Homework 5 MVP Cumulative Returns

library(tidyverse)

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library(lubridate)
library(ggplot2)

# Load the data
sector_returns <- read_csv("C:\\Users\\emman\\Downloads\\10_Industry_Portfolios.csv")

## Rows: 1173 Columns: 11
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## Delimiter: ","
## dbl (11): date, NoDur, Durbl, Manuf, Enrgy, HiTec, Telcm, Shops, Hlth, Utils...
## 
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# Convert the date column to Date type
sector_returns <- sector_returns %>%
  mutate(date = ymd(paste0(date, "01")))

# Filter data starting from 1964 (to have 5 years of data by 1969)
sector_returns <- sector_returns %>%
  filter(date >= as.Date("1969-01-01"))

# Function to calculate MVP weights
mvp_weights <- function(cov_matrix) {
  inv_cov <- solve(cov_matrix)
  ones <- rep(1, nrow(inv_cov))
  weights <- inv_cov %*% ones / sum(inv_cov %*% ones)
  return(weights)
}

# Initialize vectors to store results
dates <- sector_returns$date
num_sectors <- ncol(sector_returns) - 1
mvp_returns <- numeric(length(dates) - 60 + 1)

# Calculate rolling 5-year covariance matrices and MVP returns
for (i in 60:length(dates)) {
  ret_window <- sector_returns[(i-59):i, -1]
  cov_matrix <- cov(ret_window)
  weights <- mvp_weights(cov_matrix)
  current_returns <- as.numeric(sector_returns[i, -1])
  mvp_returns[i-59] <- sum(weights * current_returns)
}

# Create a data frame for the results
mvp_data <- data.frame(
  date = dates[60:length(dates)],
  mvp_return = mvp_returns
)

# Calculate cumulative returns
mvp_data <- mvp_data %>%
  mutate(cumulative_return = cumprod(1 + mvp_return / 100))

# Plot cumulative returns
ggplot(mvp_data, aes(x = date, y = cumulative_return)) +
  geom_line(color = "blue") +
  labs(title = "Cumulative Returns of Minimum Variance Portfolio (MVP)",
       x = "Date",
       y = "Cumulative Return") +
  theme_minimal()

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