HW3

R 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:

Including Plots

You can also embed plots, for example:

library(tidyverse)

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──

## ✓ ggplot2 3.3.5     ✓ purrr   0.3.4
## ✓ tibble  3.1.6     ✓ dplyr   1.0.8
## ✓ tidyr   1.2.0     ✓ stringr 1.4.0
## ✓ readr   2.1.2     ✓ forcats 0.5.1

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

retdata <- read_csv("FamaFrench_mon_69_98_3stocks(1) (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(retdata)

## 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…

colnames(retdata)[2]<- 'Mkt_RF'
stock.rets<-retdata %>% select(c(2,6,7,8))/100
glimpse(stock.rets)

## 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(stock.rets)[1]
Mkt.RF<-retdata %>% select(2)/100
fit = lm(formula = cbind(ge,ibm,mobil)~Mkt_RF, data = stock.rets)
sigF = as.numeric(var(Mkt.RF))
bbeta = as.matrix(fit$coefficients)
bbeta = as.matrix(bbeta[-1,])
bbeta

##            [,1]
## ge    1.0580825
## ibm   0.8149949
## mobil 0.8158072

sigeps = crossprod(fit$residuals)/(N-2)
sigeps = diag(diag(sigeps))
sigeps

##             [,1]        [,2]        [,3]
## [1,] 0.001702494 0.000000000 0.000000000
## [2,] 0.000000000 0.003225874 0.000000000
## [3,] 0.000000000 0.000000000 0.002913458

cov_1f = sigF*bbeta%*%t(bbeta)+sigeps
cov_1f

##                ge         ibm       mobil
## ge    0.004070402 0.001823896 0.001825714
## ibm   0.001823896 0.004630742 0.001406268
## mobil 0.001825714 0.001406268 0.004321127

stock.rets<-retdata %>% select(c(2,3,4,6,7,8))/100
fit3 = lm(formula = cbind(ge, ibm, mobil)~Mkt_RF + SMB + HML, data=stock.rets)
sigF3 = as.matrix(var(cbind(stock.rets$Mkt_RF,
                            stock.rets$SMB,
                            stock.rets$HML)))
bbeta3 = as.matrix(fit3$coefficients)
bbeta3 = bbeta3[-1,]
bbeta3

##                  ge        ibm      mobil
## Mkt_RF  1.134331448  0.8050676  0.9803403
## SMB    -0.369412445 -0.3099907 -0.3727822
## HML     0.009630701 -0.2981744  0.3726475

sigeps3 = crossprod(fit3$residuals)/(N-4)
sigeps3 = diag(diag(sigeps3))
cov_3f = t(bbeta3) * sigF3 * (bbeta3) + sigeps3
cov_3f

##              Mkt_RF           SMB           HML
## ge     4.332517e-03 -1.258773e-04 -4.819330e-06
## ibm   -1.258773e-04  3.199233e-03 -1.196042e-05
## mobil -4.819330e-06 -1.196042e-05  2.841930e-03

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.