library(quantmod)
## Warning: package 'quantmod' was built under R version 4.3.3
## Loading required package: xts
## Warning: package 'xts' was built under R version 4.3.3
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: TTR
## Warning: package 'TTR' was built under R version 4.3.3
## 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)
## 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 86.86008 40.73328 31.82712 52.51540 37.52378 61.13184 28.10299
## 2010-01-05 87.09000 40.73328 32.05813 52.33482 37.55686 61.52660 28.17045
## 2010-01-06 87.15133 40.48759 32.12519 52.28558 37.71561 60.70304 28.15819
## 2010-01-07 87.51920 40.51390 31.93890 52.67137 37.57009 60.80514 28.40971
## 2010-01-08 87.81044 40.84734 32.19226 52.95864 37.86773 60.77787 28.21954
## 2010-01-11 87.93307 40.68062 32.12519 52.74524 38.17861 60.44436 28.35449
##               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    0.010941312      0.002800154       0.01147251      0.008440212
## 2010-01-15   -0.008117475     -0.015037609      -0.02893486     -0.013019356
## 2010-01-22   -0.038982444     -0.036859389      -0.05578087     -0.030621777
## 2010-01-29   -0.016665245     -0.031022983      -0.03357750     -0.026243547
## 2010-02-05   -0.006797612      0.004439814      -0.02821308     -0.013973913
## 2010-02-12    0.012938191      0.018147851       0.03333329      0.029525414
##            weekly.returns.4 weekly.returns.5 weekly.returns.6 weekly.returns.7
## 2010-01-08      0.009166143    -5.790265e-03      0.004147194      0.014298722
## 2010-01-15     -0.003493573     2.004738e-02     -0.006303951     -0.004579349
## 2010-01-22     -0.055740332     1.010130e-02     -0.041785492     -0.033285246
## 2010-01-29     -0.025802804     3.369309e-03     -0.008447304     -0.011290465
## 2010-02-05     -0.019054999    -5.421506e-05      0.003223738     -0.012080019
## 2010-02-12      0.005244716    -1.946135e-02     -0.007574642      0.022544905
head(monthly_returns_df)
##            monthly.returns monthly.returns.1 monthly.returns.2
## 2010-01-29     -0.05241344       -0.07819892      -0.103722950
## 2010-02-26      0.03119445        0.04603840       0.017763815
## 2010-03-31      0.06087948        0.07710972       0.081108537
## 2010-04-30      0.01547051        0.02242502      -0.001661516
## 2010-05-28     -0.07945466       -0.07392395      -0.093935820
## 2010-06-30     -0.05174091       -0.05975684      -0.013986523
##            monthly.returns.3 monthly.returns.4 monthly.returns.5
## 2010-01-29       -0.06048786      -0.074916168       0.027836653
## 2010-02-26        0.04475159       0.002667557      -0.003424413
## 2010-03-31        0.08230673       0.063854329      -0.020572606
## 2010-04-30        0.05678500      -0.028045889       0.033216952
## 2010-05-28       -0.07536648      -0.111927971       0.051084218
## 2010-06-30       -0.07743380      -0.020619467       0.057978052
##            monthly.returns.6 monthly.returns.7
## 2010-01-29       -0.05195384      -0.034972713
## 2010-02-26        0.05457030       0.032748219
## 2010-03-31        0.09748468      -0.004386396
## 2010-04-30        0.06388132       0.058834363
## 2010-05-28       -0.05683518       0.030513147
## 2010-06-30       -0.04670133       0.023553189
#Q3
library(readxl)

# Read factor data from Excel file
factor_data <- read_excel("C:/Users/Dell/Downloads/Investments/F-F_Research_Data.xlsx")
## New names:
## • `` -> `...2`
## • `` -> `...3`
## • `` -> `...4`
## • `` -> `...5`
# 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")

# Display the first few rows of factor_data
head(factor_data)
## # A tibble: 6 × 5
##   Date                                                `Mkt-RF` SMB   HML   RF   
##   <chr>                                               <chr>    <chr> <chr> <chr>
## 1 The 1-month TBill return is from Ibbotson and Asso… Inc.     <NA>  <NA>  <NA> 
## 2 <NA>                                                <NA>     <NA>  <NA>  <NA> 
## 3 <NA>                                                Mkt-RF   SMB   HML   RF   
## 4 192607                                              2.96     -2.56 -2.4… 0.22 
## 5 192608                                              2.64     -1.17 3.82  0.25 
## 6 192609                                              0.36     -1.4  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 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] 0.002981577
#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)