hw6
2022-04-30
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install.packages("pacman")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages('curl', repos = 'http://cran.r-project.org')## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)install.packages("devtools")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──## ✔ ggplot2 3.3.5 ✔ purrr 0.3.4
## ✔ tibble 3.1.6 ✔ dplyr 1.0.9
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(readr)
ETF6_20080101_20200430 <- read_csv("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.rm(list = ls())
etf6 <- read.table('ETF6_20080101-20200430.csv', sep = ',', header = T)
#
head(etf6)## 證券代碼 簡稱 年月日 收盤價.元.
## 1 0050 元大台灣50 20080102 39.6472
## 2 0052 富邦科技 20080102 27.0983
## 3 0056 元大高股息 20080102 14.5739
## 4 0050 元大台灣50 20080103 38.9876
## 5 0052 富邦科技 20080103 26.0676
## 6 0056 元大高股息 20080103 14.3758etf6 <- etf6[, -2]
colnames(etf6) <- c('id', 'date', 'price')
head(etf6)## id date price
## 1 0050 20080102 39.6472
## 2 0052 20080102 27.0983
## 3 0056 20080102 14.5739
## 4 0050 20080103 38.9876
## 5 0052 20080103 26.0676
## 6 0056 20080103 14.3758library(pacman)
p_load(reshape2, xts, quantmod)
etf6.l <- dcast(etf6, date~id)## Using price as value column: use value.var to override.head(etf6.l)## 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# etf6.l <- na.omit(etf6.l)
# head(etf6.l)
str(etf6.l)## 'data.frame': 3041 obs. of 7 variables:
## $ date : int 20080102 20080103 20080104 20080107 20080108 20080109 20080110 20080111 20080114 20080115 ...
## $ 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 ...# convert into xts
etf6.xts <- xts(etf6.l[, -1], order.by = as.Date(as.character(etf6.l$date), format = '%Y%m%d'))
class(etf6.xts)## [1] "xts" "zoo"head(etf6.xts)## 0050 0052 0056 0061 006206 00638R
## 2008-01-02 39.6472 27.0983 14.5739 NA NA NA
## 2008-01-03 38.9876 26.0676 14.3758 NA NA NA
## 2008-01-04 38.9876 25.9346 14.4041 NA NA NA
## 2008-01-07 37.2064 24.1391 14.1777 NA NA NA
## 2008-01-08 37.5692 24.1391 14.3531 NA NA NA
## 2008-01-09 38.2619 24.2721 14.4663 NA NA NA# SIT
devtools::install_github('systematicinvestor/SIT.date')## Skipping install of 'SIT.date' from a github remote, the SHA1 (6263da60) has not changed since last install.
## Use `force = TRUE` to force installationlibrary(curl)## Using libcurl 7.68.0 with GnuTLS/3.6.13
##
## Attaching package: 'curl'
##
## The following object is masked from 'package:readr':
##
## parse_datecurl_download('https://github.com/systematicinvestor/SIT/raw/master/SIT.tar.gz', 'sit',mode = 'wb',quiet=T)
install.packages('sit', repos = NULL, type='source')## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.2'
## (as 'lib' is unspecified)library(SIT)## Loading required package: SIT.date
##
## Attaching package: 'SIT'
##
## The following object is masked from 'package:TTR':
##
## DVI
##
## The following objects are masked from 'package:dplyr':
##
## count, lst
##
## The following object is masked from 'package:purrr':
##
## cross
##
## The following object is masked from 'package:tibble':
##
## lst
##
## The following object is masked from 'package:base':
##
## close#
data <- new.env()
# 1. prices; 2. weight; 3. execution.price
# buy and hold
# etf56 <- etf6.xts$`0056`
# head(etf56)
# data$prices = data$weight = data$execution.price = etf56
# data$weight[] <- 1
# data$execution.price[] <- NA
# names(data)
#
# etf52 <- etf6.xts$`0052`
# head(etf52)
# data$prices = data$weight = data$execution.price = etf52
# data$weight[] <- 1
# data$execution.price[] <- NA
# names(data)
#
model <- list()
#
last <- xts::last
etf3 <- etf6.xts[, 1:3]
head(etf3)## 0050 0052 0056
## 2008-01-02 39.6472 27.0983 14.5739
## 2008-01-03 38.9876 26.0676 14.3758
## 2008-01-04 38.9876 25.9346 14.4041
## 2008-01-07 37.2064 24.1391 14.1777
## 2008-01-08 37.5692 24.1391 14.3531
## 2008-01-09 38.2619 24.2721 14.4663names(etf3)## [1] "0050 " "0052 " "0056 "colnames(etf3) <- c('e50', 'e52', 'e56')
names(etf3)## [1] "e50" "e52" "e56"md = 50
i = 'e50'
for (i in names(etf3)) {
data$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$prices >= sma, 1, 0)
i <- paste(i, '.sma.cross', sep = '')
model[[i]] <- bt.run(data)
}## Latest weights :
## e50
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 6.4 8 -7
##
## Latest weights :
## e50
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 5.3 7 -6.4
##
## Latest weights :
## e52
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 7.3 10 -9.2
##
## Latest weights :
## e52
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 0.9 10 -9.2
##
## Latest weights :
## e56
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 5.3 7 -6.9
##
## Latest weights :
## e56
## 2020-04-30 100
##
## Performance summary :
## CAGR Best Worst
## 9.9 7 -5.3 #-------------------------------------------------
strategy.performance.snapshoot(model, T)
## NULLplotbt(model, plotX = T, log = 'y', LeftMargin = 3)
mtext('Cumulative Performance', side = 2, line = 1)
plotbt.strategy.sidebyside(model, return.table=T, make.plot = F)## e50 e50.sma.cross e52
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "6.43" "5.3" "7.32"
## Sharpe "0.42" "0.49" "0.41"
## DVR "0.37" "0.39" "0.33"
## Volatility "20.06" "12.22" "26.2"
## MaxDD "-52.38" "-23.13" "-59.41"
## AvgDD "-3.57" "-3.08" "-5.19"
## VaR "-1.93" "-1.17" "-2.64"
## CVaR "-3.07" "-1.94" "-3.94"
## Exposure "99.97" "62.08" "99.97"
## e52.sma.cross e56 e56.sma.cross
## Period "Jan2008 - Apr2020" "Jan2008 - Apr2020" "Jan2008 - Apr2020"
## Cagr "0.93" "5.27" "9.94"
## Sharpe "0.14" "0.39" "0.99"
## DVR "0.03" "0.33" "0.93"
## Volatility "17.63" "17.17" "10.38"
## MaxDD "-56.14" "-54.36" "-14.95"
## AvgDD "-7.84" "-3.42" "-2.15"
## VaR "-1.74" "-1.61" "-0.93"
## CVaR "-2.93" "-2.86" "-1.62"
## Exposure "60.77" "99.97" "61.82"# --------------------------------------------------
# Add equal-weighted portfolio for 3 ETFs
# --------------------------------------------------
data$prices = data$weight = data$execution.price = etf3
data$execution.price[] <- NA
prices <- data$prices
n <- ncol(prices)
data$weight <- ntop(prices, n)
model$etf3.EqWeight.bh <- 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 #
strategy.performance.snapshoot(model, T)
## NULLplotbt(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"
## etf3.EqWeight.bh
## Period "Jan2008 - Apr2020"
## Cagr "6.86"
## Sharpe "0.45"
## DVR "0.4"
## Volatility "19"
## MaxDD "-54.89"
## AvgDD "-2.99"
## VaR "-1.88"
## CVaR "-2.97"
## Exposure "99.97"#=============================================================
# MVP investment strategy
#=============================================================
# monthly rebalance
# covariance matrix
# use monthly returns to compute monthly covariance matrix
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 12.9608etf3.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#
#=================================================================
# MVP portfolio
#=================================================================
# Reset inputs to SIT bt function
data$prices = data$weight = data$execution.price = etf3.m
#data$prices <- industry.price.sample
#data$weight <- industry.price.sample
#data$execution.price <- industry.price.sample
data$execution.price[] <- NA
prices <- data$prices
n <- ncol(prices)
#*****************************************************************
# Create Constraints
#*****************************************************************
constraints = new.constraints(n, lb = 0, ub = +Inf)
# SUM x.i = 1
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]) {
# using 36 historical monthly returns
hist = ret[ (i- 36 +1):i, ]
hist = na.omit(hist)
# create historical input assumptions
ia = create.historical.ia(hist, 12)
# s0 = apply(coredata(hist),2, sd)
ia$cov = cov(coredata(hist))
#ia$cov = cor(coredata(hist), use='complete.obs',method='kendall') * (s0 %*% t(s0))
# use min.risk.portfolio() to compute MVP weights
weight[i,] = min.risk.portfolio(ia, constraints)
}## Loading required package: kernlab
##
## Attaching package: 'kernlab'
##
## The following object is masked from 'package:SIT':
##
## cross
##
## The following object is masked from 'package:purrr':
##
## cross
##
## The following object is masked from 'package:ggplot2':
##
## alpha#
weight## e50 e52 e56
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## [36,] 3.548395e-01 3.249237e-06 0.645157209
## [37,] 3.501257e-01 3.383977e-06 0.649870930
## [38,] 3.954709e-01 5.865392e-05 0.604470484
## [39,] 4.192845e-01 5.503587e-05 0.580660509
## [40,] 4.492127e-01 5.870654e-05 0.550728555
## [41,] 4.660544e-01 5.882625e-05 0.533886777
## [42,] 4.141297e-01 5.637663e-05 0.585813917
## [43,] 3.558882e-01 3.327323e-06 0.644108502
## [44,] 4.180990e-01 6.984814e-05 0.581831113
## [45,] 6.707811e-05 9.737346e-06 0.999923185
## [46,] 3.603791e-05 1.255191e-05 0.999951410
## [47,] 9.264865e-05 4.022900e-05 0.999867122
## [48,] 6.367868e-05 2.478303e-05 0.999911538
## [49,] 1.868810e-03 5.399110e-05 0.998077199
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## [131,] 1.644829e-01 1.174734e-05 0.835505359
## [132,] 1.230427e-01 1.322863e-05 0.876944118
## [133,] 1.981367e-01 1.111005e-05 0.801852195
## [134,] 1.536536e-01 1.271208e-05 0.846333689
## [135,] 1.360303e-01 1.363474e-05 0.863956080
## [136,] 1.625490e-01 1.377061e-05 0.837437224
## [137,] 1.589876e-01 1.096594e-05 0.841001385
## [138,] 1.633204e-01 1.098421e-05 0.836668635
## [139,] 2.059597e-02 1.548506e-05 0.979388545
## [140,] 1.564765e-02 1.527667e-05 0.984337077
## [141,] 1.038049e-02 1.519358e-05 0.989604321
## [142,] 9.702991e-04 1.160429e-05 0.999018097
## [143,] 5.009475e-04 1.216192e-05 0.999486891
## [144,] 1.938941e-04 1.063642e-05 0.999795469
## [145,] 1.408883e-04 9.698083e-06 0.999849414
## [146,] 7.660880e-05 8.422007e-06 0.999914969
## [147,] 2.533141e-05 6.006477e-06 0.999968662
## [148,] 2.019810e-05 5.206983e-06 0.999974595weight <- round(weight, digits = 2)
#format(round(weight, 2), nsmall = 2)
#apply(weight, 1, sum)
data$weight[] = weight
#capital = 100000
#data$weight[] = (capital / prices) * data$weight
model$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"
## etf3.EqWeight.bh 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)
#====================
# multiple models
#====================
#*****************************************************************
# Create Constraints
#*****************************************************************
constraints = new.constraints(n, lb = 0, ub = 1)
# SUM x.i = 1
constraints = add.constraints(rep(1, n), 1, type = '=', constraints)
#*****************************************************************
# Create Portfolios
#*****************************************************************
ret = prices / mlag(prices) - 1
weight = coredata(prices)
weight[] = NA
#
weights = list()
# Equal Weight 1/N Benchmark
weights$equal.weight = weight
weights$equal.weight[] = ntop(prices, n)
start.i = 35
weights$equal.weight[1:start.i,] = NA
#
weights$min.var = weight
weights$min.maxloss = weight
weights$min.mad = weight
weights$min.cvar = weight
weights$min.cdar = weight
weights$min.cor.insteadof.cov = weight
weights$min.mad.downside = weight
weights$min.risk.downside = weight
#
#
for (i in 36:dim(weight)[1]) {
# using 36 historical monthly returns
hist = ret[ (i- 36 +1):i, ]
hist = na.omit(hist)
# create historical input assumptions
ia = create.historical.ia(hist, 12)
s0 = apply(coredata(hist),2, sd)
# ia$cov = cov(coredata(hist))
ia$cov = cor(coredata(hist), use='complete.obs',method='kendall') * (s0 %*% t(s0))
# use min.risk.portfolio() to compute MVP weights
weight[i,] = min.risk.portfolio(ia, constraints)
}
models = list()
# i = "equal.weight"
for(i in names(weights)) {
data$weight[] = NA
data$weight[] = weights[[i]]
models[[i]] = bt.run.share(data, clean.signal = F)
}## Latest weights :
## e50 e52 e56
## 2020-04-30 33.33 33.33 33.33
##
## Performance summary :
## CAGR Best Worst
## 5.6 12.9 -13.4
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0
##
## Latest weights :
## e50 e52 e56
## 2020-04-30 0 0 0
##
## Performance summary :
## CAGR Best Worst
## 0 0 0 # Plot perfromance
plotbt(models, plotX = T, log = 'y', LeftMargin = 3)
mtext('Cumulative Performance', side = 2, line = 1)
# Plot Strategy Statistics Side by Side
plotbt.strategy.sidebyside(models)## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Inf## Warning in cor(y, x): the standard deviation is zero## Warning in min(drawdown[x[1]:x[2]], na.rm = T): no non-missing arguments to min;
## returning Infsummary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
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