Apply it to your data 13
How much should you expect from your $100 investment after 20 years?
Liam Spurling
2022-09-19
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# Source function
source("../00_scripts/simulate_accumulation.R")1 Import stock prices
Revise the code below.
- Replace symbols with your stocks.
- Replace the from and the to arguments to date from 2012-12-31 to present.
symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")
prices <- tq_get(x = symbols,
get = "stock.prices",
from = "2012-12-31",
to = "2017-12-31")2 Convert prices to returns
asset_returns_tbl <- prices %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
type = "log") %>%
slice(-1) %>%
ungroup() %>%
set_names(c("asset", "date", "returns"))3 Assign a weight to each asset
Revise the code for weights.
- The vector weights should have a length equal to the number of assets in the portfolio.
- The values in the vector weights should sum to 1.
# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols## [1] "AGG" "EEM" "EFA" "IJS" "SPY"# weights
weights <- c(0.25, 0.25, 0.2, 0.2, 0.1)
weights## [1] 0.25 0.25 0.20 0.20 0.10w_tbl <- tibble(symbols, weights)
w_tbl## # A tibble: 5 × 2
## symbols weights
## <chr> <dbl>
## 1 AGG 0.25
## 2 EEM 0.25
## 3 EFA 0.2
## 4 IJS 0.2
## 5 SPY 0.14 Build a portfolio
portfolio_returns_tbl <- asset_returns_tbl %>%
tq_portfolio(assets_col = asset,
returns_col = returns,
weights = w_tbl,
rebalance_on = "months",
col_rename = "returns")
portfolio_returns_tbl## # A tibble: 60 × 2
## date returns
## <date> <dbl>
## 1 2013-01-31 0.0204
## 2 2013-02-28 -0.00239
## 3 2013-03-28 0.0121
## 4 2013-04-30 0.0174
## 5 2013-05-31 -0.0128
## 6 2013-06-28 -0.0247
## 7 2013-07-31 0.0321
## 8 2013-08-30 -0.0224
## 9 2013-09-30 0.0511
## 10 2013-10-31 0.0301
## # … with 50 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.005899131# 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] -0.0206612586 -0.0361148444 0.0300677617 0.0168692128 -0.0087690184
## [6] -0.0193152957 0.0188744823 -0.0398030010 -0.0190975616 -0.0245026085
## [11] -0.0074571750 0.0017925619 -0.0098009587 0.0123900555 0.0014557370
## [16] -0.0210138471 0.0265295091 0.0099020338 0.0423339032 0.0167045738
## [21] 0.0475784970 0.0206244829 -0.0037322785 0.0216034459 -0.0248968090
## [26] 0.0322749033 0.0379176860 0.0120977963 0.0244811127 -0.0290337693
## [31] -0.0083121746 0.0330731947 -0.0010023473 0.0144997781 0.0158084304
## [36] 0.0248278361 0.0527327603 -0.0044231579 0.0211878999 0.0020741353
## [41] 0.0300485105 0.0028526055 0.0407916253 0.0214686702 0.0086268309
## [46] -0.0436187738 0.0143403748 -0.0083446853 -0.0184523762 -0.0012581116
## [51] -0.0054180601 -0.0263390368 -0.0345179744 0.0029069103 0.0086155896
## [56] 0.0144103278 0.0002471582 0.0079058214 -0.0272655156 0.0034187211
## [61] 0.0114493552 0.0369282306 0.0307956683 -0.0158607357 -0.0117797186
## [66] 0.0250974175 0.0105087069 0.0350397995 0.0308572037 0.0165021697
## [71] -0.0345609158 0.0081293960 -0.0085505150 -0.0174917669 -0.0060487150
## [76] 0.0169723147 -0.0068368069 -0.0515231249 -0.0065030862 0.0659956457
## [81] -0.0007872566 -0.0009484020 0.0560451789 -0.0290428078 -0.0206696722
## [86] -0.0029383749 -0.0012660157 0.0190672161 0.0065614236 0.0060796770
## [91] -0.0365192856 0.0167920844 -0.0215465374 -0.0071831092 0.0249385776
## [96] -0.0033996091 -0.0256550250 0.0461468376 0.0126903968 0.0346301086
## [101] 0.0107327411 0.0087968376 0.0073058850 -0.0099926855 -0.0037882191
## [106] 0.0131821581 -0.0005655971 0.0554528859 0.0325998234 -0.0089194728
## [111] 0.0492167414 0.0038770320 0.0341813005 -0.0115252595 0.0051494476
## [116] -0.0122059310 -0.0147708952 0.0242564916 0.0004880337 0.0469709169# 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 0.979
## 3 0.964
## 4 1.03
## 5 1.02
## 6 0.991
## 7 0.981
## 8 1.02
## 9 0.960
## 10 0.981
## # … with 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 0.979
## 3 0.944
## 4 0.972
## 5 0.989
## 6 0.980
## 7 0.961
## 8 0.979
## 9 0.940
## 10 0.922
## # … with 111 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] 6.693794No need
6 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 results
set.seed(1234)
monte_carlo_sim_51 <- starts %>%
# Stimulate
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")
monte_carlo_sim_51## # A tibble: 6,171 × 3
## month sim growth
## <int> <chr> <dbl>
## 1 1 sim1 100
## 2 1 sim2 100
## 3 1 sim3 100
## 4 1 sim4 100
## 5 1 sim5 100
## 6 1 sim6 100
## 7 1 sim7 100
## 8 1 sim8 100
## 9 1 sim9 100
## 10 1 sim10 100
## # … 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%
## 116.78 159.29 198.28 240.34 387.828 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 $1 over 120 months")
Line Plot of Simulations with Max, Median, and Min
# Step 1 Summarize data into max, median, and min of last value
sim_summary <- monte_carlo_sim_51 %>%
group_by(sim) %>%
summarise(growth = last(growth)) %>%
ungroup() %>%
summarise(max = max(growth),
median = median(growth),
min = min(growth))
sim_summary## # A tibble: 1 × 3
## max median min
## <dbl> <dbl> <dbl>
## 1 388. 198. 117.# Step 2 Plot
monte_carlo_sim_51 %>%
# Filter for max, median, and min
group_by(sim) %>%
filter(last(growth) == sim_summary$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 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?
Based on teh Monte Carlo simulation I believe it is safe to expect a return of around $198 over the course of 20 years. With this being said I think that the best case senario based off the simulations that were run is a return of $388, with the worst case senario being $117. A limitation of the simulation is having rnorm assuming all positive normal returns.