# 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 0.10
w_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        0.1

4 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 
## # ℹ 50 more rows

5 Simulating growth of a dollar

mean_port_return <- mean(portfolio_returns_tbl$returns)
stddev_port_return <- sd(portfolio_returns_tbl$returns)
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_returns_add_1 <- tibble(returns = c(1, 1 + simulated_monthly_returns))
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  0.977
##  3  0.983
##  4  0.951
##  5  0.970
##  6  0.979
##  7  0.951
##  8  0.971
##  9  0.961
## 10  0.961
## # ℹ 111 more rows
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr
## [1] 6.810274

6 Simulation function

simulate_accumulation <- function(initial_value, n = 120, mu = mean_port_return, sigma = stddev_port_return) {
  tibble(returns = c(initial_value, 1 + rnorm(n, mu, sigma))) %>%
    mutate(growth = accumulate(returns, function(x, y) x * y)) %>%
    select(growth)
}

7 Running multiple simulations

set.seed(1234)

sims <- 51
starts <- rep(1, sims) %>% set_names(paste0("sim", 1:sims))

monte_carlo_sim_51 <- map_dfc(.x = starts, .f = ~ simulate_accumulation(initial_value = .x)) %>%
  mutate(month = 0:120) %>%
  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     0 sim1       1
##  2     0 sim2       1
##  3     0 sim3       1
##  4     0 sim4       1
##  5     0 sim5       1
##  6     0 sim6       1
##  7     0 sim7       1
##  8     0 sim8       1
##  9     0 sim9       1
## 10     0 sim10      1
## # ℹ 6,161 more rows

8 Visualize simulations

monte_carlo_sim_51 %>%
  ggplot(aes(x = month, y = growth, color = sim)) +
  geom_line(show.legend = FALSE) +
  labs(title = "Simulations of $1 Growth Over 120 Months") +
  theme(plot.title = element_text(hjust = 0.5))

9 Max, Median, Min Plot

sim_summary <- monte_carlo_sim_51 %>%
  group_by(sim) %>%
  summarize(growth = last(growth)) %>%
  ungroup()

extremes <- monte_carlo_sim_51 %>%
  group_by(sim) %>%
  filter(last(growth) %in% c(max(sim_summary$growth), median(sim_summary$growth), min(sim_summary$growth))) %>%
  ungroup()

extremes %>%
  ggplot(aes(x = month, y = growth, color = sim)) +
  geom_line() +
  labs(title = "Simulations of $1 Growth Over 120 Months",
       subtitle = "Max, Median, and Min Simulations") +
  theme(plot.title = element_text(hjust = 0.5),
        plot.subtitle = element_text(hjust = 0.5))

10 Summary Quantiles

monte_carlo_sim_51 %>%
  group_by(sim) %>%
  summarize(growth = last(growth)) %>%
  pull(growth) %>%
  quantile(probs = c(0, 0.25, 0.5, 0.75, 1)) %>%
  round(2)
##   0%  25%  50%  75% 100% 
## 1.17 1.59 1.98 2.40 3.88