Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Job Boonstoppel
2023-06-23
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# Source function
source("../00_scripts/simulate_accumulation.R")1 Import stock prices
Revise the code below.
- Replace symbols with your stocks.
- Replace the from and the to arguments to date from 2012-12-31 to present.
symbols <- c("TSLA", "META", "XOM", "AAPL", "PG", "AMZN")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31")2 Convert prices to returns
asset_returns_tbl <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("asset", "date", "returns"))3 Assign a weight to each asset
Revise the code for weights.
- The vector weights should have a length equal to the number of assets in the portfolio.
- The values in the vector weights should sum to 1.
# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols## [1] "AAPL" "AMZN" "META" "PG" "TSLA" "XOM"# weights
weights <- c(0.2, 0.2, 0.2, 0.15, 0.15, 0.1)
weights## [1] 0.20 0.20 0.20 0.15 0.15 0.10w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 6 × 2
## symbols weights
## <chr> <dbl>
## 1 AAPL 0.2
## 2 AMZN 0.2
## 3 META 0.2
## 4 PG 0.15
## 5 TSLA 0.15
## 6 XOM 0.14 Build a portfolio
portfolio_returns_tbl <- asset_returns_tbl %>%
tq_portfolio(assets_col = asset,
returns_col = returns,
weights = w_tbl,
rebalance_on = "months",
col_rename = "returns")
portfolio_returns_tbl## # A tibble: 126 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 0.0462
## 2 2013-02-28 -0.0406
## 3 2013-03-28 0.00457
## 4 2013-04-30 0.0591
## 5 2013-05-31 0.0813
## 6 2013-06-28 -0.000296
## 7 2013-07-31 0.166
## 8 2013-08-30 0.0485
## 9 2013-09-30 0.0706
## 10 2013-10-31 0.0354
## # ℹ 116 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.01881709# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.062114036 Simulation function
No need
7 Running multiple simulations
# Create a vector of 1s as a starting point
sims <- 51
starts <- rep(100, sims) %>%
set_names(paste0("sim", 1:sims))
starts## sim1 sim2 sim3 sim4 sim5 sim6 sim7 sim8 sim9 sim10 sim11 sim12 sim13
## 100 100 100 100 100 100 100 100 100 100 100 100 100
## sim14 sim15 sim16 sim17 sim18 sim19 sim20 sim21 sim22 sim23 sim24 sim25 sim26
## 100 100 100 100 100 100 100 100 100 100 100 100 100
## sim27 sim28 sim29 sim30 sim31 sim32 sim33 sim34 sim35 sim36 sim37 sim38 sim39
## 100 100 100 100 100 100 100 100 100 100 100 100 100
## sim40 sim41 sim42 sim43 sim44 sim45 sim46 sim47 sim48 sim49 sim50 sim51
## 100 100 100 100 100 100 100 100 100 100 100 100# Simulate
# for reproducible research
set.seed(1234)
monte_carle_sim_51 <- starts %>%
# Simulate
map_dfc(.x = .,
.f = ~simulate_accumulation(initial_value = .x,
N = 240,
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")
# Find quantiles
monte_carle_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%
## 772.94 3840.97 7457.23 13077.46 30666.128 Visualizing simulations with ggplot
Line Plot of Simulations with Max, Median, and Min
# Step 1 Summarize data into max, median, and min of last value
sim_summary <- monte_carle_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 30666. 7457. 773.# Step 2 Plot
monte_carle_sim_51 %>%
# Filter for max, median, 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 $100 over 240 months",
subtitle = "Maximum, Median, and Mimimum Simulation")
Questions
Based on the Monte Carlo simulation results, how much should you expect from your $100 investment after 20 years?
Based on the Monte Carlo simulation results, after 20 years (240 months), on average, I can expect my initial $100 investment to grow to $7457 (median).
What is the best-case scenario? And what is the worst-case scenario?
The best-case scenario is that my initial $100 investment grows to $30,666 in 20 years. On the other hand, the worst-case scenario is that my initial $100 investment only grows to $773 in 20 years.
What are limitations of this simulation analysis?
Examples of limitations are:
Simplified assumptions as the simulation is based on certain assumptions and simplifications (constant mean return and standard deviation). In reality, market conditions can vary significantly.
The simulation relies on historical stock price data, which may not fully capture future market conditions as these are likely to be different than those we have seen before.
Then, as you mentioned in the Apply 13 Video guide, we are assuming normal distribution of returns. But in reality, oftentimes the distribution of returns are negatively skewed, not normal, causing the results to be perhaps optimistic.