# Load packages

# Core
library(tidyverse)
library(tidyquant)

# Source function
source("../00_scripts/simulate_accumulation.R")

1 Import stock prices

Revise the code below.

symbols <- c("SPY", "QQQ", "TSLA", "XOM")

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

Revise the code for weights.

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "QQQ"  "SPY"  "TSLA" "XOM"
# weights
weights <- c(0.25, 0.25, 0.25, 0.25)
weights
## [1] 0.25 0.25 0.25 0.25
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 4 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 QQQ        0.25
## 2 SPY        0.25
## 3 TSLA       0.25
## 4 XOM        0.25

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  0.0543
##  2 2013-02-28 -0.0141
##  3 2013-03-28  0.0394
##  4 2013-04-30  0.0964
##  5 2013-05-31  0.169 
##  6 2013-06-28  0.0137
##  7 2013-07-31  0.0931
##  8 2013-08-30  0.0324
##  9 2013-09-30  0.0500
## 10 2013-10-31 -0.0138
## # ℹ 50 more rows

5 Simulating growth of a dollar

# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return
## [1] 0.01667569
# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return
## [1] 0.04388334

6 Simulation function

No need

7 Running multiple simulations

sims <- 51
starts <- rep(100, sims) %>%
    set_names(paste0("sim", 1:sims))

starts
##  sim1  sim2  sim3  sim4  sim5  sim6  sim7  sim8  sim9 sim10 sim11 sim12 sim13 
##   100   100   100   100   100   100   100   100   100   100   100   100   100 
## sim14 sim15 sim16 sim17 sim18 sim19 sim20 sim21 sim22 sim23 sim24 sim25 sim26 
##   100   100   100   100   100   100   100   100   100   100   100   100   100 
## sim27 sim28 sim29 sim30 sim31 sim32 sim33 sim34 sim35 sim36 sim37 sim38 sim39 
##   100   100   100   100   100   100   100   100   100   100   100   100   100 
## sim40 sim41 sim42 sim43 sim44 sim45 sim46 sim47 sim48 sim49 sim50 sim51 
##   100   100   100   100   100   100   100   100   100   100   100   100
# Simulate
# for reproducible research
set.seed(1234)

monte_carle_sim_51 <- starts %>%
    
    # Simulate
    map_dfc(.x = ., 
            .f = ~simulate_accumulation(initial_value = .x, 
                                       N              = 240, 
                                       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")

# 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% 
##  1044.05  3237.10  5067.03  7725.25 14124.00

8 Visualizing simulations with ggplot

Line Plot of Simulations with Max, Median, and Min

# 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 14124.  5067. 1044.
# 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 $100 over 240 months", 
         subtitle = "Maximum, Median, and Mimimum Simulation")

Based on the Monte Carlo simulation results, how much should you expect from your $100 investment after 20 years?

Based on the results of the Monte Carlo Simulation after 20 years or 240 months I should expect on average my initial $100 investment to grow to $5,067 (median).

What is the best-case scenario? What is the worst-case scenario?

The best-case scenario is that is that my $100 investment grows to $14,123 in 20 years and the worst-case scenario is that it my $100 investment grows to $1,044 in 20 years.

What are limitations of this simulation analysis?

Some examples of limitations include: