- Try to find the MVP for 4 Taiwan ETFs:
“tw0050”,“tw0056”,“tw006205”,“tw00646”. Using 2015/12/14-2018/12/28
daily returns as the insample data, you have to compute optimal weights
for 4 ETFs based on daily returns of the period. Given the derived
optimal weights, compute realized returns of MVP.
rm(list = ls())
library(readr)
library(xts)
## Warning: package 'xts' was built under R version 4.2.2
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.2.2
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## ################################### WARNING ###################################
## # We noticed you have dplyr installed. The dplyr lag() function breaks how #
## # base R's lag() function is supposed to work, which breaks lag(my_xts). #
## # #
## # If you call library(dplyr) later in this session, then calls to lag(my_xts) #
## # that you enter or source() into this session won't work correctly. #
## # #
## # All package code is unaffected because it is protected by the R namespace #
## # mechanism. #
## # #
## # Set `options(xts.warn_dplyr_breaks_lag = FALSE)` to suppress this warning. #
## # #
## # You can 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. #
## ################################### WARNING ###################################
etf4 <- read_csv("C:/Users/admin/Documents/myetf4(1).csv")
## Rows: 751 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Index
## dbl (4): tw0050, tw0056, tw006205, tw00646
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
colnames(etf4) <- c("Index","0050","0056","006205","00646")
head(etf4)
## # A tibble: 6 × 5
## Index `0050` `0056` `006205` `00646`
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 2015/12/14 53.3 18.2 31.1 19.6
## 2 2015/12/15 53.3 18.4 31.6 19.6
## 3 2015/12/16 54.1 18.6 31.6 19.9
## 4 2015/12/17 54.8 18.8 32.2 20.0
## 5 2015/12/18 54.5 19.0 32.2 19.8
## 6 2015/12/21 54.4 19.0 33 19.6
etf4.xts <- as.xts(etf4[,-1], order.by = as.POSIXct(etf4$Index) )
head(etf4.xts)
## 0050 0056 006205 00646
## 2015-12-14 53.29 18.25 31.06 19.61
## 2015-12-15 53.33 18.38 31.59 19.63
## 2015-12-16 54.14 18.56 31.60 19.89
## 2015-12-17 54.77 18.81 32.23 20.05
## 2015-12-18 54.50 18.95 32.18 19.85
## 2015-12-21 54.41 19.02 33.00 19.64
library(magrittr)
library(PerformanceAnalytics)
## Warning: package 'PerformanceAnalytics' was built under R version 4.2.2
##
## Attaching package: 'PerformanceAnalytics'
##
## The following object is masked from 'package:graphics':
##
## legend
etf4.ret <- etf4.xts %>% Return.calculate() %>% na.omit()
head(etf4.ret)
## 0050 0056 006205 00646
## 2015-12-15 0.0007506099 0.007123288 0.0170637476 0.001019888
## 2015-12-16 0.0151884493 0.009793254 0.0003165559 0.013245033
## 2015-12-17 0.0116364980 0.013469828 0.0199367089 0.008044243
## 2015-12-18 -0.0049297060 0.007442850 -0.0015513497 -0.009975062
## 2015-12-21 -0.0016513761 0.003693931 0.0254816656 -0.010579345
## 2015-12-22 0.0023892667 -0.003680336 0.0030303030 0.004073320
- By Q1, use monthly returns to recalculate the answers to Q1.
etf4.mon.ret <- etf4.xts %>% to.monthly(indexAt = "lastof", OHLC = FALSE) %>% Return.calculate() %>% na.omit()
head(etf4.mon.ret)
## 0050 0056 006205 00646
## 2016-01-31 -0.01981651 -0.013785790 -0.173070915 -0.038883350
## 2016-02-29 0.02864096 0.043548387 -0.027578391 -0.003630705
## 2016-03-31 0.05550500 -0.002575992 0.082750583 0.026028110
## 2016-04-30 -0.04724138 -0.037190083 -0.024757804 0.009639777
## 2016-05-31 0.02515382 0.016630901 0.004415011 0.022110553
## 2016-06-30 0.03636364 0.029551451 -0.025641026 -0.026057030
- Find the tangency portfolio based on Q2. Risk-free rate is assumed
to be zero