Q1. Download the data file ‘hist_prices_df.rds’ as your data set.
#This data set includes daily closing prices for all listed stocks in Taiwan stock market from 1999 to 2017. #You can use ‘readRDS(’hist_prices_df.rds’)’ to import the data. #rm(list= ls())
rm(list=ls())
data <- readRDS("C:/Users/ankhb/Downloads/hist_prices_df.rds")
str(data)## 'data.frame': 4746 obs. of 1110 variables:
## $ date : int 19990105 19990106 19990107 19990108 19990111 19990112 19990113 19990114 19990115 19990116 ...
## $ 1101 : num 9.06 9.06 9.27 9.13 8.93 8.89 8.82 8.62 8.79 8.79 ...
## $ 1102 : num 6.14 6.01 6.01 5.86 5.73 5.53 5.51 5.21 5.34 5.29 ...
## $ 1103 : num 9.85 9.65 10.12 10.33 10.12 ...
## $ 1104 : num 4.53 4.39 4.58 4.51 4.34 4.21 4.17 4.24 4.44 4.38 ...
## $ 1108 : num 7.85 7.63 7.88 7.8 7.58 7.27 7.11 6.92 7.25 7.14 ...
## $ 1109 : num 9.09 8.89 8.94 8.75 8.7 8.6 8.5 8.45 8.55 8.55 ...
## $ 1110 : num 6.73 6.73 7.2 7.36 7.2 6.98 7.11 6.98 7.17 7.04 ...
## $ 1201 : num 13.9 14.8 15.8 16.9 18 ...
## $ 1203 : num 12.2 12 12.7 12.6 12.4 ...
## $ 1204 : num 79.6 78.2 83.6 89.1 85.1 ...
## $ 1206 : num 36.7 34.2 36.5 39 41.7 40.2 40.2 40.5 43.3 46.3 ...
## $ 1207 : num 27.8 27.8 28 27.8 28 ...
## $ 1209 : num 13.2 13.1 13.4 13.4 13.4 ...
## $ 1210 : num 2.75 2.74 2.81 2.82 2.82 2.8 2.76 2.73 2.8 2.76 ...
## $ 1212 : num 14.2 14.2 14.3 14.8 15.2 ...
## $ 1213 : num 24.1 23.9 25.6 26.4 26.6 ...
## $ 1215 : num 4.99 5.03 5.32 5.21 5.36 5.25 5.25 5.12 5.28 5.34 ...
## $ 1216 : num 7.03 6.85 7.01 6.91 6.73 6.63 6.4 6.28 6.48 6.43 ...
## $ 1217 : num 13.5 13.2 13.5 13.5 13.4 ...
## $ 1218 : num 8.41 8.57 9.15 9.77 10.43 ...
## $ 1219 : num 5.94 6.25 6.5 6.69 7.12 6.62 6.5 6.32 6.62 6.5 ...
## $ 1220 : num 9.36 9.36 9.66 9.59 10.19 ...
## $ 1221 : num 7.41 7.7 8.23 8.78 8.98 8.46 8.19 8.36 8.91 9.05 ...
## $ 1222 : num 53.5 53.3 55.5 54.3 57.5 ...
## $ 1225 : num 8.04 8.19 8.73 9.31 9.92 9.35 9.42 9.46 9.85 9.85 ...
## $ 1227 : num 6.2 6.26 6.67 6.43 6.43 6.26 6.08 5.73 5.64 5.91 ...
## $ 1228 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1229 : num 5.26 5.26 5.44 5.38 5.35 5.26 5.1 5.01 5.26 5.26 ...
## $ 1230 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1231 : num 13.2 12.9 12.6 12.4 13 ...
## $ 1232 : num 3.45 3.47 3.63 3.63 3.87 3.91 3.82 3.86 4.12 4.28 ...
## $ 1233 : num 6.4 6.2 6.5 6.57 6.47 6.4 6.74 6.4 6.57 6.67 ...
## $ 1234 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1235 : num 4.85 4.85 5.18 5.16 5.06 4.82 4.57 4.37 4.63 4.51 ...
## $ 1236 : num 3.57 3.47 3.62 3.59 3.57 3.49 3.34 3.27 3.44 3.39 ...
## $ 1256 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1262 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1301 : num 10.1 10.4 11.1 11.1 11 ...
## $ 1303 : num 9.54 9.68 10.15 9.87 9.82 ...
## $ 1304 : num 5.52 5.28 5.4 5.28 5.49 5.28 5.31 5.25 5.34 5.4 ...
## $ 1305 : num 9.6 9.6 9.98 10.25 10.25 ...
## $ 1306 : num 41.6 38.7 40.1 39 38.1 ...
## $ 1307 : num 3.18 3.16 3.29 3.29 3.26 3.24 3.21 3.13 3.24 3.24 ...
## $ 1308 : num 6.65 6.38 6.83 6.65 6.67 6.59 6.59 6.44 6.71 6.59 ...
## $ 1309 : num 14.6 14.4 15.3 15.3 15.4 ...
## $ 1310 : num 14.5 14.2 14.8 14.6 15.4 ...
## $ 1311 : num 16.5 16.6 17.5 17.2 17.2 ...
## $ 1312 : num 10.1 10 10.5 10.6 10.9 ...
## $ 1313 : num 5.42 5.25 5.59 5.62 5.69 5.73 5.69 5.52 5.69 5.69 ...
## $ 1314 : num 9.92 9.59 10.15 10.2 9.92 ...
## $ 1315 : num 7.12 6.72 7.16 7.42 7.31 7.16 7.05 6.94 7.31 7.27 ...
## $ 1316 : num 29.4 29.9 31.1 32.5 32.8 ...
## $ 1319 : num 11.3 10.6 11.2 12 12.4 ...
## $ 1321 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1323 : num 3.92 3.89 3.98 3.96 3.89 3.72 3.61 3.38 3.48 3.49 ...
## $ 1324 : num 9.43 9.85 9.99 9.99 9.79 9.34 9.29 9.29 9.76 9.49 ...
## $ 1325 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1326 : num 6.36 6.43 6.61 6.64 6.5 6.34 6.17 6.17 6.41 6.27 ...
## $ 1337 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1338 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1339 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1340 : num NA NA NA NA NA NA NA NA NA NA ...
## $ 1402 : num 6.63 6.84 6.94 6.99 6.78 6.94 6.91 6.68 6.76 6.63 ...
## $ 1409 : num 7.02 7.25 7.74 7.74 7.45 7.38 7.35 7.28 7.58 7.35 ...
## $ 1410 : num 20.5 19.1 19.9 19.6 19.5 ...
## $ 1413 : num 34.6 34.5 36.9 37.4 36.6 ...
## $ 1414 : num 12.7 12.7 13.6 14.1 13.8 ...
## $ 1416 : num 11.6 11.7 12.5 13.4 13.7 ...
## $ 1417 : num 13.4 12.6 13.1 13.6 13.3 ...
## $ 1418 : num 74.6 74.3 76.9 76.9 75.4 ...
## $ 1419 : num 21.9 22.3 23.8 24.8 24.3 ...
## $ 1423 : num 7.64 8.16 8.73 8.99 8.64 8.29 8.46 8.16 8.73 8.55 ...
## $ 1431 : num 12.1 11.8 12.6 13.4 14.3 ...
## $ 1432 : num 43.1 42.7 45.5 45.1 44.6 ...
## $ 1434 : num 5.72 5.75 6 5.94 5.75 5.69 5.6 5.57 5.72 5.6 ...
## $ 1435 : num 12.3 12.5 13.3 13.7 13.7 ...
## $ 1436 : num 13.4 13.3 14.2 15.2 15.7 ...
## $ 1437 : num 20.3 20.9 22.3 23.3 22.5 ...
## $ 1438 : num 15.1 15 15.6 15.7 15.6 ...
## $ 1439 : num 9.59 10.24 10.89 11.16 10.89 ...
## $ 1440 : num 7.03 7.12 7.55 7.4 7.34 7.12 7.06 7 7.27 7.15 ...
## $ 1441 : num 42 42 44 43.1 42.2 ...
## $ 1442 : num 55.4 51.5 51.7 51.9 51.1 ...
## $ 1443 : num 21.2 21.2 22.6 23.4 23.5 ...
## $ 1444 : num 5.81 5.81 6.21 6.34 6.18 6 5.87 5.76 5.84 5.84 ...
## $ 1445 : num 9.37 9.18 9.32 9.47 9.27 9.03 9.23 9.13 9.18 9.23 ...
## $ 1446 : num 25.5 25.5 26.8 26.8 26.8 ...
## $ 1447 : num 7.38 7.51 8 8.06 7.69 8 7.9 7.64 7.74 7.53 ...
## $ 1449 : num 143 140 145 144 145 ...
## $ 1450 : num 28.9 28.6 29.5 29.3 28.6 ...
## $ 1451 : num 27.1 27.3 26.8 26.4 26.1 ...
## $ 1452 : num 8.85 8.8 9.21 9.16 8.94 8.8 8.58 8.31 8.35 8.49 ...
## $ 1453 : num 63.9 63.9 65.4 64.2 68.5 ...
## $ 1454 : num 8.78 8.51 8.78 8.74 8.6 8.55 8.65 8.46 8.46 8.65 ...
## $ 1455 : num 6.5 6.07 6.5 6.54 6.3 6.25 6.3 6.3 6.52 6.41 ...
## $ 1456 : num 155 157 162 159 155 ...
## $ 1457 : num 18.9 18.9 20 20.3 19.9 ...
## $ 1459 : num 6.07 5.79 6.03 5.92 5.79 5.79 5.73 5.6 5.73 5.92 ...
## [list output truncated]con = gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb'))
source(con)
close(con)Q2 You have to select at least 10 stocks from the data set. To avoid selecting all stocks from one specific industry, you should select stocks with ticker numbers starting with ‘1’, ‘2’, ‘3’, ‘4’, ‘5’ and ‘6’.
library(xts)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Registered S3 method overwritten by 'xts':
## method from
## as.zoo.xts zoolibrary(quantmod)## Loading required package: TTR##
## Attaching package: 'TTR'## The following object is masked _by_ '.GlobalEnv':
##
## DVI## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Version 0.4-0 included new data defaults. See ?getSymbols.library(kernlab)##
## Attaching package: 'kernlab'## The following object is masked _by_ '.GlobalEnv':
##
## crossdata.1 <- data[,c("date","1101","1102","2030","2031", "3052","6191","6005","9937", "9902","9905")]
sum(is.na(data.1))## [1] 0data.xts <- xts(data.1[,-1], order.by= as.Date(as.character(data.1[,1]),
format = '%Y%m%d'))str(data.xts)## An 'xts' object on 1999-01-05/2017-12-29 containing:
## Data: num [1:4746, 1:10] 9.06 9.06 9.27 9.13 8.93 8.89 8.82 8.62 8.79 8.79 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:10] "1101" "1102" "2030" "2031" ...
## Indexed by objects of class: [Date] TZ: UTC
## xts Attributes:
## NULLQ3. Construct equal-weighted portfolio starting from 2007 to 2017.
data.monthly <- to.monthly(data.xts, indexAt = 'lastof', OHLC=F)
data.monthly.1 <- data.monthly["2007/2017"]
data <- new.env()
data$prices <- data.monthly.1
data$weight <- data.monthly.1
data$execution.price <- data$prices
data$execution.price[] <- NA
data$symbolnames <- colnames(data$prices)
prices <- data$prices
n <- ncol(prices)
data$weight <- ntop(prices, n)
model <- list()
model$equal.weight <- bt.run(data, trade.summary = T)## Latest weights :
## 1101 1102 2030 2031 3052 6191 6005 9937 9902 9905
## 2017-12-31 10 10 10 10 10 10 10 10 10 10
##
## Performance summary :
## CAGR Best Worst
## 8.2 26.7 -30 capital = 100000
data$weight[] = (capital / prices) * data$weight
equal.weight = bt.run(data, type='share')## Latest weights :
## 1101 1102 2030 2031 3052 6191 6005 9937 9902 9905
## 2017-12-31 10 10 10 10 10 10 10 10 10 10
##
## Performance summary :
## CAGR Best Worst
## 8.2 26.7 -30 head(equal.weight$ret)## 1101
## 2007-01-31 0.00000000
## 2007-02-28 0.04404018
## 2007-03-31 0.06275091
## 2007-04-30 0.01691907
## 2007-05-31 0.00944164
## 2007-06-30 0.13928670bt.detail.summary(model$equal.weight)## $System
## $System$Period
## [1] "Jan2007 - Dec2017"
##
## $System$Cagr
## [1] 8.16
##
## $System$Sharpe
## [1] 0.44
##
## $System$DVR
## [,1]
## 1101 0.27
##
## $System$Volatility
## [1] 24.9
##
## $System$MaxDD
## [1] -56.82
##
## $System$AvgDD
## [1] -12.88
##
## $System$VaR
## 5%
## -10.48
##
## $System$CVaR
## [1] -15.45
##
## $System$Exposure
## [1] 99.24
##
##
## $Trade
## $Trade$Win.Percent
## [1] 80
##
## $Trade$Avg.Trade
## [1] 9.4
##
## $Trade$Avg.Win
## [1] 12.3
##
## $Trade$Avg.Loss
## [1] -2.5
##
## $Trade$Best.Trade
## [1] 23.17
##
## $Trade$Worst.Trade
## [1] -4.69
##
## $Trade$WinLoss.Ratio
## [1] 4.85
##
## $Trade$Avg.Len
## [1] 131
##
## $Trade$Num.Trades
## [1] 10
##
##
## $Period
## $Period$Win.Percent.Day
## [1] 59.8
##
## $Period$Best.Day
## [1] 26.7
##
## $Period$Worst.Day
## [1] -30
##
## $Period$Win.Percent.Month
## [1] 59.8
##
## $Period$Best.Month
## [1] 26.7
##
## $Period$Worst.Month
## [1] -30
##
## $Period$Win.Percent.Year
## [1] 63.6
##
## $Period$Best.Year
## [1] 124.8
##
## $Period$Worst.Year
## [1] -37.9plotbt.monthly.table(model$equal.weight$equity)
## Jan Feb Mar Apr May Jun Jul Aug
## 2007 " NA" " 4.4" " 6.3" " 1.7" " 0.9" " 13.9" " 12.5" " -2.5"
## 2008 " -3.5" " 22.1" " 7.0" " 0.8" " -4.4" "-17.4" " -3.2" " -5.1"
## 2009 " -6.5" " 6.2" " 26.7" " 12.0" " 23.7" " -3.1" " 10.0" " -1.1"
## 2010 "-11.7" " 0.5" " 7.4" " -1.5" "-10.3" " -0.1" " 7.0" " 2.9"
## 2011 " 2.9" " -6.2" " 1.9" " 5.7" " 0.0" " -0.6" " 3.4" "-10.7"
## 2012 " 9.8" " 9.5" " -2.0" " -4.2" " -5.8" " 0.7" " 1.0" " -0.1"
## 2013 " 1.0" " -1.0" " -1.3" " 2.4" " 9.5" " -5.4" " 3.7" " 1.8"
## 2014 " 0.0" " 2.4" " 0.5" " -2.8" " 1.2" " 0.2" " 3.4" " 2.1"
## 2015 " -0.8" " 1.3" " 0.4" " 2.8" " -4.9" " -7.3" " -7.5" " -5.9"
## 2016 " -4.3" " 6.6" " 1.0" " -0.2" " -3.5" " 0.9" " 5.5" " 2.0"
## 2017 " -0.2" " 7.2" " 1.3" " -3.5" " 0.1" " 1.5" " 4.3" " 4.7"
## Avg " -1.3" " 4.8" " 4.5" " 1.2" " 0.6" " -1.5" " 3.7" " -1.1"
## Sep Oct Nov Dec Year MaxDD
## 2007 " 8.7" " -7.1" " -7.9" " -4.4" " 26.8" "-18.1"
## 2008 "-30.0" "-14.9" " 11.1" " 1.8" "-37.9" "-56.8"
## 2009 " 6.7" " -1.6" " 1.8" " 14.4" "124.8" " -6.5"
## 2010 " 6.9" " -3.4" " -1.5" " 7.8" " 1.6" "-15.9"
## 2011 "-10.8" " 7.2" "-12.6" " 1.9" "-18.9" "-25.4"
## 2012 " 5.6" " -8.6" " 3.2" " 5.7" " 13.8" "-13.3"
## 2013 " 2.0" " 2.5" " 1.8" " 2.0" " 20.1" " -5.4"
## 2014 " -4.0" " -4.3" " 0.9" " 4.7" " 3.9" " -8.2"
## 2015 " 4.6" " 4.4" " -7.5" " 1.5" "-18.4" "-23.3"
## 2016 " -0.2" " 1.4" " 5.6" " 1.3" " 16.7" " -4.3"
## 2017 " -2.1" " 3.0" " -1.2" " 3.3" " 19.5" " -3.5"
## Avg " -1.1" " -1.9" " -0.6" " 3.6" " 13.8" "-16.4"plotbt.transition.map(model$equal.weight$weight)
strategy.performance.snapshoot(model, T)
## NULLQ4. Construct MVP portfolio starting from 2004-2017.
#Year 2004-2006 will be used as in sample data to compute covariance matrix for MVP.
data.monthly.2 <- data.monthly["2004/2017"]
data.monthly.3 <- data.monthly["2004/2006"]
Sigma_monthly <- cov(data.monthly.3)
head(Sigma_monthly)## 1101 1102 2030 2031 3052 6191
## 1101 7.095257 5.0740846 2.18635571 -9.092439 -1.25517857 6.0143583
## 1102 5.074085 4.2052961 2.38812929 -4.638566 -0.74942643 4.2501139
## 2030 2.186356 2.3881293 2.94821929 1.608435 0.01046071 1.3755379
## 2031 -9.092439 -4.6385658 1.60843500 25.547909 2.20173071 -10.6009413
## 3052 -1.255179 -0.7494264 0.01046071 2.201731 0.69880214 0.1811707
## 6191 6.014358 4.2501139 1.37553786 -10.600941 0.18117071 15.6384847
## 6005 9937 9902 9905
## 1101 1.14042429 2.4244268 -4.7063449 -0.4099478
## 1102 0.85780929 1.6612253 -2.6602887 0.2480113
## 2030 0.52386786 0.5523721 0.5519893 1.0783350
## 2031 -1.34739071 -3.8166471 9.4305637 4.1072866
## 3052 -0.08237929 -0.5138779 2.1867936 0.2702393
## 6191 1.05226071 1.3534447 -1.1481156 -1.0910728ones = rep(1,10)
one.vec = matrix(ones, ncol=1)
a = inv(Sigma_monthly) %*% one.vec
b = t(one.vec)%*%a
mvp.w.monthly =a / as.numeric(b)
mvp.w.monthly## [,1]
## 1101 -0.0907159873
## 1102 -0.0515201991
## 2030 -0.0004535364
## 2031 -0.0223156685
## 3052 0.6143532179
## 6191 -0.0036770687
## 6005 0.4946153094
## 9937 0.0297113804
## 9902 -0.2183613720
## 9905 0.2483639243Q5. Similar to question 4
data$prices = data$weight = data$execution.price = data.monthly.1
data$execution.price[] <- NA
prices <- data$prices
n <- ncol(prices)
constraints = new.constraints(n, lb = -Inf, ub = +Inf)
constraints = add.constraints(rep(1, n), 1, type = '=', constraints)
ret = prices / mlag(prices) - 1
weight = coredata(prices)
weight[] = NA
nrow(prices)## [1] 132hist <- na.omit(ret[1:36,])
cov(hist)## 1101 1102 2030 2031 3052
## 1101 0.025224630 0.017736344 0.008955619 0.013911524 0.009786144
## 1102 0.017736344 0.017730725 0.007152839 0.009756524 0.008230059
## 2030 0.008955619 0.007152839 0.018680911 0.018004663 0.015452262
## 2031 0.013911524 0.009756524 0.018004663 0.027504038 0.016857490
## 3052 0.009786144 0.008230059 0.015452262 0.016857490 0.027081196
## 6191 0.007984633 0.007116579 0.010996121 0.012902372 0.012445644
## 6005 0.016335182 0.014006027 0.016743330 0.021576111 0.021809001
## 9937 0.008263227 0.004435278 0.007198008 0.006573010 0.011159201
## 9902 0.017205311 0.010776307 0.018500762 0.017163931 0.018020297
## 9905 0.007637370 0.005559106 0.009326382 0.010834600 0.010762263
## 6191 6005 9937 9902 9905
## 1101 0.007984633 0.016335182 0.008263227 0.017205311 0.007637370
## 1102 0.007116579 0.014006027 0.004435278 0.010776307 0.005559106
## 2030 0.010996121 0.016743330 0.007198008 0.018500762 0.009326382
## 2031 0.012902372 0.021576111 0.006573010 0.017163931 0.010834600
## 3052 0.012445644 0.021809001 0.011159201 0.018020297 0.010762263
## 6191 0.019321391 0.011348404 0.007118646 0.009073662 0.007242802
## 6005 0.011348404 0.033026821 0.009182638 0.021034044 0.012903012
## 9937 0.007118646 0.009182638 0.010752908 0.013451627 0.005993916
## 9902 0.009073662 0.021034044 0.013451627 0.042596166 0.011841623
## 9905 0.007242802 0.012903012 0.005993916 0.011841623 0.011280463Q6 Similar to question 4, however, you need to construct MVP portfolio using Fama French three factor model to compute covariance matrix and generate backtesting results.
ia = create.historical.ia(hist,12)
s0 = apply(coredata(hist), 2 , sd)
ia$cov = cor(coredata(hist), use='complete.obs',method='pearson') * (s0 %*% t(s0))
weight[36,] = min.risk.portfolio(ia, constraints)
weight[36,]## 1101 1102 2030 2031 3052 6191
## -0.36022757 0.56440238 0.12796073 0.13352926 -0.19611934 -0.06739882
## 6005 9937 9902 9905
## -0.15946967 0.71520646 -0.13722389 0.37934046sum(weight[36,])## [1] 1model$min.var.monthly <- bt.run(data, trade.summary = T)## Latest weights :
## 1101 1102 2030 2031 3052 6191 6005 9937 9902 9905
## 2017-12-31 3355 2785 1530 2620 830 1310 1140 3950 1010 2555
##
## Performance summary :
## CAGR Best Worst
## -100 1639 -100 sum(as.numeric(weight[36,])*as.numeric(ret[37,]))## [1] -0.08070594model$min.var.monthly$ret[37, ]## 1101
## 2010-01-31 -1plotbt.strategy.sidebyside(model, return.table=T, make.plot = T)## Warning in max(mret, na.rm = T): no non-missing arguments to max; returning
## -Inf## Warning in min(mret, na.rm = T): no non-missing arguments to min; returning
## Inf
## equal.weight min.var.monthly
## Period "Jan2007 - Dec2017" "Jan2007 - Dec2017"
## Cagr "8.16" "-100"
## Sharpe "0.44" "-0.96"
## DVR "0.27" "-0.02"
## Volatility "24.9" "754.64"
## MaxDD "-56.82" "-100"
## AvgDD "-12.88" "-100"
## VaR "-10.48" "-100"
## CVaR "-15.45" "NaN"
## Exposure "99.24" "99.24"plotbt(model)