Teoría de Carteras de Markowitz en R : Media – Varianza

Codigo R

# Portfolios de Markowitz

# ** #media- varianzas/Var/Cvar

## porfolio analytics

#install.packages(«portfolio»)
library(portfolio)

library(quadprog)

args(solve.QP)

## mínimizar matriz de varianzas – covarianzas

#Dmat matrix appearing in the quadratic function to be minimized
#dvec vector appearing in the quadratic function to be minimized
#Amat matrix defining the constraints
#bvec vector holding the values of $b_0$ (defaults to zero).
#meq the first meq constraints are treated as equality constraints,
#all further as inequality constraints (defaults to

#install.packages(«quantmod»)

library(quantmod)

#getFX(«EUR/USD»)

library(«tseries»)

library(«fImport»)
library(«urca»)
library(«vars»)

getSymbols(«CADCHF=X»,src=»yahoo»,from = «2017-02-18»)
getSymbols(«AUDNZD=X»,src=»yahoo»,from = «2017-02-18»)
getSymbols(«AUDUSD=X»,src=»yahoo»,from = «2017-02-18»)
getSymbols(«EURCHF=X»,src=»yahoo»,from = «2017-02-18»)
getSymbols(«EURGBP=X»,src=»yahoo»,from = «2017-02-18»)
getSymbols(«EURCAD=X»,src=»yahoo»,from = «2017-02-18»)

getSymbols(«CADCHF=X»,src=»yahoo»,from = «2019-01-01»)
getSymbols(«AUDNZD=X»,src=»yahoo»,from = «2019-01-01»)
getSymbols(«AUDUSD=X»,src=»yahoo»,from = «2019-01-01»)
getSymbols(«EURCHF=X»,src=»yahoo»,from = «2019-01-01»)
getSymbols(«EURGBP=X»,src=»yahoo»,from = «2019-01-01»)
getSymbols(«EURCAD=X»,src=»yahoo»,from = «2019-01-01»)

CADCHF= `CADCHF=X`[,4] # precios diarios de cierre
AUDNZD= `AUDNZD=X`[,4]
AUDUSD= `AUDUSD=X`[,4]
EURCHF= `EURCHF=X`[,4]
EURGBP= `EURGBP=X`[,4]
EURCAD= `EURCAD=X`[,4]

#### tabla

forex_mark <-na.omit(cbind(CADCHF,AUDNZD,AUDUSD,EURCHF,EURGBP,EURCAD))

plot(forex_mark)

#Calculamos los retornos y x 100 para calcularlos en %

forex_mark_ret=na.omit(returns(forex_mark))
forex_mark_ret = 100 * forex_mark_ret

Forex_ret<-as.timeSeries(forex_mark_ret)

names(Forex_ret)<- cbind(«CADCHF»,»AUDNZD»,»AUDUSD»,»EURCHF»,»EURGBP»,»EURCAD»)

plot(Forex_ret)

apply(Forex_ret,2,mean) #♠ media diaria

#mu<-matrix(apply(Forex_ret,2,mean))
#mean(mu)

#head(FX)

portfolio <- function(assetReturns, targetReturn)
{
# Arguments:
# assetReturns – multivariate data set of asset returns
# target Return – the portfolios target return
# 1 Create Portfolio Settings:
nAssets = ncol(assetReturns)
Dmat = cov(assetReturns)
dvec = rep(0, times=nAssets)
Amat = t(rbind(
Return=colMeans(assetReturns),
Budget=rep(1, nAssets),
LongOnly=diag(nAssets)))
bvec = c(
Return=targetReturn,
budget=1,
LongOnly=rep(0, times=nAssets))
meq = 2
# 2 Optimize Weights:
portfolio = solve.QP(Dmat, dvec, Amat, bvec, meq)
weights = round(portfolio$solution, digits = 4)
names(weights) = colnames(assetReturns)
# Return Value:
list(
weights = 100*weights,
risk = portfolio$value,
return = targetReturn)
}

#library(fBasics)

assetReturns <- Forex_ret[, 1:6]
names(assetReturns)

targetReturn <- mean(colMeans(assetReturns))
targetReturn # media diaria todo el portfolio

#install.packages(«portfolio»)
#library(portfolio)

portfolio <- portfolio(assetReturns, targetReturn)

portfolio

weights = portfolio$weights
names(weights) = colnames(Forex_ret)
weights

sum(weights)

# c(weightedReturn = round((weights %*% colMeans(assetReturns))[[1]],
#3), targetReturn = round(100 * targetReturn, 3))

args(pie)

Weights = weights[weights > 0]
pie(Weights, labels = names(Weights))
title(main = «Cartera Forex 2020»)