# Regression - Single Factor Model Estimation of Beta, CAPM Estimation of Jensen's Alpha

#Import processed indices dataset# —> students should change the import path according to their desktop(or save CAPM text file to downloads)
library(readr)
CAPM <- read_delim("Downloads/CAPM.txt", 
                   "\t", escape_double = FALSE, trim_ws = TRUE)

View(CAPM)

#Install and load required packages#
install.packages("fBasics")
library(fBasics)

#Verify first few lines of dataset (Optional)#
da <- CAPM
head(da)


#Summarise statistics#
cols <- c("RtnInf","RtnSp500","Tb10y","InfrMTb10","Sp500MTb10")
basicStats(da[cols]) #Reference --> Tsay, 2014.  


#Run single factor model to estimate beta#
summary(lm(da$RtnInf~da$RtnSp500))
summary(aov(da$RtnInf~da$RtnSp500)) 

#Show the fitted line using scatter plot#
plot(da$RtnSp500, da$RtnInf, pch = 19, xlab = "Log Return on S&P 500 (RtnSp500)", ylab = "Log Return on Infrastructure Index(RtnInf)", col = "cadetblue3")
abline(lm(da$RtnInf~da$RtnSp500), col = "deepskyblue4")
legend("bottomright",legend = c("RtnInf","Fitted values"), pch = c(19,NA), lty = c(NA,1), col = c("cadetblue3","deepskyblue4"), cex = 0.75)


#Use CAPM to estimate Jensen's alpha --> Ri-Rf = alpha + Beta (ERP) + u#
summary(lm(da$InfrMTb10~da$Sp500MTb10))
summary(aov(da$InfrMTb10~da$Sp500MTb10))

#Show the fitted line using scatter plot#
plot(da$Sp500MTb10, da$InfrMTb10, pch = 19, xlab = "Sp500MTb10", ylab = "InfrMTb10", col = "cadetblue3")
abline(lm(da$InfrMTb10~da$Sp500MTb10), col = "deepskyblue4")
legend("bottomright",legend = c("InfrMTb10","Fitted values"), pch = c(19,NA), lty = c(NA,1), col = c("cadetblue3","deepskyblue4"), cex = 0.5)