con = gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb'))
source(con)
close(con)
library(tidyverse)
## Registered S3 methods overwritten by 'ggplot2':
## method from
## [.quosures rlang
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## print.quosures rlang
## Registered S3 method overwritten by 'rvest':
## method from
## read_xml.response xml2
## ── Attaching packages ────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 3.1.1 ✔ purrr 0.3.2
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## ✔ tidyr 0.8.3 ✔ stringr 1.4.0
## ✔ readr 1.3.1 ✔ forcats 0.4.0
## ── Conflicts ───────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
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## ✖ .GlobalEnv::lst() masks dplyr::lst(), tibble::lst()
# Q1. Try to find the min variance portfolio for three stocks
#1a Using 2007-2009 daily returns as the insample data
#1b In other words, you have to compute optimal weights for 2010-01
#1c Give me weights, realized returns and standard deviation for 2010-01.
#1a Using 2007-2009 daily returns as the insample data
library(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
##
## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
##
## first, last
## 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(plyr)
## -------------------------------------------------------------------------
## You have loaded plyr after dplyr - this is likely to cause problems.
## If you need functions from both plyr and dplyr, please load plyr first, then dplyr:
## library(plyr); library(dplyr)
## -------------------------------------------------------------------------
##
## Attaching package: 'plyr'
## The following objects are masked _by_ '.GlobalEnv':
##
## count, join
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##
## arrange, count, desc, failwith, id, mutate, rename, summarise,
## summarize
## The following object is masked from 'package:purrr':
##
## compact
tickers <- c("NKE", "ADS.DE", "PUM.DE")
data.env<-new.env()
getSymbols(tickers ,from = "2007/01/01" ,to = "2009/12/31", env = data.env, auto.assign = TRUE)
## 'getSymbols' currently uses auto.assign=TRUE by default, but will
## use auto.assign=FALSE in 0.5-0. You will still be able to use
## 'loadSymbols' to automatically load data. getOption("getSymbols.env")
## and getOption("getSymbols.auto.assign") will still be checked for
## alternate defaults.
##
## This message is shown once per session and may be disabled by setting
## options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.
## [1] "NKE" "ADS.DE" "PUM.DE"
l_ply(tickers, function(sym) try(getSymbols(sym ,from = "2007/01/01" ,to = "2009/12/31", env=data.env, auto.assign = TRUE), silent=T))
stocks <- tickers[tickers %in% ls(data.env)]
stocks
## [1] "NKE" "ADS.DE" "PUM.DE"
data <- xts()
#Take adjusted value of 3 stocks
for(i in seq_along(stocks))
{
symbol <- stocks[i]
data <- merge(data, Ad(get(symbol, envir=data.env)))}
head(data)
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 2007-01-02 NA 30.93398 12.24304
## 2007-01-03 7.266537 31.03189 12.19294
## 2007-01-04 7.340934 30.84421 11.94572
## 2007-01-05 7.352838 30.43623 11.81172
## 2007-01-08 7.330519 30.58310 11.73393
## 2007-01-09 7.422033 30.17511 11.57101
tail(data)
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 2009-12-22 11.94493 32.76583 14.13108
## 2009-12-23 12.00732 32.64684 14.08156
## 2009-12-24 11.97246 NA NA
## 2009-12-28 12.01833 32.94432 14.20716
## 2009-12-29 12.14860 32.62984 14.16731
## 2009-12-30 12.13576 32.10287 13.99944
str(data)
## An 'xts' object on 2007-01-02/2009-12-30 containing:
## Data: num [1:773, 1:3] NA 7.27 7.34 7.35 7.33 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:3] "NKE.Adjusted" "ADS.DE.Adjusted" "PUM.DE.Adjusted"
## Indexed by objects of class: [POSIXct,POSIXt] TZ: Etc/UTC
## xts Attributes:
## NULL
#data<-xts (coredata(data), order.by = as.Date(index(data), tz="", optional= TRUE))
head(data)
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 2007-01-02 NA 30.93398 12.24304
## 2007-01-03 7.266537 31.03189 12.19294
## 2007-01-04 7.340934 30.84421 11.94572
## 2007-01-05 7.352838 30.43623 11.81172
## 2007-01-08 7.330519 30.58310 11.73393
## 2007-01-09 7.422033 30.17511 11.57101
tail(data)
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 2009-12-22 11.94493 32.76583 14.13108
## 2009-12-23 12.00732 32.64684 14.08156
## 2009-12-24 11.97246 NA NA
## 2009-12-28 12.01833 32.94432 14.20716
## 2009-12-29 12.14860 32.62984 14.16731
## 2009-12-30 12.13576 32.10287 13.99944
bt.prep(data.env, align = 'remove.na', fill.gaps = T)
#1b In other words, you have to compute optimal weights for 2010-01
library(fBasics)
## Loading required package: timeDate
## Loading required package: timeSeries
##
## Attaching package: 'timeSeries'
## The following object is masked from 'package:zoo':
##
## time<-
##
## Attaching package: 'fBasics'
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##
## volatility
data.NA <- data[complete.cases(data), ]
data.NA
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 2007-01-03 7.266537 31.03189 12.192940
## 2007-01-04 7.340934 30.84421 11.945717
## 2007-01-05 7.352838 30.43623 11.811720
## 2007-01-08 7.330519 30.58310 11.733926
## 2007-01-09 7.422033 30.17511 11.571012
## 2007-01-10 7.422033 30.21591 11.536394
## 2007-01-11 7.438398 30.24039 11.810089
## 2007-01-12 7.422033 30.56679 11.974226
## 2007-01-16 7.437654 30.52598 11.833307
## 2007-01-17 7.426494 30.62390 11.748589
## 2007-01-18 7.415337 31.33381 11.735966
## 2007-01-19 7.435421 31.50516 11.648397
## 2007-01-22 7.268769 31.25221 11.573456
## 2007-01-23 7.198832 30.94214 11.658173
## 2007-01-24 7.204783 30.34647 11.596265
## 2007-01-25 7.130384 30.08535 11.428869
## 2007-01-26 7.082773 29.90584 11.273694
## 2007-01-29 7.166100 29.84056 11.342931
## 2007-01-30 7.272487 30.04455 11.167797
## 2007-01-31 7.351351 30.12615 11.351078
## 2007-02-01 7.490478 30.31383 11.790949
## 2007-02-02 7.454765 30.46071 11.817421
## 2007-02-05 7.396734 31.17060 11.811312
## 2007-02-06 7.526933 31.30117 11.900101
## 2007-02-07 7.655642 31.12981 11.824752
## 2007-02-08 7.692101 31.19509 11.773435
## 2007-02-09 7.707722 30.92582 11.786875
## 2007-02-12 7.765008 30.84421 11.811312
## 2007-02-13 7.826759 30.91765 11.811312
## 2007-02-14 7.840151 31.26037 12.055682
## 2007-02-15 7.849823 31.19509 11.984406
## 2007-02-16 7.908597 31.01557 11.810905
## 2007-02-20 7.946540 30.67285 11.281430
## 2007-02-21 7.968861 30.59126 11.419909
## 2007-02-22 8.052190 30.61574 11.402802
## 2007-02-23 8.038048 31.08902 11.581193
## 2007-02-26 8.022430 30.98294 11.517655
## 2007-02-27 7.735248 30.59942 11.145397
## 2007-02-28 7.772449 30.28935 10.935645
## 2007-03-01 7.833457 30.05271 10.874551
## 2007-03-02 7.727066 29.74264 10.856225
## 2007-03-05 7.622908 28.96746 10.834640
## 2007-03-06 7.819320 28.90218 10.711637
## 2007-03-07 7.781376 28.80426 10.823235
## 2007-03-08 8.008779 29.53864 10.891251
## 2007-03-09 8.104485 30.31383 10.961304
## 2007-03-12 8.085340 30.22407 10.839932
## 2007-03-13 8.008779 29.89767 10.792280
## 2007-03-14 8.025622 29.71000 10.595559
## 2007-03-15 8.089937 29.88951 10.741368
## 2007-03-16 8.228519 30.43623 10.827713
## 2007-03-19 8.293603 30.88502 10.867627
## 2007-03-20 8.364806 31.57861 10.988593
## 2007-03-21 8.334182 31.66020 10.874551
## 2007-03-22 8.315040 31.78259 10.895323
## 2007-03-23 8.349494 32.48435 10.952346
## 2007-03-26 8.329591 31.90500 10.888400
## 2007-03-27 8.159612 33.17793 11.152323
## 2007-03-28 8.049357 33.15346 11.032173
## 2007-03-29 8.037107 33.52065 11.119740
## 2007-03-30 8.135877 33.39825 11.147842
## 2007-04-02 8.148891 33.65936 11.228484
## 2007-04-03 8.146595 33.73281 11.324197
## 2007-04-04 8.206317 33.70832 11.607668
## 2007-04-05 8.189471 33.95312 12.798982
## 2007-04-10 8.270635 34.68751 14.007809
## 2007-04-11 8.267570 35.02205 14.259103
## 2007-04-12 8.304320 34.87518 14.934559
## 2007-04-13 8.215507 35.27501 14.956491
## 2007-04-16 8.325758 35.82172 14.885871
## 2007-04-17 8.292072 36.80091 14.912190
## 2007-04-18 8.252255 36.31131 14.912631
## 2007-04-19 8.189471 36.28684 14.912631
## 2007-04-20 8.197127 36.00940 14.874908
## 2007-04-23 8.201722 35.98492 14.737183
## 2007-04-24 8.194068 35.77276 14.719643
## 2007-04-25 8.210911 35.87068 14.756924
## 2007-04-26 8.244596 35.92780 14.752975
## 2007-04-27 8.287476 35.69933 14.722712
## 2007-04-30 8.247665 35.78093 14.693323
## 2007-05-02 8.189471 35.08734 14.759116
## 2007-05-03 8.158845 34.66303 14.684551
## 2007-05-04 8.160378 34.51615 14.737183
## 2007-05-07 8.249193 34.51615 14.693323
## 2007-05-08 8.230820 37.03754 14.561744
## 2007-05-09 8.256851 37.29050 14.605604
## 2007-05-10 8.163441 36.67035 14.592443
## 2007-05-11 8.120564 36.81861 14.592883
## 2007-05-14 8.096059 37.06572 14.616128
## 2007-05-15 8.051651 37.32106 14.605604
## 2007-05-16 8.114439 37.06572 14.561744
## 2007-05-17 8.108311 37.14808 14.620077
## 2007-05-18 8.154252 37.72466 14.531042
## 2007-05-21 8.373230 37.05747 14.535865
## 2007-05-22 8.442142 37.19750 14.561744
## 2007-05-23 8.394666 37.38695 14.540251
## 2007-05-24 8.341070 37.00806 14.552971
## 2007-05-25 8.311976 37.61758 14.557357
## 2007-05-29 8.379355 38.24359 14.543759
## 2007-05-30 8.534018 38.52363 14.558671
## 2007-05-31 8.690212 39.07550 14.534114
## 2007-06-01 8.681026 38.87781 14.597708
## 2007-06-04 8.763715 38.71308 14.539810
## 2007-06-05 8.711646 38.05413 14.561744
## 2007-06-06 8.530956 37.37872 14.539810
## 2007-06-07 8.395936 37.28811 14.511741
## 2007-06-08 8.219018 37.25516 14.515688
## 2007-06-11 8.287305 37.05747 14.552971
## 2007-06-12 8.254713 36.71977 14.517880
## 2007-06-13 8.299718 36.39853 14.507355
## 2007-06-14 8.330756 37.19750 14.506918
## 2007-06-15 8.290409 37.60111 14.511302
## 2007-06-18 8.322996 37.43637 14.520075
## 2007-06-19 8.458017 36.81861 14.513496
## 2007-06-20 8.322996 37.07395 14.476214
## 2007-06-21 8.315234 37.05747 14.476214
## 2007-06-22 8.217464 36.87627 14.476214
## 2007-06-25 8.350932 36.86802 14.478404
## 2007-06-26 8.352483 36.96687 14.479286
## 2007-06-27 9.046196 36.98334 14.495952
## 2007-06-28 9.046196 37.48579 14.495952
## 2007-06-29 9.046196 38.53187 14.482797
## 2007-07-02 9.063268 38.50715 14.474021
## 2007-07-03 9.153281 39.27319 14.475778
## 2007-07-05 9.210699 38.96018 14.474021
## 2007-07-06 9.260360 39.33908 14.476214
## 2007-07-09 9.168796 38.98490 14.476214
## 2007-07-10 9.071028 38.27652 14.474021
## 2007-07-11 9.071028 38.01295 14.474021
## 2007-07-12 9.227770 38.45774 14.409984
## 2007-07-13 9.157935 38.52363 14.292876
## 2007-07-16 9.122240 37.76584 13.947694
## 2007-07-17 9.226220 37.54345 13.870499
## 2007-07-18 9.261912 36.99983 13.766109
## 2007-07-19 9.285192 37.17279 13.573563
## 2007-07-20 9.081889 37.07395 13.686722
## 2007-07-23 9.218460 37.10690 13.645055
## 2007-07-24 9.055507 36.88450 13.442417
## 2007-07-25 8.974806 36.41500 13.336714
## 2007-07-26 8.830479 36.17613 12.787579
## 2007-07-27 8.603893 35.96198 12.939335
## 2007-07-30 8.821165 36.62917 12.901178
## 2007-07-31 8.760641 36.91745 12.901178
## 2007-08-01 8.830479 35.74782 12.938459
## 2007-08-02 8.838237 35.04769 12.851177
## 2007-08-03 8.768398 35.21243 12.656875
## 2007-08-06 8.918940 35.37716 12.705559
## 2007-08-07 9.010501 35.51719 12.745912
## 2007-08-08 8.785472 35.69841 12.917845
## 2007-08-09 8.364900 35.78077 12.965652
## 2007-08-10 8.656660 35.26185 12.502922
## 2007-08-13 8.714080 35.40187 12.379237
## 2007-08-14 8.482847 35.14653 12.298971
## 2007-08-15 8.313684 35.63250 12.195021
## 2007-08-16 8.254713 34.18282 11.658606
## 2007-08-17 8.453358 34.62762 11.704659
## 2007-08-20 8.439392 34.59467 11.961684
## 2007-08-21 8.399040 34.49582 11.941943
## 2007-08-22 8.409904 35.08887 11.900715
## 2007-08-23 8.385071 35.29479 12.106422
## 2007-08-24 8.399040 34.91590 12.403797
## 2007-08-27 8.361793 35.17125 12.408183
## 2007-08-28 8.307477 34.56995 12.493711
## 2007-08-29 8.607001 34.59467 12.536257
## 2007-08-30 8.653556 34.66880 12.634943
## 2007-08-31 8.743568 35.54190 12.927496
## 2007-09-04 8.755985 35.74782 13.167850
## 2007-09-05 8.608552 35.70664 13.211272
## 2007-09-06 8.776855 35.42658 13.245483
## 2007-09-07 8.603829 34.99004 12.945475
## 2007-09-10 8.674614 34.89943 12.752491
## 2007-09-11 8.734383 35.02298 12.912141
## 2007-09-12 8.820893 35.02298 12.912141
## 2007-09-13 8.946731 35.20419 13.029689
## 2007-09-14 9.001780 35.08887 12.859510
## 2007-09-17 8.857071 35.22067 12.634065
## 2007-09-18 9.247153 35.99493 12.812142
## 2007-09-19 9.210978 36.90097 13.247238
## 2007-09-20 9.173225 36.83508 13.175307
## 2007-09-21 9.006497 37.22221 13.822690
## 2007-09-24 9.093009 36.96687 13.684093
## 2007-09-25 9.193675 37.13161 13.444611
## 2007-09-26 9.184237 37.09866 13.158200
## 2007-09-27 9.149631 37.62582 13.253816
## 2007-09-28 9.226704 37.88940 13.217854
## 2007-10-01 9.341527 37.90586 13.280134
## 2007-10-02 9.305351 37.88116 13.434521
## 2007-10-03 9.314789 38.01295 13.371802
## 2007-10-04 9.336809 37.61758 13.313907
## 2007-10-05 9.492528 37.15632 13.276186
## 2007-10-08 9.439051 35.99493 13.195045
## 2007-10-09 9.715881 36.52208 13.193290
## 2007-10-10 9.730040 36.67035 13.119604
## 2007-10-11 9.596341 36.41500 13.145043
## 2007-10-12 9.932945 36.29146 13.158200
## 2007-10-15 10.054058 36.07730 13.235398
## 2007-10-16 10.052485 36.25027 13.120919
## 2007-10-17 9.934516 36.16790 13.289345
## 2007-10-18 9.950246 36.25027 13.026618
## 2007-10-19 9.961257 36.19262 12.936266
## 2007-10-22 9.936090 35.74782 12.850735
## 2007-10-23 10.085517 36.28322 12.974426
## 2007-10-24 9.981707 35.99493 12.887581
## 2007-10-25 10.041473 36.79390 12.978373
## 2007-10-26 10.162586 37.23869 12.908196
## 2007-10-29 10.258537 37.23045 12.946354
## 2007-10-30 10.212922 37.00806 12.997671
## 2007-10-31 10.422120 37.93058 12.979250
## 2007-11-01 10.038328 37.72466 12.865649
## 2007-11-02 10.046193 37.08219 12.717402
## 2007-11-05 9.969121 36.94216 12.588451
## 2007-11-06 10.065067 37.37872 13.065216
## 2007-11-07 9.874746 37.75761 12.983196
## 2007-11-08 9.956538 39.26494 12.851615
## 2007-11-09 9.785089 39.42968 12.811702
## 2007-11-12 9.846433 39.74268 12.885825
## 2007-11-13 10.065067 39.85800 12.806876
## 2007-11-14 9.943954 39.80034 12.849859
## 2007-11-15 9.917218 38.30948 12.570466
## 2007-11-16 9.852726 38.26005 12.560381
## 2007-11-19 9.752058 37.53521 12.478800
## 2007-11-20 9.796100 37.69171 12.477484
## 2007-11-21 9.890476 37.33753 11.995456
## 2007-11-23 10.027320 37.88940 12.072211
## 2007-11-26 9.780375 37.27987 12.021335
## 2007-11-27 9.972266 36.85980 11.965630
## 2007-11-28 10.256964 37.79880 12.009050
## 2007-11-29 10.178319 37.18927 12.091510
## 2007-11-30 10.326172 37.45285 12.054227
## 2007-12-03 10.538515 38.01295 12.013875
## 2007-12-04 10.349766 37.79056 12.068702
## 2007-12-05 10.371787 38.25182 12.193267
## 2007-12-06 10.433998 37.52697 12.369147
## 2007-12-07 10.432404 37.65053 12.421342
## 2007-12-10 10.505781 38.47421 12.328357
## 2007-12-11 10.240985 38.88605 12.368709
## 2007-12-12 10.280862 38.91077 12.340637
## 2007-12-13 10.362215 38.63895 12.280987
## 2007-12-14 10.260124 39.16610 12.346778
## 2007-12-17 10.057539 38.67189 12.039756
## 2007-12-18 10.169199 39.01784 12.128350
## 2007-12-19 10.177176 39.35555 11.989753
## 2007-12-20 10.529711 39.81681 12.039756
## 2007-12-21 10.571185 40.46753 11.936243
## 2007-12-27 10.368597 41.13470 12.017825
## 2007-12-28 10.258531 42.22197 11.973963
## 2008-01-02 10.094229 41.18413 11.985366
## 2008-01-03 10.003304 41.25827 11.911242
## 2008-01-04 9.848576 41.02763 11.750714
## 2008-01-07 9.907592 40.78051 11.009028
## 2008-01-08 9.862928 39.78386 11.274385
## 2008-01-09 9.885260 38.43303 11.554216
## 2008-01-10 9.976183 37.41990 11.503778
## 2008-01-11 9.682674 36.90097 11.404213
## 2008-01-14 9.687458 36.81037 11.381406
## 2008-01-15 9.102033 35.37716 11.066925
## 2008-01-16 9.199338 33.61449 10.388401
## 2008-01-17 8.929753 33.68038 10.351558
## 2008-01-18 9.012702 33.96867 10.472172
## 2008-01-22 9.138721 33.15323 9.933125
## 2008-01-23 9.175408 31.66236 9.530484
## 2008-01-24 9.157860 34.18282 10.439716
## 2008-01-25 8.932945 34.18282 10.488839
## 2008-01-28 9.138721 33.62272 10.404628
## 2008-01-29 9.148293 34.37228 10.494541
## 2008-01-30 9.475302 35.43483 10.584455
## 2008-01-31 9.783170 34.99004 10.537526
## 2008-02-01 9.971398 35.82196 10.787971
## 2008-02-04 9.689053 35.64075 10.837093
## 2008-02-05 9.539107 34.59467 10.431383
## 2008-02-06 9.575795 34.71822 10.602003
## 2008-02-07 9.692242 34.33109 10.371293
## 2008-02-08 9.673104 34.68527 10.366034
## 2008-02-11 9.676294 34.80882 10.195414
## 2008-02-12 9.789550 35.63250 10.437523
## 2008-02-13 9.977781 35.78077 10.504632
## 2008-02-14 9.937897 35.79724 10.434892
## 2008-02-15 9.936305 35.51719 10.187078
## 2008-02-19 9.749671 36.28322 10.202429
## 2008-02-20 9.762429 35.31951 9.809877
## 2008-02-21 9.622054 35.45130 9.950232
## 2008-02-22 9.665127 35.03945 9.983128
## 2008-02-25 9.824643 36.07730 10.166465
## 2008-02-26 9.987350 35.92903 10.784901
## 2008-02-27 9.950661 35.41011 10.702004
## 2008-02-28 9.896427 34.57819 10.465594
## 2008-02-29 9.602915 34.54524 10.331820
## 2008-03-03 9.585368 34.43816 9.971725
## 2008-03-04 9.639606 34.14164 9.835315
## 2008-03-05 9.700218 34.24872 10.044093
## 2008-03-06 9.650010 33.31796 9.973478
## 2008-03-07 9.432973 32.93907 9.917334
## 2008-03-10 9.227271 33.44150 9.863387
## 2008-03-11 9.381147 33.44150 10.257694
## 2008-03-12 9.679165 34.10046 10.524369
## 2008-03-13 9.884863 33.25206 10.338399
## 2008-03-14 9.711557 33.42504 10.255502
## 2008-03-17 9.598181 31.91770 9.853298
## 2008-03-18 9.988522 32.04125 10.223922
## 2008-03-19 10.014439 31.84357 10.250237
## 2008-03-20 10.895538 32.28012 10.418664
## 2008-03-25 11.073706 34.24872 10.833586
## 2008-03-26 10.733571 34.05927 10.647178
## 2008-03-27 10.686604 34.59467 10.757707
## 2008-03-28 10.667164 34.41345 10.756392
## 2008-03-31 11.013774 34.68527 10.699369
## 2008-04-01 11.268064 35.13006 10.965167
## 2008-04-02 11.008917 35.16300 10.894551
## 2008-04-03 11.159545 34.76764 10.948062
## 2008-04-04 11.096378 34.61114 10.934464
## 2008-04-07 10.824274 34.83354 10.993237
## 2008-04-08 10.775681 34.44640 10.826568
## 2008-04-09 10.761106 33.87807 10.609019
## 2008-04-10 10.911735 33.37561 10.607265
## 2008-04-11 10.801599 33.23558 10.361645
## 2008-04-14 10.699558 33.18617 10.248485
## 2008-04-15 10.660683 33.43327 10.105937
## 2008-04-16 10.701180 34.10046 10.167778
## 2008-04-17 10.940894 33.76275 10.128304
## 2008-04-18 10.995960 34.28167 10.451997
## 2008-04-21 11.114197 34.03456 10.295854
## 2008-04-22 11.018632 33.76275 10.223045
## 2008-04-23 10.945750 34.06751 11.634816
## 2008-04-24 11.023494 34.42169 11.505526
## 2008-04-25 11.133628 34.39698 11.629845
## 2008-04-28 10.984621 34.58643 11.564703
## 2008-04-29 11.051029 33.67215 11.268822
## 2008-04-30 10.819416 33.76275 11.375736
## 2008-05-02 10.958711 33.25206 11.472209
## 2008-05-05 10.848571 33.27678 11.231524
## 2008-05-06 10.945750 35.17125 11.259870
## 2008-05-07 10.811316 35.67368 11.413031
## 2008-05-08 10.495481 36.25851 11.213622
## 2008-05-09 10.506819 37.07499 11.276279
## 2008-05-12 10.582942 37.24162 11.488121
## 2008-05-13 10.634773 37.05832 11.492099
## 2008-05-14 10.923075 37.19163 11.610452
## 2008-05-15 11.017010 37.97479 11.934678
## 2008-05-16 10.937651 38.99122 11.884451
## 2008-05-19 10.978144 38.83293 11.969482
## 2008-05-20 10.858287 37.79150 12.157956
## 2008-05-21 10.548930 37.22495 11.967000
## 2008-05-22 10.529494 37.71650 12.688551
## 2008-05-23 10.490619 37.80816 12.431953
## 2008-05-27 10.693081 37.47490 12.431458
## 2008-05-28 10.913356 38.72462 12.468254
## 2008-05-29 11.076945 38.28305 12.508534
## 2008-05-30 11.073706 37.75817 12.498592
## 2008-06-02 10.874484 37.53322 12.188289
## 2008-06-03 10.846948 37.44157 12.191272
## 2008-06-04 11.004058 37.33326 12.035623
## 2008-06-05 11.504839 37.62487 12.332995
## 2008-06-06 11.153469 37.65819 12.167403
## 2008-06-09 11.260194 37.07499 12.009268
## 2008-06-10 11.243775 36.86671 11.836712
## 2008-06-11 11.073019 36.40847 11.631833
## 2008-06-12 10.964651 36.91670 11.817816
## 2008-06-13 11.327512 37.07499 11.700958
## 2008-06-16 11.227356 37.26661 11.551772
## 2008-06-17 11.164963 37.32494 11.748693
## 2008-06-18 11.145262 36.90836 11.586582
## 2008-06-19 11.138690 36.09187 11.454307
## 2008-06-20 10.956438 35.09211 11.288215
## 2008-06-23 10.984353 35.38370 11.219092
## 2008-06-24 10.831657 34.99212 11.127094
## 2008-06-25 10.831657 35.67531 11.139528
## 2008-06-26 9.769341 34.25896 10.838675
## 2008-06-27 9.907260 33.65909 10.646228
## 2008-06-30 9.787406 33.41748 10.599981
## 2008-07-01 9.685609 32.40937 10.180281
## 2008-07-02 9.537834 32.33439 10.172322
## 2008-07-03 9.608438 32.45103 9.995292
## 2008-07-07 9.270204 32.43437 9.969931
## 2008-07-08 9.575596 30.90138 9.791904
## 2008-07-09 9.350657 31.49291 9.880420
## 2008-07-10 9.140491 31.10967 9.473148
## 2008-07-11 9.237366 30.08490 9.421432
## 2008-07-14 9.163482 30.18487 9.344353
## 2008-07-15 9.463947 29.03513 9.234954
## 2008-07-16 9.549329 30.40982 9.337891
## 2008-07-17 9.615005 31.46792 9.589513
## 2008-07-18 9.555897 31.66787 9.723777
## 2008-07-21 9.442604 32.26774 9.909265
## 2008-07-22 9.633066 32.37605 9.790909
## 2008-07-23 9.720085 32.63432 9.993302
## 2008-07-24 9.544402 32.61766 10.253877
## 2008-07-25 9.550969 32.49269 10.293161
## 2008-07-28 9.398273 32.00113 10.172322
## 2008-07-29 9.697103 32.60100 10.194201
## 2008-07-30 9.798894 33.32584 10.445826
## 2008-07-31 9.634707 32.83427 10.321507
## 2008-08-01 9.752923 32.70097 10.415989
## 2008-08-04 9.815319 31.96780 10.400075
## 2008-08-05 10.110860 34.41725 10.836189
## 2008-08-06 10.211018 36.35015 11.105219
## 2008-08-07 9.991001 35.18375 11.188760
## 2008-08-08 10.335800 35.11710 11.122124
## 2008-08-11 10.388341 36.57510 11.194725
## 2008-08-12 10.196238 35.82527 11.176328
## 2008-08-13 10.174895 35.10876 10.873982
## 2008-08-14 10.179818 35.31705 10.615397
## 2008-08-15 10.227437 34.99212 10.817292
## 2008-08-18 10.122354 34.14232 10.688000
## 2008-08-19 10.020555 33.09255 10.194201
## 2008-08-20 9.959803 33.24252 10.392616
## 2008-08-21 9.948309 32.61766 10.178290
## 2008-08-22 10.033689 33.15921 10.353333
## 2008-08-25 9.803822 32.49269 10.358304
## 2008-08-26 9.674113 32.56767 10.431903
## 2008-08-27 9.797253 32.13444 10.294154
## 2008-08-28 10.051753 32.81762 10.514449
## 2008-08-29 9.951597 33.36749 10.693469
## 2008-09-02 10.045185 34.05067 11.070407
## 2008-09-03 10.165043 33.44248 10.817788
## 2008-09-04 9.956711 32.68430 10.741209
## 2008-09-05 9.803376 31.82616 10.486107
## 2008-09-08 10.055044 32.39271 10.632802
## 2008-09-09 10.046706 32.31772 10.515446
## 2008-09-10 9.978374 31.97614 10.353830
## 2008-09-11 10.161708 30.90971 10.335432
## 2008-09-12 10.320040 31.32628 10.442346
## 2008-09-15 10.083375 31.56790 10.069386
## 2008-09-16 10.198376 30.87638 9.978880
## 2008-09-17 9.926709 30.37650 9.846108
## 2008-09-18 10.773381 30.85972 9.867490
## 2008-09-19 10.616711 32.21775 10.685017
## 2008-09-22 10.525045 32.45936 10.572136
## 2008-09-23 10.138374 32.45103 10.449804
## 2008-09-24 9.878373 32.81762 10.542795
## 2008-09-25 10.835048 33.90903 10.362282
## 2008-09-26 11.298379 32.05946 9.840140
## 2008-09-29 10.841715 31.29295 9.377671
## 2008-09-30 11.150049 31.40960 9.533319
## 2008-10-01 11.026713 31.00968 9.362754
## 2008-10-02 10.625045 30.73475 9.205611
## 2008-10-03 10.541714 30.97637 8.950510
## 2008-10-06 10.190041 28.90183 8.081766
## 2008-10-07 9.663372 29.10179 7.757539
## 2008-10-08 9.283375 28.38528 7.396019
## 2008-10-09 8.846703 27.94371 7.555645
## 2008-10-10 9.088369 25.80252 6.963883
## 2008-10-13 9.308373 29.32673 7.918161
## 2008-10-14 9.520041 28.62689 8.023583
## 2008-10-15 8.393366 25.41095 7.353252
## 2008-10-16 9.328373 25.74421 6.772930
## 2008-10-17 9.580041 26.26076 6.749060
## 2008-10-20 9.958373 26.96893 6.857964
## 2008-10-21 9.520041 25.92750 6.862440
## 2008-10-22 8.750037 23.96127 6.539207
## 2008-10-23 8.455032 24.28620 6.327865
## 2008-10-24 7.965034 22.99482 6.026017
## 2008-10-27 7.758369 21.45351 5.608303
## 2008-10-28 8.736704 20.04549 5.651567
## 2008-10-29 8.746704 22.38663 5.920595
## 2008-10-30 9.301704 23.72799 6.402954
## 2008-10-31 9.605042 22.93650 6.535727
## 2008-11-03 9.306706 23.79465 6.646620
## 2008-11-04 9.370038 25.30264 7.332864
## 2008-11-05 8.796703 24.55281 7.204566
## 2008-11-06 8.440036 22.19500 6.964878
## 2008-11-07 8.235035 22.91151 7.017591
## 2008-11-10 7.995032 22.74488 7.165779
## 2008-11-11 7.611699 21.04526 6.911172
## 2008-11-12 7.395032 20.95361 6.441742
## 2008-11-13 8.143367 20.52038 6.496939
## 2008-11-14 7.755031 20.53705 6.400467
## 2008-11-17 7.718367 19.92885 6.200562
## 2008-11-18 7.773367 19.78721 6.118014
## 2008-11-19 7.306696 18.60415 5.922086
## 2008-11-20 7.268363 18.28755 5.941978
## 2008-11-21 7.980033 17.89597 5.943469
## 2008-11-24 8.386700 19.82054 6.451190
## 2008-11-25 8.215035 20.49539 6.610319
## 2008-11-26 8.875039 20.69534 6.271673
## 2008-11-28 8.875039 20.37875 6.664025
## 2008-12-01 8.003364 19.73722 6.384057
## 2008-12-02 8.335037 20.18712 6.563575
## 2008-12-03 8.668369 19.96217 6.549153
## 2008-12-04 8.829806 20.17879 6.368642
## 2008-12-05 9.064320 19.00406 6.290569
## 2008-12-08 9.545231 19.31232 6.454670
## 2008-12-09 8.996346 21.09525 6.731158
## 2008-12-10 8.581704 22.44495 6.862936
## 2008-12-11 8.280919 22.06170 6.929572
## 2008-12-12 8.389679 22.51160 6.777902
## 2008-12-15 8.189155 22.29498 6.631205
## 2008-12-16 8.435558 22.68656 6.787351
## 2008-12-17 8.605494 22.19500 6.715742
## 2008-12-18 8.953856 22.31998 6.738616
## 2008-12-19 8.710851 22.65323 6.738119
## 2008-12-22 8.343792 22.00338 6.599876
## 2008-12-23 8.150072 21.77843 6.566559
## 2008-12-29 8.316605 21.97006 6.762983
## 2008-12-30 8.444054 22.61158 6.976813
## 2009-01-02 9.016738 23.16979 7.276670
## 2009-01-05 9.081313 23.22811 7.384579
## 2009-01-06 8.897782 24.32786 7.682451
## 2009-01-07 8.574905 24.02792 7.528295
## 2009-01-08 8.732945 23.72799 7.519842
## 2009-01-09 8.430461 22.99482 7.384579
## 2009-01-12 8.517128 22.36996 7.409445
## 2009-01-13 8.411767 22.56159 7.257277
## 2009-01-14 7.927455 21.16190 7.052400
## 2009-01-15 7.980135 21.27855 7.125997
## 2009-01-16 7.952944 21.68679 7.157324
## 2009-01-20 7.500918 20.77866 6.847520
## 2009-01-21 7.759222 21.33686 7.104117
## 2009-01-22 7.754122 21.83675 6.938522
## 2009-01-23 7.762618 21.62846 6.825143
## 2009-01-26 7.760917 22.94484 7.203074
## 2009-01-27 7.733728 22.92817 6.862440
## 2009-01-28 8.088892 23.91962 7.011622
## 2009-01-29 7.815297 23.02815 7.015103
## 2009-01-30 7.689545 22.60325 7.026541
## 2009-02-02 7.550199 22.67823 7.207551
## 2009-02-03 7.867978 22.87818 7.145390
## 2009-02-04 7.779610 23.64468 7.285623
## 2009-02-05 8.020920 23.72799 7.235397
## 2009-02-06 8.272421 24.22788 7.375132
## 2009-02-09 8.117783 24.31953 7.480059
## 2009-02-10 7.655556 23.90295 7.355739
## 2009-02-11 7.529807 23.61968 7.226943
## 2009-02-12 7.555299 22.74488 6.921616
## 2009-02-13 7.380264 22.59491 6.956922
## 2009-02-17 7.127059 21.87841 6.601367
## 2009-02-18 7.395561 21.53682 6.311952
## 2009-02-19 7.274907 21.25355 6.358696
## 2009-02-20 7.295299 21.08692 6.167742
## 2009-02-23 7.070984 20.32043 6.010105
## 2009-02-24 7.296997 20.36209 6.095140
## 2009-02-25 7.162748 20.21212 6.272170
## 2009-02-26 6.972420 20.15380 6.141882
## 2009-02-27 7.057389 19.17068 5.943469
## 2009-03-02 6.756604 19.16235 5.766936
## 2009-03-03 6.805886 19.07904 5.673944
## 2009-03-04 7.230723 19.10403 5.665988
## 2009-03-05 6.950541 18.93740 5.668474
## 2009-03-06 6.950541 19.11236 5.287062
## 2009-03-09 6.712130 19.68724 5.123955
## 2009-03-10 7.241165 20.78699 5.359169
## 2009-03-11 7.557888 20.62869 5.509842
## 2009-03-12 7.759757 20.77866 5.569018
## 2009-03-13 7.773680 20.32043 5.619244
## 2009-03-16 7.641419 20.32043 5.767930
## 2009-03-17 7.902456 19.86220 5.720192
## 2009-03-18 7.991210 19.82054 5.868379
## 2009-03-19 8.092140 20.29544 5.948441
## 2009-03-20 7.834584 20.01216 6.017066
## 2009-03-23 8.287055 20.52871 5.943469
## 2009-03-24 7.935521 21.18690 6.002148
## 2009-03-25 8.069519 22.05337 6.017066
## 2009-03-26 8.283569 21.87841 5.871860
## 2009-03-27 8.151312 20.97028 5.666485
## 2009-03-30 8.050377 20.36209 5.497906
## 2009-03-31 8.160015 20.87863 5.682398
## 2009-04-01 8.179155 20.94529 5.607806
## 2009-04-02 8.786501 21.98672 6.009109
## 2009-04-03 9.026657 22.54493 6.288580
## 2009-04-06 8.922242 22.23666 6.534236
## 2009-04-07 8.676867 21.92007 6.504399
## 2009-04-08 8.742995 21.89507 6.680933
## 2009-04-09 9.270289 23.00315 6.929075
## 2009-04-14 8.944865 22.99482 7.323416
## 2009-04-15 9.068421 22.97816 7.536749
## 2009-04-16 9.357303 23.11147 7.703833
## 2009-04-17 9.503484 23.09480 8.006677
## 2009-04-20 9.111929 22.64490 7.814726
## 2009-04-21 9.270289 23.46139 7.967392
## 2009-04-22 9.571355 24.36118 7.807268
## 2009-04-23 9.465199 25.07769 7.877384
## 2009-04-24 9.524364 25.50259 7.933577
## 2009-04-27 9.419951 25.13601 7.885340
## 2009-04-28 9.674028 24.51115 7.700352
## 2009-04-29 9.216345 23.90295 7.744113
## 2009-04-30 9.131069 23.84463 8.068340
## 2009-05-04 9.618340 24.57780 8.247357
## 2009-05-05 9.571355 21.82842 8.113094
## 2009-05-06 9.503484 20.86197 8.113094
## 2009-05-07 9.237226 21.06193 8.055907
## 2009-05-08 9.470420 21.00243 7.638193
## 2009-05-11 9.247666 21.36791 7.583493
## 2009-05-12 8.871774 22.22636 7.719747
## 2009-05-13 8.617699 21.24892 7.749086
## 2009-05-14 8.866554 20.57745 9.136107
## 2009-05-15 8.657723 20.39046 9.132483
## 2009-05-18 8.910060 21.65690 9.451312
## 2009-05-19 9.056242 22.80434 9.796106
## 2009-05-20 8.821308 23.33131 10.067833
## 2009-05-21 8.936164 22.31136 9.885473
## 2009-05-22 9.120628 22.34536 9.663865
## 2009-05-26 9.426911 22.37936 9.730286
## 2009-05-27 9.468679 22.31986 9.994165
## 2009-05-28 9.590495 21.97138 9.629443
## 2009-05-29 9.928102 21.93738 9.825090
## 2009-06-01 10.312698 22.66834 10.049718
## 2009-06-02 10.063841 22.77034 10.038246
## 2009-06-03 10.123012 22.35386 10.009865
## 2009-06-04 10.188523 22.03938 10.030395
## 2009-06-05 10.321328 22.14137 10.047904
## 2009-06-08 10.269979 21.85239 9.881851
## 2009-06-09 10.386842 21.94588 9.771348
## 2009-06-10 10.101761 23.55230 10.064210
## 2009-06-11 10.025623 23.69679 10.326278
## 2009-06-12 10.023852 22.83834 10.355864
## 2009-06-15 9.905215 22.71084 10.126406
## 2009-06-16 9.797203 22.54085 9.875209
## 2009-06-17 9.673258 22.81284 9.367982
## 2009-06-18 9.968961 22.78734 9.437425
## 2009-06-19 10.039789 22.78734 9.581139
## 2009-06-22 9.784809 22.33686 9.174150
## 2009-06-23 9.480248 22.85534 9.144561
## 2009-06-24 9.388179 23.56930 9.625822
## 2009-06-25 9.080073 23.40781 9.367377
## 2009-06-26 9.002166 23.28031 9.115577
## 2009-06-29 9.163298 23.29731 9.467012
## 2009-06-30 9.168610 23.03383 9.418100
## 2009-07-01 9.281937 23.41631 9.543096
## 2009-07-02 9.041121 22.81284 9.473052
## 2009-07-06 9.191630 22.37086 9.046136
## 2009-07-07 9.067681 22.16687 9.063647
## 2009-07-08 9.120801 21.84389 8.825733
## 2009-07-09 9.041121 21.48690 8.784068
## 2009-07-10 9.083619 21.52940 8.703154
## 2009-07-13 9.126116 21.82689 9.046740
## 2009-07-14 9.189858 22.30286 9.014734
## 2009-07-15 9.372240 22.52385 9.537663
## 2009-07-16 9.418273 22.81284 9.534642
## 2009-07-17 9.285473 22.99983 9.484523
## 2009-07-20 9.354537 23.44180 9.634878
## 2009-07-21 9.219959 23.79879 9.952499
## 2009-07-22 9.124343 23.79879 9.970613
## 2009-07-23 9.055289 24.32576 10.213965
## 2009-07-24 9.237668 24.69124 10.239929
## 2009-07-27 9.273083 24.69974 10.326880
## 2009-07-28 9.368698 24.38526 10.338353
## 2009-07-29 9.627217 25.56670 10.495956
## 2009-07-30 9.931777 25.37970 10.744134
## 2009-07-31 10.029162 25.20122 10.738095
## 2009-08-03 10.025623 25.85568 10.977219
## 2009-08-04 10.188523 25.86418 11.140860
## 2009-08-05 10.096450 27.39410 11.627553
## 2009-08-06 10.202691 27.37711 12.013408
## 2009-08-07 10.282373 28.36306 11.462707
## 2009-08-10 10.117701 28.41406 10.929514
## 2009-08-11 10.055725 27.05412 10.755005
## 2009-08-12 10.184985 26.88413 10.587740
## 2009-08-13 10.236336 26.96063 11.269475
## 2009-08-14 10.068118 26.99462 11.678880
## 2009-08-17 9.816681 27.11362 11.491691
## 2009-08-18 9.846781 27.37711 11.629968
## 2009-08-19 10.052185 27.35160 11.580455
## 2009-08-20 10.092910 27.51310 11.987442
## 2009-08-21 9.853867 27.98057 12.007372
## 2009-08-24 9.915839 27.69159 11.877544
## 2009-08-25 9.767102 28.18457 11.986236
## 2009-08-26 9.818454 28.58404 12.227773
## 2009-08-27 10.062810 28.04857 11.935512
## 2009-08-28 9.947713 28.04857 12.160746
## 2009-08-31 9.807831 27.92957 11.907735
## 2009-09-01 9.625450 27.15612 11.876939
## 2009-09-02 9.439527 26.76514 11.561131
## 2009-09-03 9.695770 26.75664 11.841313
## 2009-09-04 9.785996 26.82463 12.440322
## 2009-09-08 9.968255 27.70859 13.163724
## 2009-09-09 9.988106 28.90703 13.425790
## 2009-09-10 10.000733 28.09106 13.410695
## 2009-09-11 9.923141 27.97208 13.159498
## 2009-09-14 9.908705 28.66904 13.344272
## 2009-09-15 9.869005 28.64354 13.284492
## 2009-09-16 10.318336 30.59844 13.827347
## 2009-09-17 10.482547 31.02341 13.913693
## 2009-09-18 10.572776 30.88743 13.432433
## 2009-09-21 10.565555 30.51344 13.404053
## 2009-09-22 10.569166 30.47095 13.467455
## 2009-09-23 10.520442 30.72594 13.625058
## 2009-09-24 10.496985 30.17347 13.585808
## 2009-09-25 10.581797 30.59844 13.556223
## 2009-09-28 10.646759 30.80242 13.375669
## 2009-09-29 10.843455 30.52194 13.408883
## 2009-09-30 11.675342 30.74293 13.702955
## 2009-10-01 11.278347 30.17347 13.319515
## 2009-10-02 11.191730 29.67199 12.770020
## 2009-10-05 11.328876 29.78248 12.861803
## 2009-10-06 11.384815 30.59844 13.465642
## 2009-10-07 11.444361 29.85898 13.587014
## 2009-10-08 11.552634 29.32351 13.561655
## 2009-10-09 11.475040 29.62099 13.652834
## 2009-10-12 11.413691 29.53600 13.754883
## 2009-10-13 11.491281 29.16202 13.592450
## 2009-10-14 11.711439 30.39445 13.984945
## 2009-10-15 11.722261 30.85343 13.908263
## 2009-10-16 11.747526 30.72594 13.652232
## 2009-10-19 11.926175 31.10841 13.947509
## 2009-10-20 11.745722 30.43695 13.583395
## 2009-10-21 11.684367 29.97797 13.193915
## 2009-10-22 11.763769 29.72299 12.940904
## 2009-10-23 11.579703 29.49350 12.988608
## 2009-10-26 11.503914 28.66904 12.821346
## 2009-10-27 11.565268 28.38855 12.498894
## 2009-10-28 11.290979 27.32611 12.053261
## 2009-10-29 11.496696 27.84458 12.653478
## 2009-10-30 11.220604 26.77364 12.542974
## 2009-11-02 11.278347 27.79359 12.764585
## 2009-11-03 11.307220 27.74258 12.638988
## 2009-11-04 11.319852 28.78803 13.219882
## 2009-11-05 11.686173 29.07702 13.422772
## 2009-11-06 11.650083 29.10252 13.465642
## 2009-11-09 11.787227 29.57850 14.065864
## 2009-11-10 11.633841 29.79948 13.948716
## 2009-11-11 11.716849 30.49645 13.907654
## 2009-11-12 11.565268 30.22447 14.085186
## 2009-11-13 11.624821 30.40295 13.930601
## 2009-11-16 11.927979 31.08291 14.089411
## 2009-11-17 11.722261 30.67493 13.888330
## 2009-11-18 11.624821 30.79393 13.700538
## 2009-11-19 11.469626 30.18196 13.387748
## 2009-11-20 11.534590 30.02046 13.426999
## 2009-11-23 11.637449 30.99792 13.976495
## 2009-11-24 11.642862 30.82793 13.929999
## 2009-11-25 11.855798 32.03486 14.242787
## 2009-11-27 11.738504 32.16236 13.972265
## 2009-11-30 11.709633 32.40886 13.815872
## 2009-12-01 11.801664 32.72333 14.102695
## 2009-12-02 11.792639 32.21336 14.243995
## 2009-12-03 11.866034 31.60989 14.193268
## 2009-12-04 11.798142 32.06037 14.536860
## 2009-12-07 11.842180 32.47684 14.314643
## 2009-12-08 11.656859 32.08586 14.042916
## 2009-12-09 11.366953 32.07737 13.889539
## 2009-12-10 11.504567 31.75438 14.077938
## 2009-12-11 11.717410 32.06037 14.189046
## 2009-12-14 11.772458 32.00087 14.170327
## 2009-12-15 11.807319 32.30685 14.050163
## 2009-12-16 11.752271 32.46834 14.281431
## 2009-12-17 11.605490 32.83383 14.176971
## 2009-12-18 11.820166 32.78283 14.019365
## 2009-12-21 11.904565 32.93583 13.954149
## 2009-12-22 11.944933 32.76583 14.131076
## 2009-12-23 12.007320 32.64684 14.081564
## 2009-12-28 12.018329 32.94432 14.207159
## 2009-12-29 12.148602 32.62984 14.167309
## 2009-12-30 12.135762 32.10287 13.999437
#Sigma = cov(data.env[,])
Sigma = cov(data.NA)
Sigma
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## NKE.Adjusted 1.498566 2.360266 1.159875
## ADS.DE.Adjusted 2.360266 35.416822 11.836347
## PUM.DE.Adjusted 1.159875 11.836347 6.462393
ones = rep(1,3)
one.vec = matrix(ones, ncol=1)
a = inv(Sigma)%*%one.vec
b = t(one.vec)%*%a
mvp.w =a / as.numeric(b)
mvp.w
## [,1]
## NKE.Adjusted 0.86895831
## ADS.DE.Adjusted -0.09597124
## PUM.DE.Adjusted 0.22701293
#1c Give me weights, realized returns and standard deviation for 2010-01.
mvp.ret<-sum((mvp.w)*colMeans(data))
mvp.ret
## [1] NA
std = sqrt(diag(mvp.w))
std
## [1] 0.9321793
# Q2. Based on Q1, you have to use weekly and monthly returns to get the answers to Q1.
NKE.monthly_return <- monthlyReturn(data.NA$NKE.Adjusted,subset=NULL, type='arithmetic',
leading=TRUE, from = "2007/01/01", to = "2009/12/31")
NKE.monthly_return
## monthly.returns
## 2007-01-31 0.011671860
## 2007-02-28 0.057281716
## 2007-03-30 0.046758493
## 2007-04-30 0.013740129
## 2007-05-31 0.053657247
## 2007-06-29 0.040963788
## 2007-07-31 -0.031566307
## 2007-08-31 -0.001948830
## 2007-09-28 0.055256161
## 2007-10-31 0.129560458
## 2007-11-30 -0.009206188
## 2007-12-28 -0.006550443
## 2008-01-31 -0.046338116
## 2008-02-29 -0.018425009
## 2008-03-31 0.146919868
## 2008-04-30 -0.017646812
## 2008-05-30 0.023503117
## 2008-06-30 -0.116158041
## 2008-07-31 -0.015601580
## 2008-08-29 0.032890466
## 2008-09-30 0.120428108
## 2008-10-31 -0.138565041
## 2008-11-28 -0.076002062
## 2008-12-30 -0.048561477
## 2009-01-30 -0.089353881
## 2009-02-27 -0.082209806
## 2009-03-31 0.156237101
## 2009-04-30 0.119001497
## 2009-05-29 0.087288027
## 2009-06-30 -0.076499214
## 2009-07-31 0.093858502
## 2009-08-31 -0.022068743
## 2009-09-30 0.190410194
## 2009-10-30 -0.038948581
## 2009-11-30 0.043583126
## 2009-12-30 0.036391320
ADS.monthly_return <- monthlyReturn(data.NA$ADS.DE.Adjusted ,subset=NULL, type='arithmetic',
leading=TRUE, from = "2007/01/01", to = "2009/12/31")
ADS.monthly_return
## monthly.returns
## 2007-01-31 -0.0291875542
## 2007-02-28 0.0054173209
## 2007-03-30 0.1026402053
## 2007-04-30 0.0713412144
## 2007-05-31 0.0920761805
## 2007-06-29 -0.0139122735
## 2007-07-31 -0.0418983580
## 2007-08-31 -0.0372601344
## 2007-09-28 0.0660488099
## 2007-10-31 0.0010868212
## 2007-11-30 -0.0125947468
## 2007-12-28 0.1273365311
## 2008-01-31 -0.1712835921
## 2008-02-29 -0.0127121332
## 2008-03-31 0.0040535254
## 2008-04-30 -0.0265968537
## 2008-05-30 0.1183380536
## 2008-06-30 -0.1149602151
## 2008-07-31 -0.0174521239
## 2008-08-29 0.0162397073
## 2008-09-30 -0.0586766887
## 2008-10-31 -0.2697613873
## 2008-11-28 -0.1115146503
## 2008-12-30 0.1095668006
## 2009-01-30 -0.0003686164
## 2009-02-27 -0.1518614694
## 2009-03-31 0.0890918701
## 2009-04-30 0.1420589995
## 2009-05-29 -0.0799865949
## 2009-06-30 0.0499806677
## 2009-07-31 0.0940959138
## 2009-08-31 0.1082629902
## 2009-09-30 0.1007304980
## 2009-10-30 -0.1291125587
## 2009-11-30 0.2104764179
## 2009-12-30 -0.0094413703
PUM.monthly_return <- monthlyReturn(data.NA$PUM.DE.Adjusted,subset=NULL, type='arithmetic',
leading=TRUE, from = "2007/01/01", to = "2009/12/31")
PUM.monthly_return
## monthly.returns
## 2007-01-31 -0.069045038
## 2007-02-28 -0.036598550
## 2007-03-30 0.019404160
## 2007-04-30 0.318041913
## 2007-05-31 -0.010835466
## 2007-06-29 -0.003530797
## 2007-07-31 -0.109206737
## 2007-08-31 0.002039969
## 2007-09-28 0.022460498
## 2007-10-31 -0.018051644
## 2007-11-30 -0.071269372
## 2007-12-28 -0.006658577
## 2008-01-31 -0.119963374
## 2008-02-29 -0.019521280
## 2008-03-31 0.035574468
## 2008-04-30 0.063215597
## 2008-05-30 0.098706229
## 2008-06-30 -0.151905991
## 2008-07-31 -0.026271179
## 2008-08-29 0.036037567
## 2008-09-30 -0.108491454
## 2008-10-31 -0.314433200
## 2008-11-28 0.019630257
## 2008-12-30 0.046936799
## 2009-01-30 0.007127610
## 2009-02-27 -0.154140138
## 2009-03-31 -0.043925694
## 2009-04-30 0.419882944
## 2009-05-29 0.217733759
## 2009-06-30 -0.041423539
## 2009-07-31 0.140155127
## 2009-08-31 0.108924348
## 2009-09-30 0.150760829
## 2009-10-30 -0.084651887
## 2009-11-30 0.101482950
## 2009-12-30 0.013286530
monthly_return <- merge(ADS.monthly_return, NKE.monthly_return, PUM.monthly_return)
monthly_return
## monthly.returns monthly.returns.1 monthly.returns.2
## 2007-01-31 -0.0291875542 0.011671860 -0.069045038
## 2007-02-28 0.0054173209 0.057281716 -0.036598550
## 2007-03-30 0.1026402053 0.046758493 0.019404160
## 2007-04-30 0.0713412144 0.013740129 0.318041913
## 2007-05-31 0.0920761805 0.053657247 -0.010835466
## 2007-06-29 -0.0139122735 0.040963788 -0.003530797
## 2007-07-31 -0.0418983580 -0.031566307 -0.109206737
## 2007-08-31 -0.0372601344 -0.001948830 0.002039969
## 2007-09-28 0.0660488099 0.055256161 0.022460498
## 2007-10-31 0.0010868212 0.129560458 -0.018051644
## 2007-11-30 -0.0125947468 -0.009206188 -0.071269372
## 2007-12-28 0.1273365311 -0.006550443 -0.006658577
## 2008-01-31 -0.1712835921 -0.046338116 -0.119963374
## 2008-02-29 -0.0127121332 -0.018425009 -0.019521280
## 2008-03-31 0.0040535254 0.146919868 0.035574468
## 2008-04-30 -0.0265968537 -0.017646812 0.063215597
## 2008-05-30 0.1183380536 0.023503117 0.098706229
## 2008-06-30 -0.1149602151 -0.116158041 -0.151905991
## 2008-07-31 -0.0174521239 -0.015601580 -0.026271179
## 2008-08-29 0.0162397073 0.032890466 0.036037567
## 2008-09-30 -0.0586766887 0.120428108 -0.108491454
## 2008-10-31 -0.2697613873 -0.138565041 -0.314433200
## 2008-11-28 -0.1115146503 -0.076002062 0.019630257
## 2008-12-30 0.1095668006 -0.048561477 0.046936799
## 2009-01-30 -0.0003686164 -0.089353881 0.007127610
## 2009-02-27 -0.1518614694 -0.082209806 -0.154140138
## 2009-03-31 0.0890918701 0.156237101 -0.043925694
## 2009-04-30 0.1420589995 0.119001497 0.419882944
## 2009-05-29 -0.0799865949 0.087288027 0.217733759
## 2009-06-30 0.0499806677 -0.076499214 -0.041423539
## 2009-07-31 0.0940959138 0.093858502 0.140155127
## 2009-08-31 0.1082629902 -0.022068743 0.108924348
## 2009-09-30 0.1007304980 0.190410194 0.150760829
## 2009-10-30 -0.1291125587 -0.038948581 -0.084651887
## 2009-11-30 0.2104764179 0.043583126 0.101482950
## 2009-12-30 -0.0094413703 0.036391320 0.013286530
monthly_return.NA <- monthly_return[complete.cases(monthly_return), ]
monthly_return.NA
## monthly.returns monthly.returns.1 monthly.returns.2
## 2007-01-31 -0.0291875542 0.011671860 -0.069045038
## 2007-02-28 0.0054173209 0.057281716 -0.036598550
## 2007-03-30 0.1026402053 0.046758493 0.019404160
## 2007-04-30 0.0713412144 0.013740129 0.318041913
## 2007-05-31 0.0920761805 0.053657247 -0.010835466
## 2007-06-29 -0.0139122735 0.040963788 -0.003530797
## 2007-07-31 -0.0418983580 -0.031566307 -0.109206737
## 2007-08-31 -0.0372601344 -0.001948830 0.002039969
## 2007-09-28 0.0660488099 0.055256161 0.022460498
## 2007-10-31 0.0010868212 0.129560458 -0.018051644
## 2007-11-30 -0.0125947468 -0.009206188 -0.071269372
## 2007-12-28 0.1273365311 -0.006550443 -0.006658577
## 2008-01-31 -0.1712835921 -0.046338116 -0.119963374
## 2008-02-29 -0.0127121332 -0.018425009 -0.019521280
## 2008-03-31 0.0040535254 0.146919868 0.035574468
## 2008-04-30 -0.0265968537 -0.017646812 0.063215597
## 2008-05-30 0.1183380536 0.023503117 0.098706229
## 2008-06-30 -0.1149602151 -0.116158041 -0.151905991
## 2008-07-31 -0.0174521239 -0.015601580 -0.026271179
## 2008-08-29 0.0162397073 0.032890466 0.036037567
## 2008-09-30 -0.0586766887 0.120428108 -0.108491454
## 2008-10-31 -0.2697613873 -0.138565041 -0.314433200
## 2008-11-28 -0.1115146503 -0.076002062 0.019630257
## 2008-12-30 0.1095668006 -0.048561477 0.046936799
## 2009-01-30 -0.0003686164 -0.089353881 0.007127610
## 2009-02-27 -0.1518614694 -0.082209806 -0.154140138
## 2009-03-31 0.0890918701 0.156237101 -0.043925694
## 2009-04-30 0.1420589995 0.119001497 0.419882944
## 2009-05-29 -0.0799865949 0.087288027 0.217733759
## 2009-06-30 0.0499806677 -0.076499214 -0.041423539
## 2009-07-31 0.0940959138 0.093858502 0.140155127
## 2009-08-31 0.1082629902 -0.022068743 0.108924348
## 2009-09-30 0.1007304980 0.190410194 0.150760829
## 2009-10-30 -0.1291125587 -0.038948581 -0.084651887
## 2009-11-30 0.2104764179 0.043583126 0.101482950
## 2009-12-30 -0.0094413703 0.036391320 0.013286530
Sigma_monthly <- cov(monthly_return.NA)
Sigma_monthly
## monthly.returns monthly.returns.1 monthly.returns.2
## monthly.returns 0.010235248 0.004069538 0.008699864
## monthly.returns.1 0.004069538 0.006262272 0.005157568
## monthly.returns.2 0.008699864 0.005157568 0.017473941
ones = rep(1,3)
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]
## monthly.returns 0.29125627
## monthly.returns.1 0.75089081
## monthly.returns.2 -0.04214708
mvp.ret.monthly<-sum((mvp.w)*colMeans(monthly_return))
mvp.ret.monthly
## [1] 0.006374629
std.monthly = sqrt(diag(mvp.w.monthly))
std.monthly
## [1] 0.5396816
NKE.weekly_return <- weeklyReturn(data.NA$NKE.Adjusted, subset=NULL, type='arithmetic',
leading=TRUE, from = "2007/01/01", to = "2009/12/31")
ADS.weekly_return <- weeklyReturn(data.NA$ADS.DE.Adjusted, subset=NULL, type='arithmetic',
leading=TRUE, from = "2007/01/01", to = "2009/12/31")
PUM.weekly_return <- weeklyReturn(data.NA$PUM.DE.Adjusted, subset=NULL, type='arithmetic',
leading=TRUE, from = "2007/01/01", to = "2009/12/31")
weekly_return <- merge(ADS.weekly_return, NKE.weekly_return, PUM.weekly_return)
weekly_return
## weekly.returns weekly.returns.1 weekly.returns.2
## 2007-01-05 -0.019195253 0.0118764963 -3.126563e-02
## 2007-01-12 0.004289691 0.0094106521 1.375803e-02
## 2007-01-19 0.030699169 0.0018038184 -2.721086e-02
## 2007-01-26 -0.050763965 -0.0474281147 -3.216777e-02
## 2007-02-02 0.018553937 0.0525206723 4.822971e-02
## 2007-02-09 0.015269245 0.0339322568 -2.584828e-03
## 2007-02-16 0.002902300 0.0260615263 2.038708e-03
## 2007-02-23 0.002367939 0.0163683900 -1.944914e-02
## 2007-03-02 -0.043307093 -0.0386887463 -6.259873e-02
## 2007-03-09 0.019204245 0.0488437655 9.679147e-03
## 2007-03-16 0.004037695 0.0153043654 -1.218751e-02
## 2007-03-23 0.067292246 0.0147019166 1.151056e-02
## 2007-03-30 0.028133734 -0.0255844246 1.784969e-02
## 2007-04-05 0.016613773 0.0065873661 1.481130e-01
## 2007-04-13 0.038932617 0.0031792041 1.685688e-01
## 2007-04-20 0.020819102 -0.0022372326 -5.454689e-03
## 2007-04-27 -0.008611001 0.0110220325 -1.023173e-02
## 2007-05-04 -0.033142783 -0.0153361530 9.829031e-04
## 2007-05-11 0.066706743 -0.0048789407 -9.791559e-03
## 2007-05-18 0.024608424 0.0041484803 -4.237751e-03
## 2007-05-25 -0.002838435 0.0193425467 1.810951e-03
## 2007-06-01 0.033501225 0.0443997913 2.771863e-03
## 2007-06-08 -0.041737171 -0.0532204373 -5.618690e-03
## 2007-06-15 0.009285880 0.0086860742 -3.021558e-04
## 2007-06-22 -0.019277143 -0.0087987215 -2.417977e-03
## 2007-06-29 0.044896027 0.1008500920 4.547460e-04
## 2007-07-06 0.020949127 0.0236744815 -4.545393e-04
## 2007-07-13 -0.020728727 -0.0110605851 -1.266478e-02
## 2007-07-20 -0.037630931 -0.0083038371 -4.240952e-02
## 2007-07-27 -0.029993272 -0.0526317818 -5.460672e-02
## 2007-08-03 -0.020842846 0.0191198333 -2.182956e-02
## 2007-08-10 0.001403567 -0.0127432628 -1.216359e-02
## 2007-08-17 -0.017986435 -0.0234850393 -6.384612e-02
## 2007-08-24 0.008325262 -0.0064256122 5.973160e-02
## 2007-08-31 0.017928680 0.0410199261 4.222086e-02
## 2007-09-07 -0.015527055 -0.0159819195 1.390757e-03
## 2007-09-14 0.002824661 0.0462527788 -6.640544e-03
## 2007-09-21 0.060798166 0.0005240075 7.490021e-02
## 2007-09-28 0.017924433 0.0244497944 -4.375675e-02
## 2007-10-05 -0.019347761 0.0288102881 4.413122e-03
## 2007-10-12 -0.023276362 0.0463961760 -8.887040e-03
## 2007-10-19 -0.002723561 0.0028503128 -1.686659e-02
## 2007-10-26 0.028902857 0.0202112043 -2.169869e-03
## 2007-11-02 -0.004202484 -0.0114530888 -1.478084e-02
## 2007-11-09 0.063305132 -0.0259903428 7.415036e-03
## 2007-11-16 -0.029663743 0.0069122519 -1.961652e-02
## 2007-11-23 -0.009687781 0.0177203751 -3.886586e-02
## 2007-11-30 -0.011521614 0.0298037761 -1.489702e-03
## 2007-12-07 0.005278050 0.0102876458 3.045529e-02
## 2007-12-14 0.040253566 -0.0165139310 -6.002894e-03
## 2007-12-21 0.033228459 0.0303174698 -3.325038e-02
## 2007-12-28 0.043354295 -0.0295760598 3.160123e-03
## 2008-01-04 -0.028287172 -0.0399623494 -1.864454e-02
## 2008-01-11 -0.100582276 -0.0168452779 -2.948765e-02
## 2008-01-18 -0.079464136 -0.0691928697 -8.172778e-02
## 2008-01-25 0.006304427 -0.0088493994 1.591551e-03
## 2008-02-01 0.047951979 0.1162497922 2.851908e-02
## 2008-02-08 -0.031731628 -0.0299149628 -3.911180e-02
## 2008-02-15 0.023984967 0.0272095700 -1.726369e-02
## 2008-02-22 -0.013450894 -0.0272916341 -2.002046e-02
## 2008-02-29 -0.014104586 -0.0064367494 3.492813e-02
## 2008-03-07 -0.046494686 -0.0176969181 -4.011742e-02
## 2008-03-14 0.014753575 0.0295330009 3.409868e-02
## 2008-03-20 -0.034253246 0.1219146425 1.590970e-02
## 2008-03-28 0.066088073 -0.0209603234 3.241567e-02
## 2008-04-04 0.005744527 0.0402369365 1.655499e-02
## 2008-04-11 -0.039743186 -0.0265653351 -5.238656e-02
## 2008-04-18 0.031474759 0.0179937248 8.719851e-03
## 2008-04-25 0.003363722 0.0125198709 1.126912e-01
## 2008-05-02 -0.033285364 -0.0157106920 -1.355444e-02
## 2008-05-09 0.114968051 -0.0412358716 -1.707866e-02
## 2008-05-16 0.051685329 0.0410049892 5.393375e-02
## 2008-05-23 -0.030341778 -0.0408709329 4.606877e-02
## 2008-05-30 -0.001322254 0.0555817536 5.360300e-03
## 2008-06-06 -0.002647877 0.0072029183 -2.649810e-02
## 2008-06-13 -0.015486645 0.0156043828 -3.833563e-02
## 2008-06-20 -0.053483037 -0.0327586499 -3.527429e-02
## 2008-06-27 -0.040835794 -0.0957590414 -5.687232e-02
## 2008-07-03 -0.035891075 -0.0301619217 -6.114241e-02
## 2008-07-11 -0.072913955 -0.0386193885 -5.741303e-02
## 2008-07-18 0.052616931 0.0344828818 3.209119e-02
## 2008-07-25 0.026045766 -0.0005157025 5.855585e-02
## 2008-08-01 0.006410273 0.0211448702 1.193297e-02
## 2008-08-08 0.073885322 0.0597643394 6.779337e-02
## 2008-08-15 -0.003558751 -0.0104842392 -2.740771e-02
## 2008-08-22 -0.052380846 -0.0189439446 -4.289049e-02
## 2008-08-29 0.006281423 -0.0081816369 3.285280e-02
## 2008-09-05 -0.046192532 -0.0148941924 -1.939146e-02
## 2008-09-12 -0.015706731 0.0527026608 -4.173236e-03
## 2008-09-19 0.028457641 0.0287470785 2.323913e-02
## 2008-09-26 -0.004913285 0.0642070788 -7.907119e-02
## 2008-10-03 -0.033783792 -0.0669711115 -9.040827e-02
## 2008-10-10 -0.167025435 -0.1378661003 -2.219568e-01
## 2008-10-17 0.017759192 0.0540990358 -3.084816e-02
## 2008-10-24 -0.124365570 -0.1685803850 -1.071324e-01
## 2008-10-31 -0.002536267 0.2059009415 8.458489e-02
## 2008-11-07 -0.001089617 -0.1426341499 7.372768e-02
## 2008-11-14 -0.103636295 -0.0582880340 -8.793958e-02
## 2008-11-21 -0.128600433 0.0290136816 -7.140073e-02
## 2008-11-28 0.138733613 0.1121556765 1.212349e-01
## 2008-12-05 -0.067457095 0.0213273429 -5.604061e-02
## 2008-12-12 0.184568083 -0.0744281976 7.747042e-02
## 2008-12-19 0.006291735 0.0382817984 -5.869515e-03
## 2008-12-23 -0.038617135 -0.0643770626 -2.546111e-02
## 2009-01-02 0.063886926 0.1063384471 1.081405e-01
## 2009-01-09 -0.007551429 -0.0650209643 1.482945e-02
## 2009-01-16 -0.056884021 -0.0566418610 -3.077427e-02
## 2009-01-23 -0.002689426 -0.0239315152 -4.641134e-02
## 2009-01-30 0.045069552 -0.0094134479 2.950825e-02
## 2009-02-06 0.071876273 0.0758011040 4.961061e-02
## 2009-02-13 -0.067400403 -0.1078471466 -5.670543e-02
## 2009-02-20 -0.066740465 -0.0115124608 -1.134381e-01
## 2009-02-27 -0.090873166 -0.0326114118 -3.636225e-02
## 2009-03-06 -0.003042093 -0.0151398768 -1.104417e-01
## 2009-03-13 0.063208560 0.1184280475 6.282922e-02
## 2009-03-20 -0.015170152 0.0078346420 7.079636e-02
## 2009-03-27 0.047876829 0.0404269072 -5.826444e-02
## 2009-04-03 0.075089207 0.1073870071 1.097850e-01
## 2009-04-09 0.020325150 0.0269902800 1.018505e-01
## 2009-04-17 0.003984149 0.0251550949 1.555189e-01
## 2009-04-24 0.104256832 0.0021970890 -9.129880e-03
## 2009-04-30 -0.065011465 -0.0412935709 1.698641e-02
## 2009-05-08 -0.119196844 0.0371644328 -5.331295e-02
## 2009-05-15 -0.029138012 -0.0858142511 1.956340e-01
## 2009-05-22 0.095873418 0.0534672916 5.818593e-02
## 2009-05-29 -0.018257928 0.0885327195 1.668328e-02
## 2009-06-05 0.009298694 0.0396073691 2.267806e-02
## 2009-06-12 0.031478087 -0.0288214850 3.064918e-02
## 2009-06-19 -0.002233218 0.0015899078 -7.481027e-02
## 2009-06-26 0.021633815 -0.1033510764 -4.859151e-02
## 2009-07-02 -0.020080271 0.0043272919 3.921584e-02
## 2009-07-10 -0.056259375 0.0047005233 -8.127243e-02
## 2009-07-17 0.068298413 0.0222217599 8.977998e-02
## 2009-07-24 0.073540382 -0.0051483645 7.964618e-02
## 2009-07-31 0.020654044 0.0856811481 4.864936e-02
## 2009-08-07 0.125463787 0.0252474733 6.748050e-02
## 2009-08-14 -0.048247022 -0.0208371161 1.885881e-02
## 2009-08-21 0.036523977 -0.0212801439 2.812701e-02
## 2009-08-28 0.002430079 0.0095237738 1.277332e-02
## 2009-09-04 -0.043636379 -0.0162567014 2.299004e-02
## 2009-09-11 0.042775761 0.0140144141 5.781008e-02
## 2009-09-18 0.104223766 0.0654666703 2.074053e-02
## 2009-09-25 -0.009356233 0.0008532291 9.215754e-03
## 2009-10-02 -0.030277655 0.0576398319 -5.799573e-02
## 2009-10-09 -0.001718995 0.0253142276 6.913176e-02
## 2009-10-16 0.037303013 0.0237459739 -4.409341e-05
## 2009-10-23 -0.040110640 -0.0142858164 -4.860919e-02
## 2009-10-30 -0.092219099 -0.0310110717 -3.430960e-02
## 2009-11-06 0.086984226 0.0382759253 7.356054e-02
## 2009-11-13 0.044684309 -0.0021683966 3.452929e-02
## 2009-11-20 -0.012580426 -0.0077619260 -3.615077e-02
## 2009-11-27 0.071347898 0.0176784784 4.060967e-02
## 2009-12-04 -0.003171098 0.0050805452 4.040827e-02
## 2009-12-11 0.000000000 -0.0068427724 -2.392635e-02
## 2009-12-18 0.022534299 0.0087695148 -1.195859e-02
## 2009-12-23 -0.004148208 0.0158334494 4.436649e-03
## 2009-12-30 -0.016662195 0.0106969748 -5.832236e-03
weekly_return.NA <- weekly_return[complete.cases(weekly_return), ]
weekly_return.NA
## weekly.returns weekly.returns.1 weekly.returns.2
## 2007-01-05 -0.019195253 0.0118764963 -3.126563e-02
## 2007-01-12 0.004289691 0.0094106521 1.375803e-02
## 2007-01-19 0.030699169 0.0018038184 -2.721086e-02
## 2007-01-26 -0.050763965 -0.0474281147 -3.216777e-02
## 2007-02-02 0.018553937 0.0525206723 4.822971e-02
## 2007-02-09 0.015269245 0.0339322568 -2.584828e-03
## 2007-02-16 0.002902300 0.0260615263 2.038708e-03
## 2007-02-23 0.002367939 0.0163683900 -1.944914e-02
## 2007-03-02 -0.043307093 -0.0386887463 -6.259873e-02
## 2007-03-09 0.019204245 0.0488437655 9.679147e-03
## 2007-03-16 0.004037695 0.0153043654 -1.218751e-02
## 2007-03-23 0.067292246 0.0147019166 1.151056e-02
## 2007-03-30 0.028133734 -0.0255844246 1.784969e-02
## 2007-04-05 0.016613773 0.0065873661 1.481130e-01
## 2007-04-13 0.038932617 0.0031792041 1.685688e-01
## 2007-04-20 0.020819102 -0.0022372326 -5.454689e-03
## 2007-04-27 -0.008611001 0.0110220325 -1.023173e-02
## 2007-05-04 -0.033142783 -0.0153361530 9.829031e-04
## 2007-05-11 0.066706743 -0.0048789407 -9.791559e-03
## 2007-05-18 0.024608424 0.0041484803 -4.237751e-03
## 2007-05-25 -0.002838435 0.0193425467 1.810951e-03
## 2007-06-01 0.033501225 0.0443997913 2.771863e-03
## 2007-06-08 -0.041737171 -0.0532204373 -5.618690e-03
## 2007-06-15 0.009285880 0.0086860742 -3.021558e-04
## 2007-06-22 -0.019277143 -0.0087987215 -2.417977e-03
## 2007-06-29 0.044896027 0.1008500920 4.547460e-04
## 2007-07-06 0.020949127 0.0236744815 -4.545393e-04
## 2007-07-13 -0.020728727 -0.0110605851 -1.266478e-02
## 2007-07-20 -0.037630931 -0.0083038371 -4.240952e-02
## 2007-07-27 -0.029993272 -0.0526317818 -5.460672e-02
## 2007-08-03 -0.020842846 0.0191198333 -2.182956e-02
## 2007-08-10 0.001403567 -0.0127432628 -1.216359e-02
## 2007-08-17 -0.017986435 -0.0234850393 -6.384612e-02
## 2007-08-24 0.008325262 -0.0064256122 5.973160e-02
## 2007-08-31 0.017928680 0.0410199261 4.222086e-02
## 2007-09-07 -0.015527055 -0.0159819195 1.390757e-03
## 2007-09-14 0.002824661 0.0462527788 -6.640544e-03
## 2007-09-21 0.060798166 0.0005240075 7.490021e-02
## 2007-09-28 0.017924433 0.0244497944 -4.375675e-02
## 2007-10-05 -0.019347761 0.0288102881 4.413122e-03
## 2007-10-12 -0.023276362 0.0463961760 -8.887040e-03
## 2007-10-19 -0.002723561 0.0028503128 -1.686659e-02
## 2007-10-26 0.028902857 0.0202112043 -2.169869e-03
## 2007-11-02 -0.004202484 -0.0114530888 -1.478084e-02
## 2007-11-09 0.063305132 -0.0259903428 7.415036e-03
## 2007-11-16 -0.029663743 0.0069122519 -1.961652e-02
## 2007-11-23 -0.009687781 0.0177203751 -3.886586e-02
## 2007-11-30 -0.011521614 0.0298037761 -1.489702e-03
## 2007-12-07 0.005278050 0.0102876458 3.045529e-02
## 2007-12-14 0.040253566 -0.0165139310 -6.002894e-03
## 2007-12-21 0.033228459 0.0303174698 -3.325038e-02
## 2007-12-28 0.043354295 -0.0295760598 3.160123e-03
## 2008-01-04 -0.028287172 -0.0399623494 -1.864454e-02
## 2008-01-11 -0.100582276 -0.0168452779 -2.948765e-02
## 2008-01-18 -0.079464136 -0.0691928697 -8.172778e-02
## 2008-01-25 0.006304427 -0.0088493994 1.591551e-03
## 2008-02-01 0.047951979 0.1162497922 2.851908e-02
## 2008-02-08 -0.031731628 -0.0299149628 -3.911180e-02
## 2008-02-15 0.023984967 0.0272095700 -1.726369e-02
## 2008-02-22 -0.013450894 -0.0272916341 -2.002046e-02
## 2008-02-29 -0.014104586 -0.0064367494 3.492813e-02
## 2008-03-07 -0.046494686 -0.0176969181 -4.011742e-02
## 2008-03-14 0.014753575 0.0295330009 3.409868e-02
## 2008-03-20 -0.034253246 0.1219146425 1.590970e-02
## 2008-03-28 0.066088073 -0.0209603234 3.241567e-02
## 2008-04-04 0.005744527 0.0402369365 1.655499e-02
## 2008-04-11 -0.039743186 -0.0265653351 -5.238656e-02
## 2008-04-18 0.031474759 0.0179937248 8.719851e-03
## 2008-04-25 0.003363722 0.0125198709 1.126912e-01
## 2008-05-02 -0.033285364 -0.0157106920 -1.355444e-02
## 2008-05-09 0.114968051 -0.0412358716 -1.707866e-02
## 2008-05-16 0.051685329 0.0410049892 5.393375e-02
## 2008-05-23 -0.030341778 -0.0408709329 4.606877e-02
## 2008-05-30 -0.001322254 0.0555817536 5.360300e-03
## 2008-06-06 -0.002647877 0.0072029183 -2.649810e-02
## 2008-06-13 -0.015486645 0.0156043828 -3.833563e-02
## 2008-06-20 -0.053483037 -0.0327586499 -3.527429e-02
## 2008-06-27 -0.040835794 -0.0957590414 -5.687232e-02
## 2008-07-03 -0.035891075 -0.0301619217 -6.114241e-02
## 2008-07-11 -0.072913955 -0.0386193885 -5.741303e-02
## 2008-07-18 0.052616931 0.0344828818 3.209119e-02
## 2008-07-25 0.026045766 -0.0005157025 5.855585e-02
## 2008-08-01 0.006410273 0.0211448702 1.193297e-02
## 2008-08-08 0.073885322 0.0597643394 6.779337e-02
## 2008-08-15 -0.003558751 -0.0104842392 -2.740771e-02
## 2008-08-22 -0.052380846 -0.0189439446 -4.289049e-02
## 2008-08-29 0.006281423 -0.0081816369 3.285280e-02
## 2008-09-05 -0.046192532 -0.0148941924 -1.939146e-02
## 2008-09-12 -0.015706731 0.0527026608 -4.173236e-03
## 2008-09-19 0.028457641 0.0287470785 2.323913e-02
## 2008-09-26 -0.004913285 0.0642070788 -7.907119e-02
## 2008-10-03 -0.033783792 -0.0669711115 -9.040827e-02
## 2008-10-10 -0.167025435 -0.1378661003 -2.219568e-01
## 2008-10-17 0.017759192 0.0540990358 -3.084816e-02
## 2008-10-24 -0.124365570 -0.1685803850 -1.071324e-01
## 2008-10-31 -0.002536267 0.2059009415 8.458489e-02
## 2008-11-07 -0.001089617 -0.1426341499 7.372768e-02
## 2008-11-14 -0.103636295 -0.0582880340 -8.793958e-02
## 2008-11-21 -0.128600433 0.0290136816 -7.140073e-02
## 2008-11-28 0.138733613 0.1121556765 1.212349e-01
## 2008-12-05 -0.067457095 0.0213273429 -5.604061e-02
## 2008-12-12 0.184568083 -0.0744281976 7.747042e-02
## 2008-12-19 0.006291735 0.0382817984 -5.869515e-03
## 2008-12-23 -0.038617135 -0.0643770626 -2.546111e-02
## 2009-01-02 0.063886926 0.1063384471 1.081405e-01
## 2009-01-09 -0.007551429 -0.0650209643 1.482945e-02
## 2009-01-16 -0.056884021 -0.0566418610 -3.077427e-02
## 2009-01-23 -0.002689426 -0.0239315152 -4.641134e-02
## 2009-01-30 0.045069552 -0.0094134479 2.950825e-02
## 2009-02-06 0.071876273 0.0758011040 4.961061e-02
## 2009-02-13 -0.067400403 -0.1078471466 -5.670543e-02
## 2009-02-20 -0.066740465 -0.0115124608 -1.134381e-01
## 2009-02-27 -0.090873166 -0.0326114118 -3.636225e-02
## 2009-03-06 -0.003042093 -0.0151398768 -1.104417e-01
## 2009-03-13 0.063208560 0.1184280475 6.282922e-02
## 2009-03-20 -0.015170152 0.0078346420 7.079636e-02
## 2009-03-27 0.047876829 0.0404269072 -5.826444e-02
## 2009-04-03 0.075089207 0.1073870071 1.097850e-01
## 2009-04-09 0.020325150 0.0269902800 1.018505e-01
## 2009-04-17 0.003984149 0.0251550949 1.555189e-01
## 2009-04-24 0.104256832 0.0021970890 -9.129880e-03
## 2009-04-30 -0.065011465 -0.0412935709 1.698641e-02
## 2009-05-08 -0.119196844 0.0371644328 -5.331295e-02
## 2009-05-15 -0.029138012 -0.0858142511 1.956340e-01
## 2009-05-22 0.095873418 0.0534672916 5.818593e-02
## 2009-05-29 -0.018257928 0.0885327195 1.668328e-02
## 2009-06-05 0.009298694 0.0396073691 2.267806e-02
## 2009-06-12 0.031478087 -0.0288214850 3.064918e-02
## 2009-06-19 -0.002233218 0.0015899078 -7.481027e-02
## 2009-06-26 0.021633815 -0.1033510764 -4.859151e-02
## 2009-07-02 -0.020080271 0.0043272919 3.921584e-02
## 2009-07-10 -0.056259375 0.0047005233 -8.127243e-02
## 2009-07-17 0.068298413 0.0222217599 8.977998e-02
## 2009-07-24 0.073540382 -0.0051483645 7.964618e-02
## 2009-07-31 0.020654044 0.0856811481 4.864936e-02
## 2009-08-07 0.125463787 0.0252474733 6.748050e-02
## 2009-08-14 -0.048247022 -0.0208371161 1.885881e-02
## 2009-08-21 0.036523977 -0.0212801439 2.812701e-02
## 2009-08-28 0.002430079 0.0095237738 1.277332e-02
## 2009-09-04 -0.043636379 -0.0162567014 2.299004e-02
## 2009-09-11 0.042775761 0.0140144141 5.781008e-02
## 2009-09-18 0.104223766 0.0654666703 2.074053e-02
## 2009-09-25 -0.009356233 0.0008532291 9.215754e-03
## 2009-10-02 -0.030277655 0.0576398319 -5.799573e-02
## 2009-10-09 -0.001718995 0.0253142276 6.913176e-02
## 2009-10-16 0.037303013 0.0237459739 -4.409341e-05
## 2009-10-23 -0.040110640 -0.0142858164 -4.860919e-02
## 2009-10-30 -0.092219099 -0.0310110717 -3.430960e-02
## 2009-11-06 0.086984226 0.0382759253 7.356054e-02
## 2009-11-13 0.044684309 -0.0021683966 3.452929e-02
## 2009-11-20 -0.012580426 -0.0077619260 -3.615077e-02
## 2009-11-27 0.071347898 0.0176784784 4.060967e-02
## 2009-12-04 -0.003171098 0.0050805452 4.040827e-02
## 2009-12-11 0.000000000 -0.0068427724 -2.392635e-02
## 2009-12-18 0.022534299 0.0087695148 -1.195859e-02
## 2009-12-23 -0.004148208 0.0158334494 4.436649e-03
## 2009-12-30 -0.016662195 0.0106969748 -5.832236e-03
colnames(weekly_return.NA)
## [1] "weekly.returns" "weekly.returns.1" "weekly.returns.2"
Sigma_weekly = cov(weekly_return.NA)
Sigma_weekly
## weekly.returns weekly.returns.1 weekly.returns.2
## weekly.returns 0.002662307 0.001049950 0.001698605
## weekly.returns.1 0.001049950 0.002489786 0.001054079
## weekly.returns.2 0.001698605 0.001054079 0.003195982
ones = rep(1,3)
one.vec = matrix(ones, ncol=1)
a = inv(Sigma_weekly)%*%one.vec
b = t(one.vec)%*%a
mvp.w.weekly =a / as.numeric(b)
mvp.w.weekly
## [,1]
## weekly.returns 0.3283104
## weekly.returns.1 0.4616641
## weekly.returns.2 0.2100254
mvp.ret.weekly<-sum((mvp.w)*colMeans(weekly_return.NA))
mvp.ret.weekly
## [1] 0.001463769
std.weekly = sqrt(diag(mvp.w.weekly))
std.weekly
## [1] 0.5729838
# Q3. Find the tangency portfolio based on Q2. Risk free 0.005
mean <- apply(data.NA, 2, mean)
mean
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 9.420327 30.810479 10.918739
var <- apply(data.NA, 2, var)
var
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 1.498566 35.416822 6.462393
summary <- apply(data.NA, 2, summary)
apply(data.NA, 2, skewness)
## NKE.Adjusted ADS.DE.Adjusted PUM.DE.Adjusted
## 0.1114019 -0.4417538 -0.4742142
cov.matrix <- matrix(Sigma, ncol =3)
cov.matrix
## [,1] [,2] [,3]
## [1,] 1.498566 2.360266 1.159875
## [2,] 2.360266 35.416822 11.836347
## [3,] 1.159875 11.836347 6.462393
mu <- matrix(mean, ncol=1)
mu
## [,1]
## [1,] 9.420327
## [2,] 30.810479
## [3,] 10.918739
rf <- 0.005
numerator <- solve(cov.matrix)%*% (mu - rf*one.vec)
denominator <-t(one.vec)%*% numerator
tangency.weight <-numerator/as.numeric(denominator)
tangency.return<- t(mu)%*% tangency.weight
tangency.var <- t(tangency.weight) %*% cov.matrix %*%tangency.weight
tangency.std <- sqrt(as.numeric(tangency.var))
Sharperatio <- (tangency.return/tangency.std)
Sharperatio
## [,1]
## [1,] 8.252372