#########################################################
#===> ((((( Trace out the efficient frontier )))))  <===#
#===> main functions <===#
#########################################################
#===> obtain a lot of tickers via included data set <===#
library(stockPortfolio)

#DATA:
ticker <-  c("C", "KEY", "WFC", "JPM",  "SO", "DUK",  "D", "HE",  "EIX",   "LUV", "AMGN",  "GILD", "CELG", "BIIB",  "CAT", "DE", "IMO", "MRO", "HES", "YPF", "^GSPC")

#===> get data <===#
gr1 <- getReturns(ticker, start='1999-12-31', end='2004-12-31')


#Single index model:
#Short sales allowed, default Rf=0.
sm1SIM  <- stockModel(gr1, model='SIM', index=21)
 # defaults:
 #    Rf = 0
 #    shortSelling = TRUE


ops1  <- optimalPort(sm1SIM)
plot(ops1)
portPossCurve(sm1SIM, add=TRUE, riskRange=5)

#Generate many values of RF:
Rfr <- seq(-5,.01,0.0005)

#Initialize the two vectors:
rbar_opt <- rep(0,length(Rfr))
risk_opt <- rep(0,length(Rfr))

#Use the single index model to find many points of tangency (one for each #value of Rf:
for(i in 1:length(Rfr)){
simn <- stockModel(gr1, model='SIM', index=21, Rf=Rfr[i], shortSelling=FALSE)
opsimn <- optimalPort(simn)
rbar_opt[i] <- opsimn$R
risk_opt[i] <- opsimn$risk
}


#Identify the efficient frontier when short sales not allowed:
points(risk_opt,rbar_opt,type="l" )

#Add the minimum risk portfolio when short sales are not allowed (this is #an approximation - but a good one!):
smnSIM_mvp <- stockModel(gr1, model='SIM', index=21, Rf=-100, shortSelling=FALSE)

opnSIM_mvp <- optimalPort(smnSIM_mvp)

points(opnSIM_mvp, optPortOnly=TRUE, colOP='#888888', cex=2)


#View only the efficient frontier when short sales are not allowed:
plot(risk_opt,rbar_opt,type="l" )

points(opnSIM_mvp, optPortOnly=TRUE, colOP='#888888', cex=2)