Homework04

library(tidyverse)

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library(quantmod)

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library(PerformanceAnalytics)

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

colnames(data)[1] <- "Date"

data$Date <- as.Date(data$Date, format="%Y/%m/%d")

selected_ETFs <- c("tw0050", "tw0056", "tw006205", "tw00646")
data_filtered <- data %>% select(Date, all_of(selected_ETFs))

data_filtered <- data_filtered %>% filter(Date >= "2015-12-14" & Date <= "2018-12-28")

returns <- data_filtered %>% 
  select(-Date) %>%
  mutate_all(~ log(. / lag(.))) %>%
  na.omit()

cov_matrix <- cov(returns)

ones <- rep(1, ncol(returns))
inv_cov_matrix <- solve(cov_matrix)
w_gmvp <- inv_cov_matrix %*% ones / sum(inv_cov_matrix %*% ones)

gmvp_return <- colMeans(returns) %*% w_gmvp
gmvp_risk <- sqrt(t(w_gmvp) %*% cov_matrix %*% w_gmvp)

cat("GMVP Weights:\n")

## GMVP Weights:

print(w_gmvp)

##                [,1]
## tw0050   -0.2241314
## tw0056    0.7298726
## tw006205  0.1080760
## tw00646   0.3861827

cat("\nGMVP Return:", gmvp_return)

## 
## GMVP Return: 0.0002263853

cat("\nGMVP Risk (Std Dev):", gmvp_risk)

## 
## GMVP Risk (Std Dev): 0.005921611

returns_monthly <- returns %>%
  mutate(Date = data_filtered$Date[-1]) %>%  # Add Date column (excluding first NA row)
  mutate(YearMonth = format(Date, "%Y-%m")) %>%
  group_by(YearMonth) %>%
  summarize(across(-Date, ~ prod(1 + ., na.rm = TRUE) - 1)) %>%
  ungroup()

head(returns_monthly)

## # A tibble: 6 × 5
##   YearMonth  tw0050   tw0056 tw006205  tw00646
##   <chr>       <dbl>    <dbl>    <dbl>    <dbl>
## 1 2015-12    0.0224  0.0332   0.0295   0.0226 
## 2 2016-01   -0.0215 -0.0148  -0.181   -0.0405 
## 3 2016-02    0.0281  0.0433  -0.0302  -0.00424
## 4 2016-03    0.0549 -0.00296  0.0797   0.0256 
## 5 2016-04   -0.0482 -0.0375  -0.0264   0.00944
## 6 2016-05    0.0241  0.0160   0.00288  0.0218

cov_matrix_monthly <- cov(returns_monthly[,-1], use="complete.obs")
gmvp_weights_monthly <- solve(cov_matrix_monthly) %*% ones / sum(solve(cov_matrix_monthly) %*% ones)
gmvp_return_monthly <- colMeans(returns_monthly[,-1]) %*% gmvp_weights_monthly
gmvp_sd_monthly <- sqrt(t(gmvp_weights_monthly) %*% cov_matrix_monthly %*% gmvp_weights_monthly)

cat("Monthly GMVP Weights:", gmvp_weights_monthly, "\n")

## Monthly GMVP Weights: 0.01064151 0.4706479 -0.009441197 0.5281518

cat("Monthly GMVP Return:", gmvp_return_monthly, "\n")

## Monthly GMVP Return: 0.005928447

cat("Monthly GMVP Standard Deviation:", gmvp_sd_monthly, "\n")

## Monthly GMVP Standard Deviation: 0.02511828

tangency_weights <- solve(cov_matrix_monthly) %*% colMeans(returns_monthly[,-1])
tangency_weights <- tangency_weights / sum(tangency_weights)

tangency_return <- colMeans(returns_monthly[,-1]) %*% tangency_weights
tangency_sd <- sqrt(t(tangency_weights) %*% cov_matrix_monthly %*% tangency_weights)

cat("Tangency Portfolio Weights:", tangency_weights, "\n")

## Tangency Portfolio Weights: 1.065822 0.09573927 -0.8225181 0.6609571

cat("Tangency Portfolio Return:", tangency_return, "\n")

## Tangency Portfolio Return: 0.01723056

cat("Tangency Portfolio Standard Deviation:", tangency_sd, "\n")

## Tangency Portfolio Standard Deviation: 0.04282222