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("HD", "TSLA", "META", "NKE", "AAPL")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2023-5-4")

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] "AAPL" "HD"   "META" "NKE"  "TSLA"

# 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 AAPL       0.25
## 2 HD         0.25
## 3 META       0.2 
## 4 NKE        0.2 
## 5 TSLA       0.1

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: 125 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.0306
##  2 2013-02-28 -0.0314
##  3 2013-03-28  0.0185
##  4 2013-04-30  0.0794
##  5 2013-05-31  0.0506
##  6 2013-06-28 -0.0139
##  7 2013-07-31  0.136 
##  8 2013-08-30  0.0517
##  9 2013-09-30  0.0821
## 10 2013-10-31  0.0190
## # … with 115 more rows

5 Simulating growth of a dollar

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

## [1] 0.01786888

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

## [1] 0.0597627

6 Simulation function

No need

7 Running multiple simulations

# Create a vector of 1s as a starting point
sims <- 51
starts <- rep(1, sims) %>%
    set_names(paste("sim", 1:sims, sep = ""))
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

# for reproducible research
set.seed(1234)

# Simulate
monte_carlo_sim_51 <- starts %>%
    # Simulate
    
    map_dfc(simulate_accumulation,
            N     = 120,
            mean  = mean_port_return,
            stdev = stddev_port_return) %>%
    # Add the column, month
    mutate(month = seq(1:nrow(.))) %>%
    # Arrange column names
    select(month, everything()) %>%
    set_names(c("month", names(starts))) %>%
    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
## # … with 6,161 more rows

# Calculate the quantiles for simulated values
probs <- c(.005, .025, .25, .5, .75, .975, .995)
monte_carlo_sim_51 %>%
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%
    # Find the quantiles
    quantile(probs = probs) %>%
    round(2)

##  0.5%  2.5%   25%   50%   75% 97.5% 99.5% 
##  1.91  2.13  4.02  7.10 11.24 19.71 34.13

8 Visualizing simulations with ggplot

Line Plot of Simulations with Max, Median, and Min

Based on the Monte Carlo simulation results, how much should you expect from your $100 investment after 10 years? What is the best-case scenario? What is the worst-case scenario? What are limitations of this simulation analysis?

Based on the Monte Carlo simulation results, you should expect to see a return of around 7% or a return of $7 on your original $100. The best-case scenario would be a return of around 37%, or a return of $37 on your original $100. The worst-case scenario is still a positive return of around 2% or $2 on the original $100. This data shows that no matter what you will still see a positive return on your investment over the span of 10 years.

monte_carlo_sim_51 %>%
    ggplot(aes(x = month, y = growth, col = sim)) +
    geom_line() +
    theme(legend.position = "none")

# Simplify the plot
sim_summary <- monte_carlo_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  38.6   7.10  1.85

monte_carlo_sim_51 %>%
    group_by(sim) %>%
    filter(last(growth) == sim_summary$max |
           last(growth) == sim_summary$median |
           last(growth) == sim_summary$min) %>%
    # Plot
    ggplot(aes(month, growth, col = sim)) +
    geom_line() +
    theme()