final
erdembileg/112035150
2024-06-10
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library(tidyquant)## Warning: package 'tidyquant' was built under R version 4.3.2## Loading required package: lubridate## Warning: package 'lubridate' was built under R version 4.3.2##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
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## date, intersect, setdiff, union## Loading required package: PerformanceAnalytics## 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##
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## legend## Loading required package: quantmod## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
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## as.zoo.data.frame zoolibrary(lubridate)
library(timetk)
library(purrr)
library(quantmod)
library(dplyr)## Warning: package 'dplyr' was built under R version 4.3.2##
## ######################### Warning from 'xts' package ##########################
## # #
## # The dplyr lag() function breaks how base R's lag() function is supposed to #
## # work, which breaks lag(my_xts). Calls to lag(my_xts) that you type or #
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## # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
## # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop #
## # dplyr from breaking base R's lag() function. #
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## Attaching package: 'dplyr'## The following objects are masked from 'package:xts':
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## first, last## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(tidyr)
# Define the ETF symbols
symbols <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
# Download the data from Yahoo Finance
prices <- getSymbols(symbols, src = 'yahoo', from = "2010-01-01", auto.assign = TRUE, warnings = FALSE) %>%
map(~ Ad(get(.))) %>%
reduce(merge) %>%
`colnames<-`(symbols)
# Convert xts to tibble
prices_tibble <- tk_tbl(prices, rename_index = "date")
# Ensure date column is in character format, then convert to Date type
prices_tibble <- prices_tibble %>%
mutate(date = as.character(date)) %>%
mutate(date = as.Date(date))
# Calculate weekly log returns
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()
# Calculate monthly log returns
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()
# Convert to tibble format
monthly_returns_tibble <- as_tibble(monthly_returns)
# Rename 'month' column to 'date'
monthly_returns_tibble <- monthly_returns_tibble %>%
rename(date = month)
# Load the Fama/French data from URL
FFdata <- read.csv("https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F_Research_Data_Factors.CSV", skip = 3)
# Clean and format the data, handling parsing errors
FFdata <- FFdata %>%
mutate(date = parse_date_time(X, orders = "Y%m", quiet = TRUE)) %>%
filter(!is.na(date)) %>%
select(date, Mkt.RF, SMB, HML, RF)
# Convert character columns to numeric
FFdata <- FFdata %>%
mutate(across(-date, ~ as.numeric(gsub(" ", "", .))))
# Ensure date columns are present and in Date format
FFdata <- FFdata %>%
mutate(date = as.Date(date))
# Merge the ETF returns with the FF factors data
merged_data <- left_join(monthly_returns_tibble, FFdata, by = 'date')
# Check the first few rows of the merged data
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># Extract the relevant returns for the CAPM model
capm_returns <- merged_data %>%
filter(date >= "2010-02-01" & date <= "2015-01-31") %>%
select(-date, -Mkt.RF, -SMB, -HML, -RF)
# Compute the covariance matrix
capm_cov_matrix <- cov(capm_returns)
print(capm_cov_matrix)## SPY QQQ EEM IWM EFA
## SPY 0.0013789570 0.0014370242 0.0017213326 0.0017634415 0.0015961631
## QQQ 0.0014370242 0.0017632708 0.0017694587 0.0018116955 0.0016582442
## EEM 0.0017213326 0.0017694587 0.0033901758 0.0023127713 0.0024955612
## IWM 0.0017634415 0.0018116955 0.0023127713 0.0026629388 0.0019648694
## EFA 0.0015961631 0.0016582442 0.0024955612 0.0019648694 0.0024254044
## TLT -0.0009663065 -0.0009584985 -0.0011821327 -0.0013080793 -0.0011039475
## IYR 0.0011816450 0.0012041823 0.0017966331 0.0015876832 0.0015471668
## GLD 0.0002043548 0.0003904106 0.0009310468 0.0005394826 0.0004417081
## TLT IYR GLD
## SPY -0.0009663065 0.0011816450 0.0002043548
## QQQ -0.0009584985 0.0012041823 0.0003904106
## EEM -0.0011821327 0.0017966331 0.0009310468
## IWM -0.0013080793 0.0015876832 0.0005394826
## EFA -0.0011039475 0.0015471668 0.0004417081
## TLT 0.0015464579 -0.0003632174 0.0001797648
## IYR -0.0003632174 0.0019945686 0.0005353319
## GLD 0.0001797648 0.0005353319 0.0029025882# Extract the relevant returns and FF factors for the FF model
ff_returns <- merged_data %>%
filter(date >= "2010-02-01" & date <= "2015-01-31")
# Compute the residuals for each ETF by regressing on the FF factors
residuals <- ff_returns %>%
select(all_of(symbols)) %>%
map_dfc(~ residuals(lm(. ~ Mkt.RF + SMB + HML, data = ff_returns)))
# Compute the covariance matrix of the residuals
ff_cov_matrix <- cov(residuals)
print(ff_cov_matrix)## SPY QQQ EEM IWM EFA
## SPY 3.259780e-06 3.622019e-06 1.784334e-06 8.352221e-07 1.903219e-06
## QQQ 3.622019e-06 2.067163e-04 -5.274706e-05 -1.248137e-05 -3.610031e-05
## EEM 1.784334e-06 -5.274706e-05 1.213626e-03 4.639607e-05 5.052329e-04
## IWM 8.352221e-07 -1.248137e-05 4.639607e-05 1.656360e-05 3.183176e-05
## EFA 1.903219e-06 -3.610031e-05 5.052329e-04 3.183176e-05 5.327993e-04
## TLT 8.488184e-06 -4.926804e-06 1.964548e-05 2.785470e-05 -2.700833e-05
## IYR 2.136827e-05 -1.638326e-05 3.328178e-04 5.932484e-05 2.082017e-04
## GLD -8.117783e-06 5.139918e-05 5.668777e-04 5.843737e-05 1.954868e-04
## TLT IYR GLD
## SPY 8.488184e-06 2.136827e-05 -8.117783e-06
## QQQ -4.926804e-06 -1.638326e-05 5.139918e-05
## EEM 1.964548e-05 3.328178e-04 5.668777e-04
## IWM 2.785470e-05 5.932484e-05 5.843737e-05
## EFA -2.700833e-05 2.082017e-04 1.954868e-04
## TLT 7.800174e-04 4.560251e-04 2.593804e-04
## IYR 4.560251e-04 1.008808e-03 3.079622e-04
## GLD 2.593804e-04 3.079622e-04 2.510801e-03# Function to compute GMV portfolio weights
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)
}
# Compute the 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 0.94117719
## QQQ -0.18088147
## EEM -0.01436988
## IWM -0.05253550
## EFA -0.01342862
## TLT 0.48106074
## IYR -0.21174222
## GLD 0.05071976print(gmv_weights_ff)## [,1]
## SPY 0.8299903675
## QQQ 0.0052288200
## EEM 0.0001159185
## IWM 0.1868598178
## EFA 0.0009316490
## TLT 0.0032724032
## IYR -0.0286069123
## GLD 0.0022079364Including Plots
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