optimization efficient frontier.Rmd

---
title: "A07_G46086231"
author: "Min Yang"
date: "10/17/2018"
output: html_document
---
##Generate data 
```{r}
## Quadratic programming using quadprog()
# Markowitz formulation
library(quadprog)
mu_return_vector <- c(0.05, 0.04, 0.06) 
sigma <- matrix(c(0.01, 0.002, 0.005, 
                  0.002, 0.008, 0.006, 
                  0.005, 0.006, 0.012), 
                nrow=3, ncol=3)
D.Matrix <- 2*sigma
d.Vector <- rep(0, 3)
A.Equality <- matrix(c(1,1,1), ncol=1)
A.Matrix <- cbind(A.Equality, mu_return_vector, 
                  diag(3))
#use for loop to generate expeted return with corresponding risk
returnval = matrix(ncol=1)
risk = matrix(ncol=1)
i=1
for (x in seq(0.035,0.06,0.001)){ 
b.Vector <- c(1, x, rep(0, 3))
out <- solve.QP(Dmat=D.Matrix, dvec=d.Vector, 
                Amat=A.Matrix, bvec=b.Vector, 
                meq=1)
returnval[i]=x
risk[i]=out$value
i=i+1
}
table(returnval)
table(risk)
```

###Plot using default plot method
```{r}
plot(risk,returnval, main="Efficient Frontier", xlab="Risk Appetite", ylab="Expected Return", type="l", col="red")
```

###Generate a data.frame for plotting using ggplot 
```{r}
library(ggplot2)
data <- cbind(returnval,risk)
data <-data.frame(data)
data
```

###using ggplot to plot the efficient frontier 
```{r}
g <- ggplot(data) + aes(x=risk,y=returnval)+labs(title="Efficient Frontier",x="Risk Appetite",y="Expected Return") + geom_line(data = data,col='red')
g
```