Hw04 Sarantuya Sharvsambuu(113035128) Investment Portfolio

Load Necessary Libraries

library(tidyverse)

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library(quantmod)

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library(PerformanceAnalytics)

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library(xts)
library(quadprog)
library(readr)

Load Data

etf_data <- read.csv("myetf4.csv")

# Convert date column to Date type
colnames(etf_data)[1] <- "Date"  # Rename 'Index' to 'Date' if necessary
etf_data$Date <- as.Date(etf_data$Date, format="%Y/%m/%d")

Select and Process ETFs

etfs <- etf_data %>%
  filter(Date >= "2015-12-14" & Date <= "2018-12-28") %>%
  select(Date, `tw0050`, `tw0056`, `tw006205`, `tw00646`)

# Convert to xts for time-series operations
etfs_xts <- xts(etfs[,-1], order.by=etfs$Date)

Compute Daily Log Returns

returns <- na.omit(Return.calculate(etfs_xts, method = "log"))

Compute GMVP (Daily Returns)

cov_matrix <- cov(returns)
mean_returns <- colMeans(returns)

n <- ncol(returns)
Dmat <- 2 * cov_matrix
dvec <- rep(0, n)
Amat <- cbind(rep(1, n))
bvec <- 1
solution <- solve.QP(Dmat, dvec, Amat, bvec, meq=1)
weights_gmvp <- solution$solution

gmvp_return <- sum(weights_gmvp * mean_returns)
gmvp_sd <- sqrt(t(weights_gmvp) %*% cov_matrix %*% weights_gmvp)

list(Weights = weights_gmvp, GMVP_Return = gmvp_return, GMVP_SD = gmvp_sd)

## $Weights
## [1] -0.2241314  0.7298726  0.1080760  0.3861827
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## $GMVP_Return
## [1] 0.0002263853
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## $GMVP_SD
##             [,1]
## [1,] 0.005921611

Compute GMVP (Monthly Returns)

monthly_returns <- apply.monthly(returns, colSums)
cov_matrix_monthly <- cov(monthly_returns)
mean_returns_monthly <- colMeans(monthly_returns)

Dmat <- 2 * cov_matrix_monthly
dvec <- rep(0, n)
solution <- solve.QP(Dmat, dvec, Amat, bvec, meq=1)
weights_gmvp_monthly <- solution$solution

gmvp_return_monthly <- sum(weights_gmvp_monthly * mean_returns_monthly)
gmvp_sd_monthly <- sqrt(t(weights_gmvp_monthly) %*% cov_matrix_monthly %*% weights_gmvp_monthly)

list(Weights_Monthly = weights_gmvp_monthly, GMVP_Return_Monthly = gmvp_return_monthly, GMVP_SD_Monthly = gmvp_sd_monthly)

## $Weights_Monthly
## [1] -0.0009382175  0.4936002513 -0.0105293618  0.5178673280
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## $GMVP_Return_Monthly
## [1] 0.006042594
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## $GMVP_SD_Monthly
##            [,1]
## [1,] 0.02499232

Compute Tangency Portfolio

w_tangency <- solve.QP(Dmat, mean_returns_monthly, Amat, bvec, meq=1)$solution

tangency_return <- sum(w_tangency * mean_returns_monthly)
tangency_sd <- sqrt(t(w_tangency) %*% cov_matrix_monthly %*% w_tangency)

list(Weights_Tangency = w_tangency, Tangency_Return = tangency_return, Tangency_SD = tangency_sd)

## $Weights_Tangency
## [1]  4.925598 -1.410903 -3.657954  1.143259
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## $Tangency_Return
## [1] 0.05775268
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## $Tangency_SD
##           [,1]
## [1,] 0.1627257