library(xts) library(PerformanceAnalytics) library(tseries) download.file("http://assets.datacamp.com/course/portfolio-analysis/prices.rds", destfile="prices.rds") # load("prices.Rdata") prices<- readRDS("prices.rds") returns <- Return.calculate(prices, method="simple") returns <- returns[(-1),] stockmu <- apply( X = returns , MARGIN = 2 , FUN="mean") stocksd <- apply( X = returns , MARGIN = 2 , FUN="sd") grid <- seq(min(stockmu),max(stockmu),length.out=50 ) # Compute the efficient frontier ## for each solution, we save the portfolio mean, ## portfolio standard deviation and the weights ## Initialize them as an empty vector vpm = vpsd = mweights = c() for( mutarget in grid ){ out <- try(portfolio.optim(x = returns,pm=mutarget, reshigh = rep(1,ncol(returns)) ),silent=TRUE) if(class(out)!="try-error"){ vpm <- c(vpm,out$pm) vpsd <- c(vpsd,out$ps) mweights <- rbind( mweights,out$pw) } } # assign the stock names to the column names of mweights colnames(mweights) <- colnames(returns) ################################################################################## # To avoid the concentration, we will impose now a max weight constraint of 30% # Compute the efficient frontier ## for each solution, we save the portfolio mean, ## portfolio standard deviation and the weights ## Initialize them as an empty vector vpm.res2 = vpsd.res2 = mweights.res2 <- c() for( mutarget in grid ){ out <- try(portfolio.optim(x = returns,pm=mutarget, reshigh = rep(0.1,ncol(returns))),silent=TRUE) if(class(out)!="try-error"){ vpm.res2 <- c(vpm.res2,out$pm) vpsd.res2 <- c(vpsd.res2,out$ps) mweights.res2 <- rbind( mweights.res2,out$pw) } } # assign the stock names to the column names of mweights colnames(mweights.res2) <- colnames(returns) ################################################################################## # To avoid the concentration, we will impose now a max weight constraint of 5% # Compute the efficient frontier ## for each solution, we save the portfolio mean, ## portfolio standard deviation and the weights ## Initialize them as an empty vector vpm.res = vpsd.res = mweights.res <- c() for( mutarget in grid ){ out = try(portfolio.optim(x = returns,pm=mutarget, reshigh = rep(0.05,ncol(returns))),silent=TRUE) if(class(out)!="try-error"){ vpm.res <- c(vpm.res,out$pm) vpsd.res <- c(vpsd.res,out$ps) mweights.res <- rbind( mweights.res,out$pw) } } # assign the stock names to the column names of mweights colnames(mweights.res) = colnames(returns) # plot(stocksd,stockmu,col="gray" , xlab="(monthly) Volatility" , ylab="(monthly) average returns", xlim=c(0.02,0.15), ylim=c(min(stockmu),max(stockmu))) text( stocksd , stockmu , labels=colnames(returns), cex= 0.7) # all portfolios offering less return than the minimum variance portfolio should be excluded minvarpm <- vpm[vpsd==min(vpsd)] minvarpm.res <- vpm.res[vpsd.res==min(vpsd.res)] minvarpm.res2 <- vpm.res2[vpsd.res2==min(vpsd.res2)] lines(vpsd,vpm,col="black",lwd=1,lty=3) lines(vpsd.res2,vpm.res2,col="red",lwd=1,lty=3) lines(vpsd.res,vpm.res,col="blue",lwd=1,lty=3) lines(vpsd[vpm>=minvarpm],vpm[vpm>=minvarpm],col="black",lwd=2) lines(vpsd.res2[vpm.res2>=minvarpm.res2],vpm.res2[vpm.res2>=minvarpm.res2],col="red",lwd=2) lines(vpsd.res[vpm.res>=minvarpm.res],vpm.res[vpm.res>=minvarpm.res],col="blue",lwd=2)

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