library(SIT)
## Loading required package: SIT.date
## Loading required package: quantmod
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
##
## Attaching package: 'SIT'
## The following object is masked from 'package:TTR':
##
## DVI
## The following object is masked from 'package:base':
##
## close
library(quantmod)
library(quadprog)
library(lpSolve)
# IMPORT DATA
industry10 <- read.table("10_Industry_Portfolios.txt", head = TRUE)
head(industry10)
## Date NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other
## 1 192607 1.45 15.55 4.69 -1.18 2.90 0.83 0.11 1.77 7.04 2.16
## 2 192608 3.97 3.68 2.81 3.47 2.66 2.17 -0.71 4.25 -1.69 4.38
## 3 192609 1.14 4.80 1.15 -3.39 -0.38 2.41 0.21 0.69 2.04 0.29
## 4 192610 -1.24 -8.23 -3.63 -0.78 -4.58 -0.11 -2.29 -0.57 -2.63 -2.85
## 5 192611 5.20 -0.19 4.10 0.01 4.71 1.63 6.43 5.42 3.71 2.11
## 6 192612 0.82 9.89 3.74 2.82 -0.02 1.99 0.62 0.11 -0.17 3.40
date <- seq(as.Date("1926-08-01"), length = 1136, by = "1 month") -1
head(date)
## [1] "1926-07-31" "1926-08-31" "1926-09-30" "1926-10-31" "1926-11-30"
## [6] "1926-12-31"
tail(date)
## [1] "2020-09-30" "2020-10-31" "2020-11-30" "2020-12-31" "2021-01-31"
## [6] "2021-02-28"
class(date)
## [1] "Date"
# convert data into xts
industry10 <- xts(industry10[, -1]/100, order.by = date)
head(industry10)
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth
## 1926-07-31 0.0145 0.1555 0.0469 -0.0118 0.0290 0.0083 0.0011 0.0177
## 1926-08-31 0.0397 0.0368 0.0281 0.0347 0.0266 0.0217 -0.0071 0.0425
## 1926-09-30 0.0114 0.0480 0.0115 -0.0339 -0.0038 0.0241 0.0021 0.0069
## 1926-10-31 -0.0124 -0.0823 -0.0363 -0.0078 -0.0458 -0.0011 -0.0229 -0.0057
## 1926-11-30 0.0520 -0.0019 0.0410 0.0001 0.0471 0.0163 0.0643 0.0542
## 1926-12-31 0.0082 0.0989 0.0374 0.0282 -0.0002 0.0199 0.0062 0.0011
## Utils Other
## 1926-07-31 0.0704 0.0216
## 1926-08-31 -0.0169 0.0438
## 1926-09-30 0.0204 0.0029
## 1926-10-31 -0.0263 -0.0285
## 1926-11-30 0.0371 0.0211
## 1926-12-31 -0.0017 0.0340
# Convert Returns into Price
industry.price <- cumprod(industry10 + 1)*100
head(industry.price)
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops
## 1926-07-31 101.4500 115.5500 104.6900 98.82000 102.9000 100.8300 100.11000
## 1926-08-31 105.4776 119.8022 107.6318 102.24905 105.6371 103.0180 99.39922
## 1926-09-30 106.6800 125.5527 108.8696 98.78281 105.2357 105.5007 99.60796
## 1926-10-31 105.3572 115.2198 104.9176 98.01231 100.4159 105.3847 97.32694
## 1926-11-30 110.8358 115.0008 109.2192 98.02211 105.1455 107.1025 103.58506
## 1926-12-31 111.7446 126.3744 113.3040 100.78633 105.1245 109.2338 104.22728
## Hlth Utils Other
## 1926-07-31 101.7700 107.0400 102.1600
## 1926-08-31 106.0952 105.2310 106.6346
## 1926-09-30 106.8273 107.3777 106.9438
## 1926-10-31 106.2184 104.5537 103.8959
## 1926-11-30 111.9754 108.4326 106.0882
## 1926-12-31 112.0986 108.2483 109.6952
## EQUAL WEIGHT PORTFOLIO RETURNS
industry.price.sample <- industry.price['1999-12/2020-03']
head(industry.price.sample)
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops
## 1999-12-31 237229.2 301031.8 196890.8 223807.9 618288.1 292170.9 255890.2
## 2000-01-31 225913.4 298412.8 181159.2 225822.1 589166.8 280367.2 227153.7
## 2000-02-29 211929.3 274689.0 173478.1 213537.4 696277.3 270302.0 218385.6
## 2000-03-31 228332.7 303558.8 187980.9 239717.1 723780.2 290763.9 247387.2
## 2000-04-30 224177.0 331698.7 189785.5 234970.7 646408.1 267793.5 236823.8
## 2000-05-31 240362.6 287848.1 187109.5 257151.9 576337.5 239916.2 230429.5
## Hlth Utils Other
## 1999-12-31 644661.4 55424.06 89942.66
## 2000-01-31 693397.8 58610.94 85769.32
## 2000-02-29 673427.9 54355.79 79782.63
## 2000-03-31 675313.5 57492.12 91047.93
## 2000-04-30 710767.5 61861.52 87943.20
## 2000-05-31 738771.7 64274.12 90986.03
#create required input parameters in using SIT package
data <- new.env()
# 4 required input elements in data
#data$prices <- industry.price.sample
#data$weight <- industry.price.sample
#data$execution.price <- industry.price.sample
#data$symbolnames : asset names
data$prices = data$weight = data$execution.price = industry.price.sample
data$execution.price[] <- NA
data$symbolnames <- colnames(data$prices)
prices <- data$prices
n <- ncol(prices)
names(data)
## [1] "prices" "weight" "symbolnames" "execution.price"
# Assign Equal Weights to 10 Assets
data$weight <-ntop(prices, n)
head(data$weight)
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other
## 1999-12-31 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
## 2000-01-31 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
## 2000-02-29 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
## 2000-03-31 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
## 2000-04-30 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
## 2000-05-31 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
# list Model
model <- list()
model$equal.weight <-bt.run(data, trade.summary = T)
## Latest weights :
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other
## 2020-03-31 10 10 10 10 10 10 10 10 10 10
##
## Performance summary :
## CAGR Best Worst
## 6.2 12 -17.5
capital = 100000
data$weight[] = (capital / prices) * data$weight
equal.weight = bt.run(data, type='share')
## Latest weights :
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other
## 2020-03-31 10 10 10 10 10 10 10 10 10 10
##
## Performance summary :
## CAGR Best Worst
## 6.2 12 -17.5
head(equal.weight$ret)
## NoDur
## 1999-12-31 0.00000
## 2000-01-31 -0.02404
## 2000-02-29 -0.03021
## 2000-03-31 0.08384
## 2000-04-30 -0.00699
## 2000-05-31 -0.01062
bt.detail.summary(model$equal.weight)
## $System
## $System$Period
## [1] "Dec1999 - Mar2020"
##
## $System$Cagr
## [1] 6.2
##
## $System$Sharpe
## [1] 0.49
##
## $System$DVR
## [,1]
## NoDur 0.42
##
## $System$Volatility
## [1] 14.5
##
## $System$MaxDD
## [1] -48.17
##
## $System$AvgDD
## [1] -7.02
##
## $System$VaR
## 5%
## -7.07
##
## $System$CVaR
## [1] -9.8
##
## $System$Exposure
## [1] 99.59
##
##
## $Trade
## $Trade$Win.Percent
## [1] 100
##
## $Trade$Avg.Trade
## [1] 23.2
##
## $Trade$Avg.Win
## [1] 23.2
##
## $Trade$Avg.Loss
## [1] NaN
##
## $Trade$Best.Trade
## [1] 44.02
##
## $Trade$Worst.Trade
## [1] 2.83
##
## $Trade$WinLoss.Ratio
## [1] NaN
##
## $Trade$Avg.Len
## [1] 243
##
## $Trade$Num.Trades
## [1] 10
##
##
## $Period
## $Period$Win.Percent.Day
## [1] 63.5
##
## $Period$Best.Day
## [1] 12
##
## $Period$Worst.Day
## [1] -17.5
##
## $Period$Win.Percent.Month
## [1] 63.5
##
## $Period$Best.Month
## [1] 12
##
## $Period$Worst.Month
## [1] -17.5
##
## $Period$Win.Percent.Year
## [1] 68.2
##
## $Period$Best.Year
## [1] 33.8
##
## $Period$Worst.Year
## [1] -35.5
plotbt.monthly.table(model$equal.weight$equity)
## Jan Feb Mar Apr May Jun Jul Aug Sep
## 1999 " NA" " NA" " NA" " NA" " NA" " NA" " NA" " NA" " NA"
## 2000 " -2.4" " -3.0" " 8.4" " -0.7" " -1.1" " 0.5" " -0.8" " 5.2" " -0.5"
## 2001 " 2.6" " -4.5" " -4.8" " 6.9" " 0.8" " -2.3" " -0.6" " -5.1" " -8.4"
## 2002 " -1.1" " 0.0" " 4.8" " -3.9" " -1.1" " -6.9" " -9.3" " 0.9" " -9.8"
## 2003 " -3.0" " -2.3" " 0.9" " 7.9" " 6.4" " 1.5" " 1.3" " 3.3" " -1.6"
## 2004 " 1.3" " 1.8" " -1.0" " -0.6" " 0.3" " 2.4" " -3.2" " 0.2" " 2.0"
## 2005 " -2.1" " 2.9" " -1.8" " -3.0" " 3.8" " 1.2" " 4.3" " -0.6" " 0.4"
## 2006 " 4.0" " 0.0" " 1.6" " 1.1" " -1.8" " 0.8" " 0.3" " 2.1" " 1.8"
## 2007 " 2.0" " -1.0" " 1.7" " 4.3" " 3.7" " -1.2" " -3.4" " 1.0" " 3.4"
## 2008 " -6.2" " -2.3" " -0.6" " 4.8" " 2.7" " -8.0" " -1.3" " 1.9" " -9.4"
## 2009 " -7.1" " -9.8" " 8.2" " 12.0" " 4.3" " 0.9" " 8.2" " 2.5" " 4.1"
## 2010 " -3.4" " 3.3" " 6.1" " 2.4" " -7.5" " -5.4" " 7.8" " -4.1" " 9.3"
## 2011 " 1.4" " 3.5" " 1.2" " 3.4" " -0.8" " -1.4" " -2.7" " -5.5" " -7.3"
## 2012 " 4.4" " 4.2" " 2.4" " -0.7" " -5.3" " 3.2" " 1.5" " 1.9" " 2.9"
## 2013 " 5.5" " 1.4" " 4.3" " 2.3" " 2.0" " -0.7" " 5.6" " -2.8" " 3.7"
## 2014 " -3.2" " 4.9" " 0.6" " 0.8" " 1.8" " 2.7" " -2.7" " 4.3" " -2.9"
## 2015 " -2.5" " 5.4" " -1.2" " 0.8" " 0.8" " -1.9" " 0.8" " -5.8" " -3.1"
## 2016 " -4.6" " 0.6" " 7.2" " 1.4" " 1.0" " 0.9" " 3.3" " -0.4" " 0.2"
## 2017 " 1.7" " 2.9" " 0.2" " 0.8" " 0.6" " 0.5" " 1.7" " -0.5" " 2.6"
## 2018 " 4.1" " -5.1" " -1.6" " 0.7" " 1.9" " 1.7" " 2.8" " 2.1" " 0.4"
## 2019 " 8.1" " 3.2" " 1.0" " 3.2" " -6.7" " 7.2" " 0.6" " -2.0" " 2.1"
## 2020 " -0.6" " -8.5" "-15.4" " NA" " NA" " NA" " NA" " NA" " NA"
## Avg " -0.1" " -0.1" " 1.1" " 2.2" " 0.3" " -0.2" " 0.7" " -0.1" " -0.5"
## Oct Nov Dec Year MaxDD
## 1999 " NA" " NA" " NA" " 0.0" " 0.0"
## 2000 " 0.1" " -5.7" " 3.2" " 2.5" " -6.1"
## 2001 " 2.1" " 6.5" " 2.1" " -6.0" "-17.4"
## 2002 " 6.7" " 6.0" " -4.4" "-18.3" "-27.0"
## 2003 " 5.6" " 1.5" " 5.9" " 30.2" " -5.3"
## 2004 " 1.4" " 4.9" " 3.4" " 13.4" " -3.2"
## 2005 " -3.0" " 2.9" " 0.1" " 4.9" " -4.7"
## 2006 " 4.1" " 2.3" " 0.8" " 18.4" " -1.8"
## 2007 " 2.1" " -3.9" " -0.3" " 8.0" " -4.6"
## 2008 "-17.5" " -6.6" " 1.7" "-35.5" "-36.5"
## 2009 " -1.8" " 5.9" " 3.4" " 32.7" "-16.2"
## 2010 " 4.2" " 1.2" " 6.4" " 20.3" "-12.5"
## 2011 " 11.5" " -0.4" " 0.9" " 2.8" "-16.6"
## 2012 " -0.8" " 0.9" " 1.2" " 16.4" " -6.0"
## 2013 " 4.0" " 2.2" " 2.3" " 33.8" " -2.8"
## 2014 " 2.6" " 2.2" " -0.1" " 11.2" " -3.2"
## 2015 " 7.5" " 0.1" " -2.6" " -2.2" " -9.6"
## 2016 " -2.5" " 4.1" " 2.3" " 13.6" " -4.6"
## 2017 " 1.1" " 3.1" " 1.2" " 17.1" " -0.5"
## 2018 " -5.9" " 2.4" " -9.4" " -6.6" "-12.7"
## 2019 " 1.7" " 2.7" " 3.2" " 26.4" " -6.7"
## 2020 " NA" " NA" " NA" "-23.0" "-23.0"
## Avg " 1.2" " 1.6" " 1.1" " 7.3" "-10.1"
plotbt.transition.map(model$equal.weight$weight)
strategy.performance.snapshoot(model, T)
## NULL
## MVP Portfolio Returns
# reset sample data range
industry.price.sample <- industry.price['1997-01/2020-03']
data$prices <- industry.price.sample
data$weight <- industry.price.sample
data$execution.price <- industry.price.sample
data$execution.price[] <- NA
prices <- data$prices
# Create Constraints
constraints = new.constraints(n, lb=-Inf, ub=+Inf)
constraints = add.constraints(rep(1,n), 1, type = '=', constraints)
ret = prices / mlag(prices) -1
# Compute MVA Weight for each month
weight = coredata(prices)
weight[] = NA
nrow(prices)
## [1] 279
hist <- na.omit(ret[1:36,])
for( i in 36 : (dim(weight)[1]) ) {
#using 36 historical monthly returns
hist = ret[ (i- 36 +1):i, ]
hist = na.omit(hist)
#create historical input assumptions
ia = create.historical.ia(hist, 12)
s0 = apply(coredata(hist),2,sd)
ia$cov = cor(coredata(hist), use='complete.obs',method='pearson') * (s0 %*% t(s0))
weight[i,] = min.risk.portfolio(ia, constraints)
}
data$weight[] = weight
ia = create.historical.ia(hist, 12)
s0 = apply(coredata(hist), 2, sd)
ia$cov = cor(coredata(hist), use = 'complete.obs', method = 'pearson') * (s0%*%t(s0))
weight[36,] = min.risk.portfolio(ia, constraints)
weight[36,]
## NoDur Durbl Manuf Enrgy HiTec Telcm
## 0.14491347 -0.21024614 -0.16569609 -0.19720645 0.15173210 0.22039628
## Shops Hlth Utils Other
## -0.05030741 0.52457948 0.50570044 0.07613432
sum(weight[36,])
## [1] 1
model$min.var.monthly <- bt.run(data, trade.summary = T)
## Latest weights :
## NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other
## 2020-03-31 -1.26 -16.4 -15.74 -12.18 13.26 31.29 -15.7 37.49 56.82 22.43
##
## Performance summary :
## CAGR Best Worst
## 6.1 8.6 -15.1
sum(as.numeric(weight[36,])*as.numeric(ret[37,]))
## [1] 0.06118331
model$min.var.monthly$ret[37, ]
## NoDur
## 2000-01-31 0.009322282
## Plot both strategies side by side and compare their performance and comment.
plotbt.custom.report.part1(model$min.var.monthly, model$equal.weight)
layout(1:2)
plotbt.transition.map(model$min.var.monthly$weight)
legend('topright', legend = 'min.var.monthly', bty = 'n')
plotbt.transition.map(model$equal.weight$weight)
legend('topright', legend = 'equal weight', bty = 'n')
strategy.performance.snapshoot(model, T)
## NULL
model <- rev(model)
plotbt.custom.report(model)
