```
setwd("C:/Users/admin/Desktop/Data Analytics/QuantitativeFinance/QFLabs")
getwd()
##baseData <- read.csv("US5.csv")
baseData <- read.csv("India5.csv")
N0 <- ncol(baseData)
Close <- baseData[, 3:N0]
logRet <- log(head(Close, -1) / tail(Close, -1))
Retn <- colMeans(logRet)
Risk <- diag(var(logRet))
RiskReturn <- as.data.frame(t(rbind(Retn,Risk)))
library(ggplot2)
plot1 <- ggplot(data = RiskReturn,aes(x = Risk, y = Retn) )
plot1 <- plot1 + geom_point()
plot1 <- plot1 + xlab("Risk / Variance") + ylab("Daily Returns") + ggtitle("Risk/Returns")
plot1
# using portfolio.optim
library(tseries)
w0 <- portfolio.optim(as.matrix(logRet),pm = 0.005,shorts = TRUE,riskless= FALSE)
w0$pw
sum(w0$pw)
# understanding the code
library(quadprog)
# the basic function that calculates the min variance portfolio with NO SHORTS
rOptPort10 <- function(hRets,pRet){
Dmat <- 2*cov(hRets)
dvec <- rep(0,ncol(hRets))
Amat <- cbind(rep(1,ncol(hRets)),colMeans(hRets))
bvec <- c(1,pRet)
result <- solve.QP(Dmat = Dmat, dvec = dvec, Amat = Amat, bvec = bvec, meq =2)
wP <- result$solution
varP <- result$value
retList <- list(wP,varP)
names(retList) <- c("wP","varP")
return(retList)
}
# testing out the function with expected return
z <- rOptPort10(logRet,0.005)
z$wP
z$varP
sum(z$wP)
# here we create the Efficient Frontier for a given range of returns
EFMinVar10 <- function(hRets, minRet, maxRet){
smuP <- seq(minRet,maxRet,length=50)
svarP <- sapply(smuP,function(x) rOptPort10(hRets,x)$varP)
EffF <- as.data.frame(cbind(smuP,svarP))
minVar <- min(EffF$svarP)
L <- EffF$svarP == minVar
minRet <- EffF[L,]$smuP
minPoint <- as.data.frame(cbind(minRet,minVar))
minVarwP <- rOptPort10(hRets,minRet)$wP
rList <-list(EffF,minPoint,minVarwP)
names(rList) <- c("EFF","minPoint","wP")
return(rList)
}
# We use the above function to get the points of the Efficient Frontier
# and numerically detect the point of minimum variance
z10 <- EFMinVar10(logRet,-0.005,.005)
z10$wp
cminRet <- (z10$minPoint)$minRet
z11 <- rOptPort10(logRet,cminRet)
z11$wP
# This function plots the Efficient Frontier and showing the point of minimum variance
EFMinVar10Plot <- function(list1){
plot2 <- ggplot(data = list1$EFF,aes(x = svarP, y = smuP) )
plot2 <- plot2 + geom_point()
plot2 <- plot2 + geom_point(data = list1$minPoint, aes(x = minVar,y = minRet),color = "red", size=3)
plot2 <- plot2 + xlab("Variance") + ylab("Returns") + ggtitle("Efficient Frontier - MinVar")
plot2
}
EFMinVar10Plot(z10)
cminRet <- (z10$minPoint)$minRet
z10a <- EFMinVar10(logRet,min(0,cminRet),0.001)
EFMinVar10Plot(z10a)
# This function calculates the Max Sharpe Ratio
# and the Tangency Portfolio weights
EFSharpe10 <- function(hRets, minRet, maxRet,RF){
smuP <- seq(minRet,maxRet,length=50)
svarP <- sapply(smuP,function(x) rOptPort10(hRets,x)$varP)
sharpe <- (smuP-RF)/svarP
EFF <- as.data.frame(cbind(smuP,svarP,sharpe,RF))
L <- EFF$sharpe == max(EFF$sharpe)
maxSharpe <- EFF[L,]
wTP <- rOptPort10(hRets,maxSharpe$smuP)$wP
rList <-list(EFF,maxSharpe,wTP)
names(rList) <- c("EFF","maxSharpe","wTP")
return(rList)
}
z11 <- EFSharpe10(logRet,min(0,cminRet),0.001,0.0001)
z11$wTP
sum(z11$wTP)
(z11$maxSharpe)$smuP
(z11$maxSharpe)$svarP
maxSharpeRet <- (z11$maxSharpe)$smuP
# This function plots the Efficient Fronter and shows
# The Tangency Point and the Capital Market Line
EFSharpe10Plot <- function(list1){
plot2 <- ggplot(data = list1$EFF,aes(x = svarP, y = smuP) )
plot2 <- plot2 + geom_point()
plot2 <- plot2 + geom_point(data = list1$maxSharpe, aes(x = svarP,y = smuP),colour = "red", pch =24, size=3)
plot2 <- plot2 + geom_point(data = list1$maxSharpe, aes(x = 0,y = RF),color = "red", pch =24, size=3)
plot2 <- plot2 + xlab("Variance") + ylab("Returns") + ggtitle("Efficient Frontier - Sharpe")
plot2 <- plot2 + geom_abline(intercept = (list1$maxSharpe)$RF, slope = (list1$maxSharpe)$sharpe, colour = "red")
plot2
}
EFSharpe10Plot(z11)
```

DONT PANIC ! This 20 minute video will explain what this code is doing

What does negative weights mean ? It means short selling. So what is short selling ? Let us explain.

If you have a Rs 100 you can invest Rs 80 in Stock A and Rs 20 in Stock B and so the weights are (0.8, 0.2). Note that the weights add up to 1.

But through a process known as short selling, you could sell Rs 80 worth of Stock B [ that you do not have, at the moment ] get Rs 80. To this you add the Rs 100 that you have and invest Rs 180 [ Rs 100 + Rs 80 ] in Stock A. In this case your weights are (180,-80) or (1.8 and -0.8) and you would note that weights add up to 1 again.

Why would you do short selling ? There are many reasons. For example, you may believe that Stock A will give you very high returns. Also if you sell "short", that is sell shares that you do not have, you will have to, at some point in future, or in the next "period" buy the shares from the market and deliver it to the person to whom you had sold the shares.

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