# Load required libraries
library(readxl)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
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## filter, lag
## The following objects are masked from 'package:base':
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## 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
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## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
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## 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. #
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## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
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## first, last
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## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
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## 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
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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
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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.