{"id":1752,"date":"2020-12-28T17:49:01","date_gmt":"2020-12-28T17:49:01","guid":{"rendered":"https:\/\/ricovictor.com\/?p=1752"},"modified":"2026-01-29T21:54:42","modified_gmt":"2026-01-29T21:54:42","slug":"teoria-de-carteras-de-markowitz-en-r-media-varianza","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2020\/12\/28\/teoria-de-carteras-de-markowitz-en-r-media-varianza\/","title":{"rendered":"Teor\u00eda de Carteras de Markowitz en R : Media – Varianza"},"content":{"rendered":"\t\t
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El modelo de carteras de Markowitz, tambi\u00e9n llamado\u00a0\u00bb Teor\u00eda moderna de carteras\u00bb<\/b>\u00a0es un m\u00e9todo que busca determinar la mejor combinaci\u00f3n entre activos para que nuestro portafolio de inversi\u00f3n sea \u00f3ptimo,teniendo en cuenta la rentabilidad esperada y el riesgo asociado a cada activo y en su conjunto.<\/span><\/div>
\u00a0<\/div>
Dentro de \u00e9sta teor\u00eda hay muchos tipos de carteras<\/a> que podemos crear,as\u00ed como usar diferentes t\u00e9cnicas para medir el riesgo. En el siguiente v\u00eddeo hago un ejemplos de una cartera base de\u00a0Media-Varianza<\/b>,utilizando 6 pares de divisas.<\/span><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Codigo R<\/strong><\/em><\/h3>

\u00a0<\/p>

# Portfolios de Markowitz<\/p>

# ** #media- varianzas\/Var\/Cvar<\/p>

## porfolio analytics<\/p>

#install.packages(\u00abportfolio\u00bb)
library(portfolio)<\/p>

library(quadprog)<\/p>

args(solve.QP)<\/p>

## m\u00ednimizar matriz de varianzas – covarianzas<\/p>

#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<\/p>

#install.packages(\u00abquantmod\u00bb)<\/p>

library(quantmod)<\/p>

#getFX(\u00abEUR\/USD\u00bb)<\/p>

library(\u00abtseries\u00bb)<\/p>

library(\u00abfImport\u00bb)
library(\u00aburca\u00bb)
library(\u00abvars\u00bb)<\/p>

getSymbols(\u00abCADCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abAUDNZD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abAUDUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURGBP=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)
getSymbols(\u00abEURCAD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2017-02-18\u00bb)<\/p>

getSymbols(\u00abCADCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2019-01-01\u00bb)
getSymbols(\u00abAUDNZD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2019-01-01\u00bb)
getSymbols(\u00abAUDUSD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2019-01-01\u00bb)
getSymbols(\u00abEURCHF=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2019-01-01\u00bb)
getSymbols(\u00abEURGBP=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2019-01-01\u00bb)
getSymbols(\u00abEURCAD=X\u00bb,src=\u00bbyahoo\u00bb,from = \u00ab2019-01-01\u00bb)<\/p>

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]<\/p>

#### tabla<\/p>

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

plot(forex_mark)<\/p>

#Calculamos los retornos y x 100 para calcularlos en %<\/p>

forex_mark_ret=na.omit(returns(forex_mark))
forex_mark_ret = 100 * forex_mark_ret<\/p>

Forex_ret<-as.timeSeries(forex_mark_ret)<\/p>

names(Forex_ret)<- cbind(\u00abCADCHF\u00bb,\u00bbAUDNZD\u00bb,\u00bbAUDUSD\u00bb,\u00bbEURCHF\u00bb,\u00bbEURGBP\u00bb,\u00bbEURCAD\u00bb)<\/p>

plot(Forex_ret)<\/p>

apply(Forex_ret,2,mean) #\u2660 media diaria<\/p>

#mu<-matrix(apply(Forex_ret,2,mean))
#mean(mu)<\/p>

#head(FX)<\/p>

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)
}<\/p>

#library(fBasics)<\/p>

assetReturns <- Forex_ret[, 1:6]
names(assetReturns)<\/p>

targetReturn <- mean(colMeans(assetReturns))
targetReturn # media diaria todo el portfolio<\/p>

#install.packages(\u00abportfolio\u00bb)
#library(portfolio)<\/p>

portfolio <- portfolio(assetReturns, targetReturn)<\/p>

portfolio<\/p>

weights = portfolio$weights
names(weights) = colnames(Forex_ret)
weights<\/p>

sum(weights)<\/p>

# c(weightedReturn = round((weights %*% colMeans(assetReturns))[[1]],
#3), targetReturn = round(100 * targetReturn, 3))<\/p>

args(pie)<\/p>

Weights = weights[weights > 0]
pie(Weights, labels = names(Weights))
title(main = \u00abCartera Forex 2020\u00bb)<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\tCurso GRATIS Multicointegraci\u00f3n en FOREX<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

El modelo de carteras de Markowitz, tambi\u00e9n llamado\u00a0\u00bb Teor\u00eda moderna de carteras\u00bb\u00a0es un m\u00e9todo que busca determinar la mejor combinaci\u00f3n entre activos para que nuestro portafolio de inversi\u00f3n sea \u00f3ptimo,teniendo en cuenta la rentabilidad esperada y el riesgo asociado a cada activo y en su conjunto.\u00a0Dentro de \u00e9sta teor\u00eda hay muchos tipos de carteras que …<\/p>\n

Teor\u00eda de Carteras de Markowitz en R : Media – Varianza<\/span> Leer m\u00e1s »<\/a><\/p>\n","protected":false},"author":19,"featured_media":1757,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[24],"tags":[],"yoast_head":"\nTeor\u00eda de Carteras de Markowitz en R : Media - Varianza - V\u00edctor A. 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