Q1

getSymbols(c("^GSPC", "PEP", "WY", "RSG", "CPRT", "PNR", "ENPH"), from="2000-01-01", periodicity="monthly")

## [1] "^GSPC" "PEP"   "WY"    "RSG"   "CPRT"  "PNR"   "ENPH"

mydata <- merge(Ad(GSPC), Ad(PEP), Ad(WY), Ad(RSG), Ad(CPRT), Ad(PNR))
myret <- 100 * diff(log(mydata))
names(myret) <- c( "GSPC", "PEP", "WY", "RSG", "CPRT", "PNR")
head(myret)

##                 GSPC       PEP         WY       RSG       CPRT       PNR
## 2000-01-01        NA        NA         NA        NA         NA        NA
## 2000-02-01 -2.031300 -6.039582 -10.892102 -8.894793  21.279611  4.081527
## 2000-03-01  9.232375  8.213574  10.511658  1.729208 -18.380834  7.527632
## 2000-04-01 -3.127991  5.508394  -6.570839 22.428543  -1.438885  3.153748
## 2000-05-01 -2.215875 10.348449  -7.284755 18.687775   2.857326  3.830267
## 2000-06-01  2.365163  8.816309 -14.032085 -3.664868 -10.379656 -9.997904

tail(myret)

##                  GSPC        PEP         WY       RSG        CPRT         PNR
## 2021-11-01 -0.8368626 -1.1326297  6.5635962 -1.753783  -6.7457682  -0.1072847
## 2021-12-01  4.2688648  8.3589387  9.0682607  5.293646   4.3540748  -0.8996837
## 2022-01-01 -5.4018230  0.5640306 -1.3853892 -8.501069 -15.9628844 -13.6685707
## 2022-02-01 -3.1862761 -5.8013054 -3.9092059 -5.954813  -5.0540268  -9.2122076
## 2022-03-01  3.5148286  2.1986844  0.9724619  9.676030   2.0858449  -6.6024706
## 2022-04-01 -0.6688424  3.6975969  0.4568546  2.418510  -0.4713442  -1.8431090

Q2

M<-cor(myret, use='complete.obs')
corrplot(M, method="number")

Discussion-> Correlation

• All the stock returns move in the same direction as the market but at varying strengths: as the market returns increases and decreases, the stock returns for the five companies increase and decrease in the same direction.
  • The “RSG” (waste disposal company) returns has the smallest positive correlation coefficient to the market returns
  • On the other hand, the “PNR” (water treatment company) returns is the most strongly correlated with the market

Q3

myret.df<-data.frame(Date=time(myret), coredata(myret))
longdf<- myret.df %>% tidyr::gather(stocks, returns,-Date,-GSPC)
ggplot(longdf, aes(GSPC, returns))+geom_point()+geom_smooth(method="lm",se=FALSE)+facet_wrap(vars(stocks))+theme_grey()

## Warning: Removed 5 rows containing non-finite values (stat_smooth).

## Warning: Removed 5 rows containing missing values (geom_point).

Q4

fit<-list()
fit$PEP<-lm(PEP~GSPC, myret)
fit$WY<-lm(WY~GSPC, myret)
fit$RSG<-lm(RSG~GSPC, myret)
fit$CPRT<-lm(CPRT~GSPC, myret)
fit$PNR<-lm(PNR~GSPC, myret)
names<-c("PEP","WY","RSG","CPRT","PNR")
reg.df<-data.frame(stock=names, beta= sapply(fit, function(x) beta = coeftest(x)[2]),
           R2=sapply(fit, function(x) R2 = summary(x)$r.squared))
print(reg.df)

##      stock      beta        R2
## PEP    PEP 0.5034126 0.2300881
## WY      WY 1.2846893 0.3172091
## RSG    RSG 0.6380280 0.1883881
## CPRT  CPRT 0.9435716 0.2008048
## PNR    PNR 1.0788246 0.3387038

knitr::kable(as.data.frame(reg.df), digits=3)

Discussion: Stock Regression

• All the stocks are affected by the S&P500’s movements since their beta is high, however there are other ommitted variables that explain the variance in their average returns since the S&P500’s R squared for them is low:
  • The regression is subject to ommitted variable bias thus, when more regressors are added, the stocks exposure to the S&P500 should reduce.
  • Due to their high beta, they’re very volatile thus allowing for high monthly average returns

Q5

p1<-ggplot(reg.df, aes(stock, beta)) +
geom_bar(stat="Identity", fill="#F9C8B0", color="darkorange4") +
geom_line(aes(x=stock, y=R2, group=1), data=reg.df, color="blue2", size=1.5) +
theme_grey() + geom_hline(yintercept = 1, color="black", linetype="dashed")+
labs(x="stock", y="beta", title="Beta and R square") +
theme(axis.text.x = element_text(angle = 90))
p<-ggplotly(p1)

## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## Please use `gather()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.

p