Assignment 5 - Group B

setwd("C:/Users/Samantha/Desktop/Financial Econometrics")

Read files

library(readr)

package 㤼㸱readr㤼㸲 was built under R version 4.0.4

portfolios<-read_csv("C:/Users/Samantha/Desktop/Financial Econometrics/portfolios.CSV")

-- Column specification --------------------------------------------------------
cols(
  .default = col_double()
)
i Use `spec()` for the full column specifications.

famafrench<-read_csv("C:/Users/Samantha/Desktop/Financial Econometrics/famafrench.CSV")

-- Column specification --------------------------------------------------------
cols(
  YearMonth = col_double(),
  `Mkt-RF` = col_double(),
  SMB = col_double(),
  HML = col_double(),
  RF = col_double()
)

#Question 1: Drop columns we do not need

library (dplyr)

Attaching package: 㤼㸱dplyr㤼㸲

The following objects are masked from 㤼㸱package:stats㤼㸲:

    filter, lag

The following objects are masked from 㤼㸱package:base㤼㸲:

    intersect, setdiff, setequal, union

portfolios2<-select(portfolios,-"<= 0", -"Lo 30", -"Med 40", -"Hi 30", -"Lo 20", -"Qnt 2", -"Qnt 3", -"Qnt 4", -"Hi 20")

#Question 2: Combine tables using inner_join from dplyr in one table called factors

factors<-inner_join(portfolios2,famafrench,by="YearMonth")

#Question 3: Create the CAPM for the Lo 10 portfolio:

size.capm_Lo10 <- lm(factors$`Lo 10` ~ factors$`Mkt-RF`)
coef(size.capm_Lo10)

     (Intercept) factors$`Mkt-RF` 
       0.6254334        0.9996396 

summary(size.capm_Lo10)

Call:
lm(formula = factors$`Lo 10` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-16.9621  -2.7728  -0.2267   2.2589  26.6354 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.62543    0.23409   2.672  0.00788 ** 
factors$`Mkt-RF`  0.99964    0.05318  18.797  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.459 on 366 degrees of freedom
Multiple R-squared:  0.4912,    Adjusted R-squared:  0.4898 
F-statistic: 353.3 on 1 and 366 DF,  p-value: < 2.2e-16

#QUestion 4: Estimate the CAPM for all 10 portfolios and summarize the resulting β0for the intercept as well as the resulting β1 for the MKT indicator. Make a similar summary for the goodness-of-fit of these 10 regression models. We run the regressions for the other remaining 9 portfolios.

Portfolio Dec 2

size.capm_Dec2<- lm(factors$`Dec 2` ~ factors$`Mkt-RF`)
coef(size.capm_Dec2)

     (Intercept) factors$`Mkt-RF` 
       0.5516835        1.1165239 

summary(size.capm_Dec2)

Call:
lm(formula = factors$`Dec 2` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-17.3812  -3.0229  -0.3127   2.3158  22.7726 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.55168    0.23100   2.388   0.0174 *  
factors$`Mkt-RF`  1.11652    0.05248  21.276   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.4 on 366 degrees of freedom
Multiple R-squared:  0.5529,    Adjusted R-squared:  0.5517 
F-statistic: 452.7 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 3

size.capm_Dec3<- lm(factors$`Dec 3` ~ factors$`Mkt-RF`)
coef(size.capm_Dec3)

     (Intercept) factors$`Mkt-RF` 
       0.5560827        1.0988465 

summary(size.capm_Dec3)

Call:
lm(formula = factors$`Dec 3` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-16.6203  -2.5112  -0.0512   2.2058  15.2685 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.5561     0.1963   2.832  0.00488 ** 
factors$`Mkt-RF`   1.0989     0.0446  24.635  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.74 on 366 degrees of freedom
Multiple R-squared:  0.6238,    Adjusted R-squared:  0.6228 
F-statistic: 606.9 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 4

size.capm_Dec4<- lm(factors$`Dec 4` ~ factors$`Mkt-RF`)
coef(size.capm_Dec4)

     (Intercept) factors$`Mkt-RF` 
        0.482102         1.071077 

summary(size.capm_Dec4)

Call:
lm(formula = factors$`Dec 4` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-16.1767  -2.2133  -0.0375   2.0520  14.4658 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.48210    0.18221   2.646   0.0085 ** 
factors$`Mkt-RF`  1.07108    0.04139  25.875   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.471 on 366 degrees of freedom
Multiple R-squared:  0.6466,    Adjusted R-squared:  0.6456 
F-statistic: 669.5 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 5

size.capm_Dec5<- lm(factors$`Dec 5` ~ factors$`Mkt-RF`)
coef(size.capm_Dec5)

     (Intercept) factors$`Mkt-RF` 
       0.5281752        1.0839636 

summary(size.capm_Dec5)

Call:
lm(formula = factors$`Dec 5` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-16.4432  -1.9591   0.0891   1.9299  12.7642 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.52818    0.16715    3.16  0.00171 ** 
factors$`Mkt-RF`  1.08396    0.03797   28.55  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.184 on 366 degrees of freedom
Multiple R-squared:  0.6901,    Adjusted R-squared:  0.6892 
F-statistic: 814.9 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 6

size.capm_Dec6<- lm(factors$`Dec 6` ~ factors$`Mkt-RF`)
coef(size.capm_Dec6)

     (Intercept) factors$`Mkt-RF` 
       0.5561633        1.0168632 

summary(size.capm_Dec6)

Call:
lm(formula = factors$`Dec 6` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-13.7738  -1.7044  -0.0535   1.5698  12.1766 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.55616    0.14492   3.838 0.000146 ***
factors$`Mkt-RF`  1.01686    0.03292  30.887  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.76 on 366 degrees of freedom
Multiple R-squared:  0.7227,    Adjusted R-squared:  0.722 
F-statistic:   954 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 7

size.capm_Dec7<- lm(factors$`Dec 7` ~ factors$`Mkt-RF`)
coef(size.capm_Dec7)

     (Intercept) factors$`Mkt-RF` 
       0.5726343        1.0209530 

summary(size.capm_Dec7)

Call:
lm(formula = factors$`Dec 7` ~ factors$`Mkt-RF`)

Residuals:
    Min      1Q  Median      3Q     Max 
-13.129  -1.349  -0.131   1.239  11.215 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.57263    0.13086   4.376 1.58e-05 ***
factors$`Mkt-RF`  1.02095    0.02973  34.344  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.492 on 366 degrees of freedom
Multiple R-squared:  0.7632,    Adjusted R-squared:  0.7625 
F-statistic:  1180 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 8

size.capm_Dec8<- lm(factors$`Dec 8` ~ factors$`Mkt-RF`)
coef(size.capm_Dec8)

     (Intercept) factors$`Mkt-RF` 
       0.5689677        1.0051850 

summary(size.capm_Dec8)

Call:
lm(formula = factors$`Dec 8` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.8374  -1.2526   0.0201   1.1779  12.7003 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.5690     0.1255   4.535 7.83e-06 ***
factors$`Mkt-RF`   1.0052     0.0285  35.266  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.39 on 366 degrees of freedom
Multiple R-squared:  0.7726,    Adjusted R-squared:  0.772 
F-statistic:  1244 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Dec 9

size.capm_Dec9<- lm(factors$`Dec 9` ~ factors$`Mkt-RF`)
coef(size.capm_Dec9)

     (Intercept) factors$`Mkt-RF` 
       0.5635456        0.9190272 

summary(size.capm_Dec9)

Call:
lm(formula = factors$`Dec 9` ~ factors$`Mkt-RF`)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.5165  -1.1190  -0.0242   1.0569  12.5852 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.56355    0.10964    5.14 4.48e-07 ***
factors$`Mkt-RF`  0.91903    0.02491   36.90  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.088 on 366 degrees of freedom
Multiple R-squared:  0.7881,    Adjusted R-squared:  0.7876 
F-statistic:  1362 on 1 and 366 DF,  p-value: < 2.2e-16

Portfolio Hi 10

size.capm_Hi10<- lm(factors$`Hi 10` ~ factors$`Mkt-RF`)
coef(size.capm_Hi10)

     (Intercept) factors$`Mkt-RF` 
       0.4518659        0.8501523 

summary(size.capm_Hi10)

Call:
lm(formula = factors$`Hi 10` ~ factors$`Mkt-RF`)

Residuals:
    Min      1Q  Median      3Q     Max 
-7.8808 -1.0944 -0.0697  1.0180  8.3507 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       0.45187    0.10270    4.40 1.42e-05 ***
factors$`Mkt-RF`  0.85015    0.02333   36.44  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.956 on 366 degrees of freedom
Multiple R-squared:  0.7839,    Adjusted R-squared:  0.7833 
F-statistic:  1328 on 1 and 366 DF,  p-value: < 2.2e-16