Import your data

symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2017-12-31")
## Convert prices to returns (monthly)
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"))

Assign 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

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")
## Warning in check_weights(weights, assets_col, map, x): Sum of weights does not
## equal 1.
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

Similuatig growth of 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] 0.02347494
# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)
simulated_monthly_returns
##   [1] -0.0033087895 -0.0042424559 -0.0246210263 -0.0207361549 -0.0206841982
##   [6]  0.0070039301  0.0035992028  0.0269577319  0.0029968246 -0.0026840615
##  [11] -0.0325819017 -0.0067267067 -0.0089475437  0.0078977011  0.0234304260
##  [16]  0.0133298306  0.0083300624 -0.0039167356 -0.0230026709 -0.0054876713
##  [21]  0.0183082556  0.0201197018  0.0028296467  0.0200378930 -0.0322601043
##  [26]  0.0117525523  0.0346486760  0.0121619242  0.0370838438  0.0132519813
##  [31] -0.0205417410  0.0047181316 -0.0142431338 -0.0188127243  0.0090851724
##  [36]  0.0156208340  0.0063323486 -0.0094460545  0.0460302655 -0.0019017857
##  [41]  0.0476230581  0.0216324813  0.0298632137  0.0467182925 -0.0298735220
##  [46]  0.0296953024  0.0145433317  0.0297917000  0.0165572539 -0.0063333380
##  [51]  0.0294203585  0.0061045598  0.0117084602  0.0382180958  0.0155339395
##  [56] -0.0239284836  0.0365760367 -0.0072438766  0.0211712951  0.0046521606
##  [61]  0.0124791279  0.0025521955 -0.0052080959  0.0047609634  0.0350563545
##  [66]  0.0395935628 -0.0187201412  0.0198242217  0.0261398595  0.0069149509
##  [71] -0.0099501741 -0.0091008151  0.0041963775 -0.0160806511 -0.0102968580
##  [76]  0.0118279463  0.0391809075  0.0415211931 -0.0324317901  0.0055056332
##  [81] -0.0160890981 -0.0240728615 -0.0441085604 -0.0202529208 -0.0058168432
##  [86] -0.0073665968  0.0102189696  0.0100573411 -0.0260167443  0.0361806534
##  [91]  0.0070846194 -0.0086102952 -0.0001407496 -0.0342253851 -0.0273649871
##  [96]  0.0150948634 -0.0049383194  0.0078395202  0.0137499101  0.0018569191
## [101]  0.0082740619  0.0284089192 -0.0016556125  0.0104324942 -0.0033777629
## [106] -0.0171560241 -0.0374572721 -0.0085889620  0.0316494186 -0.0153008875
## [111] -0.0100160354  0.0124557191 -0.0118389174 -0.0033511450  0.0355868391
## [116]  0.0182947515  0.0035310950  0.0104963574  0.0532994375 -0.0105995558
# 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   0.997
##  3   0.996
##  4   0.975
##  5   0.979
##  6   0.979
##  7   1.01 
##  8   1.00 
##  9   1.03 
## 10   1.00 
## # 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  0.997
##  3  0.992
##  4  0.968
##  5  0.948
##  6  0.928
##  7  0.935
##  8  0.938
##  9  0.964
## 10  0.966
## # ℹ 111 more rows
# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr
## [1] 5.345261

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   327.
## 2   325.
## 3   334.
## 4   334.
## 5   337.
## 6   341.
dump(list = c("simulate_accumulation"), 
     file = "../00_scripts/simulate_accumulation.R")

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_carle_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")
## New names:
## • `growth` -> `growth...1`
## • `growth` -> `growth...2`
## • `growth` -> `growth...3`
## • `growth` -> `growth...4`
## • `growth` -> `growth...5`
## • `growth` -> `growth...6`
## • `growth` -> `growth...7`
## • `growth` -> `growth...8`
## • `growth` -> `growth...9`
## • `growth` -> `growth...10`
## • `growth` -> `growth...11`
## • `growth` -> `growth...12`
## • `growth` -> `growth...13`
## • `growth` -> `growth...14`
## • `growth` -> `growth...15`
## • `growth` -> `growth...16`
## • `growth` -> `growth...17`
## • `growth` -> `growth...18`
## • `growth` -> `growth...19`
## • `growth` -> `growth...20`
## • `growth` -> `growth...21`
## • `growth` -> `growth...22`
## • `growth` -> `growth...23`
## • `growth` -> `growth...24`
## • `growth` -> `growth...25`
## • `growth` -> `growth...26`
## • `growth` -> `growth...27`
## • `growth` -> `growth...28`
## • `growth` -> `growth...29`
## • `growth` -> `growth...30`
## • `growth` -> `growth...31`
## • `growth` -> `growth...32`
## • `growth` -> `growth...33`
## • `growth` -> `growth...34`
## • `growth` -> `growth...35`
## • `growth` -> `growth...36`
## • `growth` -> `growth...37`
## • `growth` -> `growth...38`
## • `growth` -> `growth...39`
## • `growth` -> `growth...40`
## • `growth` -> `growth...41`
## • `growth` -> `growth...42`
## • `growth` -> `growth...43`
## • `growth` -> `growth...44`
## • `growth` -> `growth...45`
## • `growth` -> `growth...46`
## • `growth` -> `growth...47`
## • `growth` -> `growth...48`
## • `growth` -> `growth...49`
## • `growth` -> `growth...50`
## • `growth` -> `growth...51`
# Find quantiles 
monte_carle_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% 
## 1.17 1.59 1.98 2.40 3.88

Turn them into a function

count_ncol_numeric <- function(.data) {
    
    #body
    ncol
    
    
    
}

##Visualizing simulations with ggplot

monte_carle_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")

# Step 1 Summarize data into max, median, and min of last value
sim_summary <- monte_carle_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  3.88   1.98  1.17
# Step 2 Plot
monte_carle_sim_51 %>%
    
    # Filter for max, median, 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 = "Maximum, Median, and Mimimum Simulation")