Apply it to your data 13

# Load packages

# Core
library(tidyverse)
library(tidyquant)

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

1 Import stock prices

Revise the code below.

Replace symbols with your stocks.
Replace the from and the to arguments to date from 2012-12-31 to present.

symbols <- c("LLY", "HD", "UA", "TSLA", "NVDA")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31")

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.

The vector weights should have a length equal to the number of assets in the portfolio.
The values in the vector weights should sum to 1.

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols

## [1] "HD"   "LLY"  "NVDA" "TSLA" "UA"

# weights
weights <- c(0.2, 0.2, 0.2, 0.2, 0.2)
weights

## [1] 0.2 0.2 0.2 0.2 0.2

w_tbl <- tibble(symbols, weights)
w_tbl

## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 HD          0.2
## 2 LLY         0.2
## 3 NVDA        0.2
## 4 TSLA        0.2
## 5 UA          0.2

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: 155 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0532 
##  2 2013-02-28  0.00290
##  3 2013-03-28  0.0320 
##  4 2013-04-30  0.0899 
##  5 2013-05-31  0.137  
##  6 2013-06-28 -0.00517
##  7 2013-07-31  0.0700 
##  8 2013-08-30  0.0347 
##  9 2013-09-30  0.0381 
## 10 2013-10-31 -0.0395 
## # ℹ 145 more rows

5 Simulating growth of a dollar

# Get mean portfolio return
mean_port_return <- mean(portfolio_returns_tbl$returns)
mean_port_return

## [1] 0.01916024

# Get standard deviation of portfolio returns
stddev_port_return <- sd(portfolio_returns_tbl$returns)
stddev_port_return

## [1] 0.06584246

6 Simulation function

No need

7 Running multiple simulations

# Create a vector of 1s as a starting point
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

# Create a vector of 1s as a starting point
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% 
##   703.65  3852.30  7817.91 14099.21 34793.23

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 34793.  7818.  704.

# 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 Monte Carlo Simulation, the average return after 20 years that I can expect from a $100 initial investment would be $7818

What is the best-case scenario?

The best case scenario is that my initial investment can grow to $34,793 after 20 years

What is the worst-case scenario? What are limitations of this simulation analysis?

The worst case scenario is that my initial investment can only grow to $704 after 20 years

The limitations are that:

The results heavily depend on the assumptions: Monte Carlo simulations are only as good as the assumptions, so unrealistic distributions and incorrect means/variances will produce incorrect outputs.

They typically require a large amount of data to be accurate: You need stornger historical data to estimate realistic probable distributions. If the dataset is small or biased, then the simulated outcomes will not reflect reality.

The randomness of the analysis changes every time you run it: This means that results will vary and confidence in exact numerical outputs should be limited. You can reduce noise by running more simulations, but this increases computation.