library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ ggplot2 3.3.5 ✓ purrr 0.3.4
## ✓ tibble 3.1.6 ✓ dplyr 1.0.7
## ✓ tidyr 1.1.4 ✓ stringr 1.4.0
## ✓ readr 2.1.0 ✓ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
library(ggplot2)
library(csv)
#compute covarience matrix include these steps
threests = read_csv('/Users/macbookair/Downloads/FamaFrench_mon_69_98_3stocks(1).csv')
## Rows: 360 Columns: 9
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (9): date, Mkt-RF, SMB, HML, RF, ge, ibm, mobil, CRSP
##
## 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.
glimpse(threests)
## Rows: 360
## Columns: 9
## $ date <dbl> 196901, 196902, 196903, 196904, 196905, 196906, 196907, 19690…
## $ `Mkt-RF` <dbl> -1.20, -5.82, 2.59, 1.52, 0.02, -7.25, -7.05, 4.65, -2.88, 4.…
## $ SMB <dbl> -0.80, -3.90, -0.28, -0.85, -0.27, -5.31, -3.27, 0.89, 1.20, …
## $ HML <dbl> 1.57, 0.93, -0.45, 0.06, 0.74, -1.15, 1.36, -3.83, -3.24, -3.…
## $ RF <dbl> 0.53, 0.46, 0.46, 0.53, 0.48, 0.51, 0.53, 0.50, 0.62, 0.60, 0…
## $ ge <dbl> -1.1984, -6.0377, 6.6474, 5.9621, -3.5806, -3.8196, -4.3056, …
## $ ibm <dbl> -5.9524, -0.7004, 7.0303, 4.4586, -2.5000, 5.8777, -3.9230, 6…
## $ mobil <dbl> -1.4043, -7.8431, 21.5130, 2.9961, 2.6667, -12.9870, -6.0981,…
## $ CRSP <dbl> -0.6714, -5.3641, 3.0505, 2.0528, 0.5038, -6.7388, -6.5173, 5…
#use single index model to compute covarience matrix
#using "lm" function
colnames(threests)[2]<- 'Mkt_RF'
stockss<-threests %>% select(c(2,6,7,8))/100
glimpse(stockss)
## Rows: 360
## Columns: 4
## $ Mkt_RF <dbl> -0.0120, -0.0582, 0.0259, 0.0152, 0.0002, -0.0725, -0.0705, 0.0…
## $ ge <dbl> -0.011984, -0.060377, 0.066474, 0.059621, -0.035806, -0.038196,…
## $ ibm <dbl> -0.059524, -0.007004, 0.070303, 0.044586, -0.025000, 0.058777, …
## $ mobil <dbl> -0.014043, -0.078431, 0.215130, 0.029961, 0.026667, -0.129870, …
N <- dim(stockss)[1]
Mkt.RF<-threests %>% select(2)/100
fit = lm(formula = cbind(ge,ibm,mobil)~Mkt_RF, data = stockss)
sigF = as.numeric(var(Mkt.RF))
b_beta = as.matrix(fit$coefficients)
b_beta = as.matrix(b_beta[-1,])
b_beta
## [,1]
## ge 1.0580825
## ibm 0.8149949
## mobil 0.8158072
signi.eps = crossprod(fit$residuals)/(N-2)
signi.eps = diag(diag(signi.eps))
signi.eps
## [,1] [,2] [,3]
## [1,] 0.001702494 0.000000000 0.000000000
## [2,] 0.000000000 0.003225874 0.000000000
## [3,] 0.000000000 0.000000000 0.002913458
#covarience matrix
covarience_matr = sigF*b_beta%*%t(b_beta)+signi.eps
covarience_matr
## ge ibm mobil
## ge 0.004070402 0.001823896 0.001825714
## ibm 0.001823896 0.004630742 0.001406268
## mobil 0.001825714 0.001406268 0.004321127