Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Kate Dawson
2025-06-26
# Load packages
# Core
library(tidyverse)
library(tidyquant)
simulate_accumulation <- function(initial_value, N, mean_return, sd_return) {
simulated_returns_add_1 <- tibble(returns = c(initial_value, 1 + rnorm(N, mean_return, sd_return)))
simulated_growth <- simulated_returns_add_1 %>%
mutate(growth = accumulate(returns, function(x, y) x * y)) %>%
select(growth)
return(simulated_growth)
}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("SPY", "EFA", "IJS", "EEM", "AGG")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2017-12-31")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] "AGG" "EEM" "EFA" "IJS" "SPY"# weights
weights <- c(0.25, 0.25, 0.2, 0.2, 0.1)
weights## [1] 0.25 0.25 0.20 0.20 0.10w_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 0.14 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: 60 × 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 50 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.005899138# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.023474916 Simulation function
No need
7 Running multiple simulations
# Create a vector of 1s as starting point
sims <- 100
starts <- rep (100, sims) %>%
set_names(paste0("sim", 1:sims))
starts## sim1 sim2 sim3 sim4 sim5 sim6 sim7 sim8 sim9 sim10 sim11
## 100 100 100 100 100 100 100 100 100 100 100
## sim12 sim13 sim14 sim15 sim16 sim17 sim18 sim19 sim20 sim21 sim22
## 100 100 100 100 100 100 100 100 100 100 100
## sim23 sim24 sim25 sim26 sim27 sim28 sim29 sim30 sim31 sim32 sim33
## 100 100 100 100 100 100 100 100 100 100 100
## sim34 sim35 sim36 sim37 sim38 sim39 sim40 sim41 sim42 sim43 sim44
## 100 100 100 100 100 100 100 100 100 100 100
## sim45 sim46 sim47 sim48 sim49 sim50 sim51 sim52 sim53 sim54 sim55
## 100 100 100 100 100 100 100 100 100 100 100
## sim56 sim57 sim58 sim59 sim60 sim61 sim62 sim63 sim64 sim65 sim66
## 100 100 100 100 100 100 100 100 100 100 100
## sim67 sim68 sim69 sim70 sim71 sim72 sim73 sim74 sim75 sim76 sim77
## 100 100 100 100 100 100 100 100 100 100 100
## sim78 sim79 sim80 sim81 sim82 sim83 sim84 sim85 sim86 sim87 sim88
## 100 100 100 100 100 100 100 100 100 100 100
## sim89 sim90 sim91 sim92 sim93 sim94 sim95 sim96 sim97 sim98 sim99
## 100 100 100 100 100 100 100 100 100 100 100
## sim100
## 100# Simulate
# for reproducible research
set.seed (800)
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")
monte_carlo_sim_51## # A tibble: 24,100 × 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 24,090 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%
## 139.14 305.22 387.88 470.84 883.98
## 8 Visualizing simulations with ggplot
Line Plot of Simulations with Max, Median, and Min
``` r
monte_carlo_sim_51 %>%
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 = "Simulations 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? The best case scenario is around $600 or more while the worst case scenario is $100 or less which means our investment didn’t grow or actually costed you money. Limitations include a flat or standard distribution which does not mimic the real world’s risk and extremes.