#import data
#load libraries
library(quantmod)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
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## as.Date, as.Date.numeric## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
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## as.zoo.data.frame zoolibrary(tidyquant)## Loading required package: lubridate##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
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## date, intersect, setdiff, union## Loading required package: PerformanceAnalytics##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
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## legend## ══ Need to Learn tidyquant? ══════════════════════════════════════════════════════════════════════════════════════════
## Business Science offers a 1-hour course - Learning Lab #9: Performance Analysis & Portfolio Optimization with tidyquant!
## </> Learn more at: https://university.business-science.io/p/learning-labs-pro </>library(lubridate)
library(timetk)
library(purrr)
library(tibble)
library(readr)
library(xts)
library(PerformanceAnalytics)
library(magrittr)##
## Attaching package: 'magrittr'## The following object is masked from 'package:purrr':
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## set_nameslibrary(fBasics)## Loading required package: timeDate##
## Attaching package: 'timeDate'## The following objects are masked from 'package:PerformanceAnalytics':
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## kurtosis, skewness## Loading required package: timeSeries##
## Attaching package: 'timeSeries'## The following object is masked from 'package:zoo':
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## time<-##
## Attaching package: 'fBasics'## The following object is masked from 'package:TTR':
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## volatilitylibrary(tidyverse)## ── Attaching packages ───────────────────────────────────────────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.2 ✓ stringr 1.4.0
## ✓ tidyr 1.1.1 ✓ forcats 0.5.0
## ✓ dplyr 1.0.1## ── Conflicts ──────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## x lubridate::as.difftime() masks base::as.difftime()
## x lubridate::date() masks base::date()
## x tidyr::extract() masks magrittr::extract()
## x dplyr::filter() masks timeSeries::filter(), stats::filter()
## x dplyr::first() masks xts::first()
## x lubridate::intersect() masks base::intersect()
## x dplyr::lag() masks timeSeries::lag(), stats::lag()
## x dplyr::last() masks xts::last()
## x magrittr::set_names() masks purrr::set_names()
## x lubridate::setdiff() masks base::setdiff()
## x lubridate::union() masks base::union()tickers <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
data = new.env()
getSymbols(tickers, src = 'yahoo', from = '2010-01-01', to = '2021-04-14', 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.## pausing 1 second between requests for more than 5 symbols
## pausing 1 second between requests for more than 5 symbols
## pausing 1 second between requests for more than 5 symbols
## pausing 1 second between requests for more than 5 symbols## [1] "SPY" "QQQ" "EEM" "IWM" "EFA" "TLT" "IYR" "GLD"ETFList <- merge(Ad(SPY), Ad(QQQ),Ad(EEM), Ad(IWM),Ad(EFA),Ad(TLT),Ad(IYR),Ad(GLD))
colnames(ETFList) <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
head(ETFList)## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 90.79006 41.51847 34.10928 54.61730 41.03314 66.03745 30.41554
## 2010-01-05 91.03041 41.51847 34.35684 54.42949 41.06930 66.46396 30.48858
## 2010-01-06 91.09449 41.26806 34.42872 54.37827 41.24289 65.57423 30.47530
## 2010-01-07 91.47905 41.29489 34.22906 54.77949 41.08377 65.68450 30.74751
## 2010-01-08 91.78343 41.63475 34.50059 55.07827 41.40926 65.65512 30.54169
## 2010-01-11 91.91164 41.46482 34.42872 54.85632 41.74921 65.29481 30.68776
## GLD
## 2010-01-04 109.80
## 2010-01-05 109.70
## 2010-01-06 111.51
## 2010-01-07 110.82
## 2010-01-08 111.37
## 2010-01-11 112.85tail(ETFList)## SPY QQQ EEM IWM EFA TLT IYR GLD
## 2021-04-06 406.12 330.82 54.37 224.31 77.15 137.6382 94.20 163.22
## 2021-04-07 406.59 331.62 53.57 220.69 77.31 136.6796 94.20 162.76
## 2021-04-08 408.52 335.08 54.01 222.56 77.75 137.8079 93.97 164.51
## 2021-04-09 411.49 337.11 53.55 222.59 77.99 137.3086 93.96 163.27
## 2021-04-12 411.64 336.67 53.23 221.72 77.56 137.2487 94.47 162.28
## 2021-04-13 412.86 340.60 53.45 221.14 78.01 138.2772 95.04 163.43ETFList.xts <- xts(ETFList)
head(ETFList.xts)## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 90.79006 41.51847 34.10928 54.61730 41.03314 66.03745 30.41554
## 2010-01-05 91.03041 41.51847 34.35684 54.42949 41.06930 66.46396 30.48858
## 2010-01-06 91.09449 41.26806 34.42872 54.37827 41.24289 65.57423 30.47530
## 2010-01-07 91.47905 41.29489 34.22906 54.77949 41.08377 65.68450 30.74751
## 2010-01-08 91.78343 41.63475 34.50059 55.07827 41.40926 65.65512 30.54169
## 2010-01-11 91.91164 41.46482 34.42872 54.85632 41.74921 65.29481 30.68776
## GLD
## 2010-01-04 109.80
## 2010-01-05 109.70
## 2010-01-06 111.51
## 2010-01-07 110.82
## 2010-01-08 111.37
## 2010-01-11 112.85Weekly Returns
weekly.returns <- to.weekly(ETFList.xts, indexAt = "last", OHLC = FALSE)
ETF.weekly.returns <- na.omit(Return.calculate(weekly.returns, method = "log"))
head(ETF.weekly.returns)## SPY QQQ EEM IWM EFA
## 2010-01-15 -0.008150165 -0.015151916 -0.02936168 -0.01310462 -0.003499562
## 2010-01-22 -0.039762828 -0.037555380 -0.05739709 -0.03110062 -0.057354555
## 2010-01-29 -0.016805812 -0.031515101 -0.03415421 -0.02659356 -0.026141568
## 2010-02-05 -0.006820546 0.004430648 -0.02861835 -0.01407321 -0.019238635
## 2010-02-12 0.012854811 0.017985357 0.03278946 0.02909861 0.005230847
## 2010-02-19 0.028289444 0.024157168 0.02415967 0.03288489 0.022734954
## TLT IYR GLD
## 2010-01-15 0.019848537 -0.006324356 -0.004589865
## 2010-01-22 0.010050310 -0.042683345 -0.033851813
## 2010-01-29 0.003363789 -0.008483115 -0.011354685
## 2010-02-05 -0.000053732 0.003218256 -0.012153577
## 2010-02-12 -0.019653381 -0.007602937 0.022294528
## 2010-02-19 -0.008238932 0.048966490 0.022447943tail(ETF.weekly.returns)## SPY QQQ EEM IWM EFA
## 2021-03-12 0.026824595 0.021726770 0.002967912 0.070403521 0.0218682367
## 2021-03-19 -0.008420718 -0.007381431 0.001665587 -0.028881750 0.0019645216
## 2021-03-26 0.016551188 0.010353968 -0.015091148 -0.026410480 0.0022217614
## 2021-04-01 0.011624615 0.026759037 0.011014785 0.014088245 0.0033885475
## 2021-04-09 0.026796346 0.037907991 -0.005772328 -0.005153190 0.0145949896
## 2021-04-13 0.003323822 0.010299544 -0.001869122 -0.006535516 0.0002564615
## TLT IYR GLD
## 2021-03-12 -0.020730233 0.051252724 0.0146589405
## 2021-03-19 -0.009674828 -0.009175922 0.0107782890
## 2021-03-26 0.014074907 0.034467797 -0.0061447899
## 2021-04-01 0.007567240 0.009016849 -0.0016039051
## 2021-04-09 0.000000000 0.004052442 0.0079324505
## 2021-04-13 0.007029286 0.011428717 0.0009794246Monthly Returns
monthly.returns <- to.monthly(ETFList.xts, indexAt = "last", OHLC = FALSE)
ETF.monthly.returns <- na.omit(Return.calculate(monthly.returns, method = "log"))
head(ETF.monthly.returns)## SPY QQQ EEM IWM EFA
## 2010-02-26 0.03071793 0.04501044 0.01760802 0.04377882 0.002664268
## 2010-03-31 0.05909865 0.07428087 0.07798729 0.07909466 0.061898269
## 2010-04-30 0.01535150 0.02217754 -0.00166310 0.05523070 -0.028446722
## 2010-05-28 -0.08278878 -0.07679864 -0.09864508 -0.07835767 -0.118702355
## 2010-06-30 -0.05312741 -0.06161677 -0.01408547 -0.08059619 -0.020834896
## 2010-07-30 0.06606917 0.07006933 0.10375152 0.06514060 0.109844203
## TLT IYR GLD
## 2010-02-26 -0.003430786 0.05313334 0.032223420
## 2010-03-31 -0.020787687 0.09302102 -0.004396042
## 2010-04-30 0.032678847 0.06192375 0.057168648
## 2010-05-28 0.049821743 -0.05851441 0.030056874
## 2010-06-30 0.056359738 -0.04782683 0.023280092
## 2010-07-30 -0.009509251 0.08988455 -0.052210719tail(ETF.monthly.returns)## SPY QQQ EEM IWM EFA
## 2020-11-30 0.10325753 0.106391900 0.086097691 0.1675816003 0.133388954
## 2020-12-31 0.03637851 0.047860577 0.068867768 0.0829288210 0.048936800
## 2021-01-29 -0.01024267 0.002610233 0.031246646 0.0473172758 -0.007843178
## 2021-02-26 0.02742592 -0.001336071 0.007847555 0.0601780664 0.022132092
## 2021-03-31 0.04439891 0.017022008 -0.007284986 0.0138539151 0.024821143
## 2021-04-13 0.04086135 0.065110227 0.002060137 0.0009048001 0.027815660
## TLT IYR GLD
## 2020-11-30 0.01650211 0.082312759 -0.05560390
## 2020-12-31 -0.01235249 0.024725619 0.06778819
## 2021-01-29 -0.03700417 -0.004329307 -0.03276927
## 2021-02-26 -0.05903846 0.023983094 -0.06461193
## 2021-03-31 -0.05387845 0.056135171 -0.01149897
## 2021-04-13 0.02349013 0.033161654 0.02146089Tibble Format
ETF.monthly.returns.tibble <- as_tibble(ETF.monthly.returns)
ETF.monthly.returns.tibble## # A tibble: 135 x 8
## SPY QQQ EEM IWM EFA TLT IYR GLD
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.0307 0.0450 0.0176 0.0438 0.00266 -0.00343 0.0531 0.0322
## 2 0.0591 0.0743 0.0780 0.0791 0.0619 -0.0208 0.0930 -0.00440
## 3 0.0154 0.0222 -0.00166 0.0552 -0.0284 0.0327 0.0619 0.0572
## 4 -0.0828 -0.0768 -0.0986 -0.0784 -0.119 0.0498 -0.0585 0.0301
## 5 -0.0531 -0.0616 -0.0141 -0.0806 -0.0208 0.0564 -0.0478 0.0233
## 6 0.0661 0.0701 0.104 0.0651 0.110 -0.00951 0.0899 -0.0522
## 7 -0.0460 -0.0527 -0.0329 -0.0774 -0.0387 0.0806 -0.0131 0.0555
## 8 0.0858 0.124 0.111 0.117 0.0951 -0.0255 0.0453 0.0467
## 9 0.0375 0.0615 0.0297 0.0406 0.0373 -0.0457 0.0386 0.0362
## 10 0 -0.00173 -0.0295 0.0343 -0.0494 -0.0170 -0.0160 0.0209
## # … with 125 more rowsFAMA French
ff3.csv <- read_csv('ff3.csv')##
## ── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────
## cols(
## Date = col_double(),
## `Mkt-RF` = col_double(),
## SMB = col_double(),
## HML = col_double(),
## RF = col_double()
## )str(ff3.csv)## tibble [1,137 × 5] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Date : num [1:1137] 192607 192608 192609 192610 192611 ...
## $ Mkt-RF: num [1:1137] 2.96 2.64 0.36 -3.24 2.53 2.62 -0.06 4.18 0.13 0.46 ...
## $ SMB : num [1:1137] -2.3 -1.4 -1.32 0.04 -0.2 -0.04 -0.56 -0.1 -1.6 0.43 ...
## $ HML : num [1:1137] -2.87 4.19 0.01 0.51 -0.35 -0.02 4.83 3.17 -2.67 0.6 ...
## $ RF : num [1:1137] 0.22 0.25 0.23 0.32 0.31 0.28 0.25 0.26 0.3 0.25 ...
## - attr(*, "spec")=
## .. cols(
## .. Date = col_double(),
## .. `Mkt-RF` = col_double(),
## .. SMB = col_double(),
## .. HML = col_double(),
## .. RF = col_double()
## .. )head(ff3.csv)## # A tibble: 6 x 5
## Date `Mkt-RF` SMB HML RF
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 192607 2.96 -2.3 -2.87 0.22
## 2 192608 2.64 -1.4 4.19 0.25
## 3 192609 0.36 -1.32 0.01 0.23
## 4 192610 -3.24 0.04 0.51 0.32
## 5 192611 2.53 -0.2 -0.35 0.31
## 6 192612 2.62 -0.04 -0.02 0.28dim(ff3.csv)## [1] 1137 5tail(ff3.csv)## # A tibble: 6 x 5
## Date `Mkt-RF` SMB HML RF
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 202010 -2.1 4.44 4.03 0.01
## 2 202011 12.5 5.48 2.11 0.01
## 3 202012 4.63 4.81 -1.36 0.01
## 4 202101 -0.03 7.19 2.85 0
## 5 202102 2.78 2.11 7.08 0
## 6 202103 3.09 -2.48 7.4 0glimpse(ff3.csv)## Rows: 1,137
## Columns: 5
## $ Date <dbl> 192607, 192608, 192609, 192610, 192611, 192612, 192701, 1927…
## $ `Mkt-RF` <dbl> 2.96, 2.64, 0.36, -3.24, 2.53, 2.62, -0.06, 4.18, 0.13, 0.46…
## $ SMB <dbl> -2.30, -1.40, -1.32, 0.04, -0.20, -0.04, -0.56, -0.10, -1.60…
## $ HML <dbl> -2.87, 4.19, 0.01, 0.51, -0.35, -0.02, 4.83, 3.17, -2.67, 0.…
## $ RF <dbl> 0.22, 0.25, 0.23, 0.32, 0.31, 0.28, 0.25, 0.26, 0.30, 0.25, …colnames(ff3.csv) <- paste(c("date","Mkt-RF","SMB","HML","RF"))
ff3.digit <- ff3.csv %>% mutate(date = as.character(date))%>%
mutate(date=ymd(parse_date(date,format="%Y%m"))) %>%
mutate(date=rollback(date))
head(ff3.digit)## # A tibble: 6 x 5
## date `Mkt-RF` SMB HML RF
## <date> <dbl> <dbl> <dbl> <dbl>
## 1 1926-06-30 2.96 -2.3 -2.87 0.22
## 2 1926-07-31 2.64 -1.4 4.19 0.25
## 3 1926-08-31 0.36 -1.32 0.01 0.23
## 4 1926-09-30 -3.24 0.04 0.51 0.32
## 5 1926-10-31 2.53 -0.2 -0.35 0.31
## 6 1926-11-30 2.62 -0.04 -0.02 0.28Convert to XTS
ff3.digit.xts <- xts(ff3.digit[,-1],order.by=as.Date(ff3.digit$date))
head(ff3.digit.xts)## Mkt-RF SMB HML RF
## 1926-06-30 2.96 -2.30 -2.87 0.22
## 1926-07-31 2.64 -1.40 4.19 0.25
## 1926-08-31 0.36 -1.32 0.01 0.23
## 1926-09-30 -3.24 0.04 0.51 0.32
## 1926-10-31 2.53 -0.20 -0.35 0.31
## 1926-11-30 2.62 -0.04 -0.02 0.28Merge of Monthly Returns and FAMA French
final.data <- merge(ff3.digit,ETF.monthly.returns)
tail(final.data)## date Mkt-RF SMB HML RF SPY QQQ EEM
## 153490 2020-09-30 -2.10 4.44 4.03 0.01 0.04086135 0.06511023 0.002060137
## 153491 2020-10-31 12.47 5.48 2.11 0.01 0.04086135 0.06511023 0.002060137
## 153492 2020-11-30 4.63 4.81 -1.36 0.01 0.04086135 0.06511023 0.002060137
## 153493 2020-12-31 -0.03 7.19 2.85 0.00 0.04086135 0.06511023 0.002060137
## 153494 2021-01-31 2.78 2.11 7.08 0.00 0.04086135 0.06511023 0.002060137
## 153495 2021-02-28 3.09 -2.48 7.40 0.00 0.04086135 0.06511023 0.002060137
## IWM EFA TLT IYR GLD
## 153490 0.0009048001 0.02781566 0.02349013 0.03316165 0.02146089
## 153491 0.0009048001 0.02781566 0.02349013 0.03316165 0.02146089
## 153492 0.0009048001 0.02781566 0.02349013 0.03316165 0.02146089
## 153493 0.0009048001 0.02781566 0.02349013 0.03316165 0.02146089
## 153494 0.0009048001 0.02781566 0.02349013 0.03316165 0.02146089
## 153495 0.0009048001 0.02781566 0.02349013 0.03316165 0.02146089final.data.tibble <- as_tibble(final.data)
head(final.data.tibble)## # A tibble: 6 x 13
## date `Mkt-RF` SMB HML RF SPY QQQ EEM IWM EFA
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1926-06-30 2.96 -2.3 -2.87 0.22 0.0307 0.0450 0.0176 0.0438 0.00266
## 2 1926-07-31 2.64 -1.4 4.19 0.25 0.0307 0.0450 0.0176 0.0438 0.00266
## 3 1926-08-31 0.36 -1.32 0.01 0.23 0.0307 0.0450 0.0176 0.0438 0.00266
## 4 1926-09-30 -3.24 0.04 0.51 0.32 0.0307 0.0450 0.0176 0.0438 0.00266
## 5 1926-10-31 2.53 -0.2 -0.35 0.31 0.0307 0.0450 0.0176 0.0438 0.00266
## 6 1926-11-30 2.62 -0.04 -0.02 0.28 0.0307 0.0450 0.0176 0.0438 0.00266
## # … with 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>Based on the CAPM model, compute the Monthly MVP returns Based on the Estimated Covariance Matrix for the 8-Asset Portfolio by using the past 60-month returns from 2015/01 - 2021/03.
final.data2 <- final.data.tibble[final.data.tibble$date>="2015-01-01"&final.data.tibble$date<="2021-03-01",]
head(final.data2)## # A tibble: 6 x 13
## date `Mkt-RF` SMB HML RF SPY QQQ EEM IWM EFA
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2015-01-31 6.14 0.52 -1.81 0 0.0307 0.0450 0.0176 0.0438 0.00266
## 2 2015-02-28 -1.12 3.02 -0.41 0 0.0307 0.0450 0.0176 0.0438 0.00266
## 3 2015-03-31 0.59 -3.04 1.88 0 0.0307 0.0450 0.0176 0.0438 0.00266
## 4 2015-04-30 1.36 0.89 -1.1 0 0.0307 0.0450 0.0176 0.0438 0.00266
## 5 2015-05-31 -1.53 2.85 -0.74 0 0.0307 0.0450 0.0176 0.0438 0.00266
## 6 2015-06-30 1.54 -4.09 -4.21 0 0.0307 0.0450 0.0176 0.0438 0.00266
## # … with 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>