Week 14: Code Along 13
Eoin Hamell-Kelleher
2023-5-02
# 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
## # … with 50 more rows5 Simulating growth of a dollar
# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return## [1] 0.005899134# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return## [1] 0.02347491# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns## [1] -0.0044245195 -0.0309927137 0.0052535432 -0.0190720415 0.0155897661
## [6] -0.0224240084 0.0265818393 0.0223257801 0.0094310628 -0.0053815828
## [11] -0.0274730254 -0.0118800032 0.0552887724 0.0513274558 0.0168912176
## [16] 0.0171768566 0.0327074973 0.0116272477 -0.0167974405 -0.0716023564
## [21] 0.0219162043 -0.0217105194 -0.0043704903 0.0115717926 0.0116637240
## [26] 0.0494616465 -0.0188555636 0.0189422312 -0.0097492411 0.0290566713
## [31] 0.0019985356 0.0156409704 0.0181847909 0.0011361076 0.0315515137
## [36] -0.0048765164 -0.0112859812 0.0366860173 -0.0232484020 0.0065739732
## [41] -0.0201088153 -0.0069954974 0.0288092504 0.0147513392 -0.0431788281
## [46] 0.0103251284 0.0712530065 0.0146643048 -0.0014773843 0.0067849349
## [51] 0.0410206338 0.0115687958 -0.0092733738 0.0214806731 0.0181300340
## [56] -0.0387215330 -0.0138597285 0.0220891251 0.0287846527 -0.0434312152
## [61] 0.0339729475 0.0204613639 0.0199244016 -0.0351223823 0.0116158341
## [66] 0.0106718516 -0.0318129364 -0.0213967702 -0.0457373905 0.0124548859
## [71] 0.0044771077 0.0192677314 0.0225788544 0.0371163420 0.0242596457
## [76] 0.0360396618 -0.0389348322 -0.0150326275 -0.0140708367 -0.0027611867
## [81] 0.0213296149 -0.0162028522 0.0343545974 0.0331537396 0.0308665585
## [86] -0.0033418665 -0.0016675594 -0.0281255882 -0.0004308493 -0.0038728205
## [91] -0.0111243559 -0.0242771916 0.0179275600 0.0241356491 0.0022421867
## [96] -0.0066561332 0.0169233129 0.0052390806 -0.0046637251 -0.0064706493
## [101] -0.0222340280 0.0298302978 -0.0085828586 -0.0300533635 -0.0319592704
## [106] -0.0603150085 0.0359239840 0.0425025721 0.0268544393 -0.0002641858
## [111] 0.0203574323 0.0079712733 0.0186030940 0.0144262323 0.0042495652
## [116] -0.0242541771 0.0393186990 -0.0328176863 0.0293424890 0.0020115225# 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 0.996
## 3 0.969
## 4 1.01
## 5 0.981
## 6 1.02
## 7 0.978
## 8 1.03
## 9 1.02
## 10 1.01
## # … 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 0.996
## 3 0.965
## 4 0.970
## 5 0.951
## 6 0.966
## 7 0.944
## 8 0.970
## 9 0.991
## 10 1.00
## # … with 111 more rows# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr## [1] 4.8755636 Simulation function
simulate_accumulation <- function(init_value, N, mean, stdev) {
tibble(returns = c(init_value, 1 + rnorm(N, mean, stdev))) %>%
mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
select(growth)
}
simulate_accumulation(1, 120, mean_port_return, stddev_port_return)## # A tibble: 121 × 1
## growth
## <dbl>
## 1 1
## 2 1.02
## 3 1.03
## 4 1.01
## 5 1.00
## 6 0.983
## 7 0.986
## 8 1.04
## 9 1.07
## 10 1.09
## # … with 111 more rows# Save the function
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(paste("sim", 1:sims, sep = ""))
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
monte_carlo_sim_51 <- starts %>%
# Simulate
map_dfc(simulate_accumulation,
N = 120,
mean = mean_port_return,
stdev = stddev_port_return) %>%
# Add the column, month
mutate(month = seq(1:nrow(.))) %>%
# Arrange column names
select(month, everything()) %>%
set_names(c("month", names(starts))) %>%
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# Calculate the quantiles for simulated values
probs <- c(.005, .025, .25, .5, .75, .975, .995)
monte_carlo_sim_51 %>%
group_by(sim) %>%
summarise(growth = last(growth)) %>%
ungroup() %>%
pull(growth) %>%
# Find the quantiles
quantile(probs = probs) %>%
round(2)## 0.5% 2.5% 25% 50% 75% 97.5% 99.5%
## 1.27 1.27 1.61 1.98 2.41 3.40 4.078 Visualizing simulations with ggplot
monte_carlo_sim_51 %>%
ggplot(aes(x = month, y = growth, col = sim)) +
geom_line() +
theme(legend.position = "none")
# Simplify the plot
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 4.29 1.98 1.27monte_carlo_sim_51 %>%
group_by(sim) %>%
filter(last(growth) == sim_summary$max |
last(growth) == sim_summary$median |
last(growth) == sim_summary$min) %>%
# Plot
ggplot(aes(month, growth, col = sim)) +
geom_line() +
theme()