# Load packages

# Core
library(tidyverse)
library(tidyquant)

# Source function
simulate_accumulation <- function(initial_value, n = 240, mu, sigma) {
  tibble(returns = c(initial_value, 1 + rnorm(n, mu, sigma))) %>%
    mutate(growth = accumulate(returns, function(x, y) x * y)) %>%
    select(growth)
}

1 Import stock prices

symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = Sys.Date())

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

symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
weights <- c(0.25, 0.25, 0.2, 0.2, 0.1)
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AGG        0.25
## 2 EEM        0.25
## 3 EFA        0.2 
## 4 IJS        0.2 
## 5 SPY        0.1

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: 150 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0204 
##  2 2013-02-28 -0.00239
##  3 2013-03-28  0.0121 
##  4 2013-04-30  0.0174 
##  5 2013-05-31 -0.0128 
##  6 2013-06-28 -0.0247 
##  7 2013-07-31  0.0321 
##  8 2013-08-30 -0.0224 
##  9 2013-09-30  0.0511 
## 10 2013-10-31  0.0301 
## # ℹ 140 more rows
mu <- mean(portfolio_returns_tbl$returns)
sigma <- sd(portfolio_returns_tbl$returns)

5 Simulating growth of a dollar

mean_port_return <- mean(portfolio_returns_tbl$returns)
stddev_port_return <- sd(portfolio_returns_tbl$returns)

6 Simulation function

No need to write this; the function was loaded in step 1.

7 Running multiple simulations

set.seed(1234)
sims <- 51
starts <- rep(100, sims) %>% set_names(paste0("sim", 1:sims))

monte_carlo_sim_51 <- map_dfc(.x = starts, .f = ~ simulate_accumulation(initial_value = .x, n = 240, mu = mean_port_return, sigma = stddev_port_return)) %>%
  mutate(month = 0:240) %>%
  select(month, everything()) %>%
  pivot_longer(cols = -month, names_to = "sim", values_to = "growth")

8 Visualizing simulations with ggplot

monte_carlo_sim_51 %>%
  ggplot(aes(x = month, y = growth, color = sim)) +
  geom_line(show.legend = FALSE) +
  labs(title = "Simulated $100 Growth Over 20 Years") +
  theme(plot.title = element_text(hjust = 0.5))

sim_summary <- monte_carlo_sim_51 %>%
  group_by(sim) %>%
  summarize(growth = last(growth)) %>%
  ungroup()

extremes <- monte_carlo_sim_51 %>%
  group_by(sim) %>%
  filter(last(growth) %in% c(max(sim_summary$growth), median(sim_summary$growth), min(sim_summary$growth))) %>%
  ungroup()

extremes %>%
  ggplot(aes(x = month, y = growth, color = sim)) +
  geom_line() +
  labs(title = "Simulations of $100 Growth Over 20 Years",
       subtitle = "Max, Median, and Min Simulations") +
  theme(plot.title = element_text(hjust = 0.5),
        plot.subtitle = element_text(hjust = 0.5))

monte_carlo_sim_51 %>%
  group_by(sim) %>%
  summarize(growth = last(growth)) %>%
  pull(growth) %>%
  quantile(probs = c(0, 0.25, 0.5, 0.75, 1)) %>%
  round(2)
##     0%    25%    50%    75%   100% 
##  86.82 210.49 296.46 414.42 668.57

Summary

Based on the Monte Carlo simulation results, after 20 years, you should expect your $100 investment to grow to around the median outcome from the quantiles above. The best-case scenario is the maximum final growth, and the worst-case is the minimum value.

Limitations: - Simulated returns assume a normal distribution, which may not reflect real-world skewness or fat tails. - Returns are based on a bull market period (2012–2017), possibly overestimating future expectations. - Results vary with each run unless you set a fixed seed for reproducibility.