Week 14: Code along 13
CHAPTER 11 Monte Carlo Simulation
Alden Dimick
2024-12-11
# Load packages
# Core
library(tidyverse)
library(tidyquant)
# 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$returns)
mean_port_return## [1] 0.005899135# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$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] 0.0004703962 0.0223044578 0.0359622761 0.0296454070 0.0251913598
## [6] 0.0032738729 -0.0023500391 0.0317613901 0.0172417372 0.0288948083
## [11] 0.0223611980 -0.0055989888 -0.0161195314 0.0373404907 0.0019521409
## [16] -0.0233933872 0.0303947141 -0.0093926140 0.0139751607 0.0221815892
## [21] 0.0173640063 0.0432210702 0.0207843782 -0.0213136009 -0.0043956368
## [26] 0.0599704446 0.0101275654 0.0106589566 0.0230386880 0.0400527250
## [31] 0.0128826353 0.0293260979 -0.0355829163 -0.0459359748 -0.0085759070
## [36] -0.0175234988 0.0060044834 0.0247170604 -0.0080387848 0.0349587260
## [41] -0.0273396090 0.0139129421 0.0223638886 0.0133671104 0.0848988937
## [46] 0.0449148621 0.0107817284 0.0246660968 0.0197261591 0.0253912545
## [51] -0.0134099730 0.0323275298 -0.0324103857 -0.0259611450 -0.0165529942
## [56] 0.0316256401 0.0100343652 0.0017302412 0.0264224494 -0.0211474438
## [61] 0.0400365303 -0.0026130563 -0.0264516732 -0.0164377695 -0.0034434006
## [66] 0.0146129700 0.0318773424 -0.0180145660 0.0067254754 0.0133389330
## [71] 0.0315524983 0.0162708062 -0.0271474739 0.0556935815 0.0164109594
## [76] -0.0122414381 0.0354492216 -0.0444352901 -0.0152136182 -0.0546049080
## [81] 0.0080219807 0.0011254042 0.0184085923 -0.0067006604 -0.0128067030
## [86] 0.0105049720 0.0518120983 0.0083955631 0.0161482607 -0.0008457486
## [91] 0.0352836551 0.0279864785 -0.0048972780 -0.0057485722 -0.0250402126
## [96] 0.0524136497 0.0373606937 0.0094287117 -0.0192919781 0.0033678545
## [101] 0.0324004920 -0.0131083305 0.0205948124 0.0676164052 0.0036707424
## [106] 0.0190482827 0.0101238689 -0.0321524409 0.0070974904 -0.0227764547
## [111] -0.0255152146 0.0588043949 -0.0402389268 0.0032425451 0.0406766697
## [116] 0.0219606600 0.0215549800 0.0051557545 0.0227308694 0.0529309861# 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 1.02
## 4 1.04
## 5 1.03
## 6 1.03
## 7 1.00
## 8 0.998
## 9 1.03
## 10 1.02
## # 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 1.02
## 4 1.06
## 5 1.09
## 6 1.12
## 7 1.12
## 8 1.12
## 9 1.16
## 10 1.17
## # ℹ 111 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] 12.058486 Simulation function
simulate_accumulation <- function(initial_value, N, mean_return, sd_return) {
# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_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>
## 1 270.
## 2 271.
## 3 276.
## 4 277.
## 5 276.
## 6 277.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 <- 100
starts <- rep(1, sims) %>%
set_names(paste0("sim", 1:sims))
starts## sim1 sim2 sim3 sim4 sim5 sim6 sim7 sim8 sim9 sim10 sim11
## 1 1 1 1 1 1 1 1 1 1 1
## sim12 sim13 sim14 sim15 sim16 sim17 sim18 sim19 sim20 sim21 sim22
## 1 1 1 1 1 1 1 1 1 1 1
## sim23 sim24 sim25 sim26 sim27 sim28 sim29 sim30 sim31 sim32 sim33
## 1 1 1 1 1 1 1 1 1 1 1
## sim34 sim35 sim36 sim37 sim38 sim39 sim40 sim41 sim42 sim43 sim44
## 1 1 1 1 1 1 1 1 1 1 1
## sim45 sim46 sim47 sim48 sim49 sim50 sim51 sim52 sim53 sim54 sim55
## 1 1 1 1 1 1 1 1 1 1 1
## sim56 sim57 sim58 sim59 sim60 sim61 sim62 sim63 sim64 sim65 sim66
## 1 1 1 1 1 1 1 1 1 1 1
## sim67 sim68 sim69 sim70 sim71 sim72 sim73 sim74 sim75 sim76 sim77
## 1 1 1 1 1 1 1 1 1 1 1
## sim78 sim79 sim80 sim81 sim82 sim83 sim84 sim85 sim86 sim87 sim88
## 1 1 1 1 1 1 1 1 1 1 1
## sim89 sim90 sim91 sim92 sim93 sim94 sim95 sim96 sim97 sim98 sim99
## 1 1 1 1 1 1 1 1 1 1 1
## sim100
## 1# Simulate
# For reproducable 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: 12,100 × 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 12,090 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%
## 0.79 1.55 1.94 2.22 4.078 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 $1 over 120 months")
Line plot with max, median, and min
# Step 1 Summarise data into max, median, and min of last value
sim_summary <- monte_carlo_sim_51 %>%
group_by(sim) %>%
summarise(growth = last(growth)) %>%
ungroup() %>%
summarise(max = max(growth),
median = median(growth),
min = min(growth))
sim_summary## # A tibble: 1 × 3
## max median min
## <dbl> <dbl> <dbl>
## 1 4.07 1.94 0.785# Step 2 Plot
monte_carlo_sim_51 %>%
# Filter for max, median and min sim
group_by(sim) %>%
filter(last(growth) == sim_summary$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 = "Max, Median, and Minimum Simulation")
I am not sure why but for some reason the median line is not showing up on the gg plot however everything else is the same as in the video.