# Import data
library(readr)
retdata <- read_csv("C:/Users/DELL/Downloads/m-fac9003.csv")
## Rows: 168 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (14): AA, AGE, CAT, F, FDX, GM, HPQ, KMB, MEL, NYT, PG, TRB, TXN, SP500
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
head(retdata)
## # A tibble: 6 × 14
## AA AGE CAT F FDX GM HPQ KMB MEL NYT PG
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -16.4 -12.2 -4.44 -0.06 -2.28 -2.12 -6.19 -11.0 -10.8 -6.3 -8.89
## 2 4.04 4.95 8.84 6.02 10.5 8.97 -4.01 -5.2 0.34 -4.62 -0.84
## 3 0.12 13.1 0.17 2.06 10.8 1.57 5.67 3.21 -0.17 -0.66 5.41
## 4 -4.28 -11.1 0.25 -5.67 -2.44 -4.19 -5.29 -0.65 -2.2 -10.6 4.26
## 5 5.81 19.7 8.52 3.89 -16.2 10.9 8.81 8.83 11.8 11.6 16.4
## 6 -4.05 -1.44 -22.1 -5.79 -2.81 -2.7 -1.47 1.55 -7.76 -0.12 4.8
## # … with 3 more variables: TRB <dbl>, TXN <dbl>, SP500 <dbl>
retdata1 <- retdata / 100
head(retdata1)
## AA AGE CAT F FDX GM HPQ KMB MEL
## 1 -0.1640 -0.1217 -0.0444 -0.0006 -0.0228 -0.0212 -0.0619 -0.1101 -0.1077
## 2 0.0404 0.0495 0.0884 0.0602 0.1047 0.0897 -0.0401 -0.0520 0.0034
## 3 0.0012 0.1308 0.0017 0.0206 0.1084 0.0157 0.0567 0.0321 -0.0017
## 4 -0.0428 -0.1106 0.0025 -0.0567 -0.0244 -0.0419 -0.0529 -0.0065 -0.0220
## 5 0.0581 0.1970 0.0852 0.0389 -0.1617 0.1094 0.0881 0.0883 0.1185
## 6 -0.0405 -0.0144 -0.2210 -0.0579 -0.0281 -0.0270 -0.0147 0.0155 -0.0776
## NYT PG TRB TXN SP500
## 1 -0.0630 -0.0889 -0.1304 -0.0761 -0.0752
## 2 -0.0462 -0.0084 -0.0037 0.0497 0.0021
## 3 -0.0066 0.0541 0.0236 0.0269 0.0177
## 4 -0.1060 0.0426 -0.0798 -0.0685 -0.0334
## 5 0.1159 0.1635 0.0882 0.2288 0.0855
## 6 -0.0012 0.0480 -0.0064 -0.0587 -0.0153
# Method 1: Using lm function to estimate regression ----
stockret <- as.matrix(retdata1[, 1:13])
head(stockret)
## AA AGE CAT F FDX GM HPQ KMB MEL
## [1,] -0.1640 -0.1217 -0.0444 -0.0006 -0.0228 -0.0212 -0.0619 -0.1101 -0.1077
## [2,] 0.0404 0.0495 0.0884 0.0602 0.1047 0.0897 -0.0401 -0.0520 0.0034
## [3,] 0.0012 0.1308 0.0017 0.0206 0.1084 0.0157 0.0567 0.0321 -0.0017
## [4,] -0.0428 -0.1106 0.0025 -0.0567 -0.0244 -0.0419 -0.0529 -0.0065 -0.0220
## [5,] 0.0581 0.1970 0.0852 0.0389 -0.1617 0.1094 0.0881 0.0883 0.1185
## [6,] -0.0405 -0.0144 -0.2210 -0.0579 -0.0281 -0.0270 -0.0147 0.0155 -0.0776
## NYT PG TRB TXN
## [1,] -0.0630 -0.0889 -0.1304 -0.0761
## [2,] -0.0462 -0.0084 -0.0037 0.0497
## [3,] -0.0066 0.0541 0.0236 0.0269
## [4,] -0.1060 0.0426 -0.0798 -0.0685
## [5,] 0.1159 0.1635 0.0882 0.2288
## [6,] -0.0012 0.0480 -0.0064 -0.0587
mktret <- as.matrix(retdata1[, 14])
head(mktret)
## [,1]
## [1,] -0.0752
## [2,] 0.0021
## [3,] 0.0177
## [4,] -0.0334
## [5,] 0.0855
## [6,] -0.0153
TT <- dim(stockret)[1]
TT
## [1] 168
fit <- lm(formula = stockret ~ mktret)
fit
##
## Call:
## lm(formula = stockret ~ mktret)
##
## Coefficients:
## AA AGE CAT F FDX GM
## (Intercept) 0.005491 0.007218 0.008394 0.004544 0.007996 0.001982
## mktret 1.291591 1.514136 0.940693 1.219245 0.805117 1.045702
## HPQ KMB MEL NYT PG TRB
## (Intercept) 0.006836 0.005463 0.008849 0.004904 0.008881 0.006512
## mktret 1.627951 0.549805 1.122871 0.770649 0.468803 0.717881
## TXN
## (Intercept) 0.014389
## mktret 1.796412
sigF = as.numeric(var(mktret))
bbeta = as.matrix(fit$coefficients)
bbeta = as.matrix(bbeta[-1,])
bbeta
## [,1]
## AA 1.2915911
## AGE 1.5141359
## CAT 0.9406928
## F 1.2192453
## FDX 0.8051166
## GM 1.0457019
## HPQ 1.6279512
## KMB 0.5498052
## MEL 1.1228708
## NYT 0.7706495
## PG 0.4688034
## TRB 0.7178808
## TXN 1.7964117
sigeps = crossprod(fit$residuals)/(TT-2)
# You can use this method to compute sigeps:
# sigeps.1 = as.matrix(var(fit$residuals))
sigeps = diag(diag(sigeps))
sigeps
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.005919846 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [2,] 0.000000000 0.006095651 0.000000000 0.000000000 0.000000000 0.000000000
## [3,] 0.000000000 0.000000000 0.005966741 0.000000000 0.000000000 0.000000000
## [4,] 0.000000000 0.000000000 0.000000000 0.006791031 0.000000000 0.000000000
## [5,] 0.000000000 0.000000000 0.000000000 0.000000000 0.007839072 0.000000000
## [6,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.006609876
## [7,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [8,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [9,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [10,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [11,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [12,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [13,] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [2,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [3,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [4,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [5,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [6,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [7,] 0.008966712 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [8,] 0.000000000 0.00368461 0.000000000 0.00000000 0.000000000 0.000000000
## [9,] 0.000000000 0.00000000 0.003745483 0.00000000 0.000000000 0.000000000
## [10,] 0.000000000 0.00000000 0.000000000 0.00434329 0.000000000 0.000000000
## [11,] 0.000000000 0.00000000 0.000000000 0.00000000 0.004171711 0.000000000
## [12,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.005205835
## [13,] 0.000000000 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000
## [,13]
## [1,] 0.00000000
## [2,] 0.00000000
## [3,] 0.00000000
## [4,] 0.00000000
## [5,] 0.00000000
## [6,] 0.00000000
## [7,] 0.00000000
## [8,] 0.00000000
## [9,] 0.00000000
## [10,] 0.00000000
## [11,] 0.00000000
## [12,] 0.00000000
## [13,] 0.01316524
# Covariance matrix by single factor model
cov_1f = sigF*bbeta%*%t(bbeta)+sigeps
cov_1f
## AA AGE CAT F FDX GM
## AA 0.009046736 0.003665662 0.0022773795 0.002951744 0.0019491551 0.002531602
## AGE 0.003665662 0.010392918 0.0026697784 0.003460338 0.0022850000 0.002967804
## CAT 0.002277380 0.002669778 0.0076254044 0.002149817 0.0014196104 0.001843819
## F 0.002951744 0.003460338 0.0021498168 0.009577439 0.0018399772 0.002389800
## FDX 0.001949155 0.002285000 0.0014196104 0.001839977 0.0090540833 0.001578081
## GM 0.002531602 0.002967804 0.0018438188 0.002389800 0.0015780808 0.008659520
## HPQ 0.003941205 0.004620285 0.0028704615 0.003720446 0.0024567600 0.003190890
## KMB 0.001331056 0.001560401 0.0009694362 0.001256500 0.0008297174 0.001077654
## MEL 0.002718425 0.003186817 0.0019798858 0.002566158 0.0016945373 0.002200899
## NYT 0.001865711 0.002187179 0.0013588366 0.001761207 0.0011629960 0.001510523
## PG 0.001134954 0.001330510 0.0008266108 0.001071382 0.0007074766 0.000918885
## TRB 0.001737961 0.002037416 0.0012657930 0.001640612 0.0010833622 0.001407093
## TXN 0.004349041 0.005098393 0.0031674972 0.004105438 0.0027109857 0.003521083
## HPQ KMB MEL NYT PG
## AA 0.003941205 0.0013310564 0.0027184251 0.0018657114 0.0011349541
## AGE 0.004620285 0.0015604012 0.0031868174 0.0021871787 0.0013305099
## CAT 0.002870462 0.0009694362 0.0019798858 0.0013588366 0.0008266108
## F 0.003720446 0.0012565001 0.0025661582 0.0017612075 0.0010713820
## FDX 0.002456760 0.0008297174 0.0016945373 0.0011629960 0.0007074766
## GM 0.003190890 0.0010776539 0.0022008995 0.0015105229 0.0009188850
## HPQ 0.013934297 0.0016776942 0.0034263656 0.0023515856 0.0014305223
## KMB 0.001677694 0.0042512149 0.0011571807 0.0007941971 0.0004831279
## MEL 0.003426366 0.0011571807 0.0061088004 0.0016219938 0.0009866952
## NYT 0.002351586 0.0007941971 0.0016219938 0.0054564979 0.0006771894
## PG 0.001430522 0.0004831279 0.0009866952 0.0006771894 0.0045836602
## TRB 0.002190566 0.0007398161 0.0015109311 0.0010369833 0.0006308202
## TXN 0.005481631 0.0018513021 0.0037809262 0.0025949280 0.0015785529
## TRB TXN
## AA 0.0017379606 0.004349041
## AGE 0.0020374161 0.005098393
## CAT 0.0012657930 0.003167497
## F 0.0016406124 0.004105438
## FDX 0.0010833622 0.002710986
## GM 0.0014070929 0.003521083
## HPQ 0.0021905656 0.005481631
## KMB 0.0007398161 0.001851302
## MEL 0.0015109311 0.003780926
## NYT 0.0010369833 0.002594928
## PG 0.0006308202 0.001578553
## TRB 0.0061718134 0.002417246
## TXN 0.0024172455 0.019214110
# Method 2: Use formula "inv(X'X)*X'Y" ----
ones = rep(1, TT)
X = as.matrix(cbind(ones, mktret))
X
## ones
## [1,] 1 -0.0752
## [2,] 1 0.0021
## [3,] 1 0.0177
## [4,] 1 -0.0334
## [5,] 1 0.0855
## [6,] 1 -0.0153
## [7,] 1 -0.0116
## [8,] 1 -0.1005
## [9,] 1 -0.0573
## [10,] 1 -0.0127
## [11,] 1 0.0540
## [12,] 1 0.0192
## [13,] 1 0.0363
## [14,] 1 0.0623
## [15,] 1 0.0173
## [16,] 1 -0.0044
## [17,] 1 0.0340
## [18,] 1 -0.0525
## [19,] 1 0.0402
## [20,] 1 0.0152
## [21,] 1 -0.0235
## [22,] 1 0.0077
## [23,] 1 -0.0477
## [24,] 1 0.1082
## [25,] 1 -0.0231
## [26,] 1 0.0064
## [27,] 1 -0.0252
## [28,] 1 0.0248
## [29,] 1 -0.0021
## [30,] 1 -0.0204
## [31,] 1 0.0367
## [32,] 1 -0.0266
## [33,] 1 0.0067
## [34,] 1 -0.0003
## [35,] 1 0.0277
## [36,] 1 0.0074
## [37,] 1 0.0046
## [38,] 1 0.0080
## [39,] 1 0.0162
## [40,] 1 -0.0278
## [41,] 1 0.0203
## [42,] 1 -0.0018
## [43,] 1 -0.0079
## [44,] 1 0.0319
## [45,] 1 -0.0124
## [46,] 1 0.0169
## [47,] 1 -0.0155
## [48,] 1 0.0075
## [49,] 1 0.0300
## [50,] 1 -0.0328
## [51,] 1 -0.0487
## [52,] 1 0.0085
## [53,] 1 0.0090
## [54,] 1 -0.0303
## [55,] 1 0.0279
## [56,] 1 0.0339
## [57,] 1 -0.0308
## [58,] 1 0.0167
## [59,] 1 -0.0439
## [60,] 1 0.0076
## [61,] 1 0.0195
## [62,] 1 0.0313
## [63,] 1 0.0226
## [64,] 1 0.0233
## [65,] 1 0.0316
## [66,] 1 0.0167
## [67,] 1 0.0273
## [68,] 1 -0.0048
## [69,] 1 0.0357
## [70,] 1 -0.0094
## [71,] 1 0.0366
## [72,] 1 0.0132
## [73,] 1 0.0285
## [74,] 1 0.0029
## [75,] 1 0.0038
## [76,] 1 0.0093
## [77,] 1 0.0187
## [78,] 1 -0.0020
## [79,] 1 -0.0500
## [80,] 1 0.0146
## [81,] 1 0.0499
## [82,] 1 0.0220
## [83,] 1 0.0692
## [84,] 1 -0.0256
## [85,] 1 0.0571
## [86,] 1 0.0018
## [87,] 1 -0.0469
## [88,] 1 0.0541
## [89,] 1 0.0544
## [90,] 1 0.0393
## [91,] 1 0.0739
## [92,] 1 -0.0617
## [93,] 1 0.0490
## [94,] 1 -0.0386
## [95,] 1 0.0403
## [96,] 1 0.0114
## [97,] 1 0.0060
## [98,] 1 0.0662
## [99,] 1 0.0458
## [100,] 1 0.0050
## [101,] 1 -0.0230
## [102,] 1 0.0353
## [103,] 1 -0.0158
## [104,] 1 -0.1499
## [105,] 1 0.0586
## [106,] 1 0.0770
## [107,] 1 0.0555
## [108,] 1 0.0527
## [109,] 1 0.0374
## [110,] 1 -0.0360
## [111,] 1 0.0351
## [112,] 1 0.0344
## [113,] 1 -0.0287
## [114,] 1 0.0506
## [115,] 1 -0.0358
## [116,] 1 -0.0102
## [117,] 1 -0.0324
## [118,] 1 0.0585
## [119,] 1 0.0148
## [120,] 1 0.0535
## [121,] 1 -0.0553
## [122,] 1 -0.0247
## [123,] 1 0.0920
## [124,] 1 -0.0355
## [125,] 1 -0.0267
## [126,] 1 0.0192
## [127,] 1 -0.0213
## [128,] 1 0.0556
## [129,] 1 -0.0585
## [130,] 1 -0.0100
## [131,] 1 -0.0852
## [132,] 1 -0.0008
## [133,] 1 0.0303
## [134,] 1 -0.0964
## [135,] 1 -0.0679
## [136,] 1 0.0736
## [137,] 1 0.0021
## [138,] 1 -0.0279
## [139,] 1 -0.0137
## [140,] 1 -0.0669
## [141,] 1 -0.0839
## [142,] 1 0.0163
## [143,] 1 0.0736
## [144,] 1 0.0062
## [145,] 1 -0.0169
## [146,] 1 -0.0222
## [147,] 1 0.0352
## [148,] 1 -0.0629
## [149,] 1 -0.0105
## [150,] 1 -0.0739
## [151,] 1 -0.0804
## [152,] 1 0.0035
## [153,] 1 -0.1114
## [154,] 1 0.0851
## [155,] 1 0.0560
## [156,] 1 -0.0613
## [157,] 1 -0.0284
## [158,] 1 -0.0180
## [159,] 1 0.0074
## [160,] 1 0.0801
## [161,] 1 0.0500
## [162,] 1 0.0106
## [163,] 1 0.0155
## [164,] 1 0.0171
## [165,] 1 -0.0127
## [166,] 1 0.0542
## [167,] 1 0.0064
## [168,] 1 0.0500
Y = stockret
Y
## AA AGE CAT F FDX GM HPQ KMB MEL
## [1,] -0.1640 -0.1217 -0.0444 -0.0006 -0.0228 -0.0212 -0.0619 -0.1101 -0.1077
## [2,] 0.0404 0.0495 0.0884 0.0602 0.1047 0.0897 -0.0401 -0.0520 0.0034
## [3,] 0.0012 0.1308 0.0017 0.0206 0.1084 0.0157 0.0567 0.0321 -0.0017
## [4,] -0.0428 -0.1106 0.0025 -0.0567 -0.0244 -0.0419 -0.0529 -0.0065 -0.0220
## [5,] 0.0581 0.1970 0.0852 0.0389 -0.1617 0.1094 0.0881 0.0883 0.1185
## [6,] -0.0405 -0.0144 -0.2210 -0.0579 -0.0281 -0.0270 -0.0147 0.0155 -0.0776
## [7,] 0.0909 -0.0652 -0.0719 -0.0406 -0.0865 -0.0273 -0.0937 0.0669 -0.0552
## [8,] -0.0799 -0.0877 -0.1264 -0.1658 -0.0633 -0.1376 -0.1975 -0.0348 -0.1950
## [9,] -0.0333 -0.2747 -0.0236 -0.1208 -0.0826 -0.0942 -0.0426 -0.0838 0.0002
## [10,] -0.1513 0.0409 -0.0344 -0.0829 -0.0956 0.0078 -0.2299 0.0966 -0.0510
## [11,] 0.0271 0.1135 0.0033 -0.0194 -0.1006 0.0077 0.1480 0.0473 0.2608
## [12,] 0.0445 0.0901 0.1372 -0.0330 0.1283 -0.0638 0.0604 0.0629 -0.0056
## [13,] 0.1220 0.1973 0.0597 0.0746 0.2568 0.0494 0.2144 -0.0037 -0.0273
## [14,] -0.0088 0.1634 0.0930 0.1602 -0.0400 0.0957 0.1944 0.0173 0.1317
## [15,] 0.0165 0.1320 -0.1285 -0.0126 -0.1261 -0.0492 0.0701 0.0240 0.0047
## [16,] 0.0319 0.0146 -0.0037 0.0115 -0.0323 -0.0577 0.0178 0.0323 0.0372
## [17,] 0.0491 0.0712 0.0821 0.1301 0.1338 0.2129 0.0566 0.0600 0.1066
## [18,] -0.0556 -0.1044 -0.0505 -0.0284 -0.0451 -0.0597 -0.0669 -0.0112 -0.0088
## [19,] 0.0476 0.1942 -0.0036 -0.0630 0.0798 -0.0292 0.0545 0.0032 0.1033
## [20,] -0.0239 0.0208 -0.0375 -0.0753 -0.0553 -0.0384 -0.0207 0.0032 0.0070
## [21,] -0.0820 0.1986 -0.0649 -0.0405 -0.1211 -0.0208 -0.0658 -0.0745 -0.0006
## [22,] -0.0057 0.0722 0.0782 -0.0867 0.0958 -0.0644 0.0135 0.0699 0.0477
## [23,] -0.0807 -0.1307 -0.1444 -0.1190 -0.0980 -0.1170 -0.0485 -0.0415 -0.0688
## [24,] 0.0970 0.2963 0.0602 0.1685 0.1077 -0.0644 0.1836 0.1014 0.0738
## [25,] -0.0012 -0.0593 0.0658 0.0955 0.1259 0.1180 0.0363 -0.0636 0.1108
## [26,] 0.0786 -0.0696 0.0422 0.2017 0.1682 0.1675 0.2289 0.0887 0.0195
## [27,] 0.0129 -0.0921 0.0197 0.0409 -0.0887 -0.0267 0.1021 0.0262 -0.0129
## [28,] 0.1001 -0.1663 0.1224 0.1897 -0.0751 0.1300 -0.0093 0.0416 0.0283
## [29,] 0.0002 0.0957 0.0727 -0.0251 -0.0662 -0.0422 -0.0530 0.0330 0.0126
## [30,] -0.0256 -0.0815 -0.1128 0.0307 0.1043 0.1104 -0.0942 0.0215 0.0124
## [31,] -0.0307 -0.0088 0.0280 0.0033 -0.0553 -0.0567 0.0645 -0.0305 0.0393
## [32,] -0.1209 0.0409 -0.1293 -0.1119 -0.1049 -0.1612 -0.2237 -0.0350 -0.0408
## [33,] 0.0227 -0.0739 0.0779 -0.0331 -0.0611 -0.0746 -0.0251 -0.0162 0.0618
## [34,] 0.0504 0.1130 0.0029 -0.0682 0.2467 -0.0452 0.0178 0.0556 0.0689
## [35,] 0.0085 0.1641 0.0835 0.1481 0.0805 0.0527 0.1666 0.0660 0.0542
## [36,] 0.0187 -0.0665 -0.0578 0.0181 0.1124 -0.0027 0.0511 -0.0275 0.0817
## [37,] 0.0359 0.0874 0.0469 0.0826 0.0365 0.1680 0.0279 -0.0258 0.0589
## [38,] -0.0542 -0.0219 0.0310 -0.0079 -0.0069 -0.0104 0.0219 -0.0306 0.0803
## [39,] -0.0827 0.0777 0.0169 0.1311 -0.0025 0.0076 0.0325 -0.0171 0.0017
## [40,] 0.0228 -0.0531 0.1714 0.0582 -0.1443 0.0840 -0.0188 -0.1280 -0.0908
## [41,] 0.0244 -0.0549 0.0318 -0.0527 0.0105 -0.0159 0.1111 -0.0170 -0.0070
## [42,] 0.0345 0.0490 0.0428 0.0023 -0.0510 0.1065 -0.0280 0.0563 0.0271
## [43,] 0.0153 0.0612 0.0262 0.0147 0.1288 0.0874 -0.1136 -0.0556 -0.0047
## [44,] 0.0575 0.0076 0.0674 -0.0357 0.1302 -0.0319 0.0270 0.0428 0.0378
## [45,] -0.1089 0.0801 -0.0420 0.0809 0.0331 -0.1118 -0.0767 0.0063 -0.0562
## [46,] 0.0105 0.0441 0.1576 0.1246 0.0884 0.1382 0.0743 0.0511 -0.0161
## [47,] 0.0217 -0.0350 -0.0709 -0.0208 0.0567 0.1092 -0.0009 0.0216 0.0276
## [48,] -0.0007 -0.0344 0.0414 0.0592 -0.0113 0.0377 0.0720 -0.0133 -0.0476
## [49,] 0.1438 0.0138 0.1691 0.0425 0.0698 0.1137 0.0766 0.0939 0.0623
## [50,] -0.0517 -0.0508 0.0381 -0.0755 -0.0175 -0.0484 0.0603 -0.0235 -0.0094
## [51,] -0.0511 -0.1917 0.0340 -0.0572 -0.1098 -0.0780 -0.0939 -0.0459 0.0083
## [52,] -0.0537 -0.0171 -0.0240 -0.0018 0.1371 0.0503 -0.0259 0.0348 0.0025
## [53,] 0.0410 0.0683 -0.0308 -0.0142 -0.0002 -0.0528 -0.0253 0.0262 0.0435
## [54,] 0.0319 -0.0835 -0.0678 0.0182 -0.0263 -0.0686 -0.0410 -0.0598 -0.0419
## [55,] 0.0665 0.0109 0.0831 0.0845 -0.1140 0.0188 0.0280 0.0697 0.0241
## [56,] 0.0749 0.1463 0.0609 -0.0861 0.0621 -0.0217 0.1541 0.0425 0.0312
## [57,] 0.0051 -0.0901 -0.0656 -0.0551 -0.1308 -0.0710 -0.0283 -0.0070 -0.0545
## [58,] 0.0065 0.0096 0.1026 0.0683 -0.0223 -0.1615 0.1160 -0.1275 -0.0032
## [59,] -0.0469 -0.0644 -0.0985 -0.0849 -0.0682 -0.0342 -0.0057 -0.0311 -0.1111
## [60,] 0.0566 0.0388 0.0138 0.0230 0.0547 0.1003 0.0201 0.0091 -0.0801
## [61,] -0.0919 0.0161 -0.0682 -0.0896 0.0035 -0.0819 0.0015 -0.0494 0.1528
## [62,] -0.0128 0.2197 0.0001 0.0298 0.0672 0.0968 0.1395 0.0757 0.0845
## [63,] 0.0593 -0.0208 0.0703 0.0239 0.0336 0.0275 0.0446 0.0039 0.0641
## [64,] 0.0766 0.0351 0.0539 0.0161 0.0008 0.0209 0.0939 0.0842 -0.0292
## [65,] 0.0365 -0.0157 0.0252 0.0736 -0.1242 0.0656 -0.0066 0.0549 0.0844
## [66,] 0.0734 -0.0039 0.0618 0.0125 0.0101 -0.0280 0.1273 0.0009 -0.0309
## [67,] 0.1326 0.0844 0.0963 -0.0193 0.1066 0.0355 0.0408 0.0539 -0.0285
## [68,] 0.0016 -0.0096 -0.0507 0.0558 0.0585 -0.0317 0.0228 0.0034 0.1762
## [69,] -0.0788 0.0937 -0.1571 0.0078 0.1524 -0.0097 0.0403 0.0535 -0.0598
## [70,] -0.0399 -0.0466 -0.0004 -0.0695 -0.0149 -0.0711 0.1065 0.0775 0.1252
## [71,] 0.1470 0.0606 0.0770 -0.0219 -0.0973 0.1110 -0.1084 0.0523 0.0730
## [72,] -0.1004 -0.1200 -0.0471 0.0178 -0.0127 0.0859 0.0072 0.1112 -0.0066
## [73,] 0.0518 0.0482 0.0975 0.0296 0.0263 -0.0089 0.0078 -0.0298 -0.0125
## [74,] 0.0207 -0.0389 0.0329 0.0553 -0.0319 -0.0226 0.1848 -0.0567 0.0552
## [75,] 0.0970 0.0282 0.0146 0.0959 -0.0599 0.0349 -0.0679 -0.0243 -0.0153
## [76,] -0.0081 -0.0594 -0.0560 0.0497 0.1515 0.0147 0.1207 -0.0277 -0.0204
## [77,] -0.0109 0.0862 0.0192 0.0132 -0.0553 0.0193 0.0017 -0.0007 0.0586
## [78,] -0.0732 0.0605 0.0281 -0.1173 0.0659 -0.0541 -0.0665 0.0621 -0.0064
## [79,] 0.0124 0.0049 -0.0261 0.0076 -0.0561 -0.0735 -0.1210 -0.0205 -0.0683
## [80,] 0.0669 0.0186 0.0413 0.0305 -0.0412 0.0219 -0.0099 0.0254 0.0456
## [81,] -0.0545 0.0416 0.0901 -0.0714 0.0542 -0.0370 0.1128 0.1278 0.0657
## [82,] -0.0049 0.0216 -0.0884 0.0082 0.0116 0.1130 -0.0990 0.0540 0.1030
## [83,] 0.0811 0.0418 0.1488 0.0438 0.0952 0.0779 0.2168 0.0454 0.1073
## [84,] -0.0021 0.0770 -0.0531 -0.0194 0.0016 -0.0366 -0.0692 -0.0262 -0.0214
## [85,] 0.0782 0.0070 0.0327 0.0039 0.1475 0.0541 0.0431 0.0194 0.0553
## [86,] 0.0317 0.0399 0.0039 0.0192 0.0007 -0.0148 0.0623 0.0830 0.0729
## [87,] -0.0499 -0.1330 0.0213 -0.0499 0.0079 -0.0475 -0.0511 -0.0611 -0.0992
## [88,] 0.0269 0.1339 0.1097 0.1167 0.0317 0.0409 -0.0207 0.0259 0.1474
## [89,] 0.0495 0.0565 0.0927 0.0749 -0.0343 -0.0042 -0.0233 -0.0237 0.0484
## [90,] 0.0197 0.1523 0.0958 0.0092 0.1009 -0.0324 0.0860 -0.0093 0.0273
## [91,] 0.1699 -0.0159 0.0435 0.0825 0.1113 0.1057 0.2458 0.0146 0.1208
## [92,] -0.0721 -0.0635 0.0325 0.0477 0.0248 0.0179 -0.1257 -0.0684 -0.0501
## [93,] -0.0072 0.2932 -0.0752 0.0453 0.2000 0.0626 0.1292 0.0326 0.1335
## [94,] -0.1139 -0.0333 -0.0493 -0.0267 -0.1698 -0.0452 -0.1183 0.0572 -0.0483
## [95,] -0.0796 0.0220 -0.0689 -0.0200 0.0004 -0.0471 -0.0124 -0.0019 0.0859
## [96,] 0.0422 0.1643 0.0074 0.1251 -0.0938 0.0537 0.0184 -0.0525 0.0652
## [97,] 0.0811 -0.0514 -0.0093 0.0546 0.0613 -0.0505 -0.0403 0.0541 -0.0029
## [98,] -0.0403 0.1113 0.1325 0.1048 -0.0254 0.1942 0.1101 0.0628 0.0278
## [99,] -0.0664 0.0403 0.0050 0.1417 0.1126 -0.0214 -0.0562 -0.0996 0.0149
## [100,] 0.1221 0.0243 0.0345 0.0821 -0.0481 -0.0097 0.1852 0.0083 0.1354
## [101,] -0.1058 -0.1064 -0.0393 0.1282 -0.0612 0.0700 -0.1775 -0.0276 -0.0675
## [102,] -0.0537 0.0501 -0.0411 0.1332 -0.0256 -0.0746 -0.0407 -0.0735 0.0292
## [103,] 0.0470 -0.0891 -0.0817 -0.0309 -0.0370 0.0782 -0.0772 -0.0246 -0.0322
## [104,] -0.1348 -0.3097 -0.1381 -0.2212 -0.1792 -0.1934 -0.1291 -0.1571 -0.2323
## [105,] 0.1820 0.1188 0.0557 0.0494 -0.1087 -0.0598 0.0895 0.0668 0.0538
## [106,] 0.1129 0.1369 0.0133 0.1607 0.1696 0.1482 0.1348 0.1881 0.0964
## [107,] -0.0620 0.0723 0.0965 0.0113 0.2306 0.1101 0.0347 0.0870 0.0473
## [108,] 0.0006 0.0018 -0.0732 0.0622 0.3711 0.0205 0.0908 0.0367 0.0844
## [109,] 0.1171 -0.0942 -0.0555 0.0511 -0.0905 0.2505 0.1437 -0.0896 -0.0238
## [110,] -0.0295 -0.0424 0.0483 -0.0383 0.1659 -0.0782 -0.1560 -0.0551 0.0056
## [111,] 0.0133 0.0047 0.0045 -0.0480 -0.0273 0.0507 0.0194 0.0164 0.0370
## [112,] 0.5078 0.0672 0.4043 0.1324 0.2088 0.0201 0.1596 0.2754 0.0581
## [113,] -0.1170 -0.0430 -0.1513 -0.1103 -0.0315 -0.0750 0.1920 -0.0486 -0.0433
## [114,] 0.1212 -0.0402 0.0896 -0.0158 -0.0141 -0.0473 0.0635 -0.0260 0.0155
## [115,] -0.0361 -0.1453 -0.0213 -0.1363 -0.1789 -0.0777 0.0379 0.0664 -0.0705
## [116,] 0.0777 -0.0965 -0.0381 0.0708 -0.0556 0.0881 0.0026 -0.0705 -0.0150
## [117,] -0.0426 0.0518 -0.0359 -0.0399 -0.0878 -0.0539 -0.1412 -0.0729 0.0036
## [118,] -0.0252 0.1429 0.0110 0.0979 0.1037 0.1151 -0.1866 0.1903 0.1004
## [119,] 0.0773 -0.0208 -0.1658 -0.0840 -0.0274 0.0251 0.2746 0.0107 -0.0178
## [120,] 0.2628 0.0784 0.0105 0.0514 -0.0311 0.0052 0.1963 0.0232 -0.0695
## [121,] -0.1648 0.0287 -0.0958 -0.0619 -0.0380 0.1039 -0.0528 -0.0551 0.0088
## [122,] -0.0181 -0.0480 -0.1784 -0.1679 -0.1215 -0.0543 0.2379 -0.1757 -0.1267
## [123,] 0.0208 0.2626 0.1200 0.0989 0.1062 0.0840 -0.0156 0.0891 -0.0172
## [124,] -0.0812 -0.0641 0.0035 0.1977 -0.0337 0.1259 0.0113 0.0287 0.0825
## [125,] -0.1002 -0.0720 -0.0349 -0.1178 -0.0629 -0.2451 -0.1145 0.0394 0.1975
## [126,] -0.0122 0.1115 -0.1191 -0.0824 0.0657 -0.1826 0.2897 -0.0519 -0.0614
## [127,] 0.0381 0.3508 0.0106 0.0895 0.0378 -0.0243 -0.1306 -0.0039 0.0354
## [128,] 0.0982 -0.0186 0.0738 0.0339 0.0132 0.2715 0.1008 0.0134 0.1956
## [129,] -0.2437 0.0010 -0.0866 0.0415 0.0939 -0.1046 -0.2004 -0.0463 0.0199
## [130,] 0.1282 -0.0350 0.0439 0.0389 0.0517 -0.0493 -0.0463 0.1774 0.0401
## [131,] -0.0182 -0.1221 0.1161 -0.1343 0.0175 -0.2003 -0.3250 0.0545 -0.0336
## [132,] 0.1837 0.0573 0.1987 0.0254 -0.1709 0.0242 -0.0043 0.0098 0.0445
## [133,] 0.0969 -0.0123 -0.0625 0.2113 0.1313 0.0499 0.1632 -0.0883 -0.0524
## [134,] -0.0307 -0.1781 -0.0633 -0.0175 -0.1021 -0.0018 -0.2212 0.1002 -0.0103
## [135,] 0.0016 -0.0477 0.0631 0.0075 0.0146 -0.0313 0.0830 -0.0511 -0.1287
## [136,] 0.1484 0.0960 0.1356 0.0558 0.0061 0.0539 -0.0940 -0.1275 0.0128
## [137,] 0.0429 0.0425 0.0759 -0.1770 -0.0522 0.0442 0.0283 0.0147 0.1165
## [138,] -0.0898 0.0592 -0.0788 0.0053 0.0021 0.1280 -0.0247 -0.0735 -0.0249
## [139,] -0.0072 -0.0307 0.1050 0.0345 0.0262 -0.0146 -0.1407 0.0849 -0.1491
## [140,] -0.0273 -0.0702 -0.0954 -0.2109 0.0149 -0.1341 -0.0616 0.0176 -0.0757
## [141,] -0.1887 -0.1377 -0.1062 -0.1290 -0.1293 -0.2186 -0.3072 0.0015 -0.0850
## [142,] 0.0437 0.1244 0.0042 -0.0681 0.1160 -0.0386 0.0468 -0.1065 0.0412
## [143,] 0.1946 0.0758 0.0588 0.1785 0.1148 0.2134 0.3050 0.0464 0.1112
## [144,] -0.0804 0.0392 0.1005 -0.1714 0.1299 -0.0235 -0.0637 0.0314 0.0047
## [145,] 0.0071 -0.0390 -0.0324 -0.0217 0.0308 0.0509 0.0751 0.0070 0.0225
## [146,] 0.0507 -0.0405 0.1026 -0.0289 0.0790 0.0443 -0.0914 0.0367 -0.0639
## [147,] 0.0030 0.0790 0.0226 0.1067 0.0027 0.1395 -0.1059 0.0360 0.0704
## [148,] -0.0997 -0.0710 -0.0345 -0.0311 -0.1121 0.0598 -0.0483 0.0058 -0.0198
## [149,] 0.0309 -0.0315 -0.0445 0.1079 0.0427 -0.0248 0.1149 -0.0045 -0.0189
## [150,] -0.0537 -0.0180 -0.0649 -0.0949 -0.0107 -0.1414 -0.1968 -0.0418 -0.1542
## [151,] -0.1809 -0.1164 -0.0811 -0.1533 -0.0473 -0.1305 -0.0753 -0.0167 -0.1519
## [152,] -0.0738 0.0928 -0.0251 -0.1276 -0.0720 0.0375 -0.0522 -0.0212 0.0389
## [153,] -0.2321 -0.1475 -0.1485 -0.1687 0.0571 -0.1886 -0.1264 -0.0498 -0.0636
## [154,] 0.1417 0.0275 0.1056 -0.1278 0.0610 -0.1466 0.3526 -0.0921 0.0947
## [155,] 0.1640 0.0968 0.2205 0.3441 -0.0127 0.2080 0.2319 -0.0239 0.0612
## [156,] -0.1094 -0.0841 -0.0848 -0.1838 0.0313 -0.0725 -0.1057 -0.0517 -0.1321
## [157,] -0.1331 -0.1342 -0.0314 -0.0107 -0.0309 -0.0154 0.0019 -0.0252 -0.1201
## [158,] 0.0435 -0.0675 0.0677 -0.0877 -0.0238 -0.0577 -0.0906 -0.0116 -0.0167
## [159,] -0.0556 -0.0238 0.0459 -0.0971 0.0714 -0.0054 -0.0148 -0.0016 -0.0565
## [160,] 0.1900 0.1508 0.0753 0.3820 0.0864 0.0713 0.0473 0.0939 0.2498
## [161,] 0.0724 0.1020 -0.0095 0.0185 0.0676 -0.0070 0.1954 0.0425 0.0263
## [162,] 0.0354 0.0436 0.0665 0.0459 -0.0305 0.0182 0.0956 0.0098 0.0206
## [163,] 0.0883 0.0808 0.2177 0.0147 0.0373 0.0390 -0.0069 -0.0725 0.0944
## [164,] 0.0331 -0.0276 0.0638 0.0444 0.0413 0.1106 -0.0594 0.0552 0.0356
## [165,] -0.0848 0.0706 -0.0424 -0.0691 -0.0398 -0.0049 -0.0254 0.0100 -0.0394
## [166,] 0.2060 0.0536 0.0691 0.1348 0.1751 0.0417 0.1516 0.0283 -0.0044
## [167,] 0.0433 -0.0936 0.0370 0.0874 -0.0412 0.0135 -0.0263 0.0259 -0.0366
## [168,] 0.1574 -0.0103 0.0909 0.2114 -0.0714 0.2475 0.0595 0.0953 0.1142
## NYT PG TRB TXN
## [1,] -0.0630 -0.0889 -0.1304 -0.0761
## [2,] -0.0462 -0.0084 -0.0037 0.0497
## [3,] -0.0066 0.0541 0.0236 0.0269
## [4,] -0.1060 0.0426 -0.0798 -0.0685
## [5,] 0.1159 0.1635 0.0882 0.2288
## [6,] -0.0012 0.0480 -0.0064 -0.0587
## [7,] -0.1152 -0.0055 -0.0529 -0.1988
## [8,] -0.1160 -0.1186 -0.0735 -0.1390
## [9,] -0.0719 -0.0597 -0.0390 0.0139
## [10,] -0.0341 0.0798 -0.0910 -0.1526
## [11,] 0.0602 0.0482 0.1053 0.3118
## [12,] 0.1245 0.0396 -0.0561 0.2017
## [13,] 0.0918 -0.0846 0.2218 -0.0216
## [14,] -0.0264 0.0203 -0.0514 0.1054
## [15,] 0.0178 0.0428 0.0164 -0.0397
## [16,] -0.0158 -0.0135 0.0401 0.0047
## [17,] 0.0411 0.0103 0.0838 -0.0325
## [18,] 0.0386 -0.0957 -0.0838 -0.1502
## [19,] -0.0824 0.0454 0.0240 -0.0272
## [20,] 0.0018 0.0296 0.0232 -0.0314
## [21,] 0.0013 0.0121 -0.1161 -0.1054
## [22,] -0.1382 -0.0130 -0.0839 0.1153
## [23,] -0.0103 -0.0352 -0.0107 -0.1224
## [24,] 0.2312 0.1556 0.1047 0.1062
## [25,] 0.1556 0.1074 0.0334 0.1594
## [26,] 0.0293 -0.0237 0.0436 0.0457
## [27,] 0.0766 0.0028 -0.0090 -0.1286
## [28,] 0.0339 0.0120 0.0679 0.0582
## [29,] -0.0383 -0.0079 -0.0696 0.0836
## [30,] -0.0774 -0.1077 -0.0659 -0.0647
## [31,] -0.0116 0.1038 0.0156 0.1895
## [32,] -0.0561 -0.0767 0.0031 -0.0802
## [33,] 0.0550 0.0509 0.1054 0.1252
## [34,] -0.0567 0.0741 -0.0078 0.1302
## [35,] 0.0745 0.0234 0.0950 -0.0026
## [36,] -0.0607 -0.0142 -0.0475 -0.0499
## [37,] 0.1018 -0.0696 0.0912 0.1557
## [38,] -0.0148 0.0428 0.0045 0.0439
## [39,] 0.0761 -0.0433 0.0213 0.0317
## [40,] -0.0712 -0.0119 0.0138 -0.0239
## [41,] 0.0068 -0.0025 -0.0369 0.1335
## [42,] -0.1584 0.0560 0.0188 0.0794
## [43,] 0.0385 -0.0591 -0.0583 0.0100
## [44,] -0.0512 -0.0102 0.0121 0.1371
## [45,] 0.0340 -0.0205 0.0414 -0.0638
## [46,] -0.0528 0.1461 0.0349 -0.1333
## [47,] 0.0563 0.0435 0.0062 -0.0235
## [48,] 0.0527 0.0019 0.0759 -0.0114
## [49,] 0.0832 0.0468 -0.0025 0.0999
## [50,] -0.0153 -0.0363 -0.0296 0.1544
## [51,] -0.0252 -0.0725 0.0185 -0.0470
## [52,] -0.0761 0.0658 0.0642 -0.0160
## [53,] 0.0070 -0.0122 -0.0742 0.0490
## [54,] -0.0672 -0.0567 -0.0971 -0.0097
## [55,] -0.0141 0.0474 -0.0224 -0.0146
## [56,] 0.0392 0.0882 0.0252 -0.0133
## [57,] -0.1110 -0.0244 0.0055 -0.1274
## [58,] 0.0302 0.0563 -0.0296 0.0970
## [59,] 0.0515 -0.0104 -0.0470 0.0039
## [60,] -0.0731 -0.0127 0.0876 -0.0096
## [61,] -0.0161 0.0513 -0.0481 -0.0832
## [62,] -0.0219 0.0163 0.0674 0.1365
## [63,] 0.0773 -0.0085 -0.0160 0.1222
## [64,] -0.0263 0.0553 0.0654 0.1930
## [65,] 0.0015 0.0239 0.0085 0.0861
## [66,] 0.0341 -0.0046 0.0248 0.1562
## [67,] 0.0806 -0.0407 0.0362 0.1626
## [68,] -0.0186 0.0028 0.0488 -0.0493
## [69,] 0.0906 0.1055 -0.0137 0.0659
## [70,] 0.0093 0.0527 -0.0534 -0.1447
## [71,] 0.0636 0.0634 0.0237 -0.1596
## [72,] 0.0000 -0.0447 -0.0584 -0.1115
## [73,] -0.0253 0.0127 0.0204 -0.1037
## [74,] -0.0644 -0.0278 0.0666 0.0714
## [75,] 0.0652 0.0294 -0.0172 0.0159
## [76,] 0.1166 -0.0024 0.0547 0.1098
## [77,] 0.0117 0.0358 0.0628 -0.0086
## [78,] -0.0118 0.0270 -0.0245 -0.1176
## [79,] -0.1116 -0.0145 -0.0404 -0.1337
## [80,] 0.0736 -0.0084 0.0269 0.0767
## [81,] 0.0758 0.0928 0.0810 0.1785
## [82,] 0.0662 0.0158 0.0439 -0.1311
## [83,] 0.0346 0.0943 0.0576 0.3205
## [84,] 0.0126 -0.0144 -0.0922 -0.0014
## [85,] 0.0057 0.0708 -0.0343 0.2252
## [86,] 0.1593 0.0347 0.0262 -0.0201
## [87,] -0.0127 -0.0490 0.0276 -0.0313
## [88,] -0.0241 0.0955 0.0790 0.1877
## [89,] 0.0645 0.0922 -0.0148 0.0014
## [90,] 0.0705 0.0204 0.1072 -0.0656
## [91,] 0.0122 0.0764 0.0972 0.3638
## [92,] -0.0620 -0.1292 -0.0674 -0.0162
## [93,] 0.1070 0.0334 0.0743 0.1767
## [94,] 0.0387 -0.0159 0.0299 -0.2080
## [95,] 0.0833 0.1161 0.0213 -0.0740
## [96,] 0.1094 0.0433 0.0999 -0.0958
## [97,] -0.0203 -0.0190 -0.0283 0.2097
## [98,] 0.0041 0.0787 0.0613 0.0575
## [99,] 0.0655 -0.0101 0.0878 -0.0710
## [100,] 0.0093 -0.0271 -0.0680 0.1822
## [101,] -0.0103 0.0164 0.0117 -0.2020
## [102,] 0.1227 0.0815 0.0248 0.1295
## [103,] -0.2281 -0.1294 -0.0268 0.0155
## [104,] -0.0579 -0.0403 -0.0434 -0.2062
## [105,] -0.0556 -0.0741 -0.2230 0.1149
## [106,] 0.0240 0.2476 0.1420 0.2047
## [107,] 0.0992 -0.0157 0.1121 0.1909
## [108,] 0.1130 0.0384 0.0256 0.1175
## [109,] -0.0144 -0.0053 -0.0349 0.1521
## [110,] -0.0975 -0.0188 0.0363 -0.1017
## [111,] -0.0844 0.0906 -0.0169 0.1091
## [112,] 0.2070 -0.0428 0.2715 0.0262
## [113,] -0.0116 -0.0084 -0.0555 0.0672
## [114,] 0.0749 -0.0480 0.0999 0.3128
## [115,] 0.0641 0.0145 0.0070 -0.0032
## [116,] -0.0076 0.0920 0.0577 0.1358
## [117,] -0.0439 -0.0593 0.0624 -0.0016
## [118,] 0.0693 0.1180 0.2020 0.0877
## [119,] -0.0466 0.0303 -0.2017 0.0661
## [120,] 0.2737 0.0055 0.1413 0.0015
## [121,] -0.0744 -0.0791 -0.2383 0.1111
## [122,] -0.0776 -0.1351 -0.0793 0.5371
## [123,] 0.0115 -0.3618 -0.0657 -0.0416
## [124,] -0.0455 0.0585 0.0483 0.0135
## [125,] -0.0658 0.1081 -0.0022 -0.1176
## [126,] 0.0196 -0.1438 -0.0957 -0.0541
## [127,] 0.0378 -0.0054 -0.0764 -0.1502
## [128,] -0.0508 0.0817 0.0961 0.1355
## [129,] -0.0018 0.0789 0.2174 -0.3000
## [130,] -0.0703 0.0664 -0.1555 0.0351
## [131,] -0.0411 0.0430 -0.0041 -0.2446
## [132,] 0.1297 0.0428 0.1371 0.2649
## [133,] 0.0838 -0.0839 -0.0502 -0.0793
## [134,] 0.0126 -0.0227 0.0059 -0.3294
## [135,] -0.0768 -0.1157 -0.0002 0.0447
## [136,] -0.0018 -0.0384 0.0311 0.2467
## [137,] 0.0259 0.0668 0.0183 -0.1214
## [138,] -0.0050 -0.0098 -0.0709 -0.0680
## [139,] 0.0995 0.1162 0.0283 0.0792
## [140,] -0.0768 0.0413 -0.0447 -0.0434
## [141,] -0.0892 -0.0205 -0.2056 -0.2475
## [142,] 0.0551 0.0170 -0.0400 0.1195
## [143,] 0.1033 0.0483 0.1975 0.1435
## [144,] -0.0498 0.0202 0.0354 -0.1278
## [145,] -0.0273 0.0357 -0.0083 0.1140
## [146,] 0.0435 0.0366 0.1535 -0.0610
## [147,] 0.0887 0.0610 0.0602 0.1263
## [148,] -0.0286 0.0047 -0.0298 -0.0664
## [149,] 0.0811 -0.0093 -0.0365 -0.0745
## [150,] 0.0231 0.0040 0.0219 -0.1748
## [151,] -0.1228 -0.0003 -0.0842 -0.0237
## [152,] 0.0447 -0.0052 0.0468 -0.1504
## [153,] -0.0384 0.0069 0.0010 -0.2516
## [154,] 0.0638 -0.0071 0.1479 0.0739
## [155,] -0.0059 -0.0453 -0.0456 0.2606
## [156,] -0.0491 0.0157 -0.0084 -0.2509
## [157,] 0.0670 -0.0005 0.0637 0.0597
## [158,] -0.0469 -0.0443 -0.0720 0.0525
## [159,] -0.0722 0.0869 0.0026 -0.0236
## [160,] 0.0739 0.0126 0.0873 0.1299
## [161,] 0.0350 0.0210 0.0197 0.1078
## [162,] -0.0509 -0.0295 -0.0324 -0.1422
## [163,] -0.0205 -0.0103 -0.0231 0.0726
## [164,] -0.0023 -0.0074 -0.0190 0.2631
## [165,] -0.0217 0.0626 -0.0084 -0.0448
## [166,] 0.0929 0.0631 0.0679 0.2686
## [167,] -0.0320 -0.0216 -0.0026 0.0283
## [168,] 0.0404 0.0371 0.0555 -0.0135
b_hat = solve(t(X)%*%X)%*%t(X) %*% stockret
head(b_hat)
## AA AGE CAT F FDX GM
## ones 0.00549124 0.007218061 0.008393521 0.004543643 0.00799579 0.001982025
## 1.29159112 1.514135888 0.940692777 1.219245328 0.80511664 1.045701859
## HPQ KMB MEL NYT PG TRB
## ones 0.006835681 0.00546302 0.008849263 0.00490412 0.008880914 0.006512465
## 1.627951166 0.54980523 1.122870759 0.77064945 0.468803354 0.717880797
## TXN
## ones 0.01438887
## 1.79641173
E_hat = Y - X %*% b_hat
head(E_hat)
## AA AGE CAT F FDX
## [1,] -0.072363588 -0.015055042 0.017946575 0.086543606 0.029748981
## [2,] 0.032196419 0.039102254 0.078031024 0.053095942 0.095013465
## [3,] -0.027152402 0.096781734 -0.023343784 -0.005524285 0.086153645
## [4,] -0.005152096 -0.067245922 0.025525617 -0.020520849 -0.005504894
## [5,] -0.057822280 0.060323321 -0.003622754 -0.069889119 -0.238533263
## [6,] -0.026229896 0.001548218 -0.215000922 -0.043789190 -0.023777506
## GM HPQ KMB MEL NYT
## [1,] 0.055454755 0.053686247 -0.074217666 -0.032109382 -0.009951281
## [2,] 0.085522001 -0.050354379 -0.058617611 -0.007807291 -0.052722484
## [3,] -0.004790948 0.021049583 0.016905428 -0.030424075 -0.025144615
## [4,] -0.008955583 -0.005362112 0.006400475 0.006654621 -0.085164428
## [5,] 0.018010466 -0.057925506 0.035828633 0.013645288 0.045105352
## [6,] -0.012982786 0.003371972 0.018449000 -0.069269340 0.005686817
## PG TRB TXN
## [1,] -0.06252690 -0.082927829 0.04460129
## [2,] -0.01826540 -0.011720014 0.03153867
## [3,] 0.03692127 0.004381045 -0.01928535
## [4,] 0.04937712 -0.062335246 -0.02288872
## [5,] 0.11453640 0.020308727 0.06081793
## [6,] 0.04629178 -0.001928888 -0.04560377
# Excluding constant term
b_hat = as.matrix(b_hat[-1,])
head(b_hat)
## [,1]
## AA 1.2915911
## AGE 1.5141359
## CAT 0.9406928
## F 1.2192453
## FDX 0.8051166
## GM 1.0457019
diagD_hat = diag(t(E_hat) %*% E_hat)/(TT-2)
head(diagD_hat)
## AA AGE CAT F FDX GM
## 0.005919846 0.006095651 0.005966741 0.006791031 0.007839072 0.006609876
# Covariance matrix by single factor model
cov_1f.1 = as.numeric(var(mktret))*b_hat%*%t(b_hat) + diag(diagD_hat);
cov_1f.1
## AA AGE CAT F FDX GM
## AA 0.009046736 0.003665662 0.0022773795 0.002951744 0.0019491551 0.002531602
## AGE 0.003665662 0.010392918 0.0026697784 0.003460338 0.0022850000 0.002967804
## CAT 0.002277380 0.002669778 0.0076254044 0.002149817 0.0014196104 0.001843819
## F 0.002951744 0.003460338 0.0021498168 0.009577439 0.0018399772 0.002389800
## FDX 0.001949155 0.002285000 0.0014196104 0.001839977 0.0090540833 0.001578081
## GM 0.002531602 0.002967804 0.0018438188 0.002389800 0.0015780808 0.008659520
## HPQ 0.003941205 0.004620285 0.0028704615 0.003720446 0.0024567600 0.003190890
## KMB 0.001331056 0.001560401 0.0009694362 0.001256500 0.0008297174 0.001077654
## MEL 0.002718425 0.003186817 0.0019798858 0.002566158 0.0016945373 0.002200899
## NYT 0.001865711 0.002187179 0.0013588366 0.001761207 0.0011629960 0.001510523
## PG 0.001134954 0.001330510 0.0008266108 0.001071382 0.0007074766 0.000918885
## TRB 0.001737961 0.002037416 0.0012657930 0.001640612 0.0010833622 0.001407093
## TXN 0.004349041 0.005098393 0.0031674972 0.004105438 0.0027109857 0.003521083
## HPQ KMB MEL NYT PG
## AA 0.003941205 0.0013310564 0.0027184251 0.0018657114 0.0011349541
## AGE 0.004620285 0.0015604012 0.0031868174 0.0021871787 0.0013305099
## CAT 0.002870462 0.0009694362 0.0019798858 0.0013588366 0.0008266108
## F 0.003720446 0.0012565001 0.0025661582 0.0017612075 0.0010713820
## FDX 0.002456760 0.0008297174 0.0016945373 0.0011629960 0.0007074766
## GM 0.003190890 0.0010776539 0.0022008995 0.0015105229 0.0009188850
## HPQ 0.013934297 0.0016776942 0.0034263656 0.0023515856 0.0014305223
## KMB 0.001677694 0.0042512149 0.0011571807 0.0007941971 0.0004831279
## MEL 0.003426366 0.0011571807 0.0061088004 0.0016219938 0.0009866952
## NYT 0.002351586 0.0007941971 0.0016219938 0.0054564979 0.0006771894
## PG 0.001430522 0.0004831279 0.0009866952 0.0006771894 0.0045836602
## TRB 0.002190566 0.0007398161 0.0015109311 0.0010369833 0.0006308202
## TXN 0.005481631 0.0018513021 0.0037809262 0.0025949280 0.0015785529
## TRB TXN
## AA 0.0017379606 0.004349041
## AGE 0.0020374161 0.005098393
## CAT 0.0012657930 0.003167497
## F 0.0016406124 0.004105438
## FDX 0.0010833622 0.002710986
## GM 0.0014070929 0.003521083
## HPQ 0.0021905656 0.005481631
## KMB 0.0007398161 0.001851302
## MEL 0.0015109311 0.003780926
## NYT 0.0010369833 0.002594928
## PG 0.0006308202 0.001578553
## TRB 0.0061718134 0.002417246
## TXN 0.0024172455 0.019214110
# Calculate the global minimum variance portfolio
library(matlib)
## Warning: package 'matlib' was built under R version 4.2.3
one <- rep(1,13)
one_13_1 <- matrix(one,ncol=1)
a <- inv(cov_1f.1)%*%one_13_1
b <- t(one_13_1)%*%inv(cov_1f.1)%*%one_13_1
mvp <- a/as.vector(b)
head(mvp)
## [,1]
## [1,] 0.01171552
## [2,] -0.03060051
## [3,] 0.07924266
## [4,] 0.02246168
## [5,] 0.08020173
## [6,] 0.05326574
# Change the column name
colnames(mvp)="Weight"
mvp
## Weight
## [1,] 0.01171552
## [2,] -0.03060051
## [3,] 0.07924266
## [4,] 0.02246168
## [5,] 0.08020173
## [6,] 0.05326574
## [7,] -0.03539714
## [8,] 0.25030240
## [9,] 0.07031147
## [10,] 0.15387826
## [11,] 0.24340218
## [12,] 0.14003743
## [13,] -0.03882144