Optimasi Portofolio

Tugas Portofolio Saham

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library(tidyquant)

## Warning: package 'tidyquant' was built under R version 4.2.2

## Loading required package: lubridate

## 
## Attaching package: 'lubridate'

## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union

## Loading required package: PerformanceAnalytics

## Warning: package 'PerformanceAnalytics' was built under R version 4.2.2

## Loading required package: xts

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## 
## Attaching package: 'PerformanceAnalytics'

## The following object is masked from 'package:graphics':
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##     legend

## Loading required package: quantmod

## Loading required package: TTR

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

library(plotly)

## Warning: package 'plotly' was built under R version 4.2.2

## Loading required package: ggplot2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
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## The following object is masked from 'package:stats':
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##     filter

## The following object is masked from 'package:graphics':
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library(timetk)

## Warning: package 'timetk' was built under R version 4.2.2

tick = c('BBCA.JK','TLKM.JK','BBRI.JK','ASII.JK','UNVR.JK')

pricedata = tq_get(tick,
                   from = '2020-01-01',
                   to   = Sys.Date(),              
                   get  = 'stock.prices')
pricedata

Pengembalian

Setelah menginput 5 data saham, kita dapat menghitung pengembalian harian untuk beberapa saham ini dengan menggunakan pengembalian logaritmik yang bertujuan untuk memastikan data stasioner.

log_ret_tidy <- pricedata %>%
  group_by(symbol) %>%
  tq_transmute(select = adjusted,
               mutate_fun = periodReturn,
               period = 'daily',
               col_rename = 'ret',
               type = 'log') 

#log_ret_tidy$ret<-round(log_ret_tidy$ret,4)

library(DT)  # print data dalam tabel

## Warning: package 'DT' was built under R version 4.2.1

datatable(log_ret_tidy)

Kita dapat menggunakan fungsi spread() untuk mengubah datatable menjadi format lebar dan menggunakan xts() untuk mengubahnya menjadi objek time series.

library(tidyr)

log_ret_xts = log_ret_tidy %>%
  spread(symbol, value = ret) %>%
  tk_xts()

## Warning: Non-numeric columns being dropped: date

## Using column `date` for date_var.

datatable(log_ret_xts)

Rata-rata Pengembalian

mean_ret <- colMeans(log_ret_xts)
print ( round (mean_ret, 4))

## ASII.JK BBCA.JK BBRI.JK TLKM.JK UNVR.JK 
##  -1e-04   4e-04   3e-04   1e-04  -7e-04

Matriks Kovariansi

cov_mat <- cov(log_ret_xts) * 252
print(round(cov_mat,4))

##         ASII.JK BBCA.JK BBRI.JK TLKM.JK UNVR.JK
## ASII.JK  0.1381  0.0523  0.0689  0.0510  0.0406
## BBCA.JK  0.0523  0.0824  0.0632  0.0442  0.0342
## BBRI.JK  0.0689  0.0632  0.1445  0.0535  0.0370
## TLKM.JK  0.0510  0.0442  0.0535  0.1079  0.0322
## UNVR.JK  0.0406  0.0342  0.0370  0.0322  0.1292

Penerapan Metode Portofolio

Dalam menerapkan metode portofolio,

wts <- runif(n = length(tick))
wts <- wts/sum(wts)

port_returns <- (sum(wts * mean_ret) + 1)^252 - 1
port_risk <- sqrt(t(wts) %*% (cov_mat %*% wts))
sharpe_ratio <- port_returns/port_risk

num_port <- 5000

all_wts <- matrix(nrow = num_port, ncol = length(tick))
port_returns <- vector('numeric', length = num_port)
port_risk <- vector('numeric', length = num_port)
sharpe_ratio <- vector('numeric', length = num_port)

for (i in seq_along(port_returns)) {
  
  wts <- runif(length(tick))
  wts <- wts/sum(wts)
  
  all_wts[i,] <- wts
  
  
  port_ret <- sum(wts * mean_ret)
  port_ret <- ((port_ret + 1)^252) - 1
  
  port_returns[i] <- port_ret
  
  
  port_sd <- sqrt(t(wts) %*% (cov_mat  %*% wts))
  port_risk[i] <- port_sd
  
  sr <- port_ret/port_sd
  sharpe_ratio[i] <- sr
}

portfolio_values <- tibble(Return = port_returns,
                             Risk = port_risk,
                      SharpeRatio = sharpe_ratio)
all_wts <- tk_tbl(all_wts)

## Warning in tk_tbl.data.frame(as.data.frame(data), preserve_index,
## rename_index, : Warning: No index to preserve. Object otherwise converted to
## tibble successfully.

colnames(all_wts) <- colnames(log_ret_xts)

portfolio_values <- tk_tbl(cbind(all_wts, portfolio_values))

## Warning in tk_tbl.data.frame(cbind(all_wts, portfolio_values)): Warning: No
## index to preserve. Object otherwise converted to tibble successfully.

datatable(portfolio_values)

library(forcats)

## Warning: package 'forcats' was built under R version 4.2.1

min_var <- portfolio_values[which.min(portfolio_values$Risk),]

p <- min_var %>%
  gather(ASII.JK:UNVR.JK, key = Asset,
         value = Weights) %>%
  mutate(Asset = as.factor(Asset)) %>%
  ggplot(aes(x = fct_reorder(Asset,Weights), y = Weights, fill = Asset)) +
  geom_bar(stat = 'identity') +
  theme_minimal() +
  labs(x = 'Aset', 
       y = 'Bobot', 
       title = "Bobot Portofolio dengan Variansi Minimum") +
  scale_y_continuous(labels = scales::percent) +
  theme(legend.position = "none" )

ggplotly(p)

max_sr <- portfolio_values[which.max(portfolio_values$SharpeRatio),]

p <- max_sr %>%
  gather(ASII.JK:UNVR.JK, key = Asset,
         value = Weights) %>%
  mutate(Asset = as.factor(Asset)) %>%
  ggplot(aes(x = fct_reorder(Asset,Weights), y = Weights, fill = Asset)) +
  geom_bar(stat = 'identity') +
  theme_minimal() +
  labs(x = 'Aset', 
       y = 'Bobot', 
       title = "Bobot Portofolio Tangensi (Maksimum Sharpe Ratio)") +
  scale_y_continuous(labels = scales::percent) +
  theme(legend.position = "none" )

ggplotly(p)

Batas Efisien Portofolio

p <- portfolio_values %>%
  ggplot(aes(x = Risk, y = Return, color = SharpeRatio)) +
  geom_point() +
  theme_classic() +
  scale_y_continuous(labels = scales::percent) +
  scale_x_continuous(labels = scales::percent) +
  labs(x = 'Risiko Tahunan',
       y = 'Pengembalian Tahunan',
       title = "Optimasi Portofolio & Perbatasan yang Efisien") +
  geom_point(aes(x = Risk, y = Return), data = min_var, color = 'red') +
  geom_point(aes(x = Risk, y = Return), data = max_sr, color = 'red') +
  annotate('text', x = 0.31, y = 0.31, label = "Portofolio Tangensi") +
  annotate('text', x = 0.24, y = 0.11, label = "Portofolio Varians minimum") +
  annotate(geom = 'segment', x = 0.3023, xend = 0.3023,  y = 0.23, 
           yend = 0.29, color = 'red', arrow = arrow(type = "open")) +
  annotate(geom = 'segment', x = 0.25, xend = 0.25,  y = 0.015, 
           yend = 0.10, color = 'red', arrow = arrow(type = "open"))
  
ggplotly(p)