library(tidyquant)## Loading required package: lubridate##
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## as.Date, as.Date.numeric##
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## kurtosis, skewness## Loading required package: fAssets## Warning: package 'fAssets' was built under R version 4.2.3library(PerformanceAnalytics)
library(xts)
library(readr)
library(dplyr)## Warning: package 'dplyr' was built under R version 4.2.3##
## ######################### Warning from 'xts' package ##########################
## # #
## # The dplyr lag() function breaks how base R's lag() function is supposed to #
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## Attaching package: 'dplyr'## The following objects are masked from 'package:timeSeries':
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## first, last## The following objects are masked from 'package:stats':
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## intersect, setdiff, setequal, unionlibrary(lubridate)
library(timetk)
library(purrr)
library(kableExtra)## Warning: package 'kableExtra' was built under R version 4.2.3##
## Attaching package: 'kableExtra'## The following object is masked from 'package:dplyr':
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## group_rowslibrary(tibble)## Warning: package 'tibble' was built under R version 4.2.3symbols <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
prices <-
getSymbols(symbols, src = 'yahoo', from = "2010-01-01",
auto.assign = TRUE, warnings = FALSE) %>%
map(~Ad(get(.))) %>%
reduce(merge) %>%
`colnames<-`(symbols)
head(prices, 6)## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 88.11788 41.00547 32.42900 53.08977 37.99447 63.06118 28.77183
## 2010-01-05 88.35115 41.00547 32.66440 52.90724 38.02797 63.46839 28.84091
## 2010-01-06 88.41334 40.75814 32.73274 52.85745 38.18870 62.61876 28.82835
## 2010-01-07 88.78658 40.78463 32.54292 53.24745 38.04137 62.72409 29.08586
## 2010-01-08 89.08204 41.12030 32.80107 53.53788 38.34275 62.69599 28.89116
## 2010-01-11 89.20642 40.95247 32.73274 53.32212 38.65752 62.35199 29.02934
## 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
## 2010-01-11 112.85prices_weekly <- to.weekly(prices, indexAt = "last", OHLC = FALSE)
prices_monthly <- to.monthly(prices, indexAt = "last", OHLC = FALSE)asset_returns_wk_xts <- na.omit(Return.calculate(prices_weekly))
head(asset_returns_wk_xts,6)## SPY QQQ EEM IWM EFA
## 2010-01-15 -0.00811748 -0.015037422 -0.02893522 -0.01301943 -0.00349367
## 2010-01-22 -0.03898275 -0.036859494 -0.05578078 -0.03062162 -0.05574017
## 2010-01-29 -0.01666492 -0.031023677 -0.03357712 -0.02624350 -0.02580319
## 2010-02-05 -0.00679798 0.004440319 -0.02821328 -0.01397446 -0.01905500
## 2010-02-12 0.01293861 0.018148358 0.03333322 0.02952601 0.00524491
## 2010-02-19 0.02869326 0.024451190 0.02445373 0.03343178 0.02299528
## TLT IYR GLD
## 2010-01-15 2.004761e-02 -0.006303900 -0.004579349
## 2010-01-22 1.010088e-02 -0.041785761 -0.033285246
## 2010-01-29 3.369511e-03 -0.008447220 -0.011290465
## 2010-02-05 -5.391004e-05 0.003223757 -0.012080019
## 2010-02-12 -1.946104e-02 -0.007574272 0.022544905
## 2010-02-19 -8.205189e-03 0.050185301 0.022701796asset_returns_mon_xts <- na.omit(Return.calculate(prices_monthly))
head(asset_returns_mon_xts,6)## SPY QQQ EEM IWM EFA
## 2010-02-26 0.03119469 0.04603891 0.017763395 0.04475130 0.002667612
## 2010-03-31 0.06087986 0.07710940 0.081109172 0.08230722 0.063853990
## 2010-04-30 0.01546983 0.02242504 -0.001662106 0.05678476 -0.028045713
## 2010-05-28 -0.07945438 -0.07392361 -0.093935742 -0.07536692 -0.111928099
## 2010-06-30 -0.05174124 -0.05975683 -0.013986171 -0.07743382 -0.020619113
## 2010-07-30 0.06830062 0.07258248 0.109324772 0.06730904 0.116104271
## TLT IYR GLD
## 2010-02-26 -0.003424700 0.05457073 0.032748219
## 2010-03-31 -0.020573519 0.09748442 -0.004386396
## 2010-04-30 0.033218499 0.06388128 0.058834363
## 2010-05-28 0.051083754 -0.05683509 0.030513147
## 2010-06-30 0.057978979 -0.04670171 0.023553189
## 2010-07-30 -0.009464066 0.09404807 -0.050871157library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.2.3## Warning: package 'ggplot2' was built under R version 4.2.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.2 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks timeSeries::filter(), stats::filter()
## ✖ dplyr::first() masks xts::first()
## ✖ kableExtra::group_rows() masks dplyr::group_rows()
## ✖ dplyr::lag() masks timeSeries::lag(), stats::lag()
## ✖ dplyr::last() masks xts::last()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errorsmonthly_ret <- as_tibble(asset_returns_mon_xts, rownames = 'date')
head(monthly_ret,6)## # A tibble: 6 × 9
## date SPY QQQ EEM IWM EFA TLT IYR GLD
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010-02-26 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327
## 2 2010-03-31 0.0609 0.0771 0.0811 0.0823 0.0639 -0.0206 0.0975 -0.00439
## 3 2010-04-30 0.0155 0.0224 -0.00166 0.0568 -0.0280 0.0332 0.0639 0.0588
## 4 2010-05-28 -0.0795 -0.0739 -0.0939 -0.0754 -0.112 0.0511 -0.0568 0.0305
## 5 2010-06-30 -0.0517 -0.0598 -0.0140 -0.0774 -0.0206 0.0580 -0.0467 0.0236
## 6 2010-07-30 0.0683 0.0726 0.109 0.0673 0.116 -0.00946 0.0940 -0.0509library(readr)
data <- read_csv("C:/Users/DELL/OneDrive/Desktop/data.CSV")## New names:
## • `` -> `...1`## Warning: One or more parsing issues, call `problems()` on your data frame for details,
## e.g.:
## dat <- vroom(...)
## problems(dat)## Rows: 1263 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): ...1
## dbl (4): Mkt-RF, SMB, HML, RF
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.head(data)## # A tibble: 6 × 5
## ...1 `Mkt-RF` SMB HML RF
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 192607 2.96 -2.56 -2.43 0.22
## 2 192608 2.64 -1.17 3.82 0.25
## 3 192609 0.36 -1.4 0.13 0.23
## 4 192610 -3.24 -0.09 0.7 0.32
## 5 192611 2.53 -0.1 -0.51 0.31
## 6 192612 2.62 -0.03 -0.05 0.28colnames(data) <- paste(c('date', "mkt_rf", "smb", "hml", "rf"))
head(data,6)## # A tibble: 6 × 5
## date mkt_rf smb hml rf
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 192607 2.96 -2.56 -2.43 0.22
## 2 192608 2.64 -1.17 3.82 0.25
## 3 192609 0.36 -1.4 0.13 0.23
## 4 192610 -3.24 -0.09 0.7 0.32
## 5 192611 2.53 -0.1 -0.51 0.31
## 6 192612 2.62 -0.03 -0.05 0.28data_m1 <- data %>% mutate(date = as.character(date)) %>%
mutate(date = ymd(parse_date(date, format = "%Y%m"))) %>%
mutate(date = rollback(date))## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `date = ymd(parse_date(date, format = "%Y%m"))`.
## Caused by warning:
## ! 98 parsing failures.
## row col expected actual
## 1164 -- date like %Y%m Annual Factors: January-December
## 1166 -- date like %Y%m 1927
## 1167 -- date like %Y%m 1928
## 1168 -- date like %Y%m 1929
## 1169 -- date like %Y%m 1930
## .... ... .............. ................................
## See problems(...) for more details.head(data_m1,6)## # A tibble: 6 × 5
## date mkt_rf smb hml rf
## <date> <dbl> <dbl> <dbl> <dbl>
## 1 1926-06-30 2.96 -2.56 -2.43 0.22
## 2 1926-07-31 2.64 -1.17 3.82 0.25
## 3 1926-08-31 0.36 -1.4 0.13 0.23
## 4 1926-09-30 -3.24 -0.09 0.7 0.32
## 5 1926-10-31 2.53 -0.1 -0.51 0.31
## 6 1926-11-30 2.62 -0.03 -0.05 0.28left_join() to join the date.mergedata1 <- merge(x = data_m1, y = asset_returns_mon_xts)
head(mergedata1,5)## date mkt_rf smb hml rf SPY QQQ EEM IWM
## 1 1926-06-30 2.96 -2.56 -2.43 0.22 0.03119469 0.04603891 0.0177634 0.0447513
## 2 1926-07-31 2.64 -1.17 3.82 0.25 0.03119469 0.04603891 0.0177634 0.0447513
## 3 1926-08-31 0.36 -1.40 0.13 0.23 0.03119469 0.04603891 0.0177634 0.0447513
## 4 1926-09-30 -3.24 -0.09 0.70 0.32 0.03119469 0.04603891 0.0177634 0.0447513
## 5 1926-10-31 2.53 -0.10 -0.51 0.31 0.03119469 0.04603891 0.0177634 0.0447513
## EFA TLT IYR GLD
## 1 0.002667612 -0.0034247 0.05457073 0.03274822
## 2 0.002667612 -0.0034247 0.05457073 0.03274822
## 3 0.002667612 -0.0034247 0.05457073 0.03274822
## 4 0.002667612 -0.0034247 0.05457073 0.03274822
## 5 0.002667612 -0.0034247 0.05457073 0.03274822tail(mergedata1,5)## date mkt_rf smb hml rf SPY QQQ EEM
## 203339 <NA> 23.66 13.18 -46.56 0.45 0.02883807 0.01870746 0.05190559
## 203340 <NA> 23.56 -3.89 25.53 0.04 0.02883807 0.01870746 0.05190559
## 203341 <NA> -21.60 -6.82 25.81 1.43 0.02883807 0.01870746 0.05190559
## 203342 <NA> NA NA NA NA 0.02883807 0.01870746 0.05190559
## 203343 <NA> NA NA NA NA 0.02883807 0.01870746 0.05190559
## IWM EFA TLT IYR GLD
## 203339 0.06774699 0.03057898 -0.007759155 0.02927976 -0.001535838
## 203340 0.06774699 0.03057898 -0.007759155 0.02927976 -0.001535838
## 203341 0.06774699 0.03057898 -0.007759155 0.02927976 -0.001535838
## 203342 0.06774699 0.03057898 -0.007759155 0.02927976 -0.001535838
## 203343 0.06774699 0.03057898 -0.007759155 0.02927976 -0.001535838data_m3 <- na.omit(mergedata1)
head(data_m3,6)## date mkt_rf smb hml rf SPY QQQ EEM IWM
## 1 1926-06-30 2.96 -2.56 -2.43 0.22 0.03119469 0.04603891 0.0177634 0.0447513
## 2 1926-07-31 2.64 -1.17 3.82 0.25 0.03119469 0.04603891 0.0177634 0.0447513
## 3 1926-08-31 0.36 -1.40 0.13 0.23 0.03119469 0.04603891 0.0177634 0.0447513
## 4 1926-09-30 -3.24 -0.09 0.70 0.32 0.03119469 0.04603891 0.0177634 0.0447513
## 5 1926-10-31 2.53 -0.10 -0.51 0.31 0.03119469 0.04603891 0.0177634 0.0447513
## 6 1926-11-30 2.62 -0.03 -0.05 0.28 0.03119469 0.04603891 0.0177634 0.0447513
## EFA TLT IYR GLD
## 1 0.002667612 -0.0034247 0.05457073 0.03274822
## 2 0.002667612 -0.0034247 0.05457073 0.03274822
## 3 0.002667612 -0.0034247 0.05457073 0.03274822
## 4 0.002667612 -0.0034247 0.05457073 0.03274822
## 5 0.002667612 -0.0034247 0.05457073 0.03274822
## 6 0.002667612 -0.0034247 0.05457073 0.03274822data_m4 <- na.omit(data_m3)
head(data_m4,6)## date mkt_rf smb hml rf SPY QQQ EEM IWM
## 1 1926-06-30 2.96 -2.56 -2.43 0.22 0.03119469 0.04603891 0.0177634 0.0447513
## 2 1926-07-31 2.64 -1.17 3.82 0.25 0.03119469 0.04603891 0.0177634 0.0447513
## 3 1926-08-31 0.36 -1.40 0.13 0.23 0.03119469 0.04603891 0.0177634 0.0447513
## 4 1926-09-30 -3.24 -0.09 0.70 0.32 0.03119469 0.04603891 0.0177634 0.0447513
## 5 1926-10-31 2.53 -0.10 -0.51 0.31 0.03119469 0.04603891 0.0177634 0.0447513
## 6 1926-11-30 2.62 -0.03 -0.05 0.28 0.03119469 0.04603891 0.0177634 0.0447513
## EFA TLT IYR GLD
## 1 0.002667612 -0.0034247 0.05457073 0.03274822
## 2 0.002667612 -0.0034247 0.05457073 0.03274822
## 3 0.002667612 -0.0034247 0.05457073 0.03274822
## 4 0.002667612 -0.0034247 0.05457073 0.03274822
## 5 0.002667612 -0.0034247 0.05457073 0.03274822
## 6 0.002667612 -0.0034247 0.05457073 0.03274822data_m5 <- data_m4 %>%
filter(date >= ymd("2010-02-28") & date <= ymd("2014-12-31"))
head(data_m5,6)## date mkt_rf smb hml rf SPY QQQ EEM IWM
## 1 2010-02-28 6.31 1.48 2.21 0.01 0.03119469 0.04603891 0.0177634 0.0447513
## 2 2010-03-31 2.00 4.87 2.89 0.01 0.03119469 0.04603891 0.0177634 0.0447513
## 3 2010-04-30 -7.89 0.09 -2.44 0.01 0.03119469 0.04603891 0.0177634 0.0447513
## 4 2010-05-31 -5.57 -1.82 -4.70 0.01 0.03119469 0.04603891 0.0177634 0.0447513
## 5 2010-06-30 6.93 0.22 -0.33 0.01 0.03119469 0.04603891 0.0177634 0.0447513
## 6 2010-07-31 -4.77 -2.98 -1.93 0.01 0.03119469 0.04603891 0.0177634 0.0447513
## EFA TLT IYR GLD
## 1 0.002667612 -0.0034247 0.05457073 0.03274822
## 2 0.002667612 -0.0034247 0.05457073 0.03274822
## 3 0.002667612 -0.0034247 0.05457073 0.03274822
## 4 0.002667612 -0.0034247 0.05457073 0.03274822
## 5 0.002667612 -0.0034247 0.05457073 0.03274822
## 6 0.002667612 -0.0034247 0.05457073 0.03274822result_list <- list()
y <- NULL
for (symbol in symbols) {
diff <- data_m5[,symbol] - data_m5$rf
result_name <- paste0(symbol, "_rf")
assign(result_name, diff)
y <- cbind(y, get(result_name))
}#Calculating Beta
n <- nrow(y)
one_vec <- rep(1,n)
x <- NULL
x <- cbind(one_vec,data_m5$mkt_rf)
beta_hat = solve(t(x)%*%x)%*%t(x) %*% y
beta_hat## [,1] [,2] [,3] [,4] [,5]
## one_vec 7.618268e-03 1.177616e-02 -9.633714e-05 6.253079e-03 1.997156e-03
## 9.118814e-05 9.118814e-05 9.118814e-05 9.118814e-05 9.118814e-05
## [,6] [,7] [,8]
## one_vec 5.486656e-05 4.691208e-03 9.027284e-04
## 9.118814e-05 9.118814e-05 9.118814e-05E_hat = y - x %*% beta_hatbeta_hat = as.matrix(beta_hat[-1,])
diagD_hat = diag(t(E_hat) %*% E_hat)/(n-2)cov = as.numeric(var(data_m5$mkt_rf))*beta_hat%*%t(beta_hat) + diag(diagD_hat)
cov## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.804109e-03 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07
## [2,] 1.261442e-07 2.595991e-03 1.261442e-07 1.261442e-07 1.261442e-07
## [3,] 1.261442e-07 1.261442e-07 2.906444e-03 1.261442e-07 1.261442e-07
## [4,] 1.261442e-07 1.261442e-07 1.261442e-07 3.159851e-03 1.261442e-07
## [5,] 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07 2.175131e-03
## [6,] 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07
## [7,] 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07
## [8,] 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07 1.261442e-07
## [,6] [,7] [,8]
## [1,] 1.261442e-07 1.261442e-07 1.261442e-07
## [2,] 1.261442e-07 1.261442e-07 1.261442e-07
## [3,] 1.261442e-07 1.261442e-07 1.261442e-07
## [4,] 1.261442e-07 1.261442e-07 1.261442e-07
## [5,] 1.261442e-07 1.261442e-07 1.261442e-07
## [6,] 1.532394e-03 1.261442e-07 1.261442e-07
## [7,] 1.261442e-07 2.330579e-03 1.261442e-07
## [8,] 1.261442e-07 1.261442e-07 2.117136e-03t <- dim(data_m5)[1]
markets <- data_m5[,c(2,3,4)]
stocks1 <- data_m5[,c(-1,-2,-3,-4)]
head(stocks1,6)## rf SPY QQQ EEM IWM EFA TLT
## 1 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## 2 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## 3 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## 4 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## 5 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## 6 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## IYR GLD
## 1 0.05457073 0.03274822
## 2 0.05457073 0.03274822
## 3 0.05457073 0.03274822
## 4 0.05457073 0.03274822
## 5 0.05457073 0.03274822
## 6 0.05457073 0.03274822stocks3 <- as.matrix(stocks1)
head(stocks3,6)## rf SPY QQQ EEM IWM EFA TLT
## [1,] 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## [2,] 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## [3,] 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## [4,] 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## [5,] 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## [6,] 0.01 0.03119469 0.04603891 0.0177634 0.0447513 0.002667612 -0.0034247
## IYR GLD
## [1,] 0.05457073 0.03274822
## [2,] 0.05457073 0.03274822
## [3,] 0.05457073 0.03274822
## [4,] 0.05457073 0.03274822
## [5,] 0.05457073 0.03274822
## [6,] 0.05457073 0.03274822n <- dim(stocks3)[2]
one_vec <- rep(1,t)
p <- as.matrix(cbind(one_vec,markets))
beta <- solve(t(p)%*%p)%*%t(p)%*%stocks3
beta## rf SPY QQQ EEM IWM
## one_vec 0.0037517546 1.112323e-02 1.528112e-02 3.408622e-03 9.758038e-03
## mkt_rf -0.0002949038 2.721602e-17 3.738073e-17 8.335969e-18 2.387553e-17
## smb 0.0006417988 -2.585552e-17 -3.550304e-17 -8.028708e-18 -2.277942e-17
## hml 0.0002409029 -9.702339e-18 -1.326072e-17 -2.901935e-18 -8.414425e-18
## EFA TLT IYR GLD
## one_vec 5.502115e-03 3.559826e-03 8.196167e-03 4.407688e-03
## mkt_rf 1.346782e-17 8.719119e-18 2.005456e-17 1.078100e-17
## smb -1.276333e-17 -8.305191e-18 -1.902462e-17 -1.026538e-17
## hml -4.748043e-18 -3.083306e-18 -7.090936e-18 -3.773161e-18#Compute the residual
res <- stocks3-p%*%beta
diag.d <- diag(t(res)%*%res)/(t-6)
diag.d## rf SPY QQQ EEM IWM EFA
## 2.078442e-05 1.782448e-03 2.574663e-03 2.885247e-03 3.138761e-03 2.153626e-03
## TLT IYR GLD
## 1.510618e-03 2.309140e-03 2.095607e-03retvar <- apply(stocks3,2,var)
rsq <- 1-diag(t(res)%*%res)/((t-1)/retvar)
res.stdev <- sqrt(diag.d)
factor.cov <- var(stocks1)*t(beta)%*%beta+diag(diag.d)
stdev <- sqrt(diag(factor.cov))
factor.cor <- factor.cov/(stdev%*%t(stdev))
factor.cor## rf SPY QQQ EEM IWM
## rf 1.000000e+00 3.487705e-25 -1.113760e-24 -2.536661e-25 7.389493e-26
## SPY 3.487705e-25 1.000000e+00 1.556828e-04 2.724764e-05 9.606217e-05
## QQQ -1.113760e-24 1.556828e-04 1.000000e+00 3.396032e-05 1.145176e-04
## EEM -2.536661e-25 2.724764e-05 3.396032e-05 1.000000e+00 2.255752e-05
## IWM 7.389493e-26 9.606217e-05 1.145176e-04 2.255752e-05 1.000000e+00
## EFA 4.721642e-25 5.307188e-05 6.482837e-05 1.572667e-05 4.154175e-05
## TLT 9.363112e-26 -8.218969e-06 -4.792172e-06 -1.961608e-06 -1.084706e-05
## IYR -4.867952e-25 6.942932e-05 8.137362e-05 1.681643e-05 5.577784e-05
## GLD 1.887155e-25 4.942995e-06 8.757581e-06 4.512833e-06 1.695366e-06
## EFA TLT IYR GLD
## rf 4.721642e-25 9.363112e-26 -4.867952e-25 1.887155e-25
## SPY 5.307188e-05 -8.218969e-06 6.942932e-05 4.942995e-06
## QQQ 6.482837e-05 -4.792172e-06 8.137362e-05 8.757581e-06
## EEM 1.572667e-05 -1.961608e-06 1.681643e-05 4.512833e-06
## IWM 4.154175e-05 -1.084706e-05 5.577784e-05 1.695366e-06
## EFA 1.000000e+00 -4.145402e-06 3.138998e-05 3.726146e-06
## TLT -4.145402e-06 1.000000e+00 3.118175e-06 4.481842e-06
## IYR 3.138998e-05 3.118175e-06 1.000000e+00 7.051260e-06
## GLD 3.726146e-06 4.481842e-06 7.051260e-06 1.000000e+00cov_mon <- cov(asset_returns_mon_xts)
one <- rep(1,8)
one_m <- matrix(one, ncol=1)
a2 <- inv(cov_mon)%*%one_m
b2 <- t(one_m)%*%inv(cov_mon)%*%one_m
mvp2 <- a2/as.vector(b2)
head(mvp2)## [,1]
## SPY 0.98019954
## QQQ -0.45610362
## EEM -0.02751396
## IWM 0.06621562
## EFA 0.08560161
## TLT 0.52383354stocks_mean <- colMeans(stocks3,na.rm = TRUE)
cov.mat <- as.matrix(cov)
a6 <- inv(cov_mon)%*%one_m
b6 <- t(one_m)%*%inv(cov_mon)%*%one_m
mvp6 <- a6/as.vector(b6)
colnames(mvp6)="Weight"
mvp6## Weight
## SPY 0.98019954
## QQQ -0.45610362
## EEM -0.02751396
## IWM 0.06621562
## EFA 0.08560161
## TLT 0.52383354
## IYR -0.30024109
## GLD 0.12800837SIT package to backtest the performance of GMV
(global minimum variance) portfolios based on CAPM model and Fama-French
three-factor model. You have to use historical six monthly returns
(t-6 to t-1) to estimate the optimal weights
which will be assigned to assets to construct portfolios for investment
in next month (t). By repeating this process every month,
you can derive the monthly returns of GMV portfolios based on CAPM and
Fama-French three-factor model.con = gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb'))
source(con)
close(con)
tickers = spl('SPY,QQQ,EEM,IWM,EFA,TLT,IYR,GLD')
prices## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 88.11788 41.00547 32.42900 53.08977 37.99447 63.06118 28.77183
## 2010-01-05 88.35115 41.00547 32.66440 52.90724 38.02797 63.46839 28.84091
## 2010-01-06 88.41334 40.75814 32.73274 52.85745 38.18870 62.61876 28.82835
## 2010-01-07 88.78658 40.78463 32.54292 53.24745 38.04137 62.72409 29.08586
## 2010-01-08 89.08204 41.12030 32.80107 53.53788 38.34275 62.69599 28.89116
## 2010-01-11 89.20642 40.95247 32.73274 53.32212 38.65752 62.35199 29.02934
## 2010-01-12 88.37449 40.44010 32.20884 52.74128 38.20210 63.41926 28.53944
## 2010-01-13 89.12091 40.94363 32.30754 53.42171 38.52358 62.68195 29.07331
## 2010-01-14 89.36191 40.97896 32.22401 53.62088 38.81826 63.55969 28.97282
## 2010-01-15 88.35892 40.50196 31.85197 52.84085 38.20879 63.95290 28.70903
## ...
## 2023-05-26 420.01999 348.39999 38.69684 175.66353 70.84142 100.82204 81.06729
## 2023-05-30 420.17999 349.98001 38.25034 175.01534 70.12457 101.82936 81.41566
## 2023-05-31 417.85001 347.98999 37.89314 173.29012 69.39788 102.71700 81.84364
## 2023-06-01 421.82001 352.01001 38.56785 175.16490 70.42898 103.12000 81.89339
## 2023-06-02 427.92001 354.64999 39.23264 181.51733 71.34224 101.99000 83.72475
## 2023-06-05 427.10001 354.89999 39.22272 179.08406 70.92980 101.80000 83.16738
## 2023-06-06 428.03000 354.84000 39.57000 183.80099 71.51900 102.40000 83.88400
## 2023-06-07 426.54999 348.82001 39.40000 187.24001 70.89000 100.88000 85.20000
## 2023-06-08 429.13000 353.14999 39.68000 186.53999 71.64000 102.06000 84.76000
## 2023-06-09 429.89999 354.50000 39.86000 185.03000 71.52000 101.92000 84.24000
## 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
## 2010-01-11 112.85
## 2010-01-12 110.49
## 2010-01-13 111.54
## 2010-01-14 112.03
## 2010-01-15 110.86
## ...
## 2023-05-26 180.92
## 2023-05-30 182.04
## 2023-05-31 182.32
## 2023-06-01 183.76
## 2023-06-02 181.05
## 2023-06-05 182.14
## 2023-06-06 182.34
## 2023-06-07 180.15
## 2023-06-08 182.53
## 2023-06-09 182.04asset_returns_mon_xts <- na.omit(Return.calculate(prices_monthly))
prices_q <- to.quarterly(prices, indexAt = "last", OHLC = FALSE)
asset_q <- na.omit(Return.calculate(prices_q))
head(asset_returns_mon_xts)## SPY QQQ EEM IWM EFA
## 2010-02-26 0.03119469 0.04603891 0.017763395 0.04475130 0.002667612
## 2010-03-31 0.06087986 0.07710940 0.081109172 0.08230722 0.063853990
## 2010-04-30 0.01546983 0.02242504 -0.001662106 0.05678476 -0.028045713
## 2010-05-28 -0.07945438 -0.07392361 -0.093935742 -0.07536692 -0.111928099
## 2010-06-30 -0.05174124 -0.05975683 -0.013986171 -0.07743382 -0.020619113
## 2010-07-30 0.06830062 0.07258248 0.109324772 0.06730904 0.116104271
## TLT IYR GLD
## 2010-02-26 -0.003424700 0.05457073 0.032748219
## 2010-03-31 -0.020573519 0.09748442 -0.004386396
## 2010-04-30 0.033218499 0.06388128 0.058834363
## 2010-05-28 0.051083754 -0.05683509 0.030513147
## 2010-06-30 0.057978979 -0.04670171 0.023553189
## 2010-07-30 -0.009464066 0.09404807 -0.050871157tail(asset_returns_mon_xts)## SPY QQQ EEM IWM EFA
## 2023-01-31 0.062887396 0.106429242 0.091292802 0.098187522 0.09003651
## 2023-02-28 -0.025142710 -0.003597815 -0.075677020 -0.017234124 -0.03074776
## 2023-03-31 0.037077821 0.094927224 0.032173717 -0.048473419 0.03129052
## 2023-04-28 0.015974933 0.005079005 -0.008362893 -0.017937217 0.02936259
## 2023-05-31 0.004616194 0.078838024 -0.024022500 -0.008162042 -0.04007072
## 2023-06-09 0.028838070 0.018707463 0.051905590 0.067746988 0.03057898
## TLT IYR GLD
## 2023-01-31 0.076436435 0.099774250 0.057592574
## 2023-02-28 -0.048505534 -0.059617719 -0.053675964
## 2023-03-31 0.048393403 -0.019369783 0.079161282
## 2023-04-28 0.003383570 0.009187207 0.008623523
## 2023-05-31 -0.030152929 -0.040266046 -0.013419890
## 2023-06-09 -0.007759155 0.029279764 -0.001535838head(asset_q)## SPY QQQ EEM IWM EFA
## 2010-06-30 -0.1135806944 -0.109736684 -0.10809302 -0.09852540 -0.15463241
## 2010-09-30 0.1116161719 0.151601597 0.19962495 0.11080257 0.18082146
## 2010-12-31 0.1076081694 0.112043280 0.07301707 0.16435951 0.07006469
## 2011-03-31 0.0589736367 0.056023862 0.02162050 0.07803846 0.03194783
## 2011-06-30 0.0002587127 -0.004389145 -0.01220429 -0.01627687 0.02044919
## 2011-09-30 -0.1381722686 -0.078223734 -0.26260492 -0.21807571 -0.20552012
## TLT IYR GLD
## 2010-06-30 0.14896430 -0.04344573 0.116842622
## 2010-09-30 0.04658993 0.12985003 0.051199896
## 2010-12-31 -0.09557040 0.06966929 0.084512526
## 2011-03-31 -0.01453031 0.07072168 0.008217989
## 2011-06-30 0.03383297 0.02440122 0.043901039
## 2011-09-30 0.29631031 -0.15231108 0.082602723tail(asset_q)## SPY QQQ EEM IWM EFA
## 2022-03-31 -0.04614467 -0.087625454 -0.07574213 -0.07541704 -0.06456523
## 2022-06-30 -0.16110269 -0.225412986 -0.10430185 -0.17276598 -0.13216752
## 2022-09-30 -0.04931150 -0.044739828 -0.13017448 -0.02117924 -0.10369667
## 2022-12-30 0.07560925 -0.001281646 0.10314388 0.06211796 0.17663251
## 2023-03-31 0.07458221 0.207100892 0.04116087 0.02694574 0.08957940
## 2023-06-09 0.05009888 0.104602275 0.01805054 0.04003591 0.01833084
## TLT IYR GLD
## 2022-03-31 -0.10628835 -0.06431350 0.056679848
## 2022-06-30 -0.12593269 -0.14703214 -0.067478481
## 2022-09-30 -0.10284015 -0.10549777 -0.081859243
## 2022-12-30 -0.01879842 0.04334517 0.096786716
## 2023-03-31 0.07378896 0.01417583 0.080051886
## 2023-06-09 -0.03442204 -0.00308982 -0.006440388