{"id":1859,"date":"2021-01-05T12:59:36","date_gmt":"2021-01-05T12:59:36","guid":{"rendered":"https:\/\/ricovictor.com\/?p=1859"},"modified":"2021-01-08T15:56:11","modified_gmt":"2021-01-08T15:56:11","slug":"teoria-de-markowitz-en-r-cartera-tangencial","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2021\/01\/05\/teoria-de-markowitz-en-r-cartera-tangencial\/","title":{"rendered":"Teor\u00eda de Markowitz en R : Cartera Tangencial"},"content":{"rendered":"\t\t
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Dentro de la Teor\u00eda Moderna de Carteras de H.Markowitz hay varios tipos de portafolios que podemos crear. De uno de ellos ya habl\u00e9 en el post anterior donde expliqu\u00e9 el porftolio de Media-Varianza<\/strong><\/a> .<\/p>

Otro tipo es el llamado Tangencial<\/strong>, cuyo objetivo es encontrar aquella combinaci\u00f3n de activos y pesos que maximiza el ratio de Sharpe. En este v\u00eddeo tienes un ejemplo en R usando pares de divisas. M\u00e1s abajo tienes el c\u00f3digo usado para copiarlo si lo deseas.<\/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

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Codigo R<\/h2>

\u00a0<\/p>

## CARTERA DE MARKOWITZ — TANGENCIAL<\/p>


## C\u00d3NOCIDA COMO M\u00c1XIMO SHARPE<\/p>


### entre todo el conjunto de posibilidades que tenemos
## elegiremos aquella — max atio sharpe<\/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>

\u00a0<\/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>


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


#### pasarlo a positivo y hacer con longonly<\/p>


#### codigo sharpe<\/p>


library(quadprog)<\/p>


portfolioWeights <- function(assetReturns, targetReturn)
{
nAssets = ncol(assetReturns)
portfolio = solve.QP(
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)
weights = portfolio$solution
weights
}<\/p>

\u00a0<\/p>


tangencyPortfolio <- function (assetReturns, riskFreeRate=0)
{
# 1 Funci\u00f3n de c\u00e1lculo del Sharpe Ratio:

sharpeRatio <- function(x, assetReturns, riskFreeRate)
{
targetReturn = x
weights = portfolioWeights(assetReturns, targetReturn)
targetRisk = sqrt( weights %*% cov(assetReturns) %*% weights )[[1]]
ratio = (targetReturn – riskFreeRate)\/targetRisk
attr(ratio, \u00abweights\u00bb) <- weights
attr(ratio, \u00abtargetRisk\u00bb) <- targetRisk
ratio
}

# 2 Optimizaci\u00f3n :

nAssets = ncol(assetReturns)
mu = colMeans(assetReturns)
Cov = cov(assetReturns)
tgPortfolio <- optimize(
f=sharpeRatio, interval=range(mu), maximum=TRUE,
assetReturns=assetReturns, riskFreeRate=riskFreeRate)

# 3 Salida y caracteristica:

tgReturn = tgPortfolio$maximum
tgRisk = attr(tgPortfolio$objective, \u00abtargetRisk\u00bb)
tgWeights = attr(tgPortfolio$objective, \u00abweights\u00bb)
sharpeRatio = sharpeRatio(tgReturn, assetReturns, riskFreeRate)[[1]]
# Return Value:
list(
sharpeRatio=sharpeRatio,
tgRisk=tgRisk, tgReturn=tgReturn, tgWeights=tgWeights)
}



tangencyPortfolio(assetReturns, riskFreeRate = 0)


tangencial<- tangencyPortfolio(assetReturns, riskFreeRate = 0)

tangencial$tgWeights*100


sum(tangencial$tgWeights)<\/p>

apply(Forex_ret,2,mean) #\u2660 media diaria





abs(tangencial$tgWeights)*100


sum(abs(tangencial$tgWeights))*100

456.4795\/100

pesos_equi<- abs(tangencial$tgWeights)*100\/4.5647
pesos_equi

sum(pesos_equi)<\/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\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Dentro de la Teor\u00eda Moderna de Carteras de H.Markowitz hay varios tipos de portafolios que podemos crear. De uno de ellos ya habl\u00e9 en el post anterior donde expliqu\u00e9 el porftolio de Media-Varianza . Otro tipo es el llamado Tangencial, cuyo objetivo es encontrar aquella combinaci\u00f3n de activos y pesos que maximiza el ratio de …<\/p>\n

Teor\u00eda de Markowitz en R : Cartera Tangencial<\/span> Leer m\u00e1s »<\/a><\/p>\n","protected":false},"author":1,"featured_media":1861,"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 Markowitz en R : Cartera Tangencial - V\u00edctor A. 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