# Load libraries
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 zoo
library(PerformanceAnalytics)
##
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
##
## legend
library(readxl)
library(PortfolioAnalytics)
## 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 86.86006 40.73327 31.82712 52.51541 37.52379 61.13184 28.10297
## 2010-01-05 87.08998 40.73327 32.05812 52.33484 37.55686 61.52662 28.17045
## 2010-01-06 87.15134 40.48758 32.12519 52.28557 37.71561 60.70303 28.15819
## 2010-01-07 87.51915 40.51392 31.93890 52.67135 37.57008 60.80516 28.40972
## 2010-01-08 87.81044 40.84737 32.19227 52.95865 37.86774 60.77789 28.21954
## 2010-01-11 87.93308 40.68062 32.12519 52.74523 38.17863 60.44437 28.35450
## 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 0.010941489 0.002801091 0.01147312 0.008440284
## 2010-01-15 -0.008117388 -0.015038161 -0.02893580 -0.013019354
## 2010-01-22 -0.038982704 -0.036858820 -0.05578065 -0.030622065
## 2010-01-29 -0.016665157 -0.031023752 -0.03357712 -0.026243175
## 2010-02-05 -0.006797241 0.004439815 -0.02821327 -0.013974528
## 2010-02-12 0.012937721 0.018148159 0.03333330 0.029526053
## weekly.returns.4 weekly.returns.5 weekly.returns.6 weekly.returns.7
## 2010-01-08 0.009166141 -5.789953e-03 0.004147807 0.014298722
## 2010-01-15 -0.003493573 2.004731e-02 -0.006304356 -0.004579349
## 2010-01-22 -0.055740624 1.010019e-02 -0.041784758 -0.033285246
## 2010-01-29 -0.025802914 3.370164e-03 -0.008447940 -0.011290465
## 2010-02-05 -0.019054673 -5.409364e-05 0.003223595 -0.012080019
## 2010-02-12 0.005244716 -1.946050e-02 -0.007573860 0.022544905
head(monthly_returns_df)
## monthly.returns monthly.returns.1 monthly.returns.2
## 2010-01-29 -0.05241336 -0.07819876 -0.103722723
## 2010-02-26 0.03119464 0.04603892 0.017763746
## 2010-03-31 0.06087984 0.07710853 0.081108729
## 2010-04-30 0.01547000 0.02242576 -0.001661758
## 2010-05-28 -0.07945466 -0.07392404 -0.093935637
## 2010-06-30 -0.05174092 -0.05975628 -0.013986588
## monthly.returns.3 monthly.returns.4 monthly.returns.5
## 2010-01-29 -0.06048771 -0.074916559 0.027836653
## 2010-02-26 0.04475158 0.002667887 -0.003424473
## 2010-03-31 0.08230664 0.063853993 -0.020573703
## 2010-04-30 0.05678458 -0.028045483 0.033217987
## 2010-05-28 -0.07536637 -0.111928160 0.051084649
## 2010-06-30 -0.07743409 -0.020619587 0.057977237
## monthly.returns.6 monthly.returns.7
## 2010-01-29 -0.05195353 -0.034972713
## 2010-02-26 0.05457038 0.032748219
## 2010-03-31 0.09748503 -0.004386396
## 2010-04-30 0.06388113 0.058834363
## 2010-05-28 -0.05683523 0.030513147
## 2010-06-30 -0.04670127 0.023553189
#Q3
file_path <- "F_F_Research_Data.xlsx"
factor_data <- read_excel(file_path)
factor_data[, -1] <- factor_data[, -1] / 100 # Divide by 100 to convert percentage to decimal
names(factor_data) <- c("Date", "Mkt-RF", "SMB", "HML", "RF")
head(factor_data)
## # A tibble: 6 × 5
## Date `Mkt-RF` SMB HML RF
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 192607 0.0296 -0.0256 -0.0243 0.0022
## 2 192608 0.0264 -0.0117 0.0382 0.0025
## 3 192609 0.0036 -0.014 0.0013 0.0023
## 4 192610 -0.0324 -0.0009 0.007 0.0032
## 5 192611 0.0253 -0.001 -0.0051 0.0031
## 6 192612 0.0262 -0.0003 -0.0005 0.0028
#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 Mkt-RF SMB HML
## [13] RF
## <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] 0.00298157
#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)