# 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

# ?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 rows

5 Simulating growth of a dollar

# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return
## [1] 0.005899137
# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$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]  1.925878e-02 -1.410757e-02  3.764044e-02  1.293198e-02  2.210719e-02
##   [6]  2.492424e-02  7.026167e-03  2.412502e-02 -6.060989e-03  1.045817e-03
##  [11]  1.898053e-02  8.195020e-03 -2.168865e-02 -4.048490e-02 -2.471489e-02
##  [16]  1.642101e-02  2.752525e-03 -2.029803e-02  1.137153e-02  3.894596e-02
##  [21]  1.534567e-03  1.325983e-02  3.538859e-02 -2.520639e-02  1.238446e-04
##  [26]  6.074400e-02  4.315433e-02 -2.557662e-04 -4.809586e-04 -5.193231e-02
##  [31] -5.531001e-03  4.662863e-02  3.450598e-02  3.717184e-02  3.837188e-02
##  [36]  2.067611e-02  2.475357e-02  1.632820e-02 -1.257397e-02  7.237488e-03
##  [41] -5.379135e-03  3.549442e-02  3.199317e-02  3.919363e-03 -9.242883e-03
##  [46] -6.252011e-03  5.036846e-02 -4.484809e-02  1.120325e-02  2.900068e-02
##  [51]  1.455167e-02 -3.008494e-03  1.284299e-02  3.824448e-02 -1.123762e-02
##  [56]  1.006592e-02  1.365469e-02 -1.386300e-02 -1.072395e-02  1.174876e-02
##  [61]  3.657552e-02 -8.161554e-03 -7.871873e-03 -2.750504e-03  1.720087e-02
##  [66] -5.234228e-03 -9.647263e-03 -1.763561e-03  2.741766e-02 -1.433137e-02
##  [71] -3.468837e-02  1.559046e-02 -1.276502e-02  1.623009e-02  2.206637e-03
##  [76]  2.065292e-02  1.276640e-02  3.088752e-02  1.951169e-02 -5.889537e-02
##  [81]  2.024757e-02 -1.831284e-02  2.001946e-02 -4.880501e-02  1.539226e-02
##  [86] -4.011933e-03  9.615856e-03  1.069165e-02  9.332067e-03 -1.482332e-02
##  [91]  3.880655e-02 -2.963222e-02 -3.580350e-02 -1.009872e-02  3.172940e-02
##  [96]  3.088014e-02  2.785914e-02 -6.138887e-03 -3.282873e-02 -6.692558e-03
## [101] -1.375205e-02  1.703372e-03  1.958249e-02  4.877407e-02  2.857544e-03
## [106]  1.160805e-02  2.814247e-03  4.533987e-02  1.097591e-05  1.576837e-02
## [111]  2.607814e-02 -4.267491e-02  2.664051e-02  1.324109e-02  2.897051e-02
## [116]  1.301376e-02 -1.157099e-02  3.378581e-02  1.010688e-02  1.824567e-03
# 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   1.02 
##  3   0.986
##  4   1.04 
##  5   1.01 
##  6   1.02 
##  7   1.02 
##  8   1.01 
##  9   1.02 
## 10   0.994
## # 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   1.02
##  3   1.00
##  4   1.04
##  5   1.06
##  6   1.08
##  7   1.11
##  8   1.11
##  9   1.14
## 10   1.13
## # ℹ 111 more rows
# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr
## [1] 8.434928

6 Simulation function

simulate_accumulation <- function(initial_value, N, mean_return, sd_return) {
    
    # Add a dollar
    simulated_returns_add_1 <- tibble(returns = c(initial_value, 1 + rnorm(N, mean_return, sd_return)))

    # The first value, i whatever value we want to follow
    #rnom(time frame, etc.)
    
    # 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   325.
## 2   330.
## 3   332.
## 4   329.
## 5   328.
## 6   326.
# how to save a 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(paste0("sim", 1:sims))

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
# for reproducible research
set.seed(1234)

monte_carlo_sim51 <- starts %>%
    
    # Simulate
    map_dfc(.x = .,
            .f = ~simulate_accumulation(initial_value = .x, 
                                        N             = 120, 
                                        mean_return   = mean_port_return, 
                                        sd_return     = stddev_port_return)) %>%

    # Add
    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_sim51
## # 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
## # ℹ 6,161 more rows
# Find quantiles
monte_carlo_sim51 %>%
    
    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% 
## 1.17 1.59 1.98 2.40 3.88

8 Visualizing simulations with ggplot

monte_carlo_sim51 %>%
    
    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 12 months")

Line plot with max, median, and min

# Step 1 Summarize data into max, median, and min of last value
sim_summary <- monte_carlo_sim51 %>%
    
    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  3.88   1.98  1.17
# Step 2 Plot
monte_carlo_sim51 %>%
    
    # 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 12 months",
         subtitle = "Max, Median, and Minimum Simulation")