library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
X6portfolio <- read.csv("6portfolio.csv")
# Split into two halves
half_n <- nrow(X6portfolio) / 2
first_half <- X6portfolio[1:half_n, ]
second_half <- X6portfolio[(half_n + 1):nrow(X6portfolio), ]
# Compute statistics for both halves
summary_stats <- function(data) {
return(data.frame(
Mean = colMeans(data[,-1], na.rm=TRUE),
SD = apply(data[,-1], 2, sd, na.rm=TRUE),
Skewness = apply(data[,-1], 2, function(x) moments::skewness(x, na.rm=TRUE)),
Kurtosis = apply(data[,-1], 2, function(x) moments::kurtosis(x, na.rm=TRUE))
))
}
library(moments) # Required for skewness & kurtosis
stats_first <- summary_stats(first_half)
stats_second <- summary_stats(second_half)
print(stats_first)
## Mean SD Skewness Kurtosis
## SMALL.LoBM 0.9819132 6.411052 -0.9315746 6.371651
## ME1.BM2 1.4896987 4.879410 -1.4529046 9.185263
## SMALL.HiBM 1.6030573 4.699320 -1.7512081 10.850068
## BIG.LoBM 1.4644427 4.828790 -0.5786937 5.601247
## ME2.BM2 1.3976927 4.340999 -0.7815101 6.954528
## BIG.HiBM 1.5438009 4.074755 -0.8734925 6.352997
print(second_half)
## X SMALL.LoBM ME1.BM2 SMALL.HiBM BIG.LoBM ME2.BM2 BIG.HiBM
## 235 199907 -1.1252 -0.5169 -1.1700 -2.9887 -3.7973 -3.8208
## 236 199908 -2.7649 -3.0498 -3.4268 0.0456 -3.4353 -3.0357
## 237 199909 0.6314 -0.1897 -2.8843 -1.7866 -5.6162 -5.2602
## 238 199910 0.9525 -0.4475 -2.7004 6.6470 7.5254 3.5624
## 239 199911 13.3583 6.4205 4.3349 4.1944 -2.6936 0.9766
## 240 199912 18.3003 9.0252 6.6659 8.3424 1.2492 3.3242
## 241 200001 1.1975 -0.9354 0.3625 -4.8391 -4.0904 -7.7629
## 242 200002 28.0883 15.6498 13.1301 1.2418 -5.4572 -2.9891
## 243 200003 -13.4840 -4.8054 -1.2043 8.6671 10.7953 12.6437
## 244 200004 -14.6459 -5.7927 -4.3476 -4.2256 -0.5153 -0.0027
## 245 200005 -7.4689 -5.3605 -4.9489 -3.4721 0.3541 3.4989
## 246 200006 17.7779 9.2663 8.5776 4.7732 -4.8059 -2.8696
## 247 200007 -7.1352 1.3482 1.8849 -3.0452 3.7998 4.5455
## 248 200008 8.7960 5.1353 6.6710 7.5806 7.9300 6.9300
## 249 200009 -7.2712 -0.5730 -0.4569 -5.9659 1.5545 1.5671
## 250 200010 -8.4071 -1.3294 -1.5683 -2.0153 -0.2313 2.5737
## 251 200011 -16.5288 -4.3038 -2.9313 -10.5537 -3.4093 0.4395
## 252 200012 2.7926 8.7299 8.6265 -0.1828 8.9452 9.2058
## 253 200101 12.6089 5.0389 6.8630 3.4848 1.8940 -0.9000
## 254 200102 -12.4032 -0.6751 0.0022 -11.2013 -0.8604 1.3265
## 255 200103 -7.6214 -0.8824 -1.5864 -8.0352 -1.5624 -1.2367
## 256 200104 10.1832 5.0033 5.0816 8.9573 4.9486 4.7177
## 257 200105 3.8731 4.6138 6.3100 0.4381 2.1237 4.7252
## 258 200106 6.3064 4.6371 3.1503 -2.2317 -1.0819 -1.3252
## 259 200107 -9.3319 -4.5299 -1.0890 -1.7118 -1.1436 0.4601
## 260 200108 -7.4609 -2.6798 -1.4791 -6.9023 -3.8984 -8.2732
## 261 200109 -17.0159 -13.4339 -14.1521 -8.1659 -9.6087 -8.1314
## 262 200110 11.1180 5.4265 4.4857 3.3534 0.5583 -5.3216
## 263 200111 9.0378 7.3094 9.0717 7.8875 6.6540 12.2742
## 264 200112 6.7106 6.8199 6.6890 0.6646 2.9847 2.3635
## 265 200201 -5.1916 0.3734 3.3048 -0.9182 -1.6239 -2.5436
## 266 200202 -8.1298 -1.2577 -1.0152 -2.3962 0.1967 -5.1829
## 267 200203 8.8781 7.6614 9.9117 3.5933 5.5297 4.6840
## 268 200204 -4.0034 2.3893 4.2270 -7.1199 -0.5419 -7.5924
## 269 200205 -6.7104 -3.6309 -2.6494 -1.3862 0.4151 -2.3928
## 270 200206 -7.0903 -3.2247 -2.4015 -7.4377 -5.9293 -12.2215
## 271 200207 -14.9396 -14.5371 -15.3101 -6.4478 -8.7317 -13.7713
## 272 200208 -0.4395 0.3783 -0.4485 -0.1006 1.7138 6.4683
## 273 200209 -8.3430 -7.4921 -7.1005 -10.8017 -10.2357 -9.1350
## 274 200210 6.6600 4.6300 0.5400 9.7548 4.3438 7.9856
## 275 200211 13.2743 8.3005 7.6826 5.3780 5.8461 8.4496
## 276 200212 -8.6937 -4.6337 -3.5830 -6.1715 -3.9938 -6.9949
## 277 200301 -2.3741 -2.6034 -1.2782 -2.8369 -1.8127 -5.5572
## 278 200302 -3.9343 -1.9031 -3.7313 -1.4217 -2.3934 -4.3684
## 279 200303 1.8119 0.5505 1.0764 1.5895 0.3344 -1.5555
## 280 200304 11.0670 9.3698 9.5335 7.7629 8.7516 11.5916
## 281 200305 13.2044 10.8523 10.6693 5.0071 7.3773 8.3270
## 282 200306 2.4827 2.3886 3.5209 1.3366 1.3129 0.5109
## 283 200307 8.2183 5.6878 6.6437 1.7695 2.7525 0.8599
## 284 200308 4.8971 4.5309 6.0561 2.1260 1.5654 4.0295
## 285 200309 -1.6754 -1.9102 0.9220 -1.1320 -0.5218 -3.3924
## 286 200310 8.3925 8.0205 10.7909 5.2059 7.1717 6.7510
## 287 200311 2.9676 3.6610 4.6760 0.8079 1.6078 2.6610
## 288 200312 1.0783 2.5792 3.1070 4.6141 4.3907 5.7836
## 289 200401 3.8846 3.4793 7.2328 1.4411 2.4336 3.0770
## 290 200402 0.4228 0.9521 0.2898 1.0861 2.2999 2.9757
## 291 200403 1.2928 0.4204 0.4087 -1.8648 -0.7461 -0.4333
## 292 200404 -3.3578 -3.2731 -6.0914 -0.2311 -3.7625 -3.6398
## 293 200405 1.0182 1.2810 0.7002 1.2499 1.2698 1.0769
## 294 200406 3.1157 5.0647 4.3401 1.5136 1.5590 2.6548
## 295 200407 -9.4967 -5.6319 -5.2013 -4.3756 -2.3170 -2.1818
## 296 200408 -2.2001 -0.2903 -0.6391 -0.2820 1.4836 0.1024
## 297 200409 5.5244 5.1974 3.6371 0.8519 1.7287 2.7342
## 298 200410 2.7869 1.6822 1.2476 1.5958 0.9939 2.6893
## 299 200411 8.5101 8.6825 8.7784 3.7051 4.7825 6.2587
## 300 200412 4.4048 2.5672 3.7097 3.5207 3.4817 3.7746
## 301 200501 -5.3911 -3.2935 -2.6630 -3.0957 -1.3806 -1.7037
## 302 200502 0.7712 2.0300 2.8040 2.1229 2.0273 3.1604
## 303 200503 -4.1540 -2.4534 -1.4772 -1.2856 -2.7057 0.1157
## 304 200504 -6.3511 -6.0278 -5.7186 -1.7369 -2.3195 -2.2342
## 305 200505 7.4980 6.3501 5.7183 3.6683 3.0790 4.1685
## 306 200506 2.7806 4.0791 4.7555 -0.7926 1.7881 2.8856
## 307 200507 6.9998 6.9442 5.9866 4.5699 2.6374 3.9961
## 308 200508 -2.2529 -1.1745 -1.2413 -1.2405 -0.8856 0.3806
## 309 200509 0.3822 0.9053 0.2636 0.3871 1.1889 1.9333
## 310 200510 -3.9638 -2.6604 -2.2453 -1.2382 -1.7791 -2.1076
## 311 200511 5.1198 4.6368 4.0298 4.1346 3.7700 2.8948
## 312 200512 0.0933 -0.3940 -0.3230 -0.7290 1.2761 0.0853
## 313 200601 8.5807 9.3029 8.1654 1.8137 3.6573 4.3913
## 314 200602 -0.5483 -0.1125 -0.5208 -0.0917 0.8676 -0.8040
## 315 200603 4.0319 5.2599 5.3598 1.6908 1.0619 1.5704
## 316 200604 -0.5657 1.0112 0.8286 0.0059 2.2492 3.2858
## 317 200605 -7.6554 -4.7814 -4.0432 -2.9029 -3.0052 -1.6874
## 318 200606 -0.7189 0.4315 0.0187 -0.1141 0.1660 0.8541
## 319 200607 -5.8879 -2.8192 -2.1527 -0.7869 1.1701 0.6862
## 320 200608 3.4981 2.5366 2.5223 3.3106 1.9982 0.1641
## 321 200609 0.8236 0.8351 1.3171 2.5161 2.3538 2.1895
## 322 200610 6.1777 5.2030 4.5665 3.3829 2.9276 4.3813
## 323 200611 2.5686 2.7873 2.7404 1.8462 2.1992 1.9554
## 324 200612 -0.5996 0.6809 2.0235 0.3481 2.0059 3.1865
## 325 200701 2.5527 0.8449 1.9196 1.9159 1.8344 1.1933
## 326 200702 -0.1024 -0.0710 -1.0489 -1.9498 -1.5525 -1.2836
## 327 200703 1.7726 1.3221 0.3487 0.8422 1.7789 0.3330
## 328 200704 2.8135 2.0631 0.9535 4.8417 3.6568 3.7988
## 329 200705 4.5063 3.6801 3.1037 3.2198 4.0191 3.3277
## 330 200706 -0.5887 -1.1938 -1.6191 -1.1139 -2.3413 -2.1834
## 331 200707 -4.8084 -5.7876 -8.2207 -1.4022 -4.1777 -5.4141
## 332 200708 1.5001 2.3987 -0.6619 1.5856 2.0066 0.0271
## 333 200709 2.5885 0.9265 0.0934 4.9638 2.2985 3.0316
## 334 200710 3.5844 1.7201 0.1482 3.1527 1.4203 0.6368
## 335 200711 -7.5145 -6.6169 -7.9013 -3.1057 -5.5464 -4.5989
## 336 200712 0.1682 -0.6274 -0.9297 -0.4386 -0.8883 -0.4388
## 337 200801 -8.5654 -6.4989 -3.9366 -7.1977 -4.8299 -3.8873
## 338 200802 -4.6707 -2.8308 -3.9608 -2.1100 -3.5707 -4.4916
## 339 200803 -2.1235 1.1709 0.1903 0.6612 -2.5090 -1.0498
## 340 200804 4.7454 3.4388 1.5267 3.7378 6.0470 5.0753
## 341 200805 5.5150 5.3921 3.0015 2.3412 0.6904 1.9916
## 342 200806 -7.2838 -7.3808 -8.8965 -7.0126 -9.4254 -10.8237
## 343 200807 2.2876 2.9039 5.2999 -1.0748 -2.9991 6.7510
## 344 200808 3.1047 3.8880 7.0479 1.4728 1.0545 0.7139
## 345 200809 -11.0960 -7.2827 -6.9905 -9.7800 -9.8463 -2.0570
## 346 200810 -22.1126 -19.3522 -20.5932 -15.4972 -17.1430 -21.6172
## 347 200811 -11.7044 -11.2504 -14.3367 -6.2057 -6.3444 -16.1953
## 348 200812 4.9088 4.3153 5.3899 1.7000 1.0346 1.5085
## 349 200901 -7.8913 -10.1085 -16.0718 -5.3342 -9.2189 -19.7425
## 350 200902 -9.8277 -11.4073 -15.0774 -7.9555 -11.9113 -16.6032
## 351 200903 9.1856 10.3208 11.0487 8.3258 8.7151 13.4126
## 352 200904 16.4844 16.6446 18.3040 7.9415 10.4615 16.8494
## 353 200905 3.8848 3.1554 2.4796 4.5172 6.0893 6.4772
## 354 200906 5.4172 1.7453 0.7106 0.8703 -1.0007 0.1140
## 355 200907 6.9131 10.3276 13.3708 6.7746 8.2384 9.9829
## 356 200908 1.0155 3.0144 8.1881 1.7045 3.9404 9.8001
## 357 200909 6.3176 5.8375 7.5795 3.4573 4.7055 4.2793
## 358 200910 -6.9838 -6.3198 -9.3979 -0.4418 -2.7689 -6.4484
## 359 200911 2.0214 1.9394 4.1184 6.6381 4.7671 3.8618
## 360 200912 8.4759 8.0740 8.3772 1.9456 3.1202 1.7169
## 361 201001 -3.7834 -3.0201 -2.6859 -4.2125 -2.0265 -4.4504
## 362 201002 3.3733 4.1291 7.4536 3.0580 2.9082 5.4191
## 363 201003 7.0160 8.1488 8.9499 5.2329 6.7363 7.7161
## 364 201004 3.9334 6.2370 9.2931 0.8520 2.7427 1.2645
## 365 201005 -5.9602 -7.1246 -10.3687 -7.3779 -8.5019 -7.8501
## 366 201006 -5.7705 -7.5702 -10.8838 -4.4235 -5.6504 -8.7076
## 367 201007 6.7868 6.6902 7.2318 6.7418 7.6803 5.6834
## 368 201008 -7.1815 -7.6696 -8.6118 -4.0632 -3.9597 -6.4365
## 369 201009 14.0514 12.7735 10.9568 10.0755 8.9842 6.8510
## 370 201010 4.4471 4.2271 3.6404 4.5444 3.8611 0.5078
## 371 201011 3.7207 4.1029 3.3312 0.5094 0.3779 -1.0253
## 372 201012 7.3154 8.3352 9.4636 4.9391 7.7950 10.1774
## 373 201101 -0.4693 0.0666 0.3442 2.0293 2.5443 2.8643
## 374 201102 5.1092 5.3242 5.6043 2.5012 4.4024 4.5472
## 375 201103 3.3512 2.8300 1.4611 0.1939 1.3976 -1.5739
## 376 201104 3.2949 2.1079 1.0561 3.7506 2.7078 1.1332
## 377 201105 -1.3995 -2.1296 -3.1974 -0.5623 -1.3945 -3.0000
## 378 201106 -1.7937 -2.1296 -1.8913 -1.4636 -1.7685 -2.2103
## 379 201107 -4.5512 -3.9686 -3.0352 -0.7561 -2.9443 -4.0590
## 380 201108 -9.3859 -8.8784 -9.7399 -3.9976 -6.4878 -8.3585
## 381 201109 -11.1072 -11.4956 -10.8019 -6.3705 -6.9662 -10.1269
## 382 201110 15.6731 15.5059 13.1351 9.8325 12.0524 12.5813
## 383 201111 -1.8459 -0.2643 -0.1686 -0.0524 0.9022 -2.6363
## 384 201112 -0.5648 0.7812 1.1746 -0.1342 1.9194 1.3800
## 385 201201 8.2697 6.8063 5.8503 5.4881 3.3587 5.9724
## 386 201202 3.4330 2.3748 2.9373 4.6300 3.6923 5.9852
## 387 201203 2.4252 2.8281 3.0831 3.6960 1.2495 5.3242
## 388 201204 -1.4498 -2.0557 -0.9131 -0.4648 -0.1512 -2.5525
## 389 201205 -6.5426 -6.3568 -6.2397 -5.4838 -5.9420 -7.9175
## 390 201206 5.7113 4.2133 4.7887 2.9353 4.6708 5.0942
## 391 201207 -3.3857 -0.8420 -1.7068 1.2935 1.4434 -0.4303
## 392 201208 3.2884 3.1286 3.7404 2.3725 1.8713 4.5117
## 393 201209 3.2688 3.5176 4.1139 1.9087 3.2017 4.2734
## 394 201210 -4.0430 -1.3322 -0.8733 -2.4805 -1.8315 1.5199
## 395 201211 1.0919 1.0314 0.8674 1.1244 0.3005 -0.3317
## 396 201212 2.6308 3.4715 4.4199 -0.1907 1.2208 5.0406
## 397 201301 6.8825 6.3575 5.8106 4.4787 6.0958 7.4690
## 398 201302 1.0361 0.8591 1.3242 1.3647 1.3768 1.3000
## 399 201303 5.1794 4.5401 4.5439 3.7607 4.0516 4.0252
## 400 201304 -0.7799 -0.8766 -0.1701 1.8584 1.2847 2.1417
## 401 201305 5.0181 5.3202 5.1990 1.9508 1.4377 7.0326
## 402 201306 -0.2285 0.3531 -0.1188 -1.7702 -0.3864 -1.8251
## 403 201307 7.3800 7.1582 7.8817 5.6309 4.8920 6.2744
## 404 201308 -1.0563 -3.5344 -3.8395 -1.7433 -3.1653 -4.3434
## 405 201309 6.3876 6.2537 5.6102 4.0527 3.1904 2.3976
## 406 201310 1.0547 3.1436 3.9460 4.1757 4.7556 3.7778
## 407 201311 5.2474 3.9232 4.5237 3.2912 1.8741 4.6570
## 408 201312 1.8901 2.7539 1.8888 2.1376 3.7106 2.0897
## 409 201401 -0.1005 -4.1373 -3.6886 -3.3492 -3.3583 -3.8951
## 410 201402 4.0185 4.7223 5.1966 5.0204 4.6768 3.2149
## 411 201403 -3.4318 1.3038 1.3785 -0.5888 0.7922 4.4634
## 412 201404 -6.3726 -3.0373 -2.7400 0.3706 0.9417 -0.9228
## 413 201405 -0.6871 0.8394 0.0861 2.4590 2.0113 1.4194
## 414 201406 7.1987 5.0731 4.4407 1.6430 2.8017 3.0089
## 415 201407 -6.4083 -6.3564 -5.4594 -1.4006 -1.6522 -2.2657
## 416 201408 5.0677 4.0537 4.5295 4.7978 3.2260 4.4380
## 417 201409 -4.7034 -5.2698 -6.4390 -0.9312 -2.4773 -1.9052
## 418 201410 7.4874 5.8190 5.2151 2.8233 1.5928 1.4990
## 419 201411 1.7998 -0.2640 -1.0665 3.7087 2.5528 0.3802
## 420 201412 2.0810 2.8713 3.2662 -1.3474 0.1043 2.0002
## 421 201501 -2.8534 -4.9049 -5.1879 -1.5607 -3.2987 -6.3993
## 422 201502 7.6765 7.0046 5.0056 6.4876 5.8840 5.4379
## 423 201503 2.0609 1.8086 1.1345 -1.3767 -1.5381 -1.2115
## 424 201504 -3.2016 -2.1341 -0.7281 0.3415 1.2764 1.5106
## 425 201505 2.9169 2.7074 0.8810 1.2186 1.5029 0.9607
## 426 201506 2.7242 0.3338 0.6035 -1.8323 -1.9434 -1.2916
## 427 201507 -0.2299 -2.3624 -5.6037 2.9657 1.2570 0.0800
## 428 201508 -9.3032 -4.7374 -3.3404 -6.1721 -5.6180 -6.5880
## 429 201509 -7.8251 -4.6104 -4.7172 -2.2242 -2.8566 -4.2145
## 430 201510 5.0061 6.4663 5.7017 8.0276 8.4164 6.4103
## 431 201511 5.6571 3.3772 3.6571 0.5054 -0.2685 1.6709
## 432 201512 -3.8734 -4.9903 -6.8243 -1.3060 -2.2722 -3.5730
## 433 201601 -14.1147 -7.6824 -6.9269 -5.1637 -5.1326 -8.1763
## 434 201602 -0.7099 0.9697 0.3780 0.0215 0.6254 -2.2142
## 435 201603 7.7058 7.8565 8.4662 6.5760 6.7935 8.2047
## 436 201604 2.6434 1.1620 3.8478 -0.6295 1.2854 4.7317
## 437 201605 2.3290 1.2799 0.5247 2.1877 1.7826 0.6654
## 438 201606 0.2961 -0.4164 -0.0412 0.0131 0.5954 -2.6015
## 439 201607 7.0391 5.6284 5.6740 4.9510 2.2505 3.6762
## 440 201608 1.3009 2.6586 3.2507 -0.5452 0.4159 3.8652
## 441 201609 3.2742 1.3322 1.6892 0.4472 -0.0784 -0.4406
## 442 201610 -8.1473 -5.1409 -3.0228 -1.9605 -2.2550 1.0938
## 443 201611 9.1400 12.5651 14.9658 1.9430 5.0565 12.5388
## 444 201612 -0.4427 2.9047 4.4845 1.3517 1.8021 3.4784
## 445 201701 1.9775 -0.1849 -0.7168 3.2210 1.0026 0.4064
## 446 201702 3.3431 1.1594 0.2891 4.2757 2.6548 3.9975
## 447 201703 2.3122 0.0705 -0.6854 1.1103 -0.2497 -2.5873
## 448 201704 1.9398 1.4351 0.6314 2.0535 0.6725 -0.8974
## 449 201705 -0.8419 -1.6384 -3.8611 2.8958 0.1204 -1.6445
## 450 201706 4.8044 3.1399 3.4308 -0.1294 0.5599 4.2068
## 451 201707 0.7584 0.5109 0.4881 2.4781 1.6575 2.1367
## 452 201708 -0.6147 -2.0376 -2.3459 1.2965 -0.1186 -1.1635
## 453 201709 5.4328 8.3527 8.3274 1.3548 2.6473 4.7097
## 454 201710 0.3610 0.3246 1.0050 3.1219 1.5413 2.8620
## 455 201711 2.7001 2.7212 2.7554 3.3234 3.2685 3.2153
## 456 201712 0.8678 -0.7691 0.0149 0.9718 1.1421 1.9459
## 457 201801 3.1386 2.9959 1.8416 6.4966 5.6052 5.2253
## 458 201802 -3.0811 -3.7637 -3.7139 -2.5784 -4.7349 -4.0181
## 459 201803 1.3875 0.9719 1.9354 -2.3638 -2.2034 -3.3156
## 460 201804 1.2044 1.0672 2.4007 0.6196 0.1555 0.5007
## 461 201805 8.0057 7.5384 5.6984 3.8336 1.9238 -0.2962
## 462 201806 2.8843 0.2033 0.6187 1.0924 0.4914 -1.2985
## 463 201807 1.4298 2.1783 1.0524 3.3424 3.3649 4.6186
## 464 201808 5.7090 3.3666 2.2897 5.3918 1.7127 0.8061
## 465 201809 -1.7387 -2.7490 -2.8453 0.5834 0.6728 -1.7224
## 466 201810 -13.3209 -11.4005 -9.1791 -8.1926 -5.9586 -5.5280
## 467 201811 1.0437 2.1254 0.8349 1.4792 2.2986 2.2556
## 468 201812 -12.0918 -11.9107 -12.6489 -8.3897 -9.5705 -11.5847