Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Vincent Fosser
2025-06-26
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# Source function
source("../00_scripts/simulate_accumulation.R")1 Import stock prices
symbols <- c("Asker.st", "Atco-B.st", "Axfo.st", "Bahn-b.st", "BRK-B", "Cers", "LLY", "Embrac-b.st", "Indu-c.st", "Inve-b.st", "Inwi.st", "Novo-b.co", "NVDA", "Yubico.st")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2025-06-01")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
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols## [1] "Asker.st" "Atco-B.st" "Axfo.st" "BRK-B" "Bahn-b.st"
## [6] "Cers" "Embrac-b.st" "Indu-c.st" "Inve-b.st" "Inwi.st"
## [11] "LLY" "NVDA" "Novo-b.co" "Yubico.st"# weights
weights <- c(0.0314, 0.0133, 0.0136, 0.0589, 0.0112, 0.0068, 0.0201, 0.1858, 0.2298, 0.0584, 0.0892, 0.2504, 0.0168, 0.0143)
weights## [1] 0.0314 0.0133 0.0136 0.0589 0.0112 0.0068 0.0201 0.1858 0.2298 0.0584
## [11] 0.0892 0.2504 0.0168 0.0143w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 14 × 2
## symbols weights
## <chr> <dbl>
## 1 Asker.st 0.0314
## 2 Atco-B.st 0.0133
## 3 Axfo.st 0.0136
## 4 BRK-B 0.0589
## 5 Bahn-b.st 0.0112
## 6 Cers 0.0068
## 7 Embrac-b.st 0.0201
## 8 Indu-c.st 0.186
## 9 Inve-b.st 0.230
## 10 Inwi.st 0.0584
## 11 LLY 0.0892
## 12 NVDA 0.250
## 13 Novo-b.co 0.0168
## 14 Yubico.st 0.01434 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: 166 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 0.00846
## 2 2013-02-28 0.0317
## 3 2013-03-27 -0.00876
## 4 2013-03-28 0.0163
## 5 2013-04-30 0.0328
## 6 2013-05-31 -0.0205
## 7 2013-06-28 -0.0415
## 8 2013-07-31 0.0550
## 9 2013-08-30 -0.00525
## 10 2013-09-30 0.0128
## # ℹ 156 more rowssymbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
length(symbols)## [1] 145 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.01178762# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.037335446 Simulation function
No need
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 a 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")
monte_carlo_sim_51## # A tibble: 12,291 × 3
## month sim growth
## <int> <chr> <dbl>
## 1 1 sim1 100
## 2 1 sim2 100
## 3 1 sim3 100
## 4 1 sim4 100
## 5 1 sim5 100
## 6 1 sim6 100
## 7 1 sim7 100
## 8 1 sim8 100
## 9 1 sim9 100
## 10 1 sim10 100
## # ℹ 12,281 more rows# Find quantiles
monte_carlo_sim_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%
## 427.67 1124.18 1638.45 2357.37 3964.318 Visualizing simulations with ggplot
Line Plot of Simulations with Max, Median, and Min
# Step 1 Summarize data into max, median, 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 3964. 1638. 428.# Step 2 Plot
monte_carlo_sim_51 %>%
# Filter for max, median, 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 $100 over 240 months",
subtitle = "Max, Median, 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?
Looking at my portfolio the best case scenario would be a growth of around 40x close to $4000 after 20 years. The worst case scenario is a growth of around 5x and the mean is around 14x my initial investment after 20 years. There are some limitations however the code suggests the range if the conditions stay stable. However, it doesnt account for macroeconomic situations. It also assumes a constant mean and standard deviation which in the real market will change. Furthermore it does not account for factors like inflation. Therefore, the scenario is a bit optimistic but nevertheless a well made investment if it falls just short of the mean.