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("SBUX", "AAPL", "VZ", "T", "TSLA")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2022-12-31")

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] "AAPL" "SBUX" "T"    "TSLA" "VZ"

# 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 SBUX       0.25
## 3 T          0.2 
## 4 TSLA       0.2 
## 5 VZ         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: 120 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.00451
##  2 2013-02-28 -0.0132 
##  3 2013-03-28  0.0367 
##  4 2013-04-30  0.105  
##  5 2013-05-31  0.110  
##  6 2013-06-28  0.00257
##  7 2013-07-31  0.101  
##  8 2013-08-30  0.0514 
##  9 2013-09-30  0.0418 
## 10 2013-10-31  0.0241 
## # … with 110 more rows

5 Simulating growth of a dollar

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

## [1] 0.01509236

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

## [1] 0.05616721

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

# Simulate
set.seed(1234)
monte_carlo_sim_51 <- starts %>%
    # Simulate
    map_dfc(simulate_accumulation,
            N     = 120,
            mean  = mean_port_return,
            stdev = stddev_port_return) %>%
    # Add column month
    mutate(month = seq(1:nrow(.))) %>%
    
    # Rearrange 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

# Find quantiles 
monte_carlo_sim_51 %>%
    
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%
    
    
    quantile(probs = c(0, .25, .5, .75, 1)) %>%
    round(2)

##    0%   25%   50%   75%  100% 
##  1.47  3.05  5.22  8.05 25.70

8 Visualizing simulations with ggplot

monte_carlo_sim_51 %>%
    ggplot(aes(x = month, y = growth, col = sim)) +
    geom_line() +
    theme(legend.position = "none") +
    theme(plot.title = element_text(hjust = 0.5)) +
    
    labs(title = "Simulating Growth of 1$ over 120 months")

# 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  25.7   5.22  1.47

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(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 Minimum Simulation")

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 off of the Monte Carlo siumlation results you should expect from your $100 investment after 20 years to return $500. The best-case scenario is a return of $2600 and the worst-case scenario would be $100. The Limitations of this analysis are a max of $3900 and a minumn of $100.