Week 15: Code along 13
CHAPTER 11 Monte Carlo Simulation
Luke Moriarty
2025-11-24
# Load packages
# Core
library(tidyverse)
library(tidyquant)
library(ggplot2)
# 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$returns)
mean_port_return## [1] 0.005899132# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.02347492# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns## [1] 0.0045107597 0.0095875976 -0.0289604955 0.0128028467 -0.0192702940
## [6] -0.0178220963 0.0003519739 0.0120731503 -0.0130037207 0.0060951938
## [11] 0.0105693815 0.0246869873 -0.0049102783 0.0197181781 0.0379871598
## [16] 0.0097958453 -0.0194296829 0.0006562803 0.0067162878 0.0290938313
## [21] 0.0367915081 0.0276192889 -0.0090368697 0.0318874732 -0.0181927348
## [26] 0.0003967506 0.0059637212 0.0316263449 0.0310266533 -0.0176656172
## [31] 0.0148437540 0.0242409069 0.0134512803 0.0060300657 0.0255242834
## [36] 0.0128760561 0.0019010698 -0.0261672588 -0.0219404402 0.0024521759
## [41] 0.0011915086 0.0033500809 0.0204143060 0.0101685043 -0.0130923081
## [46] -0.0197438712 0.0252856155 0.0187025137 0.0034812074 0.0200191423
## [51] -0.0138099719 -0.0053415491 0.0558541777 0.0036122436 0.0186215543
## [56] -0.0102349677 0.0166884519 0.0147180018 0.0245199534 -0.0039138914
## [61] 0.0467063772 -0.0152115349 -0.0021307711 0.0062036832 -0.0087688654
## [66] 0.0008705858 0.0119578373 -0.0486632928 0.0405408120 0.0181493505
## [71] -0.0182507057 0.0111146440 -0.0103476826 0.0079610333 -0.0114744973
## [76] 0.0147506191 0.0002615794 0.0290533178 -0.0092102416 0.0335553075
## [81] 0.0163420179 0.0106119412 0.0373812788 -0.0164629412 0.0248325940
## [86] -0.0198303456 0.0213915650 0.0040023676 0.0073461404 -0.0373794050
## [91] 0.0360267281 0.0002631445 -0.0210143835 0.0068224435 -0.0165210390
## [96] 0.0273629058 -0.0167523742 0.0257117677 0.0133780302 0.0750447618
## [101] 0.0239240410 -0.0073496849 0.0349733892 0.0191041360 -0.0157542243
## [106] -0.0212270318 -0.0072949931 0.0126314280 0.0040696209 -0.0299581201
## [111] -0.0375158138 -0.0037136514 -0.0263616905 0.0213153729 0.0205766653
## [116] 0.0136851394 0.0170761372 0.0228103852 0.0021374182 -0.0302568036# 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 1.00
## 3 1.01
## 4 0.971
## 5 1.01
## 6 0.981
## 7 0.982
## 8 1.00
## 9 1.01
## 10 0.987
## # 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 1.00
## 3 1.01
## 4 0.985
## 5 0.997
## 6 0.978
## 7 0.961
## 8 0.961
## 9 0.973
## 10 0.960
## # ℹ 111 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] 7.1032036 Simulation function
simulate_accumulation <- function(init_value, N, mean, stdev) {
tibble(returns = c(init_value, 1 + rnorm(N, mean, stdev))) %>%
mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
select(growth)
}
simulate_accumulation(1, 120, mean_port_return, stddev_port_return)## # A tibble: 121 × 1
## growth
## <dbl>
## 1 1
## 2 1.04
## 3 1.02
## 4 1.04
## 5 1.06
## 6 1.04
## 7 1.05
## 8 1.04
## 9 1.06
## 10 1.05
## # ℹ 111 more rows# Save the function
dump(list = c("simulate_accumulation"), file = "../00_scripts/simulate_accumulation.R")7 Running multiple simulations
# Create a vector of 1s as a starting point
sims <- 51
starts <- rep(1, sims) %>%
set_names(paste("sim", 1:sims, sep = ""))
starts## sim1 sim2 sim3 sim4 sim5 sim6 sim7 sim8 sim9 sim10 sim11 sim12 sim13
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## sim14 sim15 sim16 sim17 sim18 sim19 sim20 sim21 sim22 sim23 sim24 sim25 sim26
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## sim27 sim28 sim29 sim30 sim31 sim32 sim33 sim34 sim35 sim36 sim37 sim38 sim39
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## sim40 sim41 sim42 sim43 sim44 sim45 sim46 sim47 sim48 sim49 sim50 sim51
## 1 1 1 1 1 1 1 1 1 1 1 1# Simulate
monte_carlo_sim_51 <- starts %>%
# Simulate
map_dfc(simulate_accumulation,
N = 120,
mean = mean_port_return,
stdev = stddev_port_return) %>%
# Add the column, month
mutate(month = seq(1:nrow(.))) %>%
# Arrange column names
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 1 sim1 1
## 2 1 sim2 1
## 3 1 sim3 1
## 4 1 sim4 1
## 5 1 sim5 1
## 6 1 sim6 1
## 7 1 sim7 1
## 8 1 sim8 1
## 9 1 sim9 1
## 10 1 sim10 1
## # ℹ 6,161 more rows# Calculate the quantiles for simulated values
probs <- c(.005, .025, .25, .5, .75, .975, .995)
monte_carlo_sim_51 %>%
group_by(sim) %>%
summarise(growth = last(growth)) %>%
ungroup() %>%
pull(growth) %>%
# Find the quantiles
quantile(probs = probs) %>%
round(2)## 0.5% 2.5% 25% 50% 75% 97.5% 99.5%
## 1.13 1.19 1.61 1.86 2.31 3.30 3.618 Visualizing simulations with ggplot
monte_carlo_sim_51 %>%
ggplot(aes(x = month, y = growth, col = sim)) +
geom_line() +
theme(legend.position = "none")
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 3.71 1.86 1.12monte_carlo_sim_51 %>%
group_by(sim) %>%
filter(last(growth) == sim_summary$max |
last(growth) == sim_summary$median |
last(growth) == sim_summary$min) %>%
ggplot(aes(month, growth, col = sim)) +
geom_line() +
theme()