Week 15: Code along 13
CHAPTER 11 Monte Carlo Simulation
Blake Yaffe
2024-12-11
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# time series
library(timetk)Goal
Simulate future portfolio returns
five stocks: “H”, “HSY”, “BA”, “VOO”, “NOK”
market: “SPY”
from 2012-12-31 to 2017-12-31
1 Import stock prices
symbols <- c("H", "HSY", "BA", "VOO", "NOK")
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] "BA" "H" "HSY" "NOK" "VOO"# 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 BA 0.25
## 2 H 0.25
## 3 HSY 0.2
## 4 NOK 0.2
## 5 VOO 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 0.0271
## 2 2013-02-28 0.0156
## 3 2013-03-28 0.0322
## 4 2013-04-30 0.0243
## 5 2013-05-31 0.0186
## 6 2013-06-28 0.0194
## 7 2013-07-31 0.0627
## 8 2013-08-30 -0.0225
## 9 2013-09-30 0.135
## 10 2013-10-31 0.102
## # ℹ 50 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.01312608# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.04192974# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns## [1] 7.074638e-02 3.297269e-03 7.811615e-04 2.730747e-02 4.657063e-02
## [6] 1.890332e-02 5.597453e-02 1.471058e-02 3.642172e-02 1.328472e-02
## [11] 3.651838e-02 6.388728e-02 9.031919e-03 5.070650e-03 5.383331e-02
## [16] -2.095412e-02 4.069149e-02 -1.974060e-02 1.168195e-01 -4.038401e-03
## [21] 1.481093e-02 1.908298e-02 5.452683e-03 -3.241596e-02 9.113829e-02
## [26] -2.984087e-02 4.637183e-02 5.026511e-03 6.505834e-02 1.709190e-02
## [31] 3.385905e-02 1.270700e-02 1.081171e-01 -4.016468e-02 2.412336e-03
## [36] -6.285052e-03 -6.437963e-02 3.092472e-02 -1.528128e-02 -8.963307e-03
## [41] 1.023129e-02 2.474717e-02 4.484248e-02 1.021223e-02 -3.564569e-02
## [46] 7.331054e-03 9.127615e-02 -3.032752e-02 3.591440e-02 -4.773872e-02
## [51] -1.311524e-02 -1.432753e-02 -1.920704e-02 -5.690446e-04 2.121009e-02
## [56] -4.673492e-03 8.426544e-03 -2.078351e-03 2.007348e-02 -3.785221e-02
## [61] 3.737638e-02 8.319336e-02 -8.854377e-02 2.864153e-02 9.887279e-03
## [66] 2.963828e-02 -2.655769e-02 5.515056e-02 -4.737180e-02 7.906510e-02
## [71] 6.232074e-02 5.647098e-02 -2.248299e-02 -1.439585e-02 -1.362032e-02
## [76] 8.230458e-02 -3.757097e-02 2.790524e-03 9.010735e-03 3.771651e-02
## [81] 1.570638e-02 -1.615329e-02 9.871931e-03 5.572946e-02 -2.275591e-02
## [86] 6.307607e-02 4.416988e-02 -5.653075e-03 1.124694e-02 2.302786e-02
## [91] 7.227912e-02 -2.992037e-03 4.147932e-02 3.324428e-02 -1.055987e-02
## [96] 1.954491e-02 1.768240e-02 3.748171e-02 1.975993e-02 -3.067806e-02
## [101] 4.288208e-02 1.342182e-01 -2.645289e-02 -5.166455e-04 2.245118e-02
## [106] 4.941206e-02 6.918669e-02 -8.790901e-03 3.790290e-02 3.439103e-02
## [111] 3.488814e-02 4.089509e-02 1.721101e-02 1.666256e-02 3.752796e-02
## [116] 1.681934e-02 8.644923e-05 -7.623978e-04 2.299787e-02 -9.092053e-02# 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 1.07
## 3 1.00
## 4 1.00
## 5 1.03
## 6 1.05
## 7 1.02
## 8 1.06
## 9 1.01
## 10 1.04
## # 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 1.07
## 3 1.07
## 4 1.08
## 5 1.10
## 6 1.16
## 7 1.18
## 8 1.24
## 9 1.26
## 10 1.31
## # ℹ 111 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] 21.39826 Simulation function
simulate_accumulation <- function(initial_value, N, mean_return, sd_return) {
# Add a dollar
simulated_returns_add_1 <- tibble(returns = c(initial_value, 1 + rnorm(N, mean_return, sd_return)))
# Calculate the cumulative growth of a dollar
simulated_growth <- simulated_returns_add_1 %>%
mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
select(growth)
return(simulated_growth)
}
simulate_accumulation(initial_value = 100, N = 240, mean_return = 0.005, sd_return = 0.01) %>%
tail()## # A tibble: 6 × 1
## growth
## <dbl>
## 1 371.
## 2 371.
## 3 379.
## 4 375.
## 5 374.
## 6 374.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(paste0("sim", 1:sims))
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
#For Reproducible Research
set.seed(1234)
monte_carlo_sim_51 <- starts %>%
# Simulate
map_dfc(.x = .,
.f = ~simulate_accumulation(initial_value = .x,
N = 120,
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: 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# 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%
## 1.72 2.98 4.43 6.15 14.568 Visualizing simulations with ggplot
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)) +
labs(title = "simulating growth of $1 over 120 months")
Line plot with max, median, and min
# Step 1 summarize data into max, median, and min of last value
sim_summary <- monte_carlo_sim_51 %>%
group_by(sim) %>%
summarise(growth = last(growth)) %>%
ungroup() %>%
summarise(max = max(growth),median = median(growth), min = min(growth))
sim_summary## # A tibble: 1 × 3
## max median min
## <dbl> <dbl> <dbl>
## 1 14.6 4.43 1.72#Step 2 plot
monte_carlo_sim_51 %>%
# Filter for max,median, and min sim
group_by(sim) %>%
filter(last(growth) == sim_summary$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 growht of $1 over 120 months",
subtitle = "Maximum, Median, and Minimum Simulation")