# Load required libraries
library(readxl)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(stringr)
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(PerformanceAnalytics)
## Loading required package: xts
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## 
## ######################### Warning from 'xts' package ##########################
## #                                                                             #
## # The dplyr lag() function breaks how base R's lag() function is supposed to  #
## # work, which breaks lag(my_xts). Calls to lag(my_xts) that you type or       #
## # source() into this session won't work correctly.                            #
## #                                                                             #
## # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
## # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop           #
## # dplyr from breaking base R's lag() function.                                #
## #                                                                             #
## # Code in packages is not affected. It's protected by R's namespace mechanism #
## # Set `options(xts.warn_dplyr_breaks_lag = FALSE)` to suppress this warning.  #
## #                                                                             #
## ###############################################################################
## 
## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
## 
##     first, last
## 
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
## 
##     legend
library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(tseries)
library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
library(lmtest)
library(PortfolioAnalytics)
## Loading required package: foreach
## Registered S3 method overwritten by 'PortfolioAnalytics':
##   method           from
##   print.constraint ROI
library(DEoptim)
## Loading required package: parallel
## 
## DEoptim package
## Differential Evolution algorithm in R
## Authors: D. Ardia, K. Mullen, B. Peterson and J. Ulrich
library(reshape2)
library(ggplot2)
library(quadprog)
library(quantmod)
## Loading required package: TTR
library(rugarch) # Untuk GARCH-X

# Fungsi portofolio
calculate_portfolio_return <- function(weights, returns) sum(colMeans(returns) * weights)
calculate_portfolio_var <- function(weights, returns, alpha = 0.05) {
  portfolio_returns <- returns %*% weights
  -quantile(portfolio_returns, alpha)
}

# Import BI Rate data
birate <- read_excel("Database/bi_rate.xlsx")
colnames(birate) <- c("date","bi_rate")
head(birate); tail(birate)
## # A tibble: 6 × 2
##   date              bi_rate
##   <chr>             <chr>  
## 1 18 Desember 2024  6.00   
## 2 20 November 2024  6.00   
## 3 16 Oktober 2024   6.00   
## 4 18 September 2024 6.00   
## 5 21 Agustus 2024   6.25   
## 6 17 Juli 2024      6.25
## # A tibble: 6 × 2
##   date              bi_rate
##   <chr>             <chr>  
## 1 22 September 2016 5.00   
## 2 19 Agustus 2016   5.25   
## 3 21 Juli 2016      5.25   
## 4 16 Juni 2016      5.25   
## 5 19 Mei 2016       5.50   
## 6 21 April 2016     5.50
# Replace date with month date from January 2005 - Desember 2025
Sys.setlocale("LC_TIME", "id_ID.UTF-8") 
## [1] "id_ID.UTF-8"
birate <- birate %>%
  mutate(date = dmy(date))
birate$bi_rate <- as.numeric(birate$bi_rate)
birate <- birate[order(birate$date), ]
head(birate)
## # A tibble: 6 × 2
##   date       bi_rate
##   <date>       <dbl>
## 1 2016-04-21    5.5 
## 2 2016-05-19    5.5 
## 3 2016-06-16    5.25
## 4 2016-07-21    5.25
## 5 2016-08-19    5.25
## 6 2016-09-22    5
# Import 10-year bond data
bond10 <- read.csv("Database/bond10.csv")
# Select only Date and Open.Price
bond10 <- bond10[, c("Tanggal", "Terakhir")]
# Rename columns to Open.Price and bond10
colnames(bond10) <- c("date", "bond10")
# Convert date to Date type and reoder from earliest to latest
bond10 <- bond10 %>%
  mutate(date = dmy(date))
bond10 <- bond10[order(bond10$date), ]
bond10 <- bond10 %>%
  mutate(bond10 = as.numeric(gsub(",", "", bond10)))
head(bond10)
##            date bond10
## 2756 2014-01-02   8462
## 2755 2014-01-03   8550
## 2754 2014-01-06   9103
## 2753 2014-01-07   9124
## 2752 2014-01-08   9036
## 2751 2014-01-09   9017
# Import Bitcoin data
btc_usd <- read.csv("Database/btc_usd.csv")
# Select only Date and Open.Price
btc_usd <- btc_usd[, c("Tanggal", "Terakhir")]
# Rename columns to date
colnames(btc_usd) <- c("date", "btc")
# Convert date to Date type and reoder from earliest to latest
btc_usd <- btc_usd %>%
  mutate(date = dmy(date))
btc_usd <- btc_usd[order(btc_usd$date), ]
btc_usd <- btc_usd %>%
  mutate(btc = as.numeric(gsub(",", "", btc)))
head(btc_usd)
##            date  btc
## 4015 2014-01-01 7403
## 4014 2014-01-02 7750
## 4013 2014-01-03 8121
## 4012 2014-01-04 8018
## 4011 2014-01-05 9040
## 4010 2014-01-06 9345
# Import CPI data
cpi <- read_excel("Database/inflation.xlsx")
# Rename columns to date and cpi
colnames(cpi) <- c("date", "cpi")
# Daftar nama bulan Indonesia -> Inggris
bulan_id <- c("Januari","Februari","Maret","April","Mei","Juni",
              "Juli","Agustus","September","Oktober","November","Desember")
bulan_en <- c("January","February","March","April","May","June",
              "July","August","September","October","November","December")

# Ubah nama bulan ke bahasa Inggris, lalu parse jadi date
cpi <- cpi %>%
  mutate(date = str_replace_all(date, setNames(bulan_en, bulan_id)),
         date = parse_date_time(date, orders = "my"),
         date = as.Date(date))
cpi <- cpi[order(cpi$date), ]
cpi$cpi <- as.numeric(cpi$cpi)
head(cpi)
## # A tibble: 6 × 2
##   date         cpi
##   <date>     <dbl>
## 1 2014-01-01  8.22
## 2 2014-02-01  7.75
## 3 2014-03-01  7.32
## 4 2014-04-01  7.25
## 5 2014-05-01  7.32
## 6 2014-06-01  6.7
# Import JKSE data
jkse <- read.csv("Database/jkse.csv")
# Select only Date and Open.Price
jkse <- jkse[, c("Tanggal", "Terakhir")]
# Rename columns to date and jkse
colnames(jkse) <- c("date", "jkse")
# Convert date to Date type and reoder from earliest to latest
jkse <- jkse %>%
  mutate(date = dmy(date))
jkse <- jkse[order(jkse$date), ]
jkse <- jkse %>%
  mutate(
    jkse = str_replace_all(jkse, "\\.", ""),  # hapus titik (pemisah ribuan)
    jkse = str_replace_all(jkse, ",", "."),   # ubah koma jadi titik (desimal)
    jkse = as.numeric(jkse)                   # ubah jadi numeric
  )
head(jkse)
##            date    jkse
## 2681 2014-01-01 4274.18
## 2680 2014-01-02 4327.27
## 2679 2014-01-03 4257.66
## 2678 2014-01-06 4202.81
## 2677 2014-01-07 4175.81
## 2676 2014-01-08 4200.59
# Import IDR exchange rate data
kurs_idr <- read.csv("Database/idr_kurs.csv")
# Select only Date and Open.Price
kurs_idr <- kurs_idr[, c("Tanggal", "Terakhir")]
# Rename columns to date and kurs_idr
colnames(kurs_idr) <- c("date", "kurs_idr")
# Convert date to Date type and reoder from earliest to latest
kurs_idr <- kurs_idr %>%
  mutate(date = dmy(date))
kurs_idr <- kurs_idr[order(kurs_idr$date), ]
kurs_idr <- kurs_idr %>%
  mutate(
    kurs_idr = str_replace_all(kurs_idr, "\\.", ""),  # hapus titik (pemisah ribuan)
    kurs_idr = str_replace_all(kurs_idr, ",", "."),   # ubah koma jadi titik (desimal)
    kurs_idr = as.numeric(kurs_idr)                   # ubah jadi numeric
  )
head(kurs_idr)
##            date kurs_idr
## 2815 2014-01-01  12170.0
## 2814 2014-01-02  12160.0
## 2813 2014-01-03  12170.0
## 2812 2014-01-06  12180.0
## 2811 2014-01-07  12237.5
## 2810 2014-01-08  12235.0
# Gold data
gold <- read.csv("Database/gold.csv")
# Select only Date and Open.Price
gold <- gold[, c("Tanggal", "Terakhir")]
colnames(gold) <- c("date", "gold_idr")
gold <- gold %>%
  mutate(date = dmy(date))
gold <- gold[order(gold$date), ]
gold <- gold %>%
  mutate(
    gold_idr = str_replace_all(gold_idr, "\\.", ""),  # hapus titik (pemisah ribuan)
    gold_idr = str_replace_all(gold_idr, ",", "."),   # ubah koma jadi titik (desimal)
    gold_idr = as.numeric(gold_idr)                   # ubah jadi numeric
  )
head(gold)
##            date gold_idr
## 2816 2014-01-02   1225.2
## 2815 2014-01-03   1238.6
## 2814 2014-01-06   1238.0
## 2813 2014-01-07   1229.6
## 2812 2014-01-08   1225.5
## 2811 2014-01-09   1229.4
## Monthly Data Aggregation and Preprocessing
# Load necessary packages
library(dplyr)
library(lubridate)

# Convert data to monthly format (for those that aren't already monthly)
# For bi rate - get monthly average
birate_monthly <- birate %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(bi_rate = mean(bi_rate, na.rm = TRUE)) %>%
  rename(date = year_month)

# For bond10 - get monthly average
bond10_monthly <- bond10 %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(bond10 = mean(bond10, na.rm = TRUE)) %>%
  rename(date = year_month)

# For btc_usd - get monthly average
btc_monthly <- btc_usd %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(btc = mean(btc, na.rm = TRUE)) %>%
  rename(date = year_month)

# For jkse - get monthly average
jkse_monthly <- jkse %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(jkse = mean(jkse, na.rm = TRUE)) %>%
  rename(date = year_month)

# For kurs_idr - get monthly average
kurs_idr_monthly <- kurs_idr %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(kurs_idr = mean(kurs_idr, na.rm = TRUE)) %>%
  rename(date = year_month)

# For gold - get monthly average
gold_monthly <- gold %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(gold_idr = mean(gold_idr, na.rm = TRUE)) %>%
  rename(date = year_month)

# For cpi - ensure it's monthly format
cpi_monthly <- cpi %>%
  mutate(year_month = floor_date(date, "month")) %>%
  group_by(year_month) %>%
  summarise(cpi = mean(cpi, na.rm = TRUE)) %>%
  rename(date = year_month)

# Merge all datasets
merged_data <- birate_monthly %>%
  full_join(bond10_monthly, by = "date") %>%
  full_join(btc_monthly, by = "date") %>%
  full_join(cpi_monthly, by = "date") %>%
  full_join(jkse_monthly, by = "date") %>%
  full_join(kurs_idr_monthly, by = "date") %>%
  full_join(gold_monthly, by = "date")

# Sort by date
merged_data <- merged_data %>% arrange(date)

# Check the result
head(merged_data)
## # A tibble: 6 × 8
##   date       bi_rate bond10   btc   cpi  jkse kurs_idr gold_idr
##   <date>       <dbl>  <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 2014-01-01      NA  8746. 8194.  8.22 4350.   12158.    1244.
## 2 2014-02-01      NA  8702. 6605.  7.75 4515.   11918.    1301.
## 3 2014-03-01      NA  8061. 5929.  7.32 4720.   11416.    1337.
## 4 2014-04-01      NA  7908. 4620.  7.25 4871.   11431.    1299.
## 5 2014-05-01      NA  8003. 4829.  7.32 4925.   11536.    1288.
## 6 2014-06-01      NA  8088. 6179.  6.7  4898.   11892.    1283.
tail(merged_data)
## # A tibble: 6 × 8
##   date       bi_rate bond10   btc   cpi  jkse kurs_idr gold_idr
##   <date>       <dbl>  <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 2024-07-01    6.25  6986.  62.9  2.13 7258.   16238.    2398.
## 2 2024-08-01    6.25  6714.  60.0  2.12 7417.   15735.    2474.
## 3 2024-09-01    6     6544.  60.5  1.84 7740.   15318.    2579.
## 4 2024-10-01    6     6699.  65.7  1.71 7621.   15558.    2695.
## 5 2024-11-01    6     6852.  86.5  1.55 7269.   15813.    2656.
## 6 2024-12-01    6     6994.  98.3  1.57 7216.   16036.    2650.
# Check for missing values
colSums(is.na(merged_data))
##     date  bi_rate   bond10      btc      cpi     jkse kurs_idr gold_idr 
##        0       27        0        0        0        0        0        0
# Data with non NA values
non_na_data <- merged_data %>%
  filter(complete.cases(.))
# Check the non NA data
head(non_na_data)
## # A tibble: 6 × 8
##   date       bi_rate bond10   btc   cpi  jkse kurs_idr gold_idr
##   <date>       <dbl>  <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 2016-04-01    5.5   7545  4352.  3.6  4853.   13172.    1244.
## 2 2016-05-01    5.5   7784. 4617.  3.33 4770.   13417.    1261.
## 3 2016-06-01    5.25  7660. 6445.  3.45 4871.   13338.    1279.
## 4 2016-07-01    5.25  7106. 6616.  3.21 5166.   13114.    1339.
## 5 2016-08-01    5.25  6913. 5858.  2.79 5401.   13160.    1344.
## 6 2016-09-01    5     6956. 6083.  3.07 5337.   13110.    1330.
tail(non_na_data)
## # A tibble: 6 × 8
##   date       bi_rate bond10   btc   cpi  jkse kurs_idr gold_idr
##   <date>       <dbl>  <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 2024-07-01    6.25  6986.  62.9  2.13 7258.   16238.    2398.
## 2 2024-08-01    6.25  6714.  60.0  2.12 7417.   15735.    2474.
## 3 2024-09-01    6     6544.  60.5  1.84 7740.   15318.    2579.
## 4 2024-10-01    6     6699.  65.7  1.71 7621.   15558.    2695.
## 5 2024-11-01    6     6852.  86.5  1.55 7269.   15813.    2656.
## 6 2024-12-01    6     6994.  98.3  1.57 7216.   16036.    2650.
nrow(non_na_data)
## [1] 105
# Convert BTC to IDR
btc_idr <- non_na_data %>%
  mutate(btc_idr = btc * kurs_idr) %>%
  dplyr::select(date, btc_idr)

# Add BTC_IDR to the dataset
non_na_data <- non_na_data %>%
  left_join(btc_idr, by = "date")

# Select final set of variables
non_na_data <- non_na_data %>%
  dplyr::select(date, bi_rate, bond10, btc_idr, cpi, jkse, kurs_idr, gold_idr)

# Display the final dataset
head(non_na_data); tail(non_na_data)
## # A tibble: 6 × 8
##   date       bi_rate bond10   btc_idr   cpi  jkse kurs_idr gold_idr
##   <date>       <dbl>  <dbl>     <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 2016-04-01    5.5   7545  57318032.  3.6  4853.   13172.    1244.
## 2 2016-05-01    5.5   7784. 61939403.  3.33 4770.   13417.    1261.
## 3 2016-06-01    5.25  7660. 85965931.  3.45 4871.   13338.    1279.
## 4 2016-07-01    5.25  7106. 86769238.  3.21 5166.   13114.    1339.
## 5 2016-08-01    5.25  6913. 77097435.  2.79 5401.   13160.    1344.
## 6 2016-09-01    5     6956. 79744103.  3.07 5337.   13110.    1330.
## # A tibble: 6 × 8
##   date       bi_rate bond10  btc_idr   cpi  jkse kurs_idr gold_idr
##   <date>       <dbl>  <dbl>    <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 2024-07-01    6.25  6986. 1021903.  2.13 7258.   16238.    2398.
## 2 2024-08-01    6.25  6714.  944448.  2.12 7417.   15735.    2474.
## 3 2024-09-01    6     6544.  926531.  1.84 7740.   15318.    2579.
## 4 2024-10-01    6     6699. 1021507.  1.71 7621.   15558.    2695.
## 5 2024-11-01    6     6852. 1368402.  1.55 7269.   15813.    2656.
## 6 2024-12-01    6     6994. 1576530.  1.57 7216.   16036.    2650.
# Calculate returns and changes for each variable
non_na_data$bi_rate <- as.numeric(non_na_data$bi_rate)
apt_data <- non_na_data %>%
  arrange(date) %>%
  mutate(
    jkse_return = c(NA, diff(log(jkse))),
    bond_return = c(NA, diff(log(bond10))),
    btc_return = c(NA, diff(log(btc_idr))),
    gold_return = c(NA, diff(log(gold_idr))),  # Add gold returns calculation
    birate_change = c(NA, diff(bi_rate)),
    cpi_change = c(NA, diff(cpi) / cpi[-length(cpi)]),
    kurs_change = c(NA, diff(kurs_idr) / kurs_idr[-length(kurs_idr)])
  ) %>%
  na.omit()

# Create risk-free rate variable from BI Rate
apt_data$rf_rate <- apt_data$bi_rate / 12 / 100  # Convert annual BI Rate to monthly

# Calculate excess returns
apt_data$excess_jkse <- apt_data$jkse_return - apt_data$rf_rate
apt_data$excess_bond <- apt_data$bond_return - apt_data$rf_rate
apt_data$excess_btc <- apt_data$btc_return - apt_data$rf_rate
apt_data$excess_gold <- apt_data$gold_return - apt_data$rf_rate  # Add excess returns for gold

# Check the data
head(apt_data)
## # A tibble: 6 × 20
##   date       bi_rate bond10   btc_idr   cpi  jkse kurs_idr gold_idr jkse_return
##   <date>       <dbl>  <dbl>     <dbl> <dbl> <dbl>    <dbl>    <dbl>       <dbl>
## 1 2016-05-01    5.5   7784. 61939403.  3.33 4770.   13417.    1261.     -0.0173
## 2 2016-06-01    5.25  7660. 85965931.  3.45 4871.   13338.    1279.      0.0210
## 3 2016-07-01    5.25  7106. 86769238.  3.21 5166.   13114.    1339.      0.0589
## 4 2016-08-01    5.25  6913. 77097435.  2.79 5401.   13160.    1344.      0.0445
## 5 2016-09-01    5     6956. 79744103.  3.07 5337.   13110.    1330.     -0.0120
## 6 2016-10-01    4.75  7088. 83963283.  3.31 5406.   13018.    1266.      0.0128
## # ℹ 11 more variables: bond_return <dbl>, btc_return <dbl>, gold_return <dbl>,
## #   birate_change <dbl>, cpi_change <dbl>, kurs_change <dbl>, rf_rate <dbl>,
## #   excess_jkse <dbl>, excess_bond <dbl>, excess_btc <dbl>, excess_gold <dbl>
summary(apt_data)
##       date               bi_rate          bond10        btc_idr         
##  Min.   :2016-05-01   Min.   :3.500   Min.   :6111   Min.   :    16779  
##  1st Qu.:2018-06-23   1st Qu.:4.188   1st Qu.:6597   1st Qu.:   118135  
##  Median :2020-08-16   Median :4.750   Median :6916   Median :   342069  
##  Mean   :2020-08-15   Mean   :4.886   Mean   :6998   Mean   :  8297702  
##  3rd Qu.:2022-10-08   3rd Qu.:5.750   3rd Qu.:7289   3rd Qu.:   724748  
##  Max.   :2024-12-01   Max.   :6.250   Max.   :8554   Max.   :110728567  
##       cpi             jkse         kurs_idr        gold_idr   
##  Min.   :1.320   Min.   :4599   Min.   :13018   Min.   :1154  
##  1st Qu.:2.167   1st Qu.:5853   1st Qu.:13954   1st Qu.:1298  
##  Median :3.060   Median :6237   Median :14345   Median :1726  
##  Mean   :2.997   Mean   :6248   Mean   :14459   Mean   :1672  
##  3rd Qu.:3.490   3rd Qu.:6843   3rd Qu.:15057   3rd Qu.:1907  
##  Max.   :5.950   Max.   :7740   Max.   :16335   Max.   :2695  
##   jkse_return         bond_return           btc_return      
##  Min.   :-0.201493   Min.   :-0.0785464   Min.   :-6.89749  
##  1st Qu.:-0.012833   1st Qu.:-0.0260494   1st Qu.:-0.06265  
##  Median : 0.008020   Median :-0.0050788   Median : 0.02405  
##  Mean   : 0.003815   Mean   :-0.0007297   Mean   :-0.03455  
##  3rd Qu.: 0.020662   3rd Qu.: 0.0229104   3rd Qu.: 0.14451  
##  Max.   : 0.086305   Max.   : 0.1188922   Max.   : 0.65514  
##   gold_return        birate_change         cpi_change       
##  Min.   :-0.069265   Min.   :-0.250000   Min.   :-0.302752  
##  1st Qu.:-0.011329   1st Qu.: 0.000000   1st Qu.:-0.077589  
##  Median : 0.001830   Median : 0.000000   Median :-0.013377  
##  Mean   : 0.007274   Mean   : 0.004808   Mean   :-0.002132  
##  3rd Qu.: 0.030706   3rd Qu.: 0.000000   3rd Qu.: 0.068724  
##  Max.   : 0.075923   Max.   : 0.625000   Max.   : 0.314394  
##   kurs_change           rf_rate          excess_jkse        
##  Min.   :-0.054480   Min.   :0.002917   Min.   :-0.2052429  
##  1st Qu.:-0.006061   1st Qu.:0.003490   1st Qu.:-0.0176251  
##  Median : 0.001096   Median :0.003958   Median : 0.0038237  
##  Mean   : 0.002065   Mean   :0.004072   Mean   :-0.0002566  
##  3rd Qu.: 0.011865   3rd Qu.:0.004792   3rd Qu.: 0.0164970  
##  Max.   : 0.102563   Max.   :0.005208   Max.   : 0.0831804  
##   excess_bond          excess_btc        excess_gold       
##  Min.   :-0.082088   Min.   :-6.90145   Min.   :-0.073224  
##  1st Qu.:-0.030534   1st Qu.:-0.06723   1st Qu.:-0.015524  
##  Median :-0.010287   Median : 0.01946   Median :-0.001594  
##  Mean   :-0.004801   Mean   :-0.03862   Mean   : 0.003203  
##  3rd Qu.: 0.018067   3rd Qu.: 0.14029   3rd Qu.: 0.025654  
##  Max.   : 0.115142   Max.   : 0.65159   Max.   : 0.070715
min(apt_data$date)
## [1] "2016-05-01"
max(apt_data$date)
## [1] "2024-12-01"
#Figure 1. Monthly Closing Price of Assets 
#Note :  is JKSE’s monthly closing price meanwhile  is representating the gold’s price.  is government bond’s monthly closing price,  is the bitcoin’s price.

library(ggplot2)
library(reshape2)

# Prepare data for plotting
price_data <- non_na_data %>%
  dplyr::select(date, jkse, bond10, btc_idr, gold_idr) %>%
  mutate(
    log_jkse = log(jkse),
    log_bond10 = log(bond10),
    log_btc_idr = log(btc_idr),
    log_gold = log(gold_idr)
  ) %>%
  dplyr::select(date, log_jkse, log_bond10, log_btc_idr, log_gold)

# Reshape for ggplot
price_long <- melt(price_data, id.vars = "date", variable.name = "Asset", value.name = "LogPrice")
asset_labels <- c(
  log_jkse = "JKSE",
  log_bond10 = "Bond 10Y",
  log_btc_idr = "Bitcoin (IDR)",
  log_gold = "Gold"
)
price_long$Asset <- factor(price_long$Asset, levels = names(asset_labels), labels = asset_labels)

# Plot
ggplot(price_long, aes(x = date, y = LogPrice, color = Asset)) +
  geom_line(linewidth = 1) +
  labs(title = "Monthly Log Closing Price of Assets",
       x = "Date", y = "Log Price",
       color = "Asset") +
  theme_minimal() +
  theme(legend.position = "bottom")

## GARCH(1,1)-X Model Implementation
# Calculate macroeconomic surprises using simple exponential smoothing
library(forecast)

# For BI Rate surprise
birate_model <- ses(ts(head(apt_data$bi_rate, -1)), h=1)
birate_forecasts <- c(NA, fitted(birate_model))
birate_surprise <- apt_data$bi_rate - birate_forecasts

# For CPI surprise
cpi_model <- ses(ts(head(apt_data$cpi, -1)), h=1)
cpi_forecasts <- c(NA, fitted(cpi_model))
cpi_surprise <- (apt_data$cpi - cpi_forecasts)/apt_data$cpi

# For exchange rate surprise
kurs_model <- ses(ts(head(apt_data$kurs_idr, -1)), h=1)
kurs_forecasts <- c(NA, fitted(kurs_model))
kurs_surprise <- (apt_data$kurs_idr - kurs_forecasts)/apt_data$kurs_idr

# Add surprises to the dataset
apt_data$birate_surprise <- birate_surprise
apt_data$cpi_surprise <- cpi_surprise
apt_data$kurs_surprise <- kurs_surprise

# Rate plot
p1 <- ggplot(apt_data, aes(x = 1:nrow(apt_data))) +
  geom_line(aes(y = bi_rate, color = "Actual"), linewidth = 1) +
  geom_line(aes(y = birate_forecasts, color = "Forecast"), size = 1) +
  labs(title = "BI Rate: Actual vs Forecast", x = "Time", y = "Rate") +
  scale_color_manual(values = c("blue", "red")) +
  theme_minimal()
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
# CPI plot
p2 <- ggplot(apt_data, aes(x = 1:nrow(apt_data))) +
  geom_line(aes(y = cpi, color = "Actual"), size = 1) +
  geom_line(aes(y = cpi_forecasts, color = "Forecast"), size = 1) +
  labs(title = "CPI: Actual vs Forecast", x = "Time", y = "Rate") +
  scale_color_manual(values = c("blue", "red")) +
  theme_minimal()

# Exchange Rate plot
p3 <- ggplot(apt_data, aes(x = 1:nrow(apt_data))) +
  geom_line(aes(y = kurs_idr, color = "Actual"), size = 1) +
  geom_line(aes(y = kurs_forecasts, color = "Forecast"), size = 1) +
  labs(title = "Exchange Rate: Actual vs Forecast", x = "Time", y = "IDR/USD") +
  scale_color_manual(values = c("blue", "red")) +
  theme_minimal()

# Show plots
library(gridExtra)
## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
grid.arrange(p1, p2, p3, ncol = 1)
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).
## Removed 1 row containing missing values or values outside the scale range
## (`geom_line()`).

# desctiptive table exxess for macroeconomic variables
library(psych)
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
## The following object is masked from 'package:car':
## 
##     logit
macro_vars <- apt_data %>%
  dplyr::select(birate_surprise, cpi_surprise, kurs_surprise)
describe(macro_vars)
##                 vars   n  mean   sd median trimmed  mad   min  max range  skew
## birate_surprise    1 103  0.01 0.29   0.00   -0.02 0.00 -0.50 1.00  1.50  1.23
## cpi_surprise       2 103 -0.03 0.17  -0.03   -0.02 0.16 -0.48 0.41  0.89 -0.24
## kurs_surprise      3 103  0.00 0.03   0.00    0.00 0.02 -0.11 0.12  0.24  0.20
##                 kurtosis   se
## birate_surprise     2.88 0.03
## cpi_surprise       -0.08 0.02
## kurs_surprise       5.28 0.00
summary(macro_vars)
##  birate_surprise       cpi_surprise      kurs_surprise      
##  Min.   :-5.000e-01   Min.   :-0.48487   Min.   :-0.113800  
##  1st Qu.:-2.507e-05   1st Qu.:-0.12864   1st Qu.:-0.011153  
##  Median : 0.000e+00   Median :-0.02578   Median : 0.002720  
##  Mean   : 9.716e-03   Mean   :-0.02805   Mean   : 0.003026  
##  3rd Qu.: 0.000e+00   3rd Qu.: 0.08648   3rd Qu.: 0.015861  
##  Max.   : 1.000e+00   Max.   : 0.40634   Max.   : 0.123705  
##  NA's   :1            NA's   :1          NA's   :1
# Uji Stasioneritas
# Daftar variabel yang akan diuji stasioneritasnya
variables_to_test <- c(
  "excess_jkse", "excess_bond", "excess_btc", "excess_gold",
  "birate_surprise", "cpi_surprise", "kurs_surprise"
)

# Lakukan PP test untuk setiap variabel
stationarity_results <- lapply(variables_to_test, function(var_name) {
  if (var_name %in% colnames(apt_data)) {
    x <- apt_data[[var_name]]
    
    # Pastikan numeric dan buang NA
    x <- as.numeric(x)
    x <- na.omit(x)
    
    # Jalankan pp.test dengan tryCatch untuk hindari error
    test_result <- tryCatch(
      pp.test(x, alternative = "stationary"),
      error = function(e) NULL
    )
    
    if (!is.null(test_result)) {
      data.frame(
        Variable = var_name,
        PP_Statistic = test_result$statistic,
        P_Value = test_result$p.value,
        Stationary = ifelse(test_result$p.value < 0.05, "Yes", "No")
      )
    } else {
      data.frame(
        Variable = var_name,
        PP_Statistic = NA,
        P_Value = NA,
        Stationary = "Error or non-numeric data"
      )
    }
    
  } else {
    data.frame(
      Variable = var_name,
      PP_Statistic = NA,
      P_Value = NA,
      Stationary = "Variable not found"
    )
  }
})
## Warning in pp.test(x, alternative = "stationary"): p-value smaller than printed
## p-value
## Warning in pp.test(x, alternative = "stationary"): p-value smaller than printed
## p-value
## Warning in pp.test(x, alternative = "stationary"): p-value smaller than printed
## p-value
## Warning in pp.test(x, alternative = "stationary"): p-value smaller than printed
## p-value
## Warning in pp.test(x, alternative = "stationary"): p-value smaller than printed
## p-value
## Warning in pp.test(x, alternative = "stationary"): p-value smaller than printed
## p-value
# Gabungkan hasil
stationarity_summary <- do.call(rbind, stationarity_results)
print(stationarity_summary)
##                                Variable PP_Statistic    P_Value Stationary
## Dickey-Fuller Z(alpha)      excess_jkse    -65.85094 0.01000000        Yes
## Dickey-Fuller Z(alpha)1     excess_bond    -69.67599 0.01000000        Yes
## Dickey-Fuller Z(alpha)2      excess_btc   -106.53823 0.01000000        Yes
## Dickey-Fuller Z(alpha)3     excess_gold    -73.06424 0.01000000        Yes
## Dickey-Fuller Z(alpha)4 birate_surprise    -23.25593 0.02805528        Yes
## Dickey-Fuller Z(alpha)5    cpi_surprise    -38.66798 0.01000000        Yes
## Dickey-Fuller Z(alpha)6   kurs_surprise    -41.28257 0.01000000        Yes
# Interpretasi:
# P-value < 0.05 menunjukkan bahwa kita menolak hipotesis nol (data tidak stasioner)
# dan menyimpulkan bahwa data stasioner.

# Remove rows with NA in surprise variables
apt_data <- apt_data %>% filter(!is.na(birate_surprise) & !is.na(cpi_surprise) & !is.na(kurs_surprise))

# Matriks return portofolio (termasuk gold)
return_matrix <- as.matrix(apt_data[, c("jkse_return", "bond_return", "btc_return", "gold_return")])
colnames(return_matrix) <- c("JKSE", "Bond", "BTC", "Gold")

# Contoh faktor eksogenus: suku bunga, kurs, inflasi (disimulasikan)
exog_data <- data.frame(
  birate_surprise = apt_data$birate_surprise,
  kurs_surprise = apt_data$kurs_surprise,
  cpi_surprise = apt_data$cpi_surprise
)

# Satukan dan bersihkan NA di seluruh kolom (returns + exog)
full_data <- cbind(return_matrix, exog_data)
full_data <- na.omit(full_data)

# Pisahkan kembali
returns <- full_data[, 1:4]
exog_data <- full_data[, 5:7]

# =========================================================
# 2. Estimasi GARCH(1,1)-X untuk tiap aset
# =========================================================
# Model dengan external regressors pada mean dan variance
egarch_fit <- list()
egarchx_fit <- list()

for (asset in colnames(return_matrix)) {
  spec_x <- ugarchspec(
    variance.model = list(
      model = "eGARCH",
      garchOrder = c(1, 1)),
    mean.model = list(
      armaOrder = c(1, 0),
      include.mean = TRUE,
      external.regressors = as.matrix(exog_data)  # mean equation X
    ),
    distribution.model = "sstd"
  )
  
  egarch_fit[[asset]] <- ugarchfit(spec_x, data = returns[[asset]])
}

# =========================================================
# Fungsi untuk ekstrak statistik model GARCH-X
# =========================================================
extract_garch_stats <- function(model, asset_name) {
  # cek konvergensi model
  conv <- ifelse(convergence(model) == 0, "Success", "Failed")
  
  # ambil semua koefisien
  coefs <- coef(model)
  
  # ambil nilai likelihood
  ll <- likelihood(model)
  
  # aman untuk model yang gagal konvergen
  if (conv == "Failed" || is.null(coefs)) {
    return(data.frame(
      Asset = asset_name, Convergence = conv,
      Mean_Intercept = NA, Beta_BIRate = NA, Beta_Exchange = NA, Beta_Inflation = NA,
      AR1 = NA, GARCH_Alpha1 = NA, GARCH_Beta1 = NA, Persistence = NA, Log_Likelihood = NA
    ))
  }
  
  # ambil nilai koefisien sesuai urutan (bisa disesuaikan jika nama lain)
  data.frame(
    Asset = asset_name, Convergence = conv,
    Mean_Intercept = coefs["mu"],
    Beta_BIRate = coefs["mxreg1"],
    Beta_Exchange = coefs["mxreg2"],
    Beta_Inflation = coefs["mxreg3"],
    AR1 = coefs["ar1"],
    GARCH_Alpha1 = coefs["alpha1"],
    GARCH_Beta1 = coefs["beta1"],
    Persistence = coefs["alpha1"] + coefs["beta1"],
    Log_Likelihood = ll
  )
}

for (asset in colnames(return_matrix)) {
  spec_x <- ugarchspec(
    variance.model = list(
      model = "eGARCH",
      garchOrder = c(1, 1),
      external.regressors = as.matrix(exog_data)  # varians equation X
    ),
    mean.model = list(
      armaOrder = c(1, 0),
      include.mean = TRUE,
      external.regressors = as.matrix(exog_data)  # mean equation X
    ),
    distribution.model = "sstd"
  )
  
  egarchx_fit[[asset]] <- ugarchfit(spec_x, data = returns[[asset]])
}

# =========================================================
# Ekstrak semua hasil ke satu tabel
# =========================================================
garch_stats <- do.call(rbind, lapply(names(egarch_fit), function(asset) {
  extract_garch_stats(egarch_fit[[asset]], asset)
}))
egarchx_stats <- do.call(rbind, lapply(names(egarchx_fit), function(asset) {
  extract_garch_stats(egarchx_fit[[asset]], asset)
}))

print(garch_stats)
##     Asset Convergence Mean_Intercept  Beta_BIRate Beta_Exchange Beta_Inflation
## mu   JKSE     Success    0.008229735  0.005743512    -0.7770947  -0.0057077898
## mu1  Bond     Success   -0.007972471  0.014070644     0.7264227   0.0009335524
## mu2   BTC     Success   -0.010323632 -0.040827469     0.4510218   0.0448590251
## mu3  Gold     Success    0.001468511  0.011971451    -0.1485771  -0.0384297379
##             AR1 GARCH_Alpha1 GARCH_Beta1 Persistence Log_Likelihood
## mu   0.03233501  -0.30918095   0.6096929   0.3005119      233.92480
## mu1  0.13050853   0.01947146   0.7015184   0.7209899      226.45931
## mu2  0.39431583  -0.05069688   0.7716823   0.7209855       19.14884
## mu3 -0.06245728   0.04905112   0.7811901   0.8302412      222.35485
print(egarchx_stats)
##     Asset Convergence Mean_Intercept  Beta_BIRate Beta_Exchange Beta_Inflation
## mu   JKSE     Success    0.002046534  0.000549316    -0.5772503   -0.006775565
## mu1  Bond     Success   -0.008768081  0.011128871     0.7246535    0.002335702
## mu2   BTC     Success   -0.054166012 -0.031219233     0.1783926   -0.031204555
## mu3  Gold     Success    0.007142299  0.012685929    -0.1451953   -0.005654232
##           AR1 GARCH_Alpha1 GARCH_Beta1 Persistence Log_Likelihood
## mu  0.1066122  -0.28455287   0.8688223   0.5842694      243.18204
## mu1 0.1130767  -0.01118021   0.7499201   0.7387399      228.97735
## mu2 0.2614031  -1.95728450   0.9011208  -1.0561637       24.96565
## mu3 0.1959364   0.22080323   0.8395277   1.0603309      226.88305
# Ekstraksi hasil fitting
mu_t <- sapply(egarch_fit, function(m) fitted(m))
sigma_t <- sapply(egarch_fit, function(m) sigma(m))
mu_t_egarchx <- sapply(egarchx_fit, function(m) fitted(m))
sigma_t_egarchx <- sapply(egarchx_fit, function(m) sigma(m))

mu <- colMeans(mu_t, na.rm = TRUE)       # expected return
sigma <- colMeans(sigma_t, na.rm = TRUE) # expected volatility
mu_egarchx <- colMeans(mu_t_egarchx, na.rm = TRUE)       # expected return
sigma_egarchx <- colMeans(sigma_t_egarchx, na.rm = TRUE) # expected volatility
cov_matrix <- cov(returns)               # kovarians historis

# =========================================================
# 3. Fungsi objektif: Mean–VaR berbasis distribusi GARCH-X
# =========================================================
mean_var_garch_obj <- function(w, mu, cov_matrix, alpha = 0.05, lambda = 0.5) {
  w <- w / sum(w)
  
  mu_p <- sum(w * mu)
  sigma_p <- sqrt(t(w) %*% cov_matrix %*% w)
  VaR_p <- mu_p + qnorm(alpha) * sigma_p
  
  obj <- lambda * (-mu_p) + (1 - lambda) * abs(VaR_p)
  return(obj)
}

# =========================================================
# 4. Jalankan DEOptim
# =========================================================
lower <- rep(0, 4)
upper <- rep(1, 4)

result <- DEoptim(
  fn = mean_var_garch_obj,
  lower = lower,
  upper = upper,
  control = list(NP = 50, itermax = 200),
  mu = mu,
  cov_matrix = cov_matrix,
  alpha = 0.05,
  lambda = 0.5
)
## Iteration: 1 bestvalit: 0.010041 bestmemit:    0.462390    0.405576    0.003661    0.459793
## Iteration: 2 bestvalit: 0.010041 bestmemit:    0.462390    0.405576    0.003661    0.459793
## Iteration: 3 bestvalit: 0.009886 bestmemit:    0.857062    0.809756    0.003707    0.831580
## Iteration: 4 bestvalit: 0.009886 bestmemit:    0.857062    0.809756    0.003707    0.831580
## Iteration: 5 bestvalit: 0.009820 bestmemit:    0.857062    0.809756    0.003707    0.541544
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## Iteration: 35 bestvalit: 0.009749 bestmemit:    0.946366    0.896117    0.001272    0.700468
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result_egarchx <- DEoptim(
  fn = mean_var_garch_obj,
  lower = lower,
  upper = upper,
  control = list(NP = 50, itermax = 200),
  mu = mu_egarchx,
  cov_matrix = cov_matrix,
  alpha = 0.05,
  lambda = 0.5
)
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# Bobot hasil optimasi
w_opt <- result$optim$bestmem / sum(result$optim$bestmem)
names(w_opt) <- names(returns)
w_opt_egarchx <- result_egarchx$optim$bestmem / sum(result_egarchx$optim$bestmem)
names(w_opt_egarchx) <- names(returns)

# Bobot equal-weighted
w_eq <- rep(1/4, 4)
names(w_eq) <- names(returns)

# =========================================================
# 5. Evaluasi kinerja kedua portofolio
# =========================================================
eval_portfolio <- function(w, mu, cov_matrix, alpha = 0.05) {
  mu_p <- sum(w * mu)
  sigma_p <- sqrt(t(w) %*% cov_matrix %*% w)
  VaR_p <- mu_p + qnorm(alpha) * sigma_p
  ES_p  <- mu_p + (dnorm(qnorm(alpha)) / alpha) * sigma_p
  return(c(mu_p, sigma_p, VaR_p, ES_p))
}

perf_opt <- eval_portfolio(w_opt, mu, cov_matrix)
perf_opt_egarchx <- eval_portfolio(w_opt_egarchx, mu_egarchx, cov_matrix)
perf_eq  <- eval_portfolio(w_eq,  mu, cov_matrix)

comparison <- data.frame(
  Portofolio = c("Mean–VaR (EGARCH+DEOptim)","Mean–VaR (EGARCH-X+DEOptim)", "Equal-Weighted"),
  Mean_Return = c(perf_opt[1],perf_opt_egarchx[1], perf_eq[1]),
  Volatility = c(perf_opt[2],perf_opt_egarchx[2], perf_eq[2]),
  VaR_5pct = c(perf_opt[3],perf_opt_egarchx[3], perf_eq[3]),
  ES_5pct = c(perf_opt[4],perf_opt_egarchx[4], perf_eq[4])
)

print(comparison)
##                    Portofolio   Mean_Return Volatility    VaR_5pct    ES_5pct
## 1   Mean–VaR (EGARCH+DEOptim)  0.0009587319 0.01301949 -0.02045642 0.02781419
## 2 Mean–VaR (EGARCH-X+DEOptim)  0.0010103804 0.01343221 -0.02108363 0.02871717
## 3              Equal-Weighted -0.0045430827 0.18043329 -0.30132943 0.36763897
# =========================================================
# 6. Visualisasi Perbandingan Bobot
# =========================================================
library(ggplot2)
library(reshape2)

weights_df <- data.frame(
  Asset = names(w_opt),
  GARCH_MeanVaR = w_opt,
  EGARCHX_MeanVaR = w_opt_egarchx,
  Equal_Weighted = w_eq
)

melted_weights <- melt(weights_df, id.vars = "Asset")

ggplot(melted_weights, aes(x = Asset, y = value, fill = variable)) +
  geom_bar(stat = "identity", position = "dodge") +
  geom_text(aes(label = round(value, 3)), 
            vjust = -0.5, size = 3.5, position = position_dodge(0.9)) +
  labs(
    title = "Perbandingan Bobot Portofolio: Mean–VaR (GARCH+DEOptim), Mean–VaR (EGARCH-X+DEOptim) vs Equal-Weighted",
    x = "Aset",
    y = "Bobot",
    fill = "Metode"
  ) +
  theme_minimal()

# Plot efficient frontier
n_portfolios <- 500
num_assets <- ncol(return_matrix)
weights_matrix <- matrix(0, nrow=n_portfolios, ncol=num_assets)
returns_vector <- numeric(n_portfolios)
risk_vector <- numeric(n_portfolios)

# Generate random portfolios
for (i in 1:n_portfolios) {
  weights <- runif(num_assets)
  weights <- weights / sum(weights)
  weights_matrix[i,] <- weights
  
  # Calculate portfolio return and risk
  returns_vector[i] <- calculate_portfolio_return(weights, return_matrix)
  risk_vector[i] <- calculate_portfolio_var(weights, return_matrix)
}

# Plot the efficient frontier
plot(risk_vector, returns_vector * 100, 
     pch=19, cex=0.5, col="gray",
     xlab="Value at Risk (VaR)", 
     ylab="Expected Monthly Return (%)",
     main="Portfolio Efficiency: Return vs. VaR")

# Add individual assets
asset_returns <- colMeans(return_matrix) * 100
asset_vars <- apply(return_matrix, 2, function(x) calculate_portfolio_var(1, matrix(x)))

points(asset_vars, asset_returns, col="blue", pch=17, cex=1.5)
text(asset_vars, asset_returns, labels=colnames(return_matrix), pos=4)

# Add the optimized and equal-weight portfolios
points(calculate_portfolio_var(w_opt, return_matrix), 
       calculate_portfolio_return(w_opt, return_matrix) * 100, 
       col="red", pch=18, cex=2)
text(calculate_portfolio_var(w_opt, return_matrix), 
     calculate_portfolio_return(w_opt, return_matrix) * 100, 
     "Mean-VaR+GARCH", pos=2, col="red")
points(calculate_portfolio_var(w_opt_egarchx, return_matrix), 
       calculate_portfolio_return(w_opt_egarchx, return_matrix) * 100, 
       col="yellow", pch=18, cex=2)
text(calculate_portfolio_var(w_opt_egarchx, return_matrix), 
     calculate_portfolio_return(w_opt_egarchx, return_matrix) * 100, 
     "Mean-VaR+EGARCHX", pos=2, col="yellow")

points(calculate_portfolio_var(w_eq, return_matrix), 
       calculate_portfolio_return(w_eq, return_matrix) * 100, 
       col="darkgreen", pch=18, cex=2)
text(calculate_portfolio_var(w_eq, return_matrix), 
     calculate_portfolio_return(w_eq, return_matrix) * 100, 
     "Equal-Weight", pos=4, col="darkgreen")

legend("topright", 
       legend=c("Random Portfolios", "Individual Assets", "Mean-VaR+GARCH Portfolio", "Mean-VaR+EGARCH-X Portfolio", "Equal-Weight Portfolio"), 
       col=c("gray", "blue", "red","yellow", "darkgreen"), 
       pch=c(19, 17, 18, 18),
       cex=0.8)

# Visualisasi beta GARCH-X
beta_data_garch <- data.frame(
  Asset = garch_stats$Asset,
  Factor = rep(c("BI Rate", "Exchange Rate", "Inflation"), each = nrow(garch_stats)),
  Beta = c(garch_stats$Beta_BIRate, garch_stats$Beta_Exchange, garch_stats$Beta_Inflation)
)
beta_data_egarchx <- data.frame(
  Asset = egarchx_stats$Asset,
  Factor = rep(c("BI Rate", "Exchange Rate", "Inflation"), each = nrow(egarchx_stats)),
  Beta = c(egarchx_stats$Beta_BIRate, egarchx_stats$Beta_Exchange, egarchx_stats$Beta_Inflation)
)

ggplot(beta_data_garch, aes(x = Asset, y = Beta, fill = Factor)) +
  geom_bar(stat = "identity", position = position_dodge()) +
  theme_minimal() +
  labs(title = "Factor Sensitivities (Betas) by Asset",
       subtitle = "GARCH(1,1) Model with Macroeconomic Factors",
       x = "Asset",
       y = "Beta Coefficient") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

ggplot(beta_data_egarchx, aes(x = Asset, y = Beta, fill = Factor)) +
  geom_bar(stat = "identity", position = position_dodge()) +
  theme_minimal() +
  labs(title = "Factor Sensitivities (Betas) by Asset",
       subtitle = "EGARCH(1,1)-X Model with Macroeconomic Factors",
       x = "Asset",
       y = "Beta Coefficient") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

garch_params <- garch_stats[, c("Asset", "GARCH_Alpha1", "GARCH_Beta1", "Persistence")]
egarchx_params <- egarchx_stats[, c("Asset", "GARCH_Alpha1", "GARCH_Beta1", "Persistence")]
garch_params_wide <- reshape2::dcast(
  reshape2::melt(garch_params, id.vars = "Asset"), 
  Asset ~ variable
)
egarchx_params_wide <- reshape2::dcast(
  reshape2::melt(egarchx_params, id.vars = "Asset"), 
  Asset ~ variable
)
rownames(garch_params_wide) <- garch_params_wide$Asset
rownames(egarchx_params_wide) <- egarchx_params_wide$Asset
garch_params_wide$Asset <- NULL
egarchx_params_wide$Asset <- NULL
heatmap(as.matrix(garch_params_wide), 
        Rowv = NA, Colv = NA, 
        col = colorRampPalette(c("blue", "white", "red"))(100),
        scale = "none", 
        margins = c(5, 10),
        main = "GARCH Model Parameters")

heatmap(as.matrix(egarchx_params_wide), 
        Rowv = NA, Colv = NA, 
        col = colorRampPalette(c("blue", "white", "red"))(100),
        scale = "none", 
        margins = c(5, 10),
        main = "EGARCH-X Model Parameters")

persistence_data <- data.frame(
  Asset = garch_stats$Asset,
  Persistence = garch_stats$Persistence
)
persistence_data_egarchx <- data.frame(
  Asset = egarchx_stats$Asset,
  Persistence = egarchx_stats$Persistence
)
# Urutkan data berdasarkan nilai Persistence (descending)
persistence_data <- persistence_data[order(-persistence_data$Persistence), ]
persistence_data_egarchx <- persistence_data_egarchx[order(-persistence_data_egarchx$Persistence), ]

# Buat barplot dan simpan posisi tengah tiap batang
bar_centers <- barplot(persistence_data$Persistence, 
                       names.arg = persistence_data$Asset,
                       main = "GARCH Volatility Persistence by Asset",
                       col = rainbow(nrow(persistence_data)),
                       las = 2,
                       ylim = c(0, 1.1),
                       cex.names = 0.8)

# Garis referensi di nilai 1
abline(h = 1, lty = 2, col = "red")

# Tambahkan label di atas tengah setiap batang
text(x = bar_centers,
     y = persistence_data$Persistence + 0.05,
     labels = paste0(round(persistence_data$Persistence * 100, 1), "%"),
     cex = 0.7,
     pos = 3)

# Buat barplot dan simpan posisi tengah tiap batang
bar_centers_egarchx <- barplot(persistence_data_egarchx$Persistence, 
                       names.arg = persistence_data_egarchx$Asset,
                       main = "EGARCH-X Volatility Persistence by Asset",
                       col = rainbow(nrow(persistence_data_egarchx)),
                       las = 2,
                       ylim = c(0, 1.1),
                       cex.names = 0.8)

# Garis referensi di nilai 1
abline(h = 1, lty = 2, col = "red")

# Tambahkan label di atas tengah setiap batang
text(x = bar_centers_egarchx,
     y = persistence_data_egarchx$Persistence + 0.05,
     labels = paste0(round(persistence_data_egarchx$Persistence * 100, 1), "%"),
     cex = 0.7,
     pos = 3)

## Value-at-Risk (VaR) Calculation with GARCH and Backtesting
# Helper functions for GARCH models
extract_conditional_mean <- function(garch_model) {
  if (garch_model@fit$convergence != 0) return(NULL)
  fitted(garch_model)
}

extract_conditional_volatility <- function(garch_model) {
  if (garch_model@fit$convergence != 0) return(NULL)
  sigma(garch_model)
}

# Fungsi VaR GARCH-X
calculate_garch_var <- function(garch_model, confidence_level = 0.95) {
  if (garch_model@fit$convergence != 0) return(NULL)
  cond_mean <- fitted(garch_model)
  cond_vol <- sigma(garch_model)
  df <- tryCatch(tail(coef(garch_model)["shape"], 1), error = function(e) NA)
  if (is.na(df) || df <= 2) df <- 5
  t_critical <- qt(1 - confidence_level, df = df)
  -(cond_mean + t_critical * cond_vol)
}

# =========================================================
# Fungsi backtesting GARCH–VaR
# =========================================================
perform_garch_var_backtesting <- function(returns, garch_model, confidence_level = 0.95) {
  # Cek konvergensi model
  valid_model <- (garch_model@fit$convergence == 0)
  if (!valid_model) {
    return(list(exceedances = NA, dates = NA, var_estimates = NA, n = NA))
  }
  
  var_estimates <- calculate_garch_var(garch_model, confidence_level)
  exceedances <- ifelse(-returns > var_estimates, 1, 0)
  list(
    var_estimates = var_estimates,
    exceedances = exceedances,
    dates = index(var_estimates),
    n = length(var_estimates)
  )
}

# =========================================================
# Fungsi Uji Kupiec (Unconditional Coverage Test)
# =========================================================
kupiec_test <- function(exceedances, total_obs, confidence_level) {
  alpha <- 1 - confidence_level
  x <- sum(exceedances, na.rm = TRUE)
  p_hat <- x / total_obs
  
  if (x == 0) {
    lr_stat <- -2 * log((1 - alpha)^total_obs)
  } else if (x == total_obs) {
    lr_stat <- -2 * log(alpha^total_obs)
  } else {
    lr_stat <- -2 * (log((1 - alpha)^(total_obs - x) * alpha^x) -
                       log((1 - p_hat)^(total_obs - x) * p_hat^x))
  }
  
  p_value <- 1 - pchisq(lr_stat, df = 1)
  list(
    exceptions = x,
    total_obs = total_obs,
    expected_rate = alpha,
    actual_rate = p_hat,
    lr_stat = lr_stat,
    p_value = p_value,
    result = ifelse(p_value > 0.05, "Accept H0", "Reject H0")
  )
}

# Update to use excess returns for backtesting
returns <- list(
  JKSE = apt_data$excess_jkse,
  Bond = apt_data$excess_bond,
  BTC = apt_data$excess_btc,
  Gold = apt_data$excess_gold
)

# =========================================================
# Backtesting dan Kupiec Test
# =========================================================
confidence_level <- 0.95
garch_backtest_results <- list()
garch_kupiec_results <- list()

for (asset_name in names(returns)) {
  model <- egarch_fit[[asset_name]]   # ← gunakan [[ ]] bukan [ ]
  
  backtest <- perform_garch_var_backtesting(returns[[asset_name]], model, confidence_level)
  garch_backtest_results[[asset_name]] <- backtest
  
  if (!is.na(backtest$n)) {
    kupiec <- kupiec_test(backtest$exceedances, backtest$n, confidence_level)
    garch_kupiec_results[[asset_name]] <- kupiec
  }
}

egarchx_backtest_results <- list()
egarchx_kupiec_results <- list()

for (asset_name in names(returns)) {
  model <- egarchx_fit[[asset_name]]   # ← gunakan [[ ]] bukan [ ]
  
  backtest <- perform_garch_var_backtesting(returns[[asset_name]], model, confidence_level)
  egarchx_backtest_results[[asset_name]] <- backtest
  
  if (!is.na(backtest$n)) {
    kupiec <- kupiec_test(backtest$exceedances, backtest$n, confidence_level)
    egarchx_kupiec_results[[asset_name]] <- kupiec
  }
}
garch_kupiec_summary <- do.call(rbind, lapply(names(garch_kupiec_results), function(asset) {
  result <- garch_kupiec_results[[asset]]
  if (is.null(result)) return(NULL)
  data.frame(
    Asset = asset,
    Observations = result$total_obs,
    Exceptions = result$exceptions,
    Expected_Rate = result$expected_rate,
    Actual_Rate = result$actual_rate,
    LR_Statistic = result$lr_stat,
    P_Value = result$p_value,
    Result = result$result
  )
}))
egarchx_kupiec_summary <- do.call(rbind, lapply(names(egarchx_kupiec_results), function(asset) {
  result <- egarchx_kupiec_results[[asset]]
  if (is.null(result)) return(NULL)
  data.frame(
    Asset = asset,
    Observations = result$total_obs,
    Exceptions = result$exceptions,
    Expected_Rate = result$expected_rate,
    Actual_Rate = result$actual_rate,
    LR_Statistic = result$lr_stat,
    P_Value = result$p_value,
    Result = result$result
  )
}))
print(garch_kupiec_summary)
##   Asset Observations Exceptions Expected_Rate Actual_Rate LR_Statistic
## 1  JKSE          103          8          0.05  0.07766990  1.430944806
## 2  Bond          103          6          0.05  0.05825243  0.140558279
## 3   BTC          103          2          0.05  0.01941748  2.616936109
## 4  Gold          103          5          0.05  0.04854369  0.004641804
##     P_Value    Result
## 1 0.2316103 Accept H0
## 2 0.7077266 Accept H0
## 3 0.1057284 Accept H0
## 4 0.9456815 Accept H0
print(egarchx_kupiec_summary)
##   Asset Observations Exceptions Expected_Rate Actual_Rate LR_Statistic
## 1  JKSE          103          9          0.05 0.087378641  2.501610152
## 2  Bond          103          5          0.05 0.048543689  0.004641804
## 3   BTC          103          1          0.05 0.009708738  5.195578937
## 4  Gold          103          4          0.05 0.038834951  0.291844117
##      P_Value    Result
## 1 0.11372997 Accept H0
## 2 0.94568152 Accept H0
## 3 0.02264441 Reject H0
## 4 0.58904119 Accept H0
# Compare Mean-VaR and Equal-weighted portfolio performance over time
# === CUMULATIVE RETURNS COMPARISON ===
dates <- apt_data$date
apt_data$portfolio_return_garch <- as.numeric(return_matrix %*% w_opt)
apt_data$portfolio_return_egarchx <- as.numeric(return_matrix %*% w_opt_egarchx)
apt_data$portfolio_return_equal <- as.numeric(return_matrix %*% w_eq)
garch_cumulative     <- cumprod(1 + apt_data$portfolio_return_garch)
egarchx_cumulative     <- cumprod(1 + apt_data$portfolio_return_egarchx)
equal_cumulative       <- cumprod(1 + apt_data$portfolio_return_equal)
jkse_cumulative        <- cumprod(1 + apt_data$jkse_return)
bond_cumulative        <- cumprod(1 + apt_data$bond_return)
btc_cumulative         <- cumprod(1 + apt_data$btc_return)
gold_cumulative        <- cumprod(1 + apt_data$gold_return)

# === Plot Cumulative Performance ===
plot(dates, garch_cumulative, type="l", col="red", lwd=2,
     xlab="Date", ylab="Cumulative Return (Start = 1)",
     main="Cumulative Performance Comparison",
     ylim=c(min(0.5, min(garch_cumulative, egarchx_cumulative, equal_cumulative) * 0.9),
            max(garch_cumulative, egarchx_cumulative, equal_cumulative, btc_cumulative) * 1.1))

lines(dates, egarchx_cumulative, col="orange", lwd=2, lty=2)
lines(dates, equal_cumulative, col="blue", lwd=2)
lines(dates, jkse_cumulative, col="darkgreen", lwd=1)
lines(dates, bond_cumulative, col="purple", lwd=1)
lines(dates, btc_cumulative, col="black", lwd=1)
lines(dates, gold_cumulative, col="goldenrod1", lwd=1)

legend("topleft",
       legend=c("Mean–VaR+GARCH", "Mean–VaR+EGARCH-X", "Equal-Weight",
                "JKSE", "Bond", "BTC", "Gold"),
       col=c("red", "orange", "blue", "darkgreen", "purple", "black", "goldenrod1"),
       lwd=c(2, 2, 2, 1, 1, 1, 1),
       lty=c(1, 2, 1, 1, 1, 1, 1),
       cex=0.8)

# === ROLLING METRICS ===
window <- 24 # 24-month rolling window
assets_returns <- cbind(
  apt_data$portfolio_return_garch,
  apt_data$portfolio_return_egarchx,
  apt_data$portfolio_return_equal,
  apt_data$jkse_return,
  apt_data$bond_return,
  apt_data$btc_return,
  apt_data$gold_return
)

colnames(assets_returns) <- c("MeanVar_GARCH", "MeanVar_EGARCHX", "Equal", "JKSE", "Bond", "BTC", "Gold")

rolling_returns   <- matrix(NA, nrow=length(dates) - window, ncol=ncol(assets_returns))
rolling_volatility <- matrix(NA, nrow=length(dates) - window, ncol=ncol(assets_returns))
rolling_sharpe    <- matrix(NA, nrow=length(dates) - window, ncol=ncol(assets_returns))
rolling_var       <- matrix(NA, nrow=length(dates) - window, ncol=ncol(assets_returns))

for (i in 1:(length(dates) - window)) {
  window_returns <- assets_returns[i:(i+window-1), ]
  rolling_returns[i, ]    <- colMeans(window_returns, na.rm=TRUE)
  rolling_volatility[i, ] <- apply(window_returns, 2, sd, na.rm=TRUE)
  rolling_sharpe[i, ]     <- rolling_returns[i, ] / rolling_volatility[i, ]
  rolling_var[i, ]        <- apply(window_returns, 2, function(x) -quantile(x, 0.05, na.rm=TRUE))
}

# === Plot Rolling Sharpe Ratio ===
par(mfrow=c(2,1))

plot(dates[(window+1):length(dates)], rolling_sharpe[,1], type="l", col="red", lwd=2,
     xlab="Date", ylab="Sharpe Ratio",
     main="Rolling 24-Month Sharpe Ratio",
     ylim=c(min(rolling_sharpe[,1:3]) * 1.1, max(rolling_sharpe[,1:3]) * 1.1))
lines(dates[(window+1):length(dates)], rolling_sharpe[,2], col="orange", lwd=2, lty=2)
lines(dates[(window+1):length(dates)], rolling_sharpe[,3], col="blue", lwd=2, lty=3)
abline(h=0, lty=2, col="gray")

legend("bottomright",
       legend=c("Mean–VaR+GARCH", "Mean–VaR+EGARCH-X", "Equal-Weight"),
       col=c("red", "orange", "blue"),
       lwd=2, lty=c(1,2,3),
       cex=0.8)

# === Plot Rolling VaR ===
plot(dates[(window+1):length(dates)], rolling_var[,1], type="l", col="red", lwd=2,
     xlab="Date", ylab="Value-at-Risk (95%)",
     main="Rolling 24-Month VaR (95%)",
     ylim=c(min(rolling_var[,1:3]) * 0.9, max(rolling_var[,1:3]) * 1.1))
lines(dates[(window+1):length(dates)], rolling_var[,2], col="orange", lwd=2, lty=2)
lines(dates[(window+1):length(dates)], rolling_var[,3], col="blue", lwd=2, lty=3)
legend("topright",
       legend=c("Mean–VaR+GARCH", "Mean–VaR+EGARCH-X", "Equal-Weight"),
       col=c("red", "orange", "blue"),
       lwd=2, lty=c(1,2,3),
       cex=0.8)

par(mfrow=c(1,1))

# === SUMMARY STATISTICS ===
return_stats <- data.frame(
  Mean_Return = colMeans(assets_returns, na.rm=TRUE) * 100,
  Volatility  = apply(assets_returns, 2, sd, na.rm=TRUE) * 100,
  Sharpe      = colMeans(assets_returns, na.rm=TRUE) /
    apply(assets_returns, 2, sd, na.rm=TRUE),
  VaR_95      = apply(assets_returns, 2, function(x) -quantile(x, 0.05, na.rm=TRUE)) * 100,
  Max_Drawdown = apply(assets_returns, 2, function(x) {
    cumu <- cumprod(1 + x)
    peak <- cumu[1]
    maxDD <- 0
    for (i in 2:length(cumu)) {
      if (cumu[i] > peak) peak <- cumu[i]
      DD <- (peak - cumu[i]) / peak
      if (DD > maxDD) maxDD <- DD
    }
    return(maxDD * 100)
  })
)

return_stats <- return_stats[order(-return_stats$Sharpe), ]
print(return_stats)
##                 Mean_Return Volatility      Sharpe    VaR_95 Max_Drawdown
## MeanVar_EGARCHX   0.3585308   1.343221  0.26691874  1.698267     5.138436
## MeanVar_GARCH     0.3106196   1.301949  0.23858055  1.645667     7.933005
## Gold              0.7215469   3.026203  0.23843304  4.528224    16.122314
## JKSE              0.4019900   3.525595  0.11402047  4.655023    32.465213
## Bond             -0.1039063   3.529937 -0.02943575  5.424170    30.353016
## Equal            -0.6360949  18.043329 -0.03525374  7.248948   245.898959
## BTC              -3.5640100  72.298532 -0.04929575 25.808827   145.022780
return_stats$Portfolio <- rownames(return_stats)

# === OPTIONAL: EXPORT RESULTS ===
writexl::write_xlsx(return_stats, "Portfolio_Performance_Comparison.xlsx")

# Exercise
library(DEoptim)
library(MASS)
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
# =========================================================
# 3. Fungsi Objektif Mean–VaR (berbasis distribusi GARCH-X)
# =========================================================
mean_var_garch_obj <- function(w, mu, cov_matrix, alpha = 0.05, lambda = 0.5, max_risk = NA) {
  w <- w / sum(w)  # Normalisasi bobot
  
  mu_p <- sum(w * mu)
  sigma_p <- sqrt(t(w) %*% cov_matrix %*% w)
  VaR_p <- mu_p + qnorm(alpha) * sigma_p
  
  # Jika ada batas risiko, penalti untuk portofolio melebihi batas
  if (!is.na(max_risk) && sigma_p > max_risk) {
    return(Inf)
  }
  
  # Fungsi objektif: kombinasi trade-off return dan risiko (VaR)
  obj <- lambda * (-mu_p) + (1 - lambda) * abs(VaR_p)
  return(obj)
}

# =========================================================
# 4. Simulasi Optimasi DEoptim untuk berbagai batas risiko
# =========================================================

risk_levels <- c(NA, 0.02, 0.04, 0.06, 0.08)

# Hasil disimpan dalam list
results_garch <- list()
results_egarchx <- list()

lower <- rep(0, 4)
upper <- rep(1, 4)

for (r in risk_levels) {
  label <- ifelse(is.na(r), "No_Risk_Limit", paste0("MaxRisk_", r))
  cat("\n==== Optimizing for Risk ", label, " ====\n")
  
  # --- Model GARCH ---
  result_garch <- DEoptim(
    fn = mean_var_garch_obj,
    lower = lower,
    upper = upper,
    control = list(NP = 50, itermax = 200),
    mu = mu,          # dari hasil model GARCH
    cov_matrix = cov_matrix,
    alpha = 0.05,
    lambda = 0.5,
    max_risk = r
  )
  results_garch[[label]] <- result_garch
  
  # --- Model EGARCH-X ---
  result_egarchx <- DEoptim(
    fn = mean_var_garch_obj,
    lower = lower,
    upper = upper,
    control = list(NP = 50, itermax = 200),
    mu = mu_egarchx,        # dari hasil model EGARCH-X
    cov_matrix = cov_matrix,
    alpha = 0.05,
    lambda = 0.5,
    max_risk = r
  )
  results_egarchx[[label]] <- result_egarchx
}
## 
## ==== Optimizing for Risk  No_Risk_Limit  ====
## Iteration: 1 bestvalit: 0.017360 bestmemit:    0.682382    0.572860    0.028988    0.058872
## Iteration: 2 bestvalit: 0.014265 bestmemit:    0.682382    0.572860    0.028988    0.324042
## Iteration: 3 bestvalit: 0.010765 bestmemit:    0.734025    0.976311    0.006255    0.450680
## Iteration: 4 bestvalit: 0.010223 bestmemit:    0.887158    0.846278    0.014743    0.747032
## Iteration: 5 bestvalit: 0.010223 bestmemit:    0.887158    0.846278    0.014743    0.747032
## Iteration: 6 bestvalit: 0.010223 bestmemit:    0.887158    0.846278    0.014743    0.747032
## Iteration: 7 bestvalit: 0.010223 bestmemit:    0.887158    0.846278    0.014743    0.747032
## Iteration: 8 bestvalit: 0.010223 bestmemit:    0.887158    0.846278    0.014743    0.747032
## Iteration: 9 bestvalit: 0.010218 bestmemit:    0.639011    0.761752    0.001330    0.392546
## Iteration: 10 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 11 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 12 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 13 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 14 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 15 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 16 bestvalit: 0.009809 bestmemit:    0.705609    0.694266    0.002452    0.643196
## Iteration: 17 bestvalit: 0.009787 bestmemit:    0.791644    0.745330    0.002452    0.678342
## Iteration: 18 bestvalit: 0.009787 bestmemit:    0.791644    0.745330    0.002452    0.678342
## Iteration: 19 bestvalit: 0.009755 bestmemit:    0.791644    0.745330    0.002452    0.586722
## Iteration: 20 bestvalit: 0.009755 bestmemit:    0.791644    0.745330    0.002452    0.586722
## Iteration: 21 bestvalit: 0.009755 bestmemit:    0.791644    0.745330    0.002452    0.586722
## Iteration: 22 bestvalit: 0.009755 bestmemit:    0.791644    0.745330    0.002452    0.586722
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## 
## ==== Optimizing for Risk  MaxRisk_0.02  ====
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## 
## ==== Optimizing for Risk  MaxRisk_0.04  ====
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## 
## ==== Optimizing for Risk  MaxRisk_0.06  ====
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## 
## ==== Optimizing for Risk  MaxRisk_0.08  ====
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# =========================================================
# 5. Ekstraksi hasil dan perbandingan
# =========================================================

extract_portfolio_stats <- function(opt_result, mu, cov_matrix) {
  w_opt <- opt_result$optim$bestmem / sum(opt_result$optim$bestmem)
  mu_p <- sum(w_opt * mu)
  sigma_p <- sqrt(t(w_opt) %*% cov_matrix %*% w_opt)
  VaR_p <- mu_p + qnorm(0.05) * sigma_p
  data.frame(
    Return = mu_p,
    Risk = sigma_p,
    VaR = VaR_p,
    Weights = I(list(round(w_opt, 4)))
  )
}

summary_garch <- do.call(rbind, lapply(results_garch, extract_portfolio_stats, mu = mu, cov_matrix = cov_matrix))
summary_egarchx <- do.call(rbind, lapply(results_egarchx, extract_portfolio_stats, mu = mu_egarchx, cov_matrix = cov_matrix))

summary_garch <- cbind(Model = "GARCH", Risk_Level = names(results_garch), summary_garch)
summary_egarchx <- cbind(Model = "EGARCH-X", Risk_Level = names(results_egarchx), summary_egarchx)

summary_all <- rbind(summary_garch, summary_egarchx)

print(summary_all)
##                   Model    Risk_Level       Return       Risk         VaR
## No_Risk_Limit     GARCH No_Risk_Limit 0.0009588529 0.01301963 -0.02045654
## MaxRisk_0.02      GARCH  MaxRisk_0.02 0.0009588575 0.01301964 -0.02045654
## MaxRisk_0.04      GARCH  MaxRisk_0.04 0.0009589876 0.01301980 -0.02045667
## MaxRisk_0.06      GARCH  MaxRisk_0.06 0.0009588675 0.01301965 -0.02045655
## MaxRisk_0.08      GARCH  MaxRisk_0.08 0.0009588468 0.01301963 -0.02045653
## No_Risk_Limit1 EGARCH-X No_Risk_Limit 0.0010104162 0.01343225 -0.02108367
## MaxRisk_0.021  EGARCH-X  MaxRisk_0.02 0.0010103220 0.01343214 -0.02108358
## MaxRisk_0.041  EGARCH-X  MaxRisk_0.04 0.0010104867 0.01343234 -0.02108374
## MaxRisk_0.061  EGARCH-X  MaxRisk_0.06 0.0010104568 0.01343230 -0.02108371
## MaxRisk_0.081  EGARCH-X  MaxRisk_0.08 0.0010104923 0.01343234 -0.02108375
##                     Weights
## No_Risk_Limit  0.3695, ....
## MaxRisk_0.02   0.3695, ....
## MaxRisk_0.04   0.3695, ....
## MaxRisk_0.06   0.3695, ....
## MaxRisk_0.08   0.3695, ....
## No_Risk_Limit1 0.2848, ....
## MaxRisk_0.021  0.2848, ....
## MaxRisk_0.041  0.2848, ....
## MaxRisk_0.061  0.2848, ....
## MaxRisk_0.081  0.2848, ....
library(ggplot2)
library(gridExtra)

asset_names <- c("JKSE", "Bond", "BTC", "Gold")
plots_garch <- list()
plots_egarchx <- list()

# ===== GARCH =====
for (name in names(results_garch)) {
  res <- results_garch[[name]]
  
  weights <- if(!is.null(res$optim$bestmem)) res$optim$bestmem else res
  weights <- weights / sum(weights) * 100
  
  df <- data.frame(
    Asset = asset_names,
    Weight = round(weights, 2)
  )
  
  p <- ggplot(df, aes(x = "", y = Weight, fill = Asset)) +
    geom_col(width = 1, color = "white") +
    coord_polar(theta = "y") +
    geom_text(aes(label = paste0(round(Weight, 1), "%")),
              position = position_stack(vjust = 0.5), size = 3) +
    theme_void() +
    ggtitle(paste("Mean–VaR+GARCH Portfolio\n", name)) +
    theme(plot.title = element_text(hjust = 0.5, size = 12, face = "bold"),
          legend.position = "right") +
    guides(fill = guide_legend(ncol = 1))
  
  plots_garch[[name]] <- p
}

# ===== EGARCH-X =====
for (name in names(results_egarchx)) {
  res <- results_egarchx[[name]]
  
  weights <- if(!is.null(res$optim$bestmem)) res$optim$bestmem else res
  weights <- weights / sum(weights) * 100
  
  df <- data.frame(
    Asset = asset_names,
    Weight = round(weights, 2)
  )
  
  p <- ggplot(df, aes(x = "", y = Weight, fill = Asset)) +
    geom_col(width = 1, color = "white") +
    coord_polar(theta = "y") +
    geom_text(aes(label = paste0(round(Weight, 1), "%")),
              position = position_stack(vjust = 0.5), size = 3) +
    theme_void() +
    ggtitle(paste("Mean–VaR+EGARCHX Portfolio\n", name)) +
    theme(plot.title = element_text(hjust = 0.5, size = 12, face = "bold"),
          legend.position = "right") +
    guides(fill = guide_legend(ncol = 1))
  
  plots_egarchx[[name]] <- p
}

# ===== Tampilkan pie chart =====
grid.arrange(grobs = plots_garch, ncol = 3)

grid.arrange(grobs = plots_egarchx, ncol = 3)

writexl::write_xlsx(data.frame(summary_all),"Comparison Data Frame.xlsx")
## Warning in writexl::write_xlsx(data.frame(summary_all), "Comparison Data
## Frame.xlsx"): Column 'Weights' has unrecognized data type.