Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Ethan Daly
2022-09-19
# Load packages
# Core
library(tidyverse)
library(tidyquant)
library(timetk)
# Source function
source("../00_scripts/simulateaccumulation.R")1 Import stock prices
Revise the code below.
- Replace symbols with your stocks.
- Replace the from and the to arguments to date from 2012-12-31 to present.
symbols <- c("WM", "TSLA", "BIG", "PLUG", "AMZN")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2022-12-8")2 Convert prices to returns
asset_returns_tbl <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("symbols", "date", "returns"))3 Assign a weight to each asset
Revise the code for weights.
- The vector weights should have a length equal to the number of assets in the portfolio.
- The values in the vector weights should sum to 1.
# symbols
symbols <- asset_returns_tbl %>% distinct(symbols) %>% pull()
symbols## [1] "AMZN" "BIG" "PLUG" "TSLA" "WM"# weights
weights <- c(0.2, 0.2, 0.2, 0.2, 0.2)
weights## [1] 0.2 0.2 0.2 0.2 0.2w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 5 × 2
## symbols weights
## <chr> <dbl>
## 1 AMZN 0.2
## 2 BIG 0.2
## 3 PLUG 0.2
## 4 TSLA 0.2
## 5 WM 0.24 Build a portfolio
portfolio_returns_tbl <- asset_returns_tbl %>%
tq_portfolio(assets_col = symbols,
returns_col = returns,
weights = w_tbl,
rebalance_on = "months",
col_rename = "returns")
portfolio_returns_tbl## # A tibble: 120 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 0.0501
## 2 2013-02-28 -0.198
## 3 2013-03-28 0.0934
## 4 2013-04-30 0.0126
## 5 2013-05-31 0.295
## 6 2013-06-28 0.00354
## 7 2013-07-31 0.126
## 8 2013-08-30 0.0576
## 9 2013-09-30 0.130
## 10 2013-10-31 -0.0494
## # … with 110 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.01859362# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.092969446 Simulation function
No need
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
## # … with 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%
## 0.72 2.43 5.94 12.20 84.386 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>
## 1 325.
## 2 326.
## 3 320.
## 4 312.
## 5 315.
## 6 314.## 8 Visualizing simulations with ggplotLine Plot of Simulations with Max, Median, and Min
# Step 1 Summarize data into maximum, median, and minimum 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 84.4 5.94 0.724# 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 growth of $1 over 120 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? Around 7% can be expexted the best case would be
roughlt 90% and the worst would be around 1% growth.