Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Nils Skogestig
2025-11-28
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# Source function
source("../00_scripts/simulate_accumulation.R")1 Import stock prices
Revise the code below.
- Replace symbols with your stocks.
- Replace the from and the to arguments to date from 2012-12-31 to present.
symbols <- c("TSLA", "META", "XOM", "AAPL", "PG", "AMZN")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31")2 Convert prices to returns
asset_returns_tbl <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("asset", "date", "returns"))3 Assign a weight to each asset
Revise the code for weights.
- The vector weights should have a length equal to the number of assets in the portfolio.
- The values in the vector weights should sum to 1.
# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols## [1] "AAPL" "AMZN" "META" "PG" "TSLA" "XOM"# weights
weights <- c(0.2, 0.2, 0.2, 0.15, 0.15, 0.1)
weights## [1] 0.20 0.20 0.20 0.15 0.15 0.10w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 6 × 2
## symbols weights
## <chr> <dbl>
## 1 AAPL 0.2
## 2 AMZN 0.2
## 3 META 0.2
## 4 PG 0.15
## 5 TSLA 0.15
## 6 XOM 0.14 Build a portfolio
portfolio_returns_tbl <- asset_returns_tbl %>%
tq_portfolio(assets_col = asset,
returns_col = returns,
weights = w_tbl,
rebalance_on = "months",
col_rename = "returns")
portfolio_returns_tbl## # A tibble: 155 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 0.0462
## 2 2013-02-28 -0.0406
## 3 2013-03-28 0.00457
## 4 2013-04-30 0.0591
## 5 2013-05-31 0.0813
## 6 2013-06-28 -0.000296
## 7 2013-07-31 0.166
## 8 2013-08-30 0.0485
## 9 2013-09-30 0.0706
## 10 2013-10-31 0.0354
## # ℹ 145 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.01822719# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.059335176 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_carle_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_carle_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%
## 763.84 3533.43 6632.16 11403.01 25748.018 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_carle_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 25748. 6632. 764.# Step 2 Plot
monte_carle_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 = "Maximum, Median, and Mimimum Simulation")
Based on the Monte Carlo simulation results, how much should you expect from your $100 investment after 20 years?
Based on the Monte Carlo simulation results, after 20 years (240 months), on average, I can expect my initial $100 investment to grow to $6632 (median).
What is the best-case scenario?
The best-case scenario is that my initial $100 investment grows to $25,748 in 20 years. On the other hand, the worst-case scenario is that my initial $100 investment only grows to $764 in 20 years.
What is the worst-case scenario? What are limitations of this simulation analysis?
Some examples are:
Simplified assumptions: The simulation uses fixed assumptions such as constant average returns and standard deviations. In reality, markets fluctuate unpredictably and do not behave in a consistent manner.
Dependence on historical data: The model relies on past market performance, which may not accurately reflect future conditions. Future markets can behave very differently from what historical data suggests.
Assuming normally distributed returns: As noted in the Apply 13 Video, the simulation assumes returns follow a normal distribution. In reality, returns are often negatively skewed and not truly normal, which can make the simulation results appear more optimistic than they should be.