PORTFOLIO ANALYSIS:  INPUT MEANS, VARIANCES, COVARIANCE
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#Mean, variances, and covariances:

r1_bar <- 0.01
r2_bar <- 0.013
var1 <- 0.0061
var2 <- 0.0046
cov_12 <- 0.00062
 

#Short sales NOT allowed:
a <- seq(0,1, 0.01)
b <- 1-a
cbind(a,b)

rp_bar_ns <- a*r1_bar+b*r2_bar
var_p_ns <- a^2*var1+b^2*var2+2*a*b*cov_12
sd_p_ns <- var_p_ns^0.5


#Short sales allowed:
a1 <- seq(-2,2, 0.01)
b1 <- 1-a1

cbind(a1,b1)

rp_bar_s <- a1*r1_bar+b1*r2_bar
var_p_s <- a1^2*var1+b1^2*var2+2*a1*b1*cov_12
sd_p_s <- var_p_s^0.5
 
#Plot the two portfolios possibilities curves:
#Green:  Short sales allowed.
#Blue:  Short sales not allowed.
plot(sd_p_s, rp_bar_s, col="green")
points(sd_p_ns, rp_bar_ns, col="blue")
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PORTFOLIO ANALYSIS:  READ .csv FILES
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#Read the two files:
a1 <- read.table("table_1.csv", header=T, sep=",")
a2 <- read.table("table_2.csv", header=T, sep=",")

#Or access from the course website:
a1 <- read.table("http://www.stat.ucla.edu/~nchristo/statistics_c183_c283/
      table_1.csv", header=TRUE, sep=",")

a2 <- read.table("http://www.stat.ucla.edu/~nchristo/statistics_c183_c283/
      table_2.csv", header=TRUE, sep=",")


#Select only the close prices from each file:
prices <- as.data.frame(cbind(a1$Close, a2$Close))

class(prices)

#You can rename the Close prices as follows:
names(prices) <-c("p1", "p2")

#You can see your data:
prices$p1
prices$p2

#Convert the close prices into returns:
r1 <- (prices$p1[-length(prices$p1)]-prices$p1[-1])/prices$p1[-1]
r2 <- (prices$p2[-length(prices$p2)]-prices$p2[-1])/prices$p2[-1]

#Place the returns together in a data frame:
returns <- as.data.frame(cbind(r1,r2))

#Construct a histogram of the returns:
hist(r1)
hist(r2)

#The following 5 lines will save the histograms in a pdf file on your 
#current working directory: 
pdf("hist_r1_r2.pdf", h=3.0)
par(mfrow=c(1,2))
hist(r1, main="Histogram 1", xlab="Stock1")
hist(r2, main="Histogram2", xlab="Stock2")
dev.off()


#Get summary statistics of the returns:
summary(returns)

#Get the mean returns:
mean(returns)

#Get the variance covariance matrix of the returns:
cov(returns)

#Create many portfolios (combinations of the two stocks):
a <- seq(0,1,.01)
b <- seq(1,0,-.01)
#Or simply
b <- 1-a

#Compute the expected return of each portfolio:
rp_bar <- a*mean(returns$r1)+b*mean(returns$r2)

#Compute the variance and standard deviation of each portfolio:
var_p <- a^2*var(returns$r1)+b^2*var(returns$r2)+
         2*a*b*cov(returns$r1,returns$r2)

sd_p <- var_p^.5

#Create a data frame of the standard deviation and expected return of 
#each portfolio:
qq <- as.data.frame(cbind(sd_p, rp_bar))

#Plot the portfolio possibilities curve:
plot(sd_p, rp_bar, xlab="Portfolio risk (standard deviation)", 
     ylab="Expected return")

#You can get the same plot by simply doing this:
plot(qq, xlab="Portfolio risk (standard deviation)", 
     ylab="Expected return")

#If you want a line instead of points:
plot(qq, xlab="Portfolio risk (standard deviation)", 
     ylab="Expected return", type="l")

#Find the composition of the minimum risk portfolio:
x1 <- (var(returns$r2)-cov(returns$r1,returns$r2))/
      (var(returns$r1)+var(returns$r2)-2*cov(returns$r1,returns$r2))
x2 <- 1-x1

#Compute the expected return and standard deviation of the minimum risk 
#portfolio:
rp_bar_min <- x1*mean(returns$r1)+x2*mean(returns$r2)

sd_p_min <- (x1^2*var(returns$r1)+x2^2*var(returns$r2)+
             2*x1*x2*cov(returns$r1,returns$r2))^0.5

#Add the minimum risk portfolio on the previous plot:
points(sd_p_min, rp_bar_min, col="green", pch=19)


#Identify the efficient frontier.
#First find the portfolios that have expected return above the expected return 
#of the minimum risk portfolio:
qqq <- qq[qq$rp_bar > rp_bar_min, ]

#And then draw the efficient frontier:
points(qqq, col="blue", type="l", lwd=5)

#Save the graph in a pdf file:
pdf("portfolio_curve_s10.pdf")
plot(qq, xlab="Portfolio risk (standard deviation)", 
     ylab="Portfolio expected return", type="l")
points(sd_p_min,rp_bar_min, col="green", pch=19)
points(qqq, col="blue", type="l", lwd=5)
dev.off()