Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Zach Marve,
2024-12-04
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# Source function
source("../00_scripts/simulate_accumulation.R")1 Import stock prices
Revise the code below.
- Replace symbols with your stocks.
- Replace the from and the to arguments to date from 2012-12-31 to present.
symbols <- c("MSFT", "AAPL", "F", "JPM", "SBUX")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31")2 Convert prices to returns
asset_returns_tbl <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("asset", "date", "returns"))3 Assign a weight to each asset
Revise the code for weights.
- The vector weights should have a length equal to the number of assets in the portfolio.
- The values in the vector weights should sum to 1.
# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols## [1] "AAPL" "F" "JPM" "MSFT" "SBUX"# weights
weights <- c(0.3, 0.2, 0.2, 0.15, 0.15)
weights## [1] 0.30 0.20 0.20 0.15 0.15w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 5 × 2
## symbols weights
## <chr> <dbl>
## 1 AAPL 0.3
## 2 F 0.2
## 3 JPM 0.2
## 4 MSFT 0.15
## 5 SBUX 0.154 Build a portfolio
portfolio_returns_tbl <- asset_returns_tbl %>%
tq_portfolio(assets_col = asset,
returns_col = returns,
weights = w_tbl,
rebalance_on = "months",
col_rename = "returns")
portfolio_returns_tbl## # A tibble: 144 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 -0.0194
## 2 2013-02-28 -0.00494
## 3 2013-03-28 0.0131
## 4 2013-04-30 0.0479
## 5 2013-05-31 0.0716
## 6 2013-06-28 -0.0432
## 7 2013-07-31 0.0710
## 8 2013-08-30 0.00322
## 9 2013-09-30 0.0188
## 10 2013-10-31 0.0495
## # ℹ 134 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.01376893# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.054298576 Simulation function
No need
7 Running multiple simulations
# Create a vector of its as a starting point
sims <- 51
starts <- rep(1, sims) %>%
set_names(paste0("sims", 1:sims))
starts## sims1 sims2 sims3 sims4 sims5 sims6 sims7 sims8 sims9 sims10 sims11
## 1 1 1 1 1 1 1 1 1 1 1
## sims12 sims13 sims14 sims15 sims16 sims17 sims18 sims19 sims20 sims21 sims22
## 1 1 1 1 1 1 1 1 1 1 1
## sims23 sims24 sims25 sims26 sims27 sims28 sims29 sims30 sims31 sims32 sims33
## 1 1 1 1 1 1 1 1 1 1 1
## sims34 sims35 sims36 sims37 sims38 sims39 sims40 sims41 sims42 sims43 sims44
## 1 1 1 1 1 1 1 1 1 1 1
## sims45 sims46 sims47 sims48 sims49 sims50 sims51
## 1 1 1 1 1 1 1# Simulate
# for reproducable research
set.seed(1234)
monte_carlo_sims_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()) %>%
# Rearrand column names
set_names(c("month", names(starts))) %>%
# Transform to long form
pivot_longer(cols = -month, names_to = "sim", values_to = "growth")
monte_carlo_sims_51## # A tibble: 12,291 × 3
## month sim growth
## <int> <chr> <dbl>
## 1 1 sims1 1
## 2 1 sims2 1
## 3 1 sims3 1
## 4 1 sims4 1
## 5 1 sims5 1
## 6 1 sims6 1
## 7 1 sims7 1
## 8 1 sims8 1
## 9 1 sims9 1
## 10 1 sims10 1
## # ℹ 12,281 more rows# Find quantiles
monte_carlo_sims_51 %>%
group_by(sim) %>%
summarise(growth = last(growth)) %>%
ungroup() %>%
pull(growth) %>%
quantile(probs = c(0, 0.25, 0.5, 0.75, 1)) %>%
round(2)## 0% 25% 50% 75% 100%
## 3.31 13.53 23.95 39.74 84.008 Visualizing simulations with ggplot
Line Plot of Simulations with Max, Median, and Min
# Step 1 Summarize data into max, median, and min of last value
sim_summary <- monte_carlo_sims_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 84.0 24.0 3.31# Step 2 Plot
monte_carlo_sims_51 %>%
# Fitler 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, color = 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 $1 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 simulation, a 100 investment could grow to about 22.5 in 20 years in the median case, up to 64 in the best case, or stay at 100 in the worst case. However, this assumes consistent growth and doesn’t account for inflation, taxes, fees, or unexpected market changes, which can affect real outcomes.