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

# Choose stocks

symbols <- c("AAPL", "NVDA", "ADBE", "AVGO", "AMD")

# Using tq_get() ----
prices <- tq_get(x = symbols,
                 get = "stock.prices",
                 from = "2012-12-31",
                 to = "2023-12-13")

2 Convert prices to returns (monthly)

asset_returns_tbl <- prices %>%

    # Calculate monthly returns
    group_by(symbol) %>%
    tq_transmute(select = adjusted,
                 mutate_fun = periodReturn,
                 period = "monthly",
                 type = "log") %>%
    slice(-1) %>%
    ungroup() %>%

    # remane
    set_names(c("asset", "date", "returns"))

# period_returns = c("yearly", "quarterly", "monthly", "weekly")

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" "ADBE" "AMD"  "AVGO" "NVDA"

# 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 ADBE       0.25
## 3 AMD        0.2 
## 4 AVGO       0.2 
## 5 NVDA       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: 132 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.00258
##  2 2013-02-28 -0.0105 
##  3 2013-03-28  0.0430 
##  4 2013-04-30  0.0127 
##  5 2013-05-31  0.102  
##  6 2013-06-28 -0.0162 
##  7 2013-07-31  0.0255 
##  8 2013-08-30 -0.00421
##  9 2013-09-30  0.0858 
## 10 2013-10-31  0.0156 
## # ℹ 122 more rows

5 Simulating growth of a dollar

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

## [1] 0.02584519

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

## [1] 0.07587188

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

# 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
## # ℹ 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% 
##  3.41  3.88  7.84 11.70 18.42 57.82 60.17

8 Visualizing simulations with ggplot

Line Plot of Simulations with Max, Median, and Min

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  60.2   11.7  3.27

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()

Based on the Monte Carlo simulation results, how much should you expect from your $100 investment after 20 years? What is the best-case scenario? What is the worst-case scenario? What are limitations of this simulation analysis?