sp500 <- GetSP500Stocks()
sp500tickers <- sp500[,c(1,2,4)]
#We select 5 Leading Tech Hardware Stocks and download the price data for those
stocks1 <- c("amc.ax","cba.ax","col.ax","csl.ax","gmg.ax","ltr.ax","wbc.ax","wes.ax")
prices1 <- getSymbols(stocks1[1], source="yahoo", auto.assign=FALSE,
return.class="xts")[,6]
for (i in 2:length(stocks1)){
prices.tmp <- getSymbols(stocks1[i], source="yahoo", auto.assign=FALSE,
return.class="xts")[,6]
prices1 <- cbind(prices1, prices.tmp)
}
## Warning: ltr.ax contains missing values. Some functions will not work if objects
## contain missing values in the middle of the series. Consider using na.omit(),
## na.approx(), na.fill(), etc to remove or replace them.
colnames(prices1) <- c("amc.ax","cba.ax","col.ax","csl.ax","gmg.ax","ltr.ax","wbc.ax","wes.ax")
plot(prices1$amc.ax)
plot(prices1$cba.ax)
plot(prices1$col.ax)
plot(prices1$csl.ax)
plot(prices1$gmg.ax)
plot(prices1$ltr.ax)
plot(prices1$wbc.ax)
plot(prices1$wes.ax)
#Since we will be working with returns, let us convert the price data to returns
Portfolio1 <- na.omit(diff(log(prices1)))
#Trimming the Data to get recent data post 12-31-2014
Portfolio1 <- Portfolio1["2015/"]
mean(Portfolio1$amc.ax)
## [1] 0.0005013187
var(Portfolio1$amc.ax)
## amc.ax
## amc.ax 0.000187823
mean(Portfolio1$cba.ax)|
var(Portfolio1$cba.ax)
## cba.ax
## cba.ax TRUE
mean(Portfolio1$col.ax)|
var(Portfolio1$col.ax)
## col.ax
## col.ax TRUE
mean(Portfolio1$csl.ax)|
var(Portfolio1$csl.ax)
## csl.ax
## csl.ax TRUE
mean(Portfolio1$gmg.ax)|
var(Portfolio1$gmg.ax)
## gmg.ax
## gmg.ax TRUE
mean(Portfolio1$ltr.ax)|
var(Portfolio1$ltr.ax)
## ltr.ax
## ltr.ax TRUE
mean(Portfolio1$cba.ax)|
var(Portfolio1$cba.ax)
## cba.ax
## cba.ax TRUE
mean(Portfolio1$wbc.ax)|
var(Portfolio1$wbc.ax)
## wbc.ax
## wbc.ax TRUE
mean(Portfolio1$wes.ax)|
var(Portfolio1$wes.ax)
## wes.ax
## wes.ax TRUE
means <- c(mean(Portfolio1$amc.ax),mean(Portfolio1$cba.ax),mean(Portfolio1$col.ax),mean(Portfolio1$csl.ax),mean(Portfolio1$gmg.ax),mean(Portfolio1$ltr.ax),mean(Portfolio1$cba.ax),mean(Portfolio1$wbc.ax),mean(Portfolio1$wes.ax))
vars <- c(var(Portfolio1$amc.ax),var(Portfolio1$cba.ax),var(Portfolio1$col.ax),var(Portfolio1$csl.ax),var(Portfolio1$gmg.ax),var(Portfolio1$ltr.ax),var(Portfolio1$cba.ax),var(Portfolio1$wbc.ax),var(Portfolio1$wes.ax))
Stockplot <- as.data.frame(t(cbind(vars, means)))
colnames(Stockplot)<- c("amc.ax", "cba.ax", "col.ax", "csl.ax", "gmg.ax", "ltr.ax", "cba.ax", "wbc.ax", "wes.ax")
Stockplot <- t(Stockplot)
plot(Stockplot, col = rainbow(5), pch= 15, xlab = "Variance", ylab = "Mean Returns", main = "Risk vs Return")
legend("bottomright", legend=c("amc.ax", "cba.ax", "col.ax", "csl.ax", "gmg.ax", "ltr.ax", "cba.ax", "wbc.ax", "wes.ax"),
col=rainbow(5), lty=1:2, cex=0.8, pch = 15)
#Convert the numeric vectors to timeseries vectors
Portfolio1 <- as.timeSeries(Portfolio1)
#Let us build portfolio using each of the stock combinations to obtain the minimum variance portfolio in each of the cases
#Set Specs
Spec = portfolioSpec()
setNFrontierPoints(Spec)<-100
#Portfolio 1 - Tech Stocks
##Determine the efficient frontier and plot the same
effFrontier1 <- portfolioFrontier(Portfolio1, Spec ,constraints = "LongOnly")
effFrontier1
##
## Title:
## MV Portfolio Frontier
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
## Portfolio Points: 5 of 99
##
## Portfolio Weights:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 1 0.0000 0.0000 0.0712 0.0000 0.0000 0.0000 0.9288 0.0000
## 25 0.3929 0.0000 0.3080 0.0708 0.0702 0.1238 0.0000 0.0343
## 50 0.2360 0.0000 0.2225 0.0566 0.0662 0.4188 0.0000 0.0000
## 74 0.0784 0.0000 0.1287 0.0333 0.0575 0.7021 0.0000 0.0000
## 99 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
##
## Covariance Risk Budgets:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 1 0.0000 0.0000 0.0193 0.0000 0.0000 0.0000 0.9807 0.0000
## 25 0.2785 0.0000 0.2182 0.0528 0.0581 0.3677 0.0000 0.0247
## 50 0.0322 0.0000 0.0302 0.0096 0.0161 0.9119 0.0000 0.0000
## 74 0.0031 0.0000 0.0051 0.0021 0.0064 0.9832 0.0000 0.0000
## 99 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 1 -0.0001 0.0174 0.0433 0.0230
## 25 0.0010 0.0123 0.0287 0.0190
## 50 0.0021 0.0250 0.0494 0.0359
## 74 0.0031 0.0400 0.0767 0.0560
## 99 0.0042 0.0562 0.1071 0.0774
##
## Description:
## Mon Jul 11 15:31:11 2022 by user:
plot(effFrontier1, c(1))
##Plot the weights for all the portfolio in the efficient frontier
frontierWeights1 <- getWeights(effFrontier1)
barplot(t(frontierWeights1), main="Frontier Weights", col=cm.colors(ncol(frontierWeights1)+2), legend=colnames(frontierWeights1))
##Obtain the weights for each stock for the portfolio with the least variance
mvp1 <- minvariancePortfolio(Portfolio1, spec=portfolioSpec(),constraints="LongOnly")
mvp1
##
## Title:
## MV Minimum Variance Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.4113 0.0000 0.3154 0.0586 0.0479 0.0135 0.0805 0.0727
##
## Covariance Risk Budgets:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.4113 0.0000 0.3154 0.0586 0.0479 0.0135 0.0805 0.0727
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0005 0.0106 0.0261 0.0156
##
## Description:
## Mon Jul 11 15:31:11 2022 by user:
##Obtain the weights for each stock for the tangency portfolio
tanPort1 <- tangencyPortfolio(Portfolio1, spec=portfolioSpec(), constraints="LongOnly")
tanPort1
##
## Title:
## MV Tangency Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.3335 0.0000 0.2806 0.0710 0.0716 0.2433 0.0000 0.0000
##
## Covariance Risk Budgets:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.1185 0.0000 0.0996 0.0282 0.0353 0.7185 0.0000 0.0000
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0014 0.0166 0.0359 0.0252
##
## Description:
## Mon Jul 11 15:31:11 2022 by user:
#Let us tabulate the weights for the two portfolios for comparison
minvarweights1 <- getWeights(mvp1)
tanportweights1 <- getWeights(tanPort1)
weights1 <- (cbind(minvarweights1, tanportweights1))
colnames(weights1) <- c("Minimum Variance Portfolio", "Tangency Portfolio")
Portfolio1 <- as.timeSeries(Portfolio1)
plot(Portfolio1)
mvp1 <- minvariancePortfolio(Portfolio1, spec=portfolioSpec(),constraints="LongOnly")
mvp1
##
## Title:
## MV Minimum Variance Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.4113 0.0000 0.3154 0.0586 0.0479 0.0135 0.0805 0.0727
##
## Covariance Risk Budgets:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.4113 0.0000 0.3154 0.0586 0.0479 0.0135 0.0805 0.0727
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0005 0.0106 0.0261 0.0156
##
## Description:
## Mon Jul 11 15:31:12 2022 by user:
tanPort1 <- tangencyPortfolio(Portfolio1, spec=portfolioSpec(), constraints="LongOnly")
tanPort1
##
## Title:
## MV Tangency Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.3335 0.0000 0.2806 0.0710 0.0716 0.2433 0.0000 0.0000
##
## Covariance Risk Budgets:
## amc.ax cba.ax col.ax csl.ax gmg.ax ltr.ax wbc.ax wes.ax
## 0.1185 0.0000 0.0996 0.0282 0.0353 0.7185 0.0000 0.0000
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0014 0.0166 0.0359 0.0252
##
## Description:
## Mon Jul 11 15:31:12 2022 by user:
minvarweights1 <- getWeights(mvp1)
tanportweights1 <- getWeights(tanPort1)
weights1 <- (cbind(minvarweights1, tanportweights1))
colnames(weights1) <- c("Minimum Variance Portfolio", "Tangency Portfolio")
weights1
## Minimum Variance Portfolio Tangency Portfolio
## amc.ax 0.41134109 0.33351819
## cba.ax 0.00000000 0.00000000
## col.ax 0.31539298 0.28059092
## csl.ax 0.05863499 0.07098561
## gmg.ax 0.04794209 0.07162252
## ltr.ax 0.01348886 0.24328276
## wbc.ax 0.08047864 0.00000000
## wes.ax 0.07272135 0.00000000
weights1 <- data.frame(minvarweights1)
assets <- colnames(frontierWeights1)
ggplot(data=weights1, aes(x=assets, y=minvarweights1, fill=assets)) +
geom_bar(stat="identity", position=position_dodge(),colour="black") +
geom_text(aes(label=sprintf("%.02f %%",minvarweights1*100)),
position=position_dodge(width=0.9), vjust=-0.25, check_overlap = TRUE) +
ggtitle("Minimum Variance Portfolio Optimal Weights")+ theme(plot.title = element_text(hjust = 0.5)) +
labs(x= "Assets", y = "Weight (%)")
tanwt1 <- data.frame(tanportweights1)
assets <- colnames(frontierWeights1)
ggplot(data=tanwt1, aes(x=assets, y=tanportweights1, fill=assets)) +
geom_bar(stat="identity", position=position_dodge(),colour="black") +
geom_text(aes(label=sprintf("%.02f %%",tanportweights1*100)),
position=position_dodge(width=0.9), vjust=-0.25, check_overlap = TRUE) +
ggtitle("Tangency Portfolio Optimal Weights")+ theme(plot.title = element_text(hjust = 0.5)) +
labs(x= "Assets", y = "Weight (%)")
