Week 15: Code along 13
CHAPTER 11 Monte Carlo Simulation
Will Petro
2025-06-26
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# time series
library(timetk)Goal
Simulate future portfolio returns
five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG”
market: “SPY”
from 2012-12-31 to 2017-12-31
1 Import stock prices
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
# 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
# ?tq_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$returns)
mean_port_return## [1] 0.005899128# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.0234749# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns## [1] -0.0119289787 0.0248803101 0.0070925250 0.0017355149 -0.0125435115
## [6] 0.0097962814 0.0272328902 -0.0065500616 0.0081258324 0.0034690051
## [11] 0.0363668895 -0.0121488815 -0.0043616891 0.0528124988 0.0229473138
## [16] -0.0219244543 -0.0044566840 0.0367613869 0.0293236944 0.0330488814
## [21] 0.0289866375 0.0159577548 -0.0267733637 -0.0157568184 -0.0153873565
## [26] -0.0122445831 0.0045198259 0.0277468654 0.0221593556 -0.0264126459
## [31] 0.0090764208 -0.0368587595 -0.0192030192 -0.0041077605 -0.0110927750
## [36] 0.0171907839 -0.0176138880 -0.0195730479 0.0241806807 0.0196732687
## [41] 0.0271270442 0.0066637072 0.0053440406 -0.0269443715 0.0146610968
## [46] -0.0153156752 0.0014188435 0.0252321245 0.0174909375 0.0446893781
## [51] -0.0111376122 -0.0002239654 0.0116347166 -0.0136996474 0.0260365414
## [56] -0.0122949742 0.0204862768 -0.0152470324 0.0255498530 0.0051998637
## [61] 0.0199839081 0.0083605073 0.0084261088 0.0115632641 -0.0003362293
## [66] 0.0120567324 0.0460377010 0.0099702684 -0.0368276218 0.0334887896
## [71] 0.0076180524 0.0288262224 0.0134662988 -0.0072901387 0.0263591006
## [76] 0.0420067172 0.0052278989 0.0079640677 -0.0099611313 -0.0007714796
## [81] -0.0228736753 0.0055703372 -0.0188962221 0.0037827325 -0.0533166953
## [86] -0.0291540848 -0.0088558398 -0.0144620685 0.0354928827 0.0077410524
## [91] 0.0021734339 0.0088045618 0.0116885338 -0.0028757396 0.0254778410
## [96] 0.0278855930 0.0126268896 0.0145409837 0.0064902481 0.0265212576
## [101] -0.0240621862 -0.0146681901 0.0327159445 0.0009665242 -0.0038937955
## [106] 0.0504854836 -0.0503848495 0.0600292627 -0.0344236003 0.0050661209
## [111] -0.0096488363 0.0243022706 0.0359048236 0.0018120438 -0.0221499335
## [116] 0.0233547598 -0.0117029380 0.0100652561 -0.0209325572 -0.0171418243# Add a dollar
simulated_returns_add_1 <- tibble(returns = c(1, 1 + simulated_monthly_returns))
simulated_returns_add_1## # A tibble: 121 × 1
## returns
## <dbl>
## 1 1
## 2 0.988
## 3 1.02
## 4 1.01
## 5 1.00
## 6 0.987
## 7 1.01
## 8 1.03
## 9 0.993
## 10 1.01
## # ℹ 111 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: 121 × 1
## growth
## <dbl>
## 1 1
## 2 0.988
## 3 1.01
## 4 1.02
## 5 1.02
## 6 1.01
## 7 1.02
## 8 1.05
## 9 1.04
## 10 1.05
## # ℹ 111 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] 6.0888436 Simulation function
simulate_accumulation <- function(initial_value, n = 120, 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)
}
dump(list = c("simulation_accumulation"), file = "../00_scripts/simulate_accumulation.R")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 = 0:120) %>%
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: 6,171 × 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 6,161 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 $1 Growth Over 120 Months") +
theme(plot.title = element_text(hjust = 0.5))
9 Max, Median, Min Plot
sim_summary <- monte_carlo_sim_51 %>%
group_by(sim) %>%
summarize(growth = last(growth)) %>%
ungroup()
extremes <- monte_carlo_sim_51 %>%
group_by(sim) %>%
filter(last(growth) %in% c(max(sim_summary$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 120 Months",
subtitle = "Max, Median, and Min Simulations") +
theme(plot.title = element_text(hjust = 0.5),
plot.subtitle = element_text(hjust = 0.5))
10 Summary Quantiles
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%
## 1.17 1.59 1.98 2.40 3.88