Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Will Petro
2025-06-26
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# Source function
# source("../00_scripts/simulate_accumulation.R")1 Import stock prices
Revise the code below.
- Replace symbols with your stocks.
- Replace the from and the to arguments to date from 2012-12-31 to present.
symbols <- c("UAL", "LUV", "DAL", "AAL")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31")2 Convert prices to returns
asset_returns_tbl <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("asset", "date", "returns"))3 Assign a weight to each asset
Revise the code for weights.
- The vector weights should have a length equal to the number of assets in the portfolio.
- The values in the vector weights should sum to 1.
# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols## [1] "AAL" "DAL" "LUV" "UAL"# weights
weights <- c(0.4, 0.3, 0.2, 0.1)
weights## [1] 0.4 0.3 0.2 0.1w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 4 × 2
## symbols weights
## <chr> <dbl>
## 1 AAL 0.4
## 2 DAL 0.3
## 3 LUV 0.2
## 4 UAL 0.14 Build a portfolio
portfolio_returns_tbl <- asset_returns_tbl %>%
tq_portfolio(assets_col = asset,
returns_col = returns,
weights = w_tbl,
rebalance_on = "months",
col_rename = "returns")
portfolio_returns_tbl## # A tibble: 150 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 0.0910
## 2 2013-02-28 0.00218
## 3 2013-03-28 0.184
## 4 2013-04-30 0.0137
## 5 2013-05-31 0.0376
## 6 2013-06-28 -0.0377
## 7 2013-07-31 0.128
## 8 2013-08-30 -0.128
## 9 2013-09-30 0.151
## 10 2013-10-31 0.136
## # ℹ 140 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.00516951# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.103914# Construct a normal distribution
simulated_monthly_returns <- rnorm(240, mean_port_return, stddev_port_return)
simulated_monthly_returns## [1] -0.0645389063 -0.1204551172 0.0118087008 0.0218728654 0.2348337993
## [6] -0.1116935645 -0.1301102373 -0.1335867589 0.0651687604 0.1369131307
## [11] 0.0126115755 -0.0423985951 -0.0583294679 0.0609237111 0.0967588417
## [16] 0.1202649307 0.0600305591 -0.2519171845 0.1668204649 0.0523589414
## [21] -0.1182400524 -0.0322181915 -0.0344530390 -0.2818467292 -0.0447543857
## [26] 0.1419295611 -0.0575303248 -0.0346783514 0.0129618771 -0.0546539843
## [31] -0.0042800064 0.0695415751 -0.1800634385 0.0916422270 0.1572451601
## [36] 0.1516561922 0.0843807679 0.1515496005 0.0042901754 0.0792726999
## [41] 0.0885973730 -0.0197342968 -0.0971212650 -0.0754243628 0.0854720739
## [46] 0.0034563040 0.0459504255 -0.0234847679 0.1527849786 0.0692410199
## [51] -0.0713946413 -0.0778078865 0.1630212582 0.0475355795 0.0265904273
## [56] -0.0793946601 0.0420936815 -0.0301924332 -0.0728314396 0.0260782373
## [61] -0.0427799139 -0.0713992067 -0.0338401316 0.0752777385 -0.0795071739
## [66] 0.0297612524 0.1088983381 0.1124001062 0.0556158585 0.0404075736
## [71] -0.0441250279 0.0638440112 0.1104491731 0.0589298584 -0.0869511131
## [76] -0.1954588724 -0.0054973131 -0.0506316323 -0.0504222913 0.1427201505
## [81] -0.1334196971 -0.1551462208 -0.1044697743 0.1467234454 0.0852206643
## [86] -0.0376403705 0.1557107044 -0.0733117094 0.1839668169 -0.0377154525
## [91] -0.1186814145 -0.0257692090 -0.0485089721 0.0823226659 -0.0813087012
## [96] -0.0218203641 0.0685167243 0.0516171259 0.1565290948 -0.0480559838
## [101] 0.0235723389 0.1083372624 -0.0779521674 0.0926631236 0.1401468375
## [106] -0.0643749828 0.2453351774 0.1387554080 0.0789184472 0.0685145718
## [111] 0.0526574618 0.1469114164 0.1070500744 -0.0056847404 -0.0477757891
## [116] -0.0263835395 -0.1445118798 0.0086363850 -0.0611387932 -0.1033371008
## [121] 0.0002226198 0.1834776995 0.2070400256 -0.0202635010 -0.1084336721
## [126] -0.0422081174 0.0348200730 -0.0811491338 0.0311614022 0.3301899698
## [131] -0.2707473505 0.1720928250 -0.0137443432 0.0182843260 -0.0218645379
## [136] 0.1263369639 0.1029327868 0.2348577661 -0.1304875798 -0.0171059679
## [141] 0.1106440231 0.0194295869 0.0633577072 -0.0095884502 -0.1381132062
## [146] -0.0666907778 0.2220334889 0.1256533182 0.0261061012 -0.0696255127
## [151] 0.0040457630 0.0008981494 -0.1305507850 -0.1437196150 -0.0146577928
## [156] -0.1032793568 0.0020191621 -0.1726372644 0.0004726234 -0.1580498604
## [161] 0.0776113664 0.0703885001 0.1059917049 -0.1110379920 -0.0380755636
## [166] -0.0535149023 0.0217367451 0.1917589454 0.1900939868 0.0395872283
## [171] 0.1900666371 -0.1197023510 -0.1652089241 -0.0751328792 -0.0761689687
## [176] 0.0696480568 0.0270041934 -0.0239328291 0.0324719491 0.1416313358
## [181] -0.0817788146 -0.1636826698 -0.0271774974 -0.1083015714 0.0610953157
## [186] 0.0201331421 -0.0241752790 0.2792940208 -0.0465130601 0.0552936341
## [191] -0.0266695281 0.0631702350 0.0499792297 0.1358084738 0.0673945817
## [196] -0.1769297904 -0.0981526276 -0.0645784443 -0.0946074794 -0.0256588209
## [201] -0.0102259002 -0.1155005059 0.0518880405 -0.0827658401 0.0258512423
## [206] 0.0397308738 -0.2068173947 -0.1605522590 0.0683688910 -0.0016218167
## [211] 0.0814743482 -0.1042481854 0.0484414756 -0.0243207713 0.0308561997
## [216] 0.0904259824 -0.1569174276 0.0137943967 -0.0303163931 -0.0329601441
## [221] -0.0016799117 -0.1097780343 -0.0227719869 -0.1097450583 -0.0674261956
## [226] -0.0600158611 0.1096735191 0.1167355633 0.0242460951 -0.1253581272
## [231] -0.0019124132 -0.1273292896 0.0819287234 -0.0075337380 -0.0483479399
## [236] -0.0893686270 0.0676245069 -0.1932349297 0.0088250021 0.1433915393# Add a dollar
simulated_returns_add_1 <- tibble(returns = c(1, 1 + simulated_monthly_returns))
simulated_returns_add_1## # A tibble: 241 × 1
## returns
## <dbl>
## 1 1
## 2 0.935
## 3 0.880
## 4 1.01
## 5 1.02
## 6 1.23
## 7 0.888
## 8 0.870
## 9 0.866
## 10 1.07
## # ℹ 231 more rows# Calculate the cumulative growth of a dollar
simulated_growth <- simulated_returns_add_1 %>%
mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
select(growth)
simulated_growth## # A tibble: 241 × 1
## growth
## <dbl>
## 1 1
## 2 0.935
## 3 0.823
## 4 0.832
## 5 0.851
## 6 1.05
## 7 0.933
## 8 0.812
## 9 0.703
## 10 0.749
## # ℹ 231 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] -3.0332916 Simulation function
No need
simulate_accumulation <- function(initial_value, n = 240, mu = mean_port_return, sigma = stddev_port_return) {
tibble(returns = c(initial_value, 1 + rnorm(n, mu, sigma))) %>%
mutate(growth = accumulate(returns, function(x, y) x * y)) %>%
select(growth)
}7 Running multiple simulations
set.seed(1234)
sims <- 51
starts <- rep(1, sims) %>% set_names(paste0("sim", 1:sims))
monte_carlo_sim_51 <- map_dfc(.x = starts, .f = ~ simulate_accumulation(initial_value = .x)) %>%
mutate(month = 0:240) %>%
select(month, everything()) %>%
set_names(c("month", names(starts))) %>%
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 0 sim1 1
## 2 0 sim2 1
## 3 0 sim3 1
## 4 0 sim4 1
## 5 0 sim5 1
## 6 0 sim6 1
## 7 0 sim7 1
## 8 0 sim8 1
## 9 0 sim9 1
## 10 0 sim10 1
## # ℹ 12,281 more rows8 Visualizing simulations with ggplot
monte_carlo_sim_51 %>%
ggplot(aes(x = month, y = growth, color = sim)) +
geom_line(show.legend = FALSE) +
labs(title = "Simulations of $1 Growth Over 240 Months") +
theme(plot.title = element_text(hjust = 0.5))
10 Line Plot of Simulations with Max, Median, and Min
sim_summary <- monte_carlo_sim_51 %>%
group_by(sim) %>%
summarize(growth = last(growth)) %>%
ungroup()
extremes <- monte_carlo_sim_51 %>%
group_by(sim) %>%
filter(last(growth) %in% c(max(sim_summary$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 $1 Growth Over 240 Months",
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%
## 0.03 0.49 1.58 3.90 16.56Based 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 off of the simulation, I can expect my best-case scenario growth to be at around 16.56, with my worst-case scenario sitting at 0.03. The limitation of running a simulation analysis is the lack of accounting for major events that could impact these investments. Analyzing historical data to make future inferences is an educated guess at best, rather than a direct play-out.