0427
-0.0462
0.0615
-0.0198
0.0299
-0.0260
0.0571
0.0769
0.1072
0.1530
0.0063
-0.0162
0.0182
-0.0097
0.0369
-0.0360
0.0049
0.0390
0.0049
-0.0133
0.0775
-0.1100
-0.0124
0.0111
-0.0650
0.1019
0.0295
0.0015
0.0664
0.1625
0.0400
-0.0427
-0.0105
0.0150
-0.0690
-0.0035
-0.0047
0.004000
0.003000
0.002000
0.001000
0.000000
0.015
-0.001000
-0.002000
With shortsale
-0.02
min
0.05
max
MVP
0.0003937015 R_p
0.0198419132 Sigma_p
-0.02
0.1870617952
0.06
0.05
0.04
0.03
0.02
0.01
0
0.03
0.02
-0.0127
0.0259
-0.0446
-0.0019
0.0384
-0.0022
-0.0479
-0.0174
-0.0507
0.0065
-0.0143
-0.0375
-0.0086
0.0244
0.0027
0.0070
-0.0031
-0.0876
0.0074
-0.0208
-0.0129
0.0478
-0.0101
-0.1181
-0.0590
0.0470
-0.0125
0.0005
-0.1423
-0.0201
-0.0152
0.0376
-0.0087
-0.0037
0.01
0
-0.01
-0.02
-0.03
0.05
0.1
BMW
Lufthansa
PetroChina
BritishTobacco Gold
0.000684
0.000085
-0.001551
0.000525
0.002125
0.001915
0.001723
0.002180
0.000811
0.002821
0.043756
0.041513
0.046685
0.028482
0.053115
0.36834632
-0.02794527
-1.11288952
-0.43131826
0.46613583
1.60698851
Samsung
0.0002495
0.0010957
0.0005432
-0.0000145
0.0005463
0.0001656
0.0000622
0.36834632
BMW
0.0006567
0.0005432
0.0018962
0.0006914
0.0011651
0.0003833
-0.0002392
5.239253E-005
0.0028294417
0.0003215357
0.000000652
-0.0009769469
-0.0001148009
4.657410E-005
3.161118E-005
0.0003215357
0.0002572682
-7.117388E-006
-0.0004776103
-6.090452E-005
-4.107084E-005
-0.02794527
Lufthansa
0.0002954
-0.0000145
0.0006914
0.0017068
0.0003256
0.0002001
-0.0000280
-1.11288952
-0.43131826
PetroChina
BritishTobacco
0.0004076
0.0002873
0.0005463
0.0001656
0.0011651
0.0003833
0.0003256
0.0002001
0.0021586
0.0003077
0.0003077
0.0008034
0.0002468
0.0004998
-1.07887E-006 -5.9274260E-005 -1.6194426E-005
0.000000652 -0.0009769469 -0.0001148009
-7.11739E-006 -0.0004776103 -6.0904518E-005
1.332878E-006 1.0125281E-005 2.4114566E-006
1.012528E-005
0.0026734305
0.0001476827
2.411457E-006
0.0001476827
0.0001494616
0.000000365 -0.0001280425 -0.0001004765
0.0037721689
0.0614179855
10
no
-0.001075
0.0367450273
X/Y
st dev
mean
0.0004759828
width of one segment
-0.000599
-0.000124
0.029314843 0.0244085859
0.000352
0.0220501004
0.000828
0.0206100827
Without short sale
0.004000
0.003000
Without short sale
0.004000
0.003000
0.002000
0.001000
0.000000
0.015
0.02
0.025
0.03
0.035
0.04
-0.001000
-0.002000
0.070000
distance
no
-0.013
0.126532596
10
0.007
width of one segment
-0.006
0.001
0.0669446736 0.0200535873
0.008
0.0614179856
0.015
0.1207959317
With shortsale
0.045
0.0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Min
Max
-0.001551
0.000811
0.028482
1
0.003208
0.002821
0.053115
0.46613583
Gold
-0.0002332
0.0000622
-0.0002392
-0.0000280
0.0002468
0.0004998
0.0027941
-1.420650E-005
4.657410E-005
-4.107084E-005
0.000000365
-0.0001280425
-0.0001004765
0.0006071033
Apple
Samsung
BMW
Lufthansa
PetroChina
0.0367786535 0.0332610271 0.0437557162 0.0415130793 0.0466853322
0.0008009571 0.0032083625 0.0006844527 8.499628E-005 -0.0015514654
0.001304
0.001780
0.002256
0.002732
0.003208
0.0199919247 0.0205256846 0.0227378339 0.0263365969 0.0331007321
t short sale
t short sale
0.045
X/Y
st dev
mean
0.05
0.055
0.06
Efficient Frontier
Apple
Samsung
BMW
Lufthansa
PetroChina
BritishTobacco
Gold
MVP
Apple
Samsung
BMW
Lufthansa
0.0367786535 0.0332610271 0.0437557162 0.0415130793
0.0008009571 0.0032083625 0.0006844527 8.499628E-005
0.022
0.029
0.036
0.043
0.1812662929 0.2420310519 0.3028888322 0.3638102951
e
Efficient Frontier
Apple
Samsung
BMW
Lufthansa
PetroChina
BritishTobacco
Gold
MVP
0.05
0.42476309
BMW
Lufthansa
PetroChina
BritishTobacco
Gold
MVP
0.35
0.4
0.45
BritishTobaccoGold
0.028481645 0.05311496
0.000524576 0.00212478
PetroChina
BritishTobacc Gold
0.046685332 0.02848164 0.05311496
-0.001551465 0.00052458 0.00212478
Apple
Samsung
BMW
Lufthansa
PetroChina
BritishTobacco
Gold
Apple
Samsung
BMW
Lufthansa
PetroChina
BritishTobacco
Gold
Apple
0.0013396629
0.0002494822
0.0006567005
0.0002954213
0.0004075652
0.00028731
-0.0002332157
Samsung
0.0002494822
0.0010956585
0.0005432004
-1.45183E-005
0.0005462685
0.0001656283
6.217549E-005
BMW
0.0006567005
0.0005432004
0.0018961534
0.0006914424
0.0011651056
0.0003833499
-0.000239202
Lufthansa
0.0002954213
-1.45183E-005
0.0006914424
0.0017067652
0.0003255718
0.000200066
-2.80234E-005
Apple
Samsung
BMW
Lufthansa
0.0013396629 0.0002494822 0.0006567005 0.0002954213
0.0010956585 0.0005432004 -1.45183E-005
0.0018961534 0.0006914424
0.0017067652
PetroChina
0.0004075652
0.0005462685
0.0011651056
0.0003255718
0.0021585633
0.0003076662
0.0002468253
BritishTobacco
0.00028731
0.0001656283
0.0003833499
0.000200066
0.0003076662
0.0008034041
0.0004997517
Gold
-0.0002332157
6.217549E-005
-0.000239202
-2.80234E-005
0.0002468253
0.0004997517
0.0027940721
PetroChina
BritishTobacco
Gold
0.0004075652
0.00028731 -0.0002332157
0.0005462685
0.0001656283 6.217549E-005
0.0011651056
0.0003833499 -0.000239202
0.0003255718
0.000200066 -2.80234E-005
0.0021585633
0.0003076662 0.0002468253
0.0008034041 0.0004997517
0.0027940721
Date
Apple
Samsung BMW
LufthansaPetroChinBritishTo Gold
12/22/2014
0.0198
0.0181
0.0060
0.0236
0.0330
0.0112
-0.0188
12/29/2014
-0.0409
-0.0163
-0.0300
0.0130
0.0121
-0.0393
0.0407
1/5/2015
0.0245
-0.0120
0.0087
0.0018
0.0359
-0.0077
0.0863
1/12/2015
-0.0537
0.0015
0.0565
0.0132
0.0346
0.0330
0.0800
1/20/2015
0.0659
-0.0068
0.0555
0.0102
-0.0264
0.0416
-0.0032
1/26/2015
0.0370
0.0444
0.0486
0.0462
-0.0104
-0.0057
0.0573
2/2/2015
0.0151
0.0051
0.0222
-0.0790
0.0263
-0.0156
-0.0479
2/9/2015
0.0685
-0.0080
0.0141
-0.0285
0.0133
0.0022
-0.0355
2/17/2015
0.0190
-0.0020
0.0295
-0.0200
0.0121
0.0209
-0.0280
2/23/2015
-0.0080
-0.0009
0.0207
-0.0076
0.0450
0.0266
0.0405
3/2/2015
-0.0145
0.0626
0.0203
-0.0011
-0.0421
-0.0159
-0.1255
3/9/2015
-0.0238
0.0104
0.0421
-0.0034
-0.0020
-0.0592
-0.0139
3/16/2015
0.0187
0.0048
-0.0263
0.0713
-0.0070
0.0098
0.0570
3/23/2015
-0.0210
-0.0294
-0.0057
-0.0659
0.0030
-0.0260
-0.0169
3/30/2015
0.0168
0.0091
-0.0083
-0.0257
0.0442
0.0026
-0.0004
4/6/2015
0.0142
0.0391
0.0199
0.0189
0.1694
0.0219
0.0037
4/13/2015
-0.0185
-0.0268
-0.0614
-0.0583
-0.0008
0.0274
0.0486
4/20/2015
0.0443
-0.0276
0.0000
0.0066
-0.0231
0.0143
-0.0013
4/27/2015
-0.0102
0.0000
-0.0417
0.0098
-0.0312
-0.0179
0.0166
5/4/2015
-0.0103
-0.0511
0.0354
0.0673
-0.0339
0.0094
-0.0322
5/11/2015
0.0090
-0.0090
-0.0633
0.0416
-0.0351
0.0139
0.0384
5/18/2015
0.0293
0.0181
0.0224
-0.0334
0.0448
-0.0144
-0.0341
5/26/2015
-0.0171
-0.0017
-0.0433
-0.0259
-0.0527
-0.0130
-0.0182
6/1/2015
-0.0125
-0.0050
-0.0071
-0.0474
-0.0406
-0.0544
-0.0324
6/8/2015
-0.0115
-0.0477
0.0046
-0.0137
0.0147
0.0178
0.0226
6/15/2015
-0.0045
-0.0086
-0.0268
-0.0472
-0.0368
0.0556
-0.0161
6/22/2015
0.0012
0.0095
0.0638
0.0185
0.0292
-0.0037
-0.0201
6/29/2015
-0.0024
-0.0078
-0.0402
-0.0194
0.0010
-0.0234
-0.0342
7/6/2015
-0.0250
-0.0071
-0.0374
0.0573
-0.0908
0.0281
-0.0359
7/13/2015
0.0514
0.0365
0.0013
0.0448
0.0204
0.0179
-0.0355
7/20/2015
-0.0395
-0.0582
-0.0498
-0.0039
-0.0158
-0.0366
-0.0231
7/27/2015
-0.0257
-0.0358
0.0055
-0.0329
-0.0235
0.0785
-0.0013
8/3/2015
-0.0477
-0.0414
0.0128
-0.0170
-0.0340
-0.0073
-0.0018
8/10/2015
0.0038
0.0035
-0.0640
-0.0239
-0.0363
-0.0115
0.0292
8/17/2015
-0.0880
-0.0342
-0.0765
-0.0848
-0.0894
-0.0692
0.0601
8/24/2015
0.0712
-0.0182
0.0383
0.0171
-0.0310
-0.0135
-0.0686
8/31/2015
-0.0355
0.0444
-0.0394
0.0390
-0.1067
-0.0409
-0.0668
9/8/2015
0.0452
0.0299
0.0313
0.0035
-0.0149
0.0301
0.0121
9/14/2015
-0.0067
0.0234
0.0434
0.0213
0.0182
0.0434
0.0450
9/21/2015
0.0111
-0.0655
-0.0803
0.0072
-0.0208
-0.0106
-0.0141
9/28/2015
-0.0377
0.0063
-0.0045
0.0714
-0.0426
0.0257
0.0631
10/5/2015
0.0158
0.1349
0.1183
0.0607
0.1397
0.0282
0.0712
10/12/2015
-0.0096
-0.0039
-0.0098
0.0123
0.0292
0.0269
0.0211
10/19/2015
0.0724
0.0190
0.0706
0.0224
-0.0149
-0.0034
0.0274
10/26/2015
0.0035
0.0644
-0.0005
-0.0349
-0.0247
0.0006
-0.0607
11/2/2015
0.0131
-0.0248
0.0294
0.0387
0.0028
-0.0276
-0.1066
11/9/2015
11/16/2015
11/23/2015
11/30/2015
12/7/2015
12/14/2015
12/21/2015
12/28/2015
1/4/2016
1/11/2016
1/19/2016
1/25/2016
2/1/2016
2/8/2016
2/16/2016
2/22/2016
2/29/2016
3/7/2016
3/14/2016
3/21/2016
3/28/2016
4/4/2016
4/11/2016
4/18/2016
4/25/2016
5/2/2016
5/9/2016
5/16/2016
5/23/2016
5/31/2016
6/6/2016
6/13/2016
6/20/2016
6/27/2016
7/5/2016
7/11/2016
7/18/2016
7/25/2016
8/1/2016
8/8/2016
8/15/2016
8/22/2016
8/29/2016
9/6/2016
9/12/2016
-0.0720
0.0620
-0.0125
0.0104
-0.0491
-0.0632
0.0189
-0.0256
-0.0789
0.0018
0.0442
-0.0402
-0.0341
-0.0003
0.0218
0.0091
0.0629
-0.0073
0.0358
-0.0024
0.0409
-0.0121
0.0110
-0.0380
-0.1130
-0.0109
-0.0237
0.0519
0.0539
-0.0242
0.0093
-0.0354
-0.0202
0.0267
0.0082
0.0217
-0.0012
0.0563
0.0314
0.0065
0.0109
-0.0221
0.0074
-0.0427
0.1143
-0.0284
-0.0115
0.0327
-0.0437
0.0118
-0.0047
0.0055
-0.0195
-0.0706
-0.0333
0.0049
0.0110
0.0122
-0.0292
0.0239
0.0129
0.0367
0.0280
0.0192
0.0118
-0.0070
-0.0258
0.0433
-0.0154
-0.0273
0.0361
-0.0287
0.0128
0.0102
0.0779
0.0175
0.0142
-0.0182
0.0471
0.0185
0.0167
-0.0013
0.0152
0.0143
-0.0102
0.0841
-0.0376
-0.0093
-0.0135
-0.0308
-0.0124
0.0474
0.0212
-0.0219
-0.0541
0.0282
0.0206
-0.0033
-0.1490
-0.0747
-0.0015
-0.0013
-0.0547
-0.0378
0.0373
0.0139
0.1238
-0.0481
0.0321
-0.0169
-0.0187
-0.0501
0.0484
0.0603
-0.0216
-0.0619
-0.0354
-0.0254
0.0483
-0.0343
-0.0235
-0.0192
-0.0133
-0.0067
0.0668
0.0272
0.0117
0.0200
0.0083
0.0267
-0.0307
-0.0141
0.0307
-0.0339
-0.0280
-0.0427
0.0285
-0.0262
0.0359
-0.0383
0.0585
0.0266
0.0059
0.0244
-0.0878
-0.0081
-0.0026
-0.0434
-0.0377
0.0472
0.0516
0.0615
0.0338
-0.0307
-0.0348
0.0025
-0.0142
0.0249
-0.0180
-0.0273
-0.0804
-0.0108
0.0012
0.0251
-0.0450
-0.0629
-0.0071
-0.0262
-0.0046
0.0271
0.0179
-0.0956
0.0310
-0.0141
0.0525
-0.0571
-0.0014
0.0323
-0.0065
-0.0178
-0.0590
0.0045
-0.0045
-0.0507
-0.0676
0.0422
0.0113
-0.0240
-0.0721
-0.0936
0.0136
0.0462
-0.0074
-0.0278
0.1238
0.0492
0.0662
-0.1091
0.0731
-0.0380
-0.0478
-0.0329
0.0823
0.0512
0.0047
-0.0610
0.0133
-0.0395
0.0445
0.0164
0.0387
-0.0171
-0.0521
-0.0333
0.0517
0.0328
-0.0159
-0.0226
0.0132
-0.0081
-0.0115
0.0050
0.0083
-0.0492
-0.0172
-0.0207
0.0391
0.0023
-0.0154
-0.0547
-0.0011
0.0263
-0.0117
-0.0523
-0.0265
0.0194
0.0686
-0.0243
0.0057
0.0091
-0.0131
0.0601
0.0183
-0.0196
-0.0127
0.0262
0.0132
0.0210
-0.0052
0.0204
-0.0029
-0.0101
-0.0027
0.0225
-0.0015
-0.0180
-0.0137
0.0065
0.0818
-0.0176
0.0044
-0.0091
0.0088
-0.0128
0.0183
-0.0063
-0.0127
0.0259
-0.0446
-0.0019
0.0057
-0.0043
0.0060
0.0831
-0.0427
-0.0462
0.0615
-0.0198
0.0299
-0.0260
0.0571
0.0769
0.1072
0.1530
0.0063
-0.0162
0.0182
-0.0097
0.0369
-0.0360
0.0049
0.0390
0.0049
-0.0133
0.0775
-0.1100
-0.0124
0.0111
-0.0650
0.1019
0.0295
0.0015
0.0664
0.1625
0.0400
-0.0427
-0.0105
0.0150
-0.0690
-0.0035
-0.0047
-0.0876
0.0074
-0.0208
-0.0129
9/19/2016
9/26/2016
10/3/2016
10/10/2016
10/17/2016
10/24/2016
10/31/2016
11/7/2016
11/14/2016
11/21/2016
11/28/2016
12/5/2016
12/12/2016
-0.0192
0.0030
0.0089
0.0313
-0.0088
-0.0247
-0.0429
-0.0038
0.0150
0.0157
-0.0169
0.0369
-0.0057
0.0288
0.0172
0.0676
-0.0756
0.0076
0.0157
0.0081
-0.0178
-0.0075
0.0404
0.0467
0.0307
-0.0157
0.0245
-0.0073
0.0348
-0.0054
0.0233
0.0120
-0.0518
0.0571
0.0111
0.0217
-0.0361
0.1227
-0.0203
0.0024
-0.0553
-0.0611
0.1005
0.1031
0.0368
-0.0017
0.0916
0.0098
-0.0202
-0.0384
0.0490
-0.0185
0.0281
0.0222
0.0451
-0.0096
0.0435
-0.0201
-0.0410
-0.0082
0.0348
0.0353
0.0279
0.0000
0.0090
0.0384
-0.0022
-0.0479
-0.0174
-0.0507
0.0065
-0.0143
-0.0375
-0.0086
0.0244
0.0027
0.0070
-0.0031
0.0478
-0.0101
-0.1181
-0.0590
0.0470
-0.0125
0.0005
-0.1423
-0.0201
-0.0152
0.0376
-0.0087
-0.0037
Year
Month
2014
2014
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
2015
12
12
1
1
1
1
2
2
2
2
3
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
6
7
7
7
7
8
8
8
8
8
9
9
9
9
10
10
10
10
11
Data
Month
Average - Apple
Average - Samsung
1
0.0001
-0.0076
2
0.0171
0.0056
3
0.0048
0.0122
4
-0.0153
-0.0051
5
0.0064
0.0072
6
-0.0055
0.0001
7
0.0058
-0.0019
8
-0.0062
-0.0005
9
0.0084
-0.0005
10
0.0051
0.0264
11
0.0012
-0.0016
12
-0.0136
0.0012
Total Result
0.0008
0.0032
Year
2014
2015
2016
Total
Data
Average - Apple
Average - Samsung
-0.0106
0.0009
-0.0001
-0.0005
0.0022
0.0071
Result
0.0008
0.0032
2015
2015
2015
2015
2015
2015
2015
2015
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
11
11
11
11
12
12
12
12
1
1
1
1
2
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
8
9
9
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
2016
9
9
10
10
10
10
10
11
11
11
11
12
12
Average - BMW
Average - Lufthansa
Average - PetroChina
-0.0072
-0.0003
-0.0090
0.0188
-0.0062
0.0334
-0.0033
-0.0060
-0.0140
-0.0058
-0.0072
0.0275
-0.0175
-0.0067
-0.0115
-0.0076
-0.0233
-0.0107
0.0057
0.0057
-0.0080
-0.0108
-0.0058
-0.0291
-0.0069
0.0033
-0.0095
0.0213
0.0265
0.0164
0.0130
0.0086
-0.0019
0.0087
0.0150
0.0020
0.0007
0.0001
-0.0016
Average - BMW
Average - Lufthansa
Average - PetroChina
-0.0120
0.0183
0.0225
0.0030
0.0014
-0.0068
-0.0012
-0.0021
0.0029
0.0007
0.0001
-0.0016
Average - BritishTobacco
Average - Gold
0.0088
0.0448
0.0079
0.0220
-0.0085
-0.0115
0.0119
0.0220
0.0001
-0.0134
0.0054
0.0200
0.0093
-0.0117
-0.0130
-0.0205
0.0098
0.0138
-0.0080
-0.0093
-0.0046
-0.0174
-0.0082
-0.0047
0.0005
0.0021
Average - BritishTobacco
Average - Gold
-0.0141
0.0110
0.0012
-0.0010
0.0004
0.0050
0.0005
0.0021
MEAN
ST dev
x_i
R_p
sigma_p
Samsung
PetroChina
R_p
sigma_p
Samsung PetroChina
0.003208 -0.0015514654
0.033261
0.0466853322
0
1
-0.001551
0.04646
1
0
0.003208
0.033101
0
1
0.9
0.8
0.7
0.1
0.2
0.3
0.0027323797 0.002256 0.00178
0.0317395229 0.031022 0.030993
Name
Samsung
PetroChina
0.6
0.4
0.0013044314
0.0316546371
Without shortsale
0.004
0.003
0.002
0.001
0
0.03
0.032
0.034
0.036
0.038
0.04
0.042
0.044
-0.001
-0.002
MEAN
ST dev
x_i
R_p
sigma_p
Samsung
BritishT
R_p
Sigma_p
Samsung PetroChina
0.003208 -0.0015514654
0.033261
0.0466853322
-0.4
1.4
-0.003455
0.061598
1.4
-0.4
0.005112
0.043371
-0.4
1.4
1.3
1.2
1.1
-0.3
-0.2
-0.1
0.0046363109 0.00416 0.003684
0.0402472868 0.037442 0.035031
Name
Samsung
PetroChina
1
0
0.0032083625
0.0331007321
With shortsale
0.006
0.005
0.004
0.003
0.046
0.
With shortsale
0.006
0.005
0.004
0.003
0.002
0.001
0
0.025
-0.001
-0.002
-0.003
-0.004
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.0
0
1
Samsung PetroChina
0.001096
0.0005462685
0.000546
0.0021585633
0.5
0.5
0.000828
0.032965
0.4
0.6
0.0003524658
0.0348510691
0
0
0.3
0.2
0.7
0.8
-0.000123517 -0.0005994998
0.0372255027 0.0400014097
0
0.0021585633
0.1
0
0.9
1
-0.0010754826 -0.001551
0.04310129 0.04646
42
Portfolio
Samsung
PetroChina
0.044
0.046
0.048
-0.4
1.4
Samsung PetroChina
0.001096
0.0005462685
0.000546
0.0021585633
0.9
0.1
0.002732
0.03174
0.8
0.2
0.0022563969
0.0310220867
0.0001753054
-0.0003059103
0.7
0.6
0.3
0.4
0.0017804141 0.0013044314
0.0309931623 0.0316546371
Portfolio
-0.0003059103
0.0042307841
0.5
0.4
0.5
0.6
0.0008284486 0.000352
0.0329649766 0.034851
Portfolio
Samsung
PetroChina
0.055
0.06
0.065
sigma^2_p 0.002159
sigma_p
0.04646
sigma^2_p
sigma_p
0.003794
0.061598
0.3
0.2
0.1
0
0.7
0.8
0.9
1
-0.0001235 -0.000599 -0.001075 -0.00155147
0.0372255 0.040001 0.043101 0.046460341
-0.1
-0.2
-0.3
1.1
1.2
1.3
-0.0020274482 -0.002503 -0.002979
0.0500263844 0.053758 0.057624
-0.4
1.4
-0.003455
0.061598
