# Load packages

# Core
library(tidyverse)
library(tidyquant)

1 Import stock prices

Revise the code below.

symbols <- c("UNH", "LLY", "JNJ", "PFE", "MRK")

prices <- tq_get(x = symbols, 
                 get = "stock.prices", 
                 from = "2000-12-31", 
                 to = "2025-06-11")

2 Convert prices to returns

asset_returns_tbl <- prices %>%
    
    group_by(symbol) %>%
    
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly",
                 type       = "log") %>%
    
    slice(-1) %>%
    
    ungroup() %>%
    
    set_names(c("asset", "date", "returns"))

3 Assign a weight to each asset

Revise the code for weights.

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "JNJ" "LLY" "MRK" "PFE" "UNH"
# weights
weights <- c(0.3, 0.25, 0.20, 0.13, 0.12)
weights
## [1] 0.30 0.25 0.20 0.13 0.12
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 JNJ        0.3 
## 2 LLY        0.25
## 3 MRK        0.2 
## 4 PFE        0.13
## 5 UNH        0.12

4 Build a portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    
    tq_portfolio(assets_col = asset, 
                 returns_col = returns, 
                 weights = w_tbl, 
                 rebalance_on = "months", 
                 col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 293 × 2
##    date        returns
##    <date>        <dbl>
##  1 2001-02-28  0.0181 
##  2 2001-03-30 -0.0633 
##  3 2001-04-30  0.0746 
##  4 2001-05-31 -0.0211 
##  5 2001-06-29 -0.0516 
##  6 2001-07-31  0.0677 
##  7 2001-08-31 -0.0268 
##  8 2001-09-28  0.0323 
##  9 2001-10-31 -0.00428
## 10 2001-11-30  0.0495 
## # ℹ 283 more rows

5 Simulating growth of a dollar

# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return
## [1] 0.006613693
# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return
## [1] 0.04269281
# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns
##   [1]  0.0373071048  0.0695062937  0.0200155577 -0.0478303377  0.0308181215
##   [6]  0.0051529833  0.0342871770  0.0648030275 -0.0266919465 -0.0066777267
##  [11]  0.0757438211  0.0622701445  0.0568764512  0.0477924465 -0.0548640413
##  [16]  0.0227610663  0.0969714675  0.0456995892 -0.0082245374 -0.0646131937
##  [21] -0.0456965473 -0.0608850485 -0.0236562699 -0.0036044922  0.0462678215
##  [26] -0.0367311819 -0.0533563860 -0.0914199847 -0.0269468421  0.0139145097
##  [31] -0.0496054191  0.0632986104 -0.0037795271  0.0912453411  0.0122206671
##  [36]  0.0106407704 -0.0186782318  0.0566637520  0.0290115146  0.0670794800
##  [41] -0.0324800164  0.0558990673 -0.0094100537  0.0466126864  0.0226367651
##  [46]  0.0566751210  0.0932165826 -0.0362111190  0.0166780299  0.0844173002
##  [51]  0.0277568746  0.0241420683  0.0442178868 -0.0207610204 -0.0630135532
##  [56]  0.0846165106  0.0592659988  0.0682518659  0.0646254276  0.0139034800
##  [61] -0.0466900709 -0.0141614927 -0.0561805795  0.0260703844 -0.0262718658
##  [66] -0.0826922755 -0.0184779044  0.0476726785  0.0062847757  0.1079801652
##  [71]  0.0001456179  0.0272207866 -0.0330306801  0.0085659835 -0.0025796686
##  [76]  0.0287747143 -0.0172585804 -0.0094856722  0.0443898430 -0.0053161342
##  [81] -0.0539379055 -0.0017325324  0.0051797471  0.1089114825 -0.0013172914
##  [86]  0.0947706009  0.0395205589  0.0673130124 -0.0007264524  0.0170994926
##  [91] -0.0019303013  0.0283529078  0.0431703906  0.0310322667 -0.0322235845
##  [96]  0.0157846263 -0.0474380193  0.1074461464 -0.0509222216  0.0051980217
## [101] -0.0369486463 -0.0436060159  0.0118111805  0.0738618023 -0.0075977076
## [106] -0.0029953136  0.0113654987 -0.0356535004 -0.0330746878 -0.0423341200
## [111]  0.0239360743 -0.1166659059 -0.0568957854 -0.0169779658  0.0192347750
## [116]  0.0314872233 -0.0461656389  0.0131866191  0.0354387678  0.0699062137
# Add a dollar
simulated_returns_add_1 <- tibble(returns = c(1, 1 + simulated_monthly_returns))
simulated_returns_add_1
## # A tibble: 121 × 1
##    returns
##      <dbl>
##  1   1    
##  2   1.04 
##  3   1.07 
##  4   1.02 
##  5   0.952
##  6   1.03 
##  7   1.01 
##  8   1.03 
##  9   1.06 
## 10   0.973
## # ℹ 111 more rows
# Calculate the cumulative growth of a dollar
simulated_growth <- simulated_returns_add_1 %>%
    mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
    select(growth)

simulated_growth
## # A tibble: 121 × 1
##    growth
##     <dbl>
##  1   1   
##  2   1.04
##  3   1.11
##  4   1.13
##  5   1.08
##  6   1.11
##  7   1.12
##  8   1.15
##  9   1.23
## 10   1.20
## # ℹ 111 more rows
# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr
## [1] 11.76057

6 Simulation function

simulate_accumulation <- function(initial_value, N, mean_return, sd_return) {

    # Add a dollar
    simulated_returns_add_1 <- tibble(returns = c(initial_value, 1 + rnorm(N, mean_return, sd_return)))

    # Calculate the cumulative growth of a dollar
    simulated_growth <- simulated_returns_add_1 %>%
        mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
        select(growth)
    
    return(simulated_growth)
}

simulate_accumulation(initial_value = 100, N = 240, mean_return = 0.005, sd_return = 0.01) %>% tail()
## # A tibble: 6 × 1
##   growth
##    <dbl>
## 1   425.
## 2   436.
## 3   440.
## 4   440.
## 5   448.
## 6   450.

7 Running multiple simulations

# Create a Vector of 1s as a Starting Point
sims <- 51
starts <- rep(100, sims) %>%
    set_names(paste0("sim", 1:sims))

starts
##  sim1  sim2  sim3  sim4  sim5  sim6  sim7  sim8  sim9 sim10 sim11 sim12 sim13 
##   100   100   100   100   100   100   100   100   100   100   100   100   100 
## sim14 sim15 sim16 sim17 sim18 sim19 sim20 sim21 sim22 sim23 sim24 sim25 sim26 
##   100   100   100   100   100   100   100   100   100   100   100   100   100 
## sim27 sim28 sim29 sim30 sim31 sim32 sim33 sim34 sim35 sim36 sim37 sim38 sim39 
##   100   100   100   100   100   100   100   100   100   100   100   100   100 
## sim40 sim41 sim42 sim43 sim44 sim45 sim46 sim47 sim48 sim49 sim50 sim51 
##   100   100   100   100   100   100   100   100   100   100   100   100
# Simulate
# For Reproducible Research
set.seed(1234)
monte_carlo_sim_51 <- starts %>%
    
    # Simulate
    map_dfc(.x = ., 
            .f = ~simulate_accumulation(initial_value = .x, 
                                        N             = 240, 
                                        mean_return   = mean_port_return, 
                                        sd_return     = stddev_port_return)) %>%
    
    # Add Column Month
    mutate(month = 1:nrow(.)) %>%
    select(month, everything()) %>%
    
    # Rearrange Column Names
    set_names(c("month", names(starts))) %>%
    
    # Transform to Long Form
    pivot_longer(cols = -month, names_to = "sim", values_to = "growth")

# Find quantiles
monte_carlo_sim_51 %>%
    
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%
    
    quantile(probs = c(0.3, 0.25, 0.20, 0.13, 0.12)) %>%
    round(2)
##    30%    25%    20%    13%    12% 
## 321.92 301.18 237.19 194.95 180.84

8 Visualizing simulations with ggplot

monte_carlo_sim_51 %>%
    
    ggplot(aes(x = month, y = growth, colour = sim)) +
    geom_line() +
    theme(legend.position = "none") +
    theme(plot.title = element_text(hjust = 0.5)) +
    
    labs(title = "Simulating Growth of $100 Over 240 Months")

Line Plot With Max, Median, and Min

# Step 1 Summarize Data into Max, Median, and Min of Last Value
sim_summary <- monte_carlo_sim_51 %>%
    
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    
    summarise(max = max(growth), 
              median = median(growth), 
              min = min(growth))

sim_summary
## # A tibble: 1 × 3
##     max median   min
##   <dbl>  <dbl> <dbl>
## 1 1281.   467.  99.1
# Step 2 Plot 
monte_carlo_sim_51 %>%
    
    # Filter for Max, Median, and Min Sim
    group_by(sim) %>%
    filter(last(growth) == sim_summary$max |
               last(growth) == sim_summary$median |
               last(growth) == sim_summary$min) %>%
    ungroup() %>%
    
    # Plot
    ggplot(aes(x = month, y = growth, colour = sim)) +
    geom_line() +
    
    theme(legend.position = "none") +
    theme(plot.title = element_text(hjust = 0.5)) +
    theme(plot.subtitle = element_text(hjust = 0.5)) +
    
    labs(title = "Simulating Growth of $100 Over 240 Months",
         subtitle = "Maximum, Median, and Minimum Simulation")

Based on the Monte Carlo simulation results, how much should you expect from your $100 investment after 20 years? What is the best-case scenario? What is the worst-case scenario? What are limitations of this simulation analysis?

Based on the Monte Carlo simulation I would expect an initial investment of $100 to grow to approximately $467 in 20 years as this was the median. In the best case scenario my original $100 investment would grow to $1,281 and in the worst case scenario I would expect my initial investment to shrink down to $99.10. One of the limitations of this simulation analysis is that past preformance is not indiciative of future preformance especially with individual stock selections. A second limitation is that we assumed a normal distribution of returns but in reality the returns of this portfolio are certainly not a normal distribution. A third limitation is the simulation only looks at the past 25 years of stock preformance data. Although this is significantly more time than in our code along assignment it still provides some limitations.