MIDTERM 2
ENKHJIN
4/18/2019
rm(list=ls())
options(digits=5)
firm_data1 = read.csv("Fama_N.CSV")
head(firm_data1)## Date Mkt.RF SMB HML RF
## 1 192607 2.96 -2.3 -2.87 0.22
## 2 192608 2.64 -1.4 4.19 0.25
## 3 192609 0.36 -1.32 0.01 0.23
## 4 192610 -3.24 0.04 0.51 0.32
## 5 192611 2.53 -0.2 -0.35 0.31
## 6 192612 2.62 -0.04 -0.02 0.28names(firm_data1)## [1] "Date" "Mkt.RF" "SMB" "HML" "RF"attach(firm_data1)
library("Ecdat")## Loading required package: Ecfun##
## Attaching package: 'Ecfun'## The following object is masked from 'package:base':
##
## sign##
## Attaching package: 'Ecdat'## The following object is masked from 'package:datasets':
##
## Orangelibrary("robust")## Loading required package: fit.modelsstocks5=cbind(N=Mkt.RF,SMB,HML)
fit = lm(cbind(Mkt.RF,SMB,HML)~RF)
options(digits=3)
SMB## [1] -2.3 -1.4 -1.32 0.04 -0.2 -0.04 -0.56 -0.1 -1.6
## [10] 0.43 1.41 0.47 -3.23 -0.72 -3.57 2.13 2.76 0.93
## [19] 4.25 -2.03 -0.26 3.82 2.98 -3.5 -1.35 -2.07 2.18
## [28] 2.27 -1.81 -0.85 -3.54 -0.39 -4.78 -0.99 -5.46 -2.17
## [37] -3.88 -9.52 1.17 -4.08 -1.91 -4.2 3.58 0.12 3.44
## [46] -0.17 -2.04 -3.22 -0.37 -2.22 -2.22 -0.1 2.21 -4.68
## [55] 3.81 3.39 3.07 -4.61 5.16 -5.38 1.43 -1.97 0.56
## [64] -1.87 4.3 -0.56 3.94 -2.77 2.27 1.44 3.72 0.35
## [73] -4.44 14.29 -2.43 -2.76 2.08 -8.27 0.69 -2.75 3.9
## [82] 4.56 36.7 8.67 -1.01 -5.45 -0.32 -0.08 -6.48 0.66
## [91] 12.53 5.19 2.51 2.8 -0.26 -2.14 -6.94 5.42 -1.52
## [100] 1.24 6.49 3.08 1.07 0.42 -3.54 -1.56 -3.34 -2.51
## [109] 1.47 6.28 1.57 2.65 4.3 0.22 5.1 1.14 0.66
## [118] -6.03 0.81 -3.25 1.14 0.72 3.07 -2.39 9.01 3.61
## [127] 4.31 1.23 -1.78 -3.77 -0.66 -3.65 0.85 0.42 -6.89
## [136] 0.45 -3.65 -7.76 4.97 0.35 -4.24 6.37 -2.47 4.05
## [145] 6.66 -2.44 -2.72 5.83 -2.56 -1.8 -1.56 0.63 -4.76
## [154] 1.66 2.81 -1.02 4.32 -4.61 20.23 -0.01 -5.07 0.79
## [163] 0.24 2.51 1.25 3.92 -6.66 -2.13 1.01 -0.11 3.22
## [172] 0.28 1.94 -2.15 1 -1.57 0.1 -1.69 -0.66 1.32
## [181] 5.7 -0.41 -0.99 -2.02 -1.21 -2.98 7.52 1.72 1.78
## [190] -0.6 -3.05 -1.22 -0.16 -0.09 0.66 1.82 -1.54 -2.49
## [199] 8.78 4.84 5.03 2.06 4.41 -1.06 -2.41 -0.62 1.28
## [208] 0.58 -1.64 3.34 2.56 -0.1 1.71 -1.35 1.67 4.04
## [217] 0.55 2.41 0.47 -0.14 0.37 2.24 2.44 1.56 -1.61
## [226] 0.32 1.51 3.1 -1.46 1.61 1.71 2.46 4.16 2.12
## [235] 4.02 -0.73 0.31 2.37 1.46 -1.53 -2.06 -1.78 -4.41
## [244] 0.09 -0.4 0.06 2.18 0.68 -1.61 -3.97 -3.26 -0.31
## [253] 1.43 0.3 1.64 0.51 -1.74 -2.48 2.49 -1.71 0.13
## [262] -1.66 0.93 -1.86 -0.32 -1.1 -1.23 -1.5 -0.62 -2.8
## [271] 1.81 -1.89 2.48 -0.89 -0.77 -0.88 0.57 0.13 1.05
## [280] 1.03 -0.93 2.07 3.36 0.04 -1.41 1.99 -2.12 -2.38
## [289] 0.51 0.73 0.57 -0.58 -0.84 1.49 1.73 0.09 -0.64
## [298] -1.49 -0.01 -1.95 -1.99 0.99 1.9 -0.22 -0.29 -2.25
## [307] -0.61 0.79 -2.99 0.48 -1.01 -1.61 -0.4 1.18 1.15
## [316] -1.06 -0.71 -1.48 3.58 2.15 -0.19 0.28 -0.07 -1.86
## [325] -1.05 0.36 -0.85 -1.37 -1.29 -0.84 0.46 -0.17 -0.49
## [334] -3.48 0.39 0.41 1.07 2.66 -2.54 0.59 -2.62 2.14
## [343] 0.25 1.54 -0.66 -1.79 -0.29 -4.65 -1.36 -0.38 0.3
## [352] 1.5 -2.46 2.08 0.44 -1.04 -2.42 0.07 1.5 -1.46
## [361] -1.68 1.9 1.56 -0.09 -0.22 -0.03 3.4 -0.72 0.27
## [370] -1.6 -1.07 0.55 -0.76 0.06 0.08 -2.52 0.4 -0.93
## [379] 4.36 0.7 0.63 -0.59 2.24 -0.24 0.47 1.19 0.15
## [388] 1.13 2.06 -2.07 3.02 1.49 1.48 -0.58 -2.15 0.68
## [397] -0.32 -0.78 -0.09 1.43 1.24 -0.6 2.09 0.51 -0.51
## [406] 0.31 1.21 -0.22 -0.52 0.9 -1.11 -3.95 0.35 -1.56
## [415] 0.66 3.98 3.27 0.1 1.95 -2.47 -1.88 -1.75 -1.05
## [424] -1.61 1.24 -0.83 1.78 -1.16 0.53 -0.68 -3.33 -0.57
## [433] 1.49 1.23 -2.43 -3.97 2.61 -3.8 3.06 0.5 -2.62
## [442] -1.31 1.12 -0.25 -0.56 -0.94 -0.31 -0.54 -1.13 -1.97
## [451] -0.19 0.1 0.99 -1.37 -0.9 -0.26 0.28 0.09 -0.51
## [460] 0.43 0.61 -0.26 2.7 3.48 1.79 1.2 0.04 -4.35
## [469] 0.87 2.81 0.61 2.48 4.68 2.08 3.89 4.54 0.94
## [478] 3.45 -4.7 1.02 -0.44 -3.23 -1.07 -6.64 4.22 1.86
## [487] 8.32 3.34 1.63 0.62 1.98 5.96 3.08 0.47 3.1
## [496] 1.42 0.2 5.73 3.91 -2.95 -1.28 5.73 6.43 -0.17
## [505] -1.3 2.34 2.76 -0.47 2.36 3.44 -0.78 -3.89 -0.25
## [514] -0.88 -0.27 -5.39 -3.21 0.94 1.2 3.81 -2.53 -3.67
## [523] 2.9 -2.4 -2.32 -6.11 -4.52 -2.16 -0.54 1.52 8.62
## [532] -4.28 -4.07 2.97 7.37 1.88 2.54 -0.49 -1.1 -1.42
## [541] -1.5 -0.16 0.41 -1.8 -2.85 3.32 6.12 1.37 -0.27
## [550] 0.01 -2.79 0.33 -2.89 -4.09 -2.67 -2.74 -1.11 -1.86
## [559] -3.48 -3.99 -2.82 -3.99 -6.12 -2.95 7.91 -2.03 2.94
## [568] -0.23 -7.7 -5.29 9.76 0.05 2.51 -0.71 -3.01 -0.2
## [577] 0.92 -0.68 0.27 -3.51 -1.17 -4.84 11.01 0.16 3.75
## [586] -0.54 3.83 0.76 2.69 -3.2 -0.13 -4.02 -1.19 -0.76
## [595] 4.8 7.03 -1.17 -0.03 -1.24 -1.35 0.31 -2.01 -0.01
## [604] 0.25 2.32 3.01 4.78 1.08 0.99 -0.12 1.18 2.13
## [613] 2.12 1.52 1.45 1.27 3.72 1.35 2.22 3.59 3.48
## [622] 0.4 4.56 1.69 0.26 5.06 -0.39 -9.88 3.01 1.24
## [631] 3.66 0.45 3.19 2.18 0.57 1.17 1.26 2.08 -0.25
## [640] -3.34 2.74 4.17 1.65 -1.82 -6.64 0.97 2.16 1.67
## [649] 4.25 3.92 0.89 2.47 -3.45 -0.28 3 -0.31 3.58
## [658] 4.42 2 -0.85 -2.18 -1.95 -2.66 2.13 -0.96 1.17
## [667] -1.29 0.49 -0.19 1.51 0.47 -0.4 0.84 -4.11 2.88
## [676] 2.35 4.77 -0.18 2.7 3.23 1.77 0.53 6.16 0.91
## [685] 1.46 -4.3 0.56 -3.6 2.04 -0.29 -0.43 -1.71 0.07
## [694] -1.2 0.03 -0.32 -2.21 -0.25 0.2 -1.2 -0.62 -0.6
## [703] 3.27 0.76 -1.15 0.14 -2.25 0.65 2.85 -0.34 -1.58
## [712] -1.57 0.23 -0.49 1.22 -0.65 -0.52 2.84 -1.32 -0.91
## [721] -3.38 -4.17 2.28 -2.48 -1.92 0.08 -1.81 3.49 0.37
## [730] -1.69 -0.53 -2.18 -0.67 -0.72 0.52 -8.43 2.77 0.13
## [739] -0.77 3.36 6.16 0.96 -2.64 2.16 -0.21 0.04 -1.25
## [748] -2.9 -1.74 1.95 -2.14 2.76 0.74 -0.59 -0.04 -1.01
## [757] -4.02 0.5 0.28 -3.3 -1.24 -2.41 -1.29 1.03 1.52
## [766] -0.5 -2.57 1.43 -3.21 -3.58 -3.67 -5.51 0.33 0.79
## [775] 3.79 3.95 3.89 0.5 -0.34 0.07 -0.93 1.59 1.63
## [784] 0.9 -0.48 -2.24 8.47 0.88 -1.03 -6.12 0.39 -3.09
## [793] -0.44 -0.12 0.56 2.05 3.7 1.64 2.03 -3.43 0.23
## [802] -0.7 1.96 -0.31 0.93 0.32 3.11 1.45 -1.43 1.22
## [811] 0.14 2.73 -0.98 -0.93 -2.02 -0.45 -1.73 1.34 2.82
## [820] -2.34 0.27 0.04 -2.65 -0.67 -0.7 -0.62 -2.2 2.93
## [829] 2.09 1.6 -2.1 -3.74 -1.17 0.57 -2.62 1.88 1.3
## [838] 4.92 3.04 -3.58 -3.83 2.3 -0.88 -4.44 -3.89 3.2
## [847] -1.84 -2.9 -0.38 -5.66 4.89 1.32 -2.8 7.31 2.61
## [856] -0.68 -4.94 -2.35 -1.15 0 -0.94 0.21 -3.75 -3.16
## [865] -5.12 -5.3 -0.12 -3.32 1.07 -0.33 0.39 -5.68 -3.94
## [874] 3.99 3.42 3.06 2.66 -1.27 3.33 -6.94 7.38 7.15
## [883] 4.95 21.71 -16.87 -7.75 -5.11 13.86 -2.79 -1.13 -1.39
## [892] -3.76 -2.79 0.97 6.57 -0.74 0.34 0.52 2.6 6.05
## [901] -4.35 2.49 -6.13 7.63 -0.41 4.57 1.19 -1.1 4.23
## [910] 5.94 -3.21 4.26 -5.3 -2.44 2.57 -2.9 2.84 0
## [919] 1.39 -0.34 0.89 0.57 4.7 1.67 5.25 2.6 0.79
## [928] 2.68 2.01 -3.01 2.8 -1.43 1.75 -2.06 -0.21 2.26
## [937] -3.8 -1.63 3.03 0.31 3.91 0.12 -1.51 -0.51 -1.39
## [946] -3.99 2.89 2.62 2.93 -0.92 -0.58 -1.21 0.91 -0.46
## [955] 5.42 -0.38 3.55 -1.34 -3.04 -0.35 -4.08 0.9 -1.37
## [964] 1.73 0.86 -1.1 0.1 1.32 -0.06 -2.06 0.03 0.77
## [973] -2.51 -0.13 -2.29 0.22 -2.63 0.2 -0.89 -0.23 0.94
## [982] -1.64 3.22 1.27 2.47 3.61 -1.13 -2.34 -2.99 3.59
## [991] -0.01 0.16 -0.08 4.83 -2.33 2.61 2.07 -0.9 2.45
## [1000] -4.23 -2.49 6.11 0.38 1.21 1.43 4.98 0.05 -1.98
## [1009] 0.17 -3 3.92 1.14 3.71 0.69 -2.46 1.52 2.6
## [1018] -0.35 -0.71 -0.17 -1.3 -3.06 -3.49 3.41 -0.17 -0.71
## [1027] 2.15 -1.75 -0.6 -0.51 0.02 0.77 -2.59 0.42 0.51
## [1036] -1.14 0.58 1.47 0.39 -0.45 0.78 -2.42 1.67 1.22
## [1045] 1.86 0.3 2.93 -1.49 1.24 -0.5 0.86 0.32 -1.89
## [1054] -4.25 -1.85 3.07 -4.24 0.36 -3.83 4.23 -2.09 2.54
## [1063] -0.56 0.48 3.02 -2.97 0.87 2.83 -4.14 0.48 -2.64
## [1072] -1.97 3.64 -2.82 -3.36 0.78 0.87 0.68 -0.26 0.65
## [1081] 2.65 1.14 2.01 -4.36 5.51 0.05 -1.01 -2 1.19
## [1090] 0.73 -2.54 2.15 -1.4 -1.69 4.52 -1.94 -0.66 -1.26
## [1099] -3.03 0.28 3.93 1.1 5.24 1.17 -2.17 1.27 -2.35
## [1108] -4.69 -0.78 -2.58 3.02 2.03 SMB -2.46
## [1117] 4.2 -30.8 -5.13 3.53 4.67 49.07 25.44 10.05 17.87
## [1126] -14 9.35 5.85 0.79 -4.04 5.05 33.35 17.98 25.56
## [1135] -3.79 -7.08 -9.14 3.93 0.93 -4.93 -6.66 -1.16 -2.18
## [1144] -6.71 -1.17 -2.72 14.81 5.43 -2.75 1.4 -8.25 -5.88
## [1153] -0.99 21.8 2.59 50.69 24.5 -13.98 -11.79 5.62 -11.95
## [1162] -23.44 -0.6 15.28 14.69 22.93 14.38 21.69 5.57 7.23
## [1171] 8.89 13.67 -8.31 0.38 -9.6 -11 5.9 -12.72 -14.19
## [1180] 16.13 7.58 5.8 -1.07 -9.1 -3.71 -6.77 -26 14.87
## [1189] -1.59 18.08 4.71 26.17 4.9 -1.96 0.24 -7.19 3.2
## [1198] 9.23 13.8 -6.01 -1.15 7.27 -8.08 -4.05 6.6 -4.77
## [1207] -3.32
## 747 Levels: -0.01 -0.03 -0.04 -0.06 -0.07 -0.08 -0.09 -0.1 -0.11 ... SMBpairs(cbind(Mkt.RF,SMB,HML))
cor(fit$residuals)## Mkt.RF SMB HML
## Mkt.RF 1.00000 0.196 0.00851
## SMB 0.19587 1.000 0.08405
## HML 0.00851 0.084 1.00000covRob(fit$residuals,cor=F)## Call:
## covRob(data = fit$residuals, corr = F)
##
## Robust Estimate of Covariance:
## Mkt.RF SMB HML
## Mkt.RF 65455 15102 -1617
## SMB 15102 46715 2983
## HML -1617 2983 42811
##
## Robust Estimate of Location:
## Mkt.RF SMB HML
## 0.0825 -2.9358 -2.1468cor.test(fit$residuals[,1], fit$residuals[,2])##
## Pearson's product-moment correlation
##
## data: fit$residuals[, 1] and fit$residuals[, 2]
## t = 7, df = 1000, p-value = 6e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.141 0.249
## sample estimates:
## cor
## 0.196cor.test(fit$residuals[,1], fit$residuals[,3])##
## Pearson's product-moment correlation
##
## data: fit$residuals[, 1] and fit$residuals[, 3]
## t = 0.3, df = 1000, p-value = 0.8
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.0479 0.0649
## sample estimates:
## cor
## 0.00851cor.test(fit$residuals[,2], fit$residuals[,3])##
## Pearson's product-moment correlation
##
## data: fit$residuals[, 2] and fit$residuals[, 3]
## t = 3, df = 1000, p-value = 0.003
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.0278 0.1398
## sample estimates:
## cor
## 0.084pairs(fit$residuals)
n=dim(firm_data1)[1]
sigF = as.matrix(var(cbind(Mkt.RF,SMB,HML)))
sigF## Mkt.RF SMB HML
## Mkt.RF 64390 12045 819
## SMB 12045 45654 4482
## HML 819 4482 44628bbeta = as.matrix(fit$coef)
bbeta = t( bbeta[-1,])
bbeta## RF-0.01 RF-0.02 RF-0.03 RF-0.06 RF0 RF0.01 RF0.02 RF0.03 RF0.04
## Mkt.RF 327 409 132 92 428 496 449 488 499
## SMB 275 540 223 211 332 410 418 348 317
## HML 401 212 214 104 226 369 370 371 335
## RF0.05 RF0.06 RF0.07 RF0.08 RF0.09 RF0.1 RF0.11 RF0.12 RF0.13
## Mkt.RF 505 359 476 505 490 530 493 297 511
## SMB 470 277 418 237 336 318 328 329 322
## HML 394 332 357 342 259 337 306 210 342
## RF0.14 RF0.15 RF0.16 RF0.17 RF0.18 RF0.19 RF0.2 RF0.21 RF0.22
## Mkt.RF 383 478 373 437 455 410 470 404 464
## SMB 379 351 273 342 358 263 262 332 343
## HML 253 362 295 285 207 348 273 248 300
## RF0.23 RF0.24 RF0.25 RF0.26 RF0.27 RF0.28 RF0.29 RF0.3 RF0.31
## Mkt.RF 432 355 427 360 330 481 461 501 421
## SMB 397 287 277 270 305 333 248 311 304
## HML 349 319 336 257 355 382 266 381 311
## RF0.32 RF0.33 RF0.34 RF0.35 RF0.36 RF0.37 RF0.38 RF0.39 RF0.4
## Mkt.RF 481 484 274 327 335 357 356 480 389
## SMB 328 496 354 442 392 349 301 324 340
## HML 310 333 330 393 393 269 328 277 354
## RF0.41 RF0.42 RF0.43 RF0.44 RF0.45 RF0.46 RF0.47 RF0.48 RF0.49
## Mkt.RF 488 426 533 497 502 445 493 326 515
## SMB 399 328 340 331 425 334 308 253 407
## HML 262 310 309 256 411 348 391 437 263
## RF0.5 RF0.51 RF0.52 RF0.53 RF0.54 RF0.55 RF0.56 RF0.57 RF0.58
## Mkt.RF 532 255 474 445 529 438 447 362 324
## SMB 371 299 285 294 438 208 428 254 370
## HML 487 395 364 397 289 440 317 426 427
## RF0.59 RF0.6 RF0.61 RF0.62 RF0.63 RF0.64 RF0.65 RF0.66 RF0.67
## Mkt.RF 362 416 500 335 375 471 467 440 561
## SMB 457 281 376 298 582 418 238 227 231
## HML 391 383 311 371 335 271 286 271 276
## RF0.68 RF0.69 RF0.7 RF0.71 RF0.72 RF0.73 RF0.74 RF0.75 RF0.76
## Mkt.RF 360 431 463 388 47 204 354 398 256
## SMB 331 359 390 209 370 211 440 190 260
## HML 282 123 319 511 624 482 544 276 589
## RF0.77 RF0.78 RF0.79 RF0.8 RF0.81 RF0.82 RF0.83 RF0.86 RF0.87
## Mkt.RF 645 365 658 404 474 165 273 403 281
## SMB 545 410 3 363 407 297 22 279 354
## HML 382 273 73 419 439 435 114 633 277
## RF0.89 RF0.92 RF0.95 RF0.96 RF0.98 RF0.99 RF1 RF1.02 RF1.04 RF1.05
## Mkt.RF 60 296 464 480 99 778 42 697 275 205
## SMB 146 402 610 323 16 578 97 602 603 428
## HML 393 700 187 429 625 240 382 681 711 352
## RF1.06 RF1.07 RF1.08 RF1.1 RF1.13 RF1.15 RF1.2 RF1.21 RF1.24 RF1.26
## Mkt.RF 234 446 146 541 654 373 568 518 204 695
## SMB 400 245 671 649 483 530 561 503 201 440
## HML 485 361 539 287 218 38 656 255 367 428
## RF1.28 RF1.31 RF1.35 RF1.49 RF1.54 RF1.57 RF1.6 RF1.65 RF1.66
## Mkt.RF 326 259 158 542 764 618 238 192 519
## SMB 156 25 71 314 523 338 614 679 337
## HML 665 564 674 308 506 693 408 720 605
## RF1.81 RF1.82 RF10.38 RF10.54 RF11.24 RF14.71 RF2.13 RF2.41 RF2.46
## Mkt.RF 323 50 527 508 617 139 621 235 804
## SMB 253 94 595 741 703 727 472 319 95
## HML 332 321 108 507 230 585 682 168 134
## RF2.66 RF2.73 RF2.9 RF2.95 RF2.98 RF3.12 RF3.14 RF3.51 RF3.54
## Mkt.RF 75 123 865 881 639 585 124 818 524
## SMB 223 348 707 701 157 266 221 733 81
## HML 293 733 518 488 728 386 313 583 741
## RF3.56 RF3.83 RF3.84 RF3.9 RF3.93 RF4.21 RF4.39 RF4.66 RF4.68
## Mkt.RF 703 131 526 244 506 620 518 438 612
## SMB 661 529 163 88 597 713 704 343 524
## HML 311 520 480 58 717 328 165 173 268
## RF4.75 RF4.76 RF4.8 RF4.86 RF5.08 RF5.12 RF5.21 RF5.26 RF5.47 RF5.6
## Mkt.RF 140 127 507 543 616 347 703 623 228 663
## SMB 284 568 378 237 522 598 434 339 161 439
## HML 503 60 509 330 584 721 609 515 137 425
## RF5.8 RF5.89 RF6.16 RF6.35 RF6.52 RF6.58 RF6.93 RF7.18 RF7.72
## Mkt.RF 700 137 502 516 316 136 195 437 622
## SMB 525 130 355 710 162 165 236 521 391
## HML 735 637 736 510 581 335 516 371 478
## RF7.81 RF8 RF8.37 RF8.8 RF9.85 RFRF
## Mkt.RF 130 237 611 531 306 883
## SMB 167 53 164 517 350 746
## HML 334 738 281 579 521 742resig2 = apply((fit$resid)^2, 2, sum)/(n-3-1)
resig2 = diag(resig2)
cov_ff3 = sigF
cov_ff3## Mkt.RF SMB HML
## Mkt.RF 64390 12045 819
## SMB 12045 45654 4482
## HML 819 4482 44628cov2cor(cov_ff3)## Mkt.RF SMB HML
## Mkt.RF 1.0000 0.2222 0.0153
## SMB 0.2222 1.0000 0.0993
## HML 0.0153 0.0993 1.0000cov_hist = cov(stocks5)
cov2cor(cov_hist)## N SMB HML
## N 1.0000 0.2222 0.0153
## SMB 0.2222 1.0000 0.0993
## HML 0.0153 0.0993 1.0000one.vec=rep(1,3)
a = solve(cov_ff3)%*%one.vec
b = t(one.vec)%*%a
mvp.w =a / as.numeric(b)
mvp.w## [,1]
## Mkt.RF 0.246
## SMB 0.338
## HML 0.416a1 = solve(cov_hist)%*%one.vec
b1 = t(one.vec)%*%a1
mvp.w1 =a1 / as.numeric(b1)
mvp.w1## [,1]
## N 0.246
## SMB 0.338
## HML 0.416R Markdown
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.
When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:
summary(cars)## speed dist
## Min. : 4.0 Min. : 2
## 1st Qu.:12.0 1st Qu.: 26
## Median :15.0 Median : 36
## Mean :15.4 Mean : 43
## 3rd Qu.:19.0 3rd Qu.: 56
## Max. :25.0 Max. :120Including Plots
You can also embed plots, for example:
Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.