# 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$returns)
mean_port_return
## [1] 0.005899133
# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return
## [1] 0.02347489
# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns
##   [1] -0.0084868919  0.0312228518  0.0280970305 -0.0082001505  0.0018584719
##   [6] -0.0258792309  0.0345958176  0.0180622747  0.0059517662  0.0028183118
##  [11] -0.0680182078 -0.0001613288  0.0259980709 -0.0159437905  0.0093500418
##  [16]  0.0264809956  0.0448856505  0.0071531298 -0.0042016483  0.0049936724
##  [21] -0.0011954927 -0.0040526641 -0.0033360873 -0.0229403022  0.0357044763
##  [26]  0.0419644020 -0.0064802373  0.0058513503  0.0290480583  0.0407778499
##  [31]  0.0383974807  0.0125616428 -0.0013686006  0.0009777797  0.0044943318
##  [36]  0.0187498324  0.0055222855  0.0664791764  0.0345033009  0.0194096081
##  [41] -0.0237587614  0.0333556529 -0.0381133912 -0.0034315801  0.0213932859
##  [46] -0.0130155299 -0.0058145517 -0.0302385822  0.0449990505  0.0315130761
##  [51] -0.0043706158  0.0181166909 -0.0042180063 -0.0031562121  0.0314127696
##  [56] -0.0278016233  0.0339874256  0.0236191058  0.0381409742  0.0153325958
##  [61]  0.0171861316 -0.0131673444  0.0491985477  0.0092468391  0.0201637402
##  [66]  0.0258153473 -0.0294316860  0.0016665759 -0.0215407056 -0.0142887032
##  [71]  0.0030197727  0.0051517473 -0.0193010070  0.0005276612 -0.0176749324
##  [76]  0.0544549587 -0.0268113758 -0.0488230641  0.0030921468 -0.0166007671
##  [81]  0.0210035680 -0.0401946446  0.0042704901 -0.0186983832  0.0095065508
##  [86]  0.0176529787  0.0151628674  0.0304172852 -0.0045587373  0.0269712491
##  [91] -0.0098624716  0.0444366283  0.0320230418  0.0061614626 -0.0062567165
##  [96]  0.0045415358  0.0082756264  0.0427171572  0.0081493847  0.0059001569
## [101] -0.0219585579 -0.0006505693  0.0337360408 -0.0009205105 -0.0009967471
## [106]  0.0286919584 -0.0184559054 -0.0082824781  0.0213109045  0.0029454695
## [111]  0.0410511044 -0.0247455954  0.0277141128  0.0223369876  0.0050996197
## [116]  0.0168498562 -0.0063857639 -0.0348241599 -0.0043820948  0.0360062492
# 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   0.992
##  3   1.03 
##  4   1.03 
##  5   0.992
##  6   1.00 
##  7   0.974
##  8   1.03 
##  9   1.02 
## 10   1.01 
## # 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  0.992
##  3  1.02 
##  4  1.05 
##  5  1.04 
##  6  1.04 
##  7  1.02 
##  8  1.05 
##  9  1.07 
## 10  1.08 
## # ℹ 111 more rows
# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr
## [1] 8.560687

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)))
    
    # 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   286.
## 2   284.
## 3   287.
## 4   285.
## 5   290.
## 6   295.

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_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: 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

8 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")