library(tidyquant)
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library(lubridate)
library(timetk)
library(purrr)
library(quantmod)
library(dplyr)
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library(tidyr)
symbols <- 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)
prices_tibble <- tk_tbl(prices, rename_index = "date")
prices_tibble <- prices_tibble %>%
mutate(date = as.character(date)) %>%
mutate(date = as.Date(date))
weekly_prices <- prices_tibble %>%
group_by(week = floor_date(date, "week")) %>%
summarize(across(all_of(symbols), last))
weekly_returns <- weekly_prices %>%
mutate(across(all_of(symbols), ~ log(. / lag(.)))) %>%
drop_na()
monthly_prices <- prices_tibble %>%
group_by(month = floor_date(date, "month")) %>%
summarize(across(all_of(symbols), last))
monthly_returns <- monthly_prices %>%
mutate(across(all_of(symbols), ~ log(. / lag(.)))) %>%
drop_na()
monthly_returns_tibble <- as_tibble(monthly_returns)
monthly_returns_tibble <- monthly_returns_tibble %>%
rename(date = month)
FFdata <- read.csv("https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F_Research_Data_Factors.CSV", skip = 3)
FFdata <- FFdata %>%
mutate(date = parse_date_time(X, orders = "Y%m", quiet = TRUE)) %>%
filter(!is.na(date)) %>%
select(date, Mkt.RF, SMB, HML, RF)
FFdata <- FFdata %>%
mutate(across(-date, ~ as.numeric(gsub(" ", "", .))))
FFdata <- FFdata %>%
mutate(date = as.Date(date))
merged_data <- left_join(monthly_returns_tibble, FFdata, by = 'date')
head(merged_data)
## # A tibble: 6 × 13
## date SPY QQQ EEM IWM EFA TLT IYR GLD
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010-02-01 0.0307 0.0450 0.0176 0.0438 0.00266 -0.00343 0.0531 0.0322
## 2 2010-03-01 0.0591 0.0743 0.0780 0.0791 0.0619 -0.0208 0.0930 -0.00440
## 3 2010-04-01 0.0154 0.0222 -0.00166 0.0552 -0.0284 0.0327 0.0619 0.0572
## 4 2010-05-01 -0.0828 -0.0768 -0.0986 -0.0784 -0.119 0.0498 -0.0585 0.0301
## 5 2010-06-01 -0.0531 -0.0616 -0.0141 -0.0806 -0.0208 0.0564 -0.0478 0.0233
## 6 2010-07-01 0.0661 0.0701 0.104 0.0651 0.110 -0.00951 0.0899 -0.0522
## # ℹ 4 more variables: Mkt.RF <dbl>, SMB <dbl>, HML <dbl>, RF <dbl>
capm_returns <- merged_data %>%
filter(date >= "2010-02-01" & date <= "2015-01-31") %>%
select(-date, -Mkt.RF, -SMB, -HML, -RF)
capm_cov_matrix <- cov(capm_returns)
print(capm_cov_matrix)
## SPY QQQ EEM IWM EFA
## SPY 0.0013789602 0.0014370254 0.0017213307 0.0017634403 0.0015961643
## QQQ 0.0014370254 0.0017632643 0.0017694588 0.0018116905 0.0016582425
## EEM 0.0017213307 0.0017694588 0.0033901713 0.0023127658 0.0024955582
## IWM 0.0017634403 0.0018116905 0.0023127658 0.0026629374 0.0019648664
## EFA 0.0015961643 0.0016582425 0.0024955582 0.0019648664 0.0024254008
## TLT -0.0009663098 -0.0009584985 -0.0011821362 -0.0013080833 -0.0011039521
## IYR 0.0011816476 0.0012041849 0.0017966290 0.0015876828 0.0015471657
## GLD 0.0002043547 0.0003904110 0.0009310461 0.0005394833 0.0004417098
## TLT IYR GLD
## SPY -0.0009663098 0.0011816476 0.0002043547
## QQQ -0.0009584985 0.0012041849 0.0003904110
## EEM -0.0011821362 0.0017966290 0.0009310461
## IWM -0.0013080833 0.0015876828 0.0005394833
## EFA -0.0011039521 0.0015471657 0.0004417098
## TLT 0.0015464571 -0.0003632229 0.0001797655
## IYR -0.0003632229 0.0019945611 0.0005353326
## GLD 0.0001797655 0.0005353326 0.0029025882
ff_returns <- merged_data %>%
filter(date >= "2010-02-01" & date <= "2015-01-31")
residuals <- ff_returns %>%
select(all_of(symbols)) %>%
map_dfc(~ residuals(lm(. ~ Mkt.RF + SMB + HML, data = ff_returns)))
ff_cov_matrix <- cov(residuals)
print(ff_cov_matrix)
## SPY QQQ EEM IWM EFA
## SPY 3.259893e-06 3.622669e-06 1.782061e-06 8.350488e-07 1.903389e-06
## QQQ 3.622669e-06 2.067128e-04 -5.274325e-05 -1.248068e-05 -3.609896e-05
## EEM 1.782061e-06 -5.274325e-05 1.213625e-03 4.639486e-05 5.052333e-04
## IWM 8.350488e-07 -1.248068e-05 4.639486e-05 1.656402e-05 3.183169e-05
## EFA 1.903389e-06 -3.609896e-05 5.052333e-04 3.183169e-05 5.327998e-04
## TLT 8.487284e-06 -4.925863e-06 1.964390e-05 2.785543e-05 -2.701148e-05
## IYR 2.136860e-05 -1.638066e-05 3.328135e-04 5.932457e-05 2.082001e-04
## GLD -8.118385e-06 5.140062e-05 5.668770e-04 5.843797e-05 1.954886e-04
## TLT IYR GLD
## SPY 8.487284e-06 2.136860e-05 -8.118385e-06
## QQQ -4.925863e-06 -1.638066e-05 5.140062e-05
## EEM 1.964390e-05 3.328135e-04 5.668770e-04
## IWM 2.785543e-05 5.932457e-05 5.843797e-05
## EFA -2.701148e-05 2.082001e-04 1.954886e-04
## TLT 7.800130e-04 4.560221e-04 2.593836e-04
## IYR 4.560221e-04 1.008799e-03 3.079621e-04
## GLD 2.593836e-04 3.079621e-04 2.510801e-03
compute_gmv_weights <- function(cov_matrix) {
inv_cov <- solve(cov_matrix)
ones <- rep(1, nrow(inv_cov))
weights <- inv_cov %*% ones / sum(inv_cov %*% ones)
return(weights)
}
gmv_weights_capm <- compute_gmv_weights(capm_cov_matrix)
gmv_weights_ff <- compute_gmv_weights(ff_cov_matrix)
print(gmv_weights_capm)
## [,1]
## SPY 0.94116869
## QQQ -0.18088543
## EEM -0.01436733
## IWM -0.05252635
## EFA -0.01342610
## TLT 0.48106449
## IYR -0.21174619
## GLD 0.05071822
print(gmv_weights_ff)
## [,1]
## SPY 0.8299884705
## QQQ 0.0052266843
## EEM 0.0001191034
## IWM 0.1868640572
## EFA 0.0009288430
## TLT 0.0032739372
## IYR -0.0286086812
## GLD 0.0022075855