#install.packages(c("readxl", "quadprog"))
source("portfolio.R")
library("quadprog")
library("readxl")
library(PerformanceAnalytics)

#Calcula o retorno simples de 1 ativo
getRts <- function(aux.quotes){
  idx <- 2:length(aux.quotes)
  return((aux.quotes[idx] - aux.quotes[idx-1])/ aux.quotes[idx-1])
}

#Calcula o retorno continuamente composto de 1 ativo
getRtcc <- function(aux.quotes){
  return(log(1 + getRts(aux.quotes)))
}

close.df <- as.data.frame(read_xlsx("close.xlsx", col_names = TRUE))
row_names <- close.df[,1]
close.df <- close.df[,2:ncol(close.df)]
rownames(close.df) <- as.Date(row_names, origin = "1970-01-01")
weights.vec = c(0.19434, 0.13030, 0.09964, 0.06222, 0.03914, 0.02704,
                  0.02509, 0.02502, 0.01907, 0.01783, 0.00960, 0.00914)
risk.free <- 0

ret.df <- apply(close.df, 2, getRtcc)
mu.vec <- apply(ret.df, 2, mean)
sig.vec <- apply(ret.df, 2, sd)
sigma.mat <- cov(ret.df)
num_rows <- nrow(ret.df)
num_cols <- ncol(ret.df)
one.vec <- rep(1, num_cols)
zero.vec <- rep(0, num_cols)

getPortRet <- function(){

  ret <- rep(0, num_rows)

  for(i in 1:num_cols){
    ret <- ret + weights.vec[i]*ret.df[,i]
  }


  return(ret)
}

portfolio <- getPortfolio(er = mu.vec, cov.mat = sigma.mat, weights = weights.vec)

gmvp.portfolio <- globalMin.portfolio(er = mu.vec, cov.mat = sigma.mat)
gmvp.portfolio

tan.portfolio <- tangency.portfolio(er = mu.vec, cov.mat = sigma.mat, risk.free = risk.free, shorts = TRUE)
tan.portfolio

################# QUESTAO 1 #################
## Traçando a fronteira da bala de Markowitz com posições curtas permitidas ##

ef.frontier.s <- efficient.frontier(er = mu.vec, cov.mat = sigma.mat,
                                    nport = 100, alpha.min = -2, alpha.max = 3,
                                    shorts = TRUE)
plot(ef.frontier.s, col = "blue")

################# QUESTAO 2 #################
## Traçando a fronteira da bala de Markowitz com posições curtas não permitidas ##

ef.frontier.ns <- efficient.frontier(er = mu.vec, cov.mat = sigma.mat,
                                     nport = 100, alpha.min = -2, alpha.max = 3,
                                     shorts = FALSE)
points(ef.frontier.ns$sd, ef.frontier.ns$er, col = "red")

################# QUESTAO 3 #################
## Determinando pesos do GMVP com posições curtas não permitidas ##

A <- cbind(one.vec, diag(num_cols), -diag(num_cols))
b <- c(1, zero.vec, -0.5*one.vec)
gmvp.ns.mw <- solve.QP(Dmat = 2*sigma.mat, dvec = zero.vec,
                      Amat = A, bvec = b, meq = 1)
gmvp.ns.mw$solution
points(sqrt(gmvp.ns.mw$value), t(gmvp.ns.mw$solution)%*%mu.vec,
       pch=16, col='orange', cex=2)

################# QUESTAO 4 #################
## Determinando pesos das ações no TP com posições curtas não permitidas ##

tan.port.ns <- tangency.portfolio(er = mu.vec, cov.mat = sigma.mat,
                                  risk.free = risk.free, shorts = FALSE)
tan.port.ns
points(tan.port.ns$sd, tan.port.ns$er, col = "black", pch = 16, cex = 2)
################# QUESTAO 5 #################
## Determinando reta dos investimentos eficientes posições curtas não permitidas ##

abline(a = risk.free, b = (tan.port.ns$er - risk.free)/tan.port.ns$sd, col = 'pink', lwd = 3)

################# QUESTAO 6 #################
## Determinando posição no grafico do port. do E2M ##

points(portfolio$sd, portfolio$er, col="green", pch=16, cex=2)

################# QUESTAO 7 #################
##  Obtendo os pesos das ações no portfolio no portfolio eficiente ##

x = portfolio$sd
y = (((tan.port.ns$er - risk.free)/tan.port.ns$sd) * x) + risk.free
points(x, y, col = 'yellow', pch = 16, cex = 2)

################# QUESTAO 8 #################
## Obtendo os gráficos do retorno acumulado/drawdown ##

charts.PerformanceSummary(getPortRet(), Rf = 0)