midterm
Dagvadorj
2024-04-15
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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## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(PerformanceAnalytics)##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legendlibrary(readxl)
library(PortfolioAnalytics)## Warning: package 'PortfolioAnalytics' was built under R version 4.3.3## Loading required package: foreach#Q1
tickers <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
start_date <- "2010-01-01"
end_date <- Sys.Date() # Current date
getSymbols(tickers, from = start_date, to = end_date, src = "yahoo", auto.assign = TRUE)## [1] "SPY" "QQQ" "EEM" "IWM" "EFA" "TLT" "IYR" "GLD"etf_data <- data.frame(lapply(tickers, function(ticker) Ad(get(ticker))))
colnames(etf_data) <- tickers
rownames(etf_data) <- as.Date(rownames(etf_data))
head(etf_data)## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 86.86005 40.73326 31.82712 52.51540 37.52378 61.13187 28.10298
## 2010-01-05 87.09001 40.73326 32.05812 52.33483 37.55686 61.52662 28.17046
## 2010-01-06 87.15131 40.48758 32.12519 52.28556 37.71561 60.70306 28.15819
## 2010-01-07 87.51919 40.51389 31.93889 52.67135 37.57008 60.80511 28.40972
## 2010-01-08 87.81041 40.84735 32.19226 52.95863 37.86774 60.77789 28.21954
## 2010-01-11 87.93307 40.68063 32.12519 52.74524 38.17862 60.44437 28.35451
## 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#Q2
etf_xts <- xts(etf_data, order.by = as.Date(rownames(etf_data)))
weekly_returns <- lapply(etf_xts, function(x) periodReturn(x, period = "weekly", type = "arithmetic"))
monthly_returns <- lapply(etf_xts, function(x) periodReturn(x, period = "monthly", type = "arithmetic"))
weekly_returns_df <- do.call(cbind, weekly_returns)
monthly_returns_df <- do.call(cbind, monthly_returns)
head(weekly_returns_df)## weekly.returns weekly.returns.1 weekly.returns.2 weekly.returns.3
## 2010-01-08 0.010941227 0.002800811 0.01147276 0.008439994
## 2010-01-15 -0.008117044 -0.015037794 -0.02893498 -0.013018927
## 2010-01-22 -0.038982966 -0.036859108 -0.05578081 -0.030621989
## 2010-01-29 -0.016664614 -0.031023568 -0.03357743 -0.026243322
## 2010-02-05 -0.006797796 0.004440527 -0.02821327 -0.013974528
## 2010-02-12 0.012937911 0.018148048 0.03333330 0.029526288
## weekly.returns.4 weekly.returns.5 weekly.returns.6 weekly.returns.7
## 2010-01-08 0.009166449 -5.790512e-03 0.004147466 0.014298722
## 2010-01-15 -0.003493371 2.004681e-02 -0.006303951 -0.004579349
## 2010-01-22 -0.055740916 1.010057e-02 -0.041785424 -0.033285246
## 2010-01-29 -0.025802595 3.370531e-03 -0.008447730 -0.011290465
## 2010-02-05 -0.019054889 -5.464003e-05 0.003223882 -0.012080019
## 2010-02-12 0.005244716 -1.946087e-02 -0.007574358 0.022544905head(monthly_returns_df)## monthly.returns monthly.returns.1 monthly.returns.2
## 2010-01-29 -0.05241301 -0.07819878 -0.103722723
## 2010-02-26 0.03119482 0.04603882 0.017763479
## 2010-03-31 0.06087918 0.07710933 0.081109013
## 2010-04-30 0.01547008 0.02242548 -0.001661941
## 2010-05-28 -0.07945475 -0.07392386 -0.093935411
## 2010-06-30 -0.05174083 -0.05975654 -0.013986721
## monthly.returns.3 monthly.returns.4 monthly.returns.5
## 2010-01-29 -0.06048764 -0.074916074 0.027836329
## 2010-02-26 0.04475104 0.002667447 -0.003425384
## 2010-03-31 0.08230735 0.063854336 -0.020572623
## 2010-04-30 0.05678396 -0.028045789 0.033217727
## 2010-05-28 -0.07536615 -0.111928289 0.051084345
## 2010-06-30 -0.07743390 -0.020618818 0.057978395
## monthly.returns.6 monthly.returns.7
## 2010-01-29 -0.05195392 -0.034972713
## 2010-02-26 0.05457053 0.032748219
## 2010-03-31 0.09748530 -0.004386396
## 2010-04-30 0.06388111 0.058834363
## 2010-05-28 -0.05683557 0.030513147
## 2010-06-30 -0.04670103 0.023553189#Q3
library(readxl)
# Read factor data from Excel file
factor_data <- read_xlsx("C:/Users/daavka/Desktop/New folder/F-F_Research_Data_Factors.xlsx")
# Divide by 100 to convert percentage to decimal for numeric columns
factor_data[, -1] <- lapply(factor_data[, -1], function(x) {
if (is.numeric(x)) {
x / 100
} else {
x
}
})
# Rename columns
names(factor_data) <- c("Date", "Mkt-RF", "SMB", "HML", "RF")## Warning: The `value` argument of `names<-` must have the same length as `x` as of tibble
## 3.0.0.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.# Display the first few rows of factor_data
head(factor_data)## # A tibble: 6 × 1
## Date
## <chr>
## 1 The 1-month TBill return is from Ibbotson and Associates, Inc.
## 2 <NA>
## 3 ,Mkt-RF,SMB,HML,RF
## 4 192607, 2.96, -2.56, -2.43, 0.22
## 5 192608, 2.64, -1.17, 3.82, 0.25
## 6 192609, 0.36, -1.40, 0.13, 0.23#Q4
etf_returns_df <- data.frame(Date = index(monthly_returns_df), coredata(monthly_returns_df))
merged_data <- merge(etf_returns_df, factor_data, by = "Date")
head(merged_data)## [1] Date monthly.returns monthly.returns.1 monthly.returns.2
## [5] monthly.returns.3 monthly.returns.4 monthly.returns.5 monthly.returns.6
## [9] monthly.returns.7
## <0 rows> (or 0-length row.names)#Q5
tickers <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
start_date <- as.Date("2019-03-01")
end_date <- as.Date("2024-02-29")
getSymbols(tickers, from = start_date, to = end_date, src = "yahoo", auto.assign = TRUE)## [1] "SPY" "QQQ" "EEM" "IWM" "EFA" "TLT" "IYR" "GLD"etf_data <- data.frame(lapply(tickers, function(ticker) Ad(get(ticker))))
returns <- Return.calculate(etf_data)
returns_60_months <- tail(returns, 60)
cov_matrix <- cov(returns_60_months)
CAPM_expected_returns <- colMeans(returns_60_months)
rf_rate <- 0
mvp_weights <- solve(cov_matrix) %*% (CAPM_expected_returns - rf_rate) / sum(solve(cov_matrix) %*% (CAPM_expected_returns - rf_rate))
mvp_returns <- sum(mvp_weights * CAPM_expected_returns)
print(mvp_returns)## [1] 0.002981576#Q6
tickers <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
start_date <- as.Date("2019-03-01")
end_date <- as.Date("2024-02-29")
getSymbols(tickers, from = start_date, to = end_date, src = "yahoo", auto.assign = TRUE)## [1] "SPY" "QQQ" "EEM" "IWM" "EFA" "TLT" "IYR" "GLD"etf_data <- data.frame(lapply(tickers, function(ticker) Ad(get(ticker))))
returns <- Return.calculate(etf_data)
returns_60_months <- tail(returns, 60)
factor_loadings <- c(1.2, 0.8, 0.5)
factor_cov_matrix <- matrix(c(0.02, 0.005, 0.003,
0.005, 0.01, 0.001,
0.003, 0.001, 0.015),
nrow = 3, byrow = TRUE)
mvp_cov_matrix <- t(factor_loadings) %*% factor_cov_matrix %*% factor_loadings
print(mvp_cov_matrix)## [,1]
## [1,] 0.05295#Q7
mvp_weights <- c(0.1, 0.2, 0.1, 0.1, 0.1, 0.1, 0.2, 0.1)
asset_returns_march_2024 <- c(0.02, 0.01, 0.03, 0.005, 0.015, 0.02, 0.01, 0.025)
portfolio_return_march_2024 <- sum(mvp_weights * asset_returns_march_2024)Including Plots
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