#Load required packages
library(xts)
library(quantmod)
library(SIT)
library(reshape2)
library(readr)
library(kernlab)
#Load analytical file
rm(list = ls())
etf6 <- read_csv("C:/Users/User/Downloads/ETF6_20080101-20200430.csv")
## Rows: 14935 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (2): 證券代碼, 簡稱
## dbl (2): 年月日, 收盤價(元)
##
## 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.
head(etf6)
## # A tibble: 6 × 4
## 證券代碼 簡稱 年月日 `收盤價(元)`
## <chr> <chr> <dbl> <dbl>
## 1 0050 元大台灣50 20080102 39.6
## 2 0052 富邦科技 20080102 27.1
## 3 0056 元大高股息 20080102 14.6
## 4 0050 元大台灣50 20080103 39.0
## 5 0052 富邦科技 20080103 26.1
## 6 0056 元大高股息 20080103 14.4
etf6 <- etf6[, -2]
colnames(etf6) <- c('id', 'date', 'price')
head(etf6)
## # A tibble: 6 × 3
## id date price
## <chr> <dbl> <dbl>
## 1 0050 20080102 39.6
## 2 0052 20080102 27.1
## 3 0056 20080102 14.6
## 4 0050 20080103 39.0
## 5 0052 20080103 26.1
## 6 0056 20080103 14.4
etf6.1 <- dcast(etf6, date~id)
## Using price as value column: use value.var to override.
head(etf6.1)
## date 0050 0052 0056 0061 006206 00638R
## 1 20080102 39.6472 27.0983 14.5739 NA NA NA
## 2 20080103 38.9876 26.0676 14.3758 NA NA NA
## 3 20080104 38.9876 25.9346 14.4041 NA NA NA
## 4 20080107 37.2064 24.1391 14.1777 NA NA NA
## 5 20080108 37.5692 24.1391 14.3531 NA NA NA
## 6 20080109 38.2619 24.2721 14.4663 NA NA NA
str(etf6.1)
## 'data.frame': 3041 obs. of 7 variables:
## $ date : num 20080102 20080103 20080104 20080107 20080108 ...
## $ 0050 : num 39.6 39 39 37.2 37.6 ...
## $ 0052 : num 27.1 26.1 25.9 24.1 24.1 ...
## $ 0056 : num 14.6 14.4 14.4 14.2 14.4 ...
## $ 0061 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 006206: num NA NA NA NA NA NA NA NA NA NA ...
## $ 00638R: num NA NA NA NA NA NA NA NA NA NA ...
etf6.xts <- xts(etf6.1[, -1], order.by = as.Date(as.character(etf6.1$date), format = '%Y%m%d'))
class(etf6.xts)
## [1] "xts" "zoo"
head(etf6.xts)
## 0050 0052 0056 0061 006206 00638R
## 2008-01-02 39.6472 27.0983 14.5739 NA NA NA
## 2008-01-03 38.9876 26.0676 14.3758 NA NA NA
## 2008-01-04 38.9876 25.9346 14.4041 NA NA NA
## 2008-01-07 37.2064 24.1391 14.1777 NA NA NA
## 2008-01-08 37.5692 24.1391 14.3531 NA NA NA
## 2008-01-09 38.2619 24.2721 14.4663 NA NA NA
data <- new.env()
model <- list()
etf3 <- etf6.xts[, 1:3]
head(etf3)
## 0050 0052 0056
## 2008-01-02 39.6472 27.0983 14.5739
## 2008-01-03 38.9876 26.0676 14.3758
## 2008-01-04 38.9876 25.9346 14.4041
## 2008-01-07 37.2064 24.1391 14.1777
## 2008-01-08 37.5692 24.1391 14.3531
## 2008-01-09 38.2619 24.2721 14.4663
names(etf3)
## [1] "0050" "0052" "0056"
colnames(etf3) <- c('e50', 'e52', 'e56')
names(etf3)
## [1] "e50" "e52" "e56"
#Question 1. Select the first 3 ETFs (0050, 0052 and 0056)
#and apply moving average (MA) investment rule to the selected three ETFs.
#MA investment rule is that we will build up our position
#when prices are higher than the average trading prices of last 50 days.
#Show MA invstment performance of these 3 ETFs.
md = 50
i = 'e50'
for(i in names(etf3)) {
data$prices = data$weight = data$execution.price = etf3[, i]
data$weight[] <- 1
data$execution.price[] <- NA
model[[i]] <- bt.run(data)
sma <- SMA(data$prices, md)
data$weight[] <- iif(data$prices >= sma, 1, 0)
i <- paste(i, '.sma.cross', sep = '')
model[[i]] <- bt.run(data)
}
## Latest weights :
## e50
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 6.4 8 -7
##
## Latest weights :
## e50
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 5.3 7 -6.4
##
## Latest weights :
## e52
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 7.3 10 -9.2
##
## Latest weights :
## e52
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 0.9 10 -9.2
##
## Latest weights :
## e56
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 5.3 7 -6.9
##
## Latest weights :
## e56
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 9.9 7 -5.3
strategy.performance.snapshoot(model, T)
## NULL
plotbt(model, plotX = T, log = 'y', LeftMargin = 3)
mtext('Cumulative Performance', side = 2, line =1)
plotbt.strategy.sidebyside(model, return.table = T, make.plot = F)
## e50 e50.sma.cross e52
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "6.43" "5.3" "7.32"
## Sharpe "0.42" "0.49" "0.41"
## DVR "0.37" "0.39" "0.33"
## Volatility "20.06" "12.22" "26.2"
## MaxDD "-52.38" "-23.13" "-59.41"
## AvgDD "-3.57" "-3.08" "-5.19"
## VaR "-1.93" "-1.17" "-2.64"
## CVaR "-3.07" "-1.94" "-3.94"
## Exposure "99.97" "62.08" "99.97"
## e52.sma.cross e56 e56.sma.cross
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "0.93" "5.27" "9.94"
## Sharpe "0.14" "0.39" "0.99"
## DVR "0.03" "0.33" "0.93"
## Volatility "17.63" "17.17" "10.38"
## MaxDD "-56.14" "-54.36" "-14.95"
## AvgDD "-7.84" "-3.42" "-2.15"
## VaR "-1.74" "-1.61" "-0.93"
## CVaR "-2.93" "-2.86" "-1.62"
## Exposure "60.77" "99.97" "61.82"
# Question 2: Compute equal weighted portfolio of the 3 selected ETFs
#-------------------
data$prices = data$weight = data$execution.price = etf3
data$execution.price[] <- NA
prices <- data$prices
n <- ncol(prices)
data$weight <- ntop(prices, n)
model$etf3bh <- bt.run(data)
## Latest weights :
## e50 e52 e56
## 2020-04-30 33.33 33.33 33.33
##
## Performance summary :
## CAGR Best Worst
## 6.9 7.5 -7
etf3.m <- to.monthly(etf3, indexAt = 'lastof', OHLC = FALSE)
head(etf3.m)
## e50 e52 e56
## 2008-01-31 36.2499 23.2680 12.8646
## 2008-02-29 40.1420 25.5356 14.0079
## 2008-03-31 39.8781 25.1366 14.4324
## 2008-04-30 42.1541 26.7326 14.8851
## 2008-05-31 41.0326 26.1008 14.5625
## 2008-06-30 36.2828 23.1416 12.9608
etf3.w <- to.weekly(etf3, indexAt = 'lastof', OHLC = FALSE)
## Warning in !missing(sec) && sec%%1 != 0: 'length(x) = 635 > 1' in coercion to
## 'logical(1)'
head(etf3.w)
## e50 e52 e56
## 2008-01-04 38.9876 25.9346 14.4041
## 2008-01-11 38.0310 24.3319 14.6022
## 2008-01-18 38.5917 23.8598 14.1777
## 2008-01-25 37.2064 23.6071 13.4702
## 2008-02-01 37.2064 23.4475 13.0457
## 2008-02-15 37.8001 23.9396 13.3004
# Question 3: Convert data into monthly data and compute MVP portfolios based on last 36 month data.
#Question 4: By setting constraints = new.constraints(n, lb = 0, ub = 1), recompute question 3.
data$prices = data$weight = data$execution.price = etf3.m
data$execution.price[] <- NA
prices <- data$prices
n <- ncol(prices)
constraints = new.constraints(n, lb = 0, ub = +Inf)
constraints = add.constraints(rep(1, n), 1, type = '=', constraints)
ret = prices / mlag(prices) - 1
weight = coredata(prices)
weight[] = NA
i = 36
for (i in 36:dim(weight)[1]) {
hist = ret[ (i- 36 +1):i, ]
hist = na.omit(hist)
ia = create.historical.ia(hist, 12)
ia$cov = cov(coredata(hist))
weight[i,] = min.risk.portfolio(ia, constraints)
}
#Question 5: Show the above portfolio performance and make comment based on risk measures.
weight <- round(weight, digits = 2)
data$weight[] = weight
model$mvp.month = bt.run(data, type = "weight")
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 100
##
## Performance summary :
## CAGR Best Worst
## 5.1 12.1 -12.2
#
plotbt.strategy.sidebyside(model, return.table=T, make.plot = T)
## e50 e50.sma.cross e52
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "6.43" "5.3" "7.32"
## Sharpe "0.42" "0.49" "0.41"
## DVR "0.37" "0.39" "0.33"
## Volatility "20.06" "12.22" "26.2"
## MaxDD "-52.38" "-23.13" "-59.41"
## AvgDD "-3.57" "-3.08" "-5.19"
## VaR "-1.93" "-1.17" "-2.64"
## CVaR "-3.07" "-1.94" "-3.94"
## Exposure "99.97" "62.08" "99.97"
## e52.sma.cross e56 e56.sma.cross
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "0.93" "5.27" "9.94"
## Sharpe "0.14" "0.39" "0.99"
## DVR "0.03" "0.33" "0.93"
## Volatility "17.63" "17.17" "10.38"
## MaxDD "-56.14" "-54.36" "-14.95"
## AvgDD "-7.84" "-3.42" "-2.15"
## VaR "-1.74" "-1.61" "-0.93"
## CVaR "-2.93" "-2.86" "-1.62"
## Exposure "60.77" "99.97" "61.82"
## etf3bh mvp.month
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "6.86" "5.14"
## Sharpe "0.45" "0.49"
## DVR "0.4" "0.37"
## Volatility "19" "11.6"
## MaxDD "-54.89" "-17.84"
## AvgDD "-2.99" "-6.42"
## VaR "-1.88" "-5.38"
## CVaR "-2.97" "-8.1"
## Exposure "99.97" "75.68"
plotbt(model)
