Apply it to your data 13

# Load packages

# Core
library(tidyverse)
library(tidyquant)

# Source function
source("../00_scripts/simulate_accumlation.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("HMC", "WMT", "TGT")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2023-01-01")

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] "HMC" "TGT" "WMT"

# weights
weights <- c(0.3,0.3,0.4)
weights

## [1] 0.3 0.3 0.4

w_tbl <- tibble(symbols, weights)
w_tbl

## # A tibble: 3 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 HMC         0.3
## 2 TGT         0.3
## 3 WMT         0.4

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  0.0222 
##  2 2013-02-28  0.0168 
##  3 2013-03-28  0.0578 
##  4 2013-04-30  0.0375 
##  5 2013-05-31 -0.0344 
##  6 2013-06-28 -0.00560
##  7 2013-07-31  0.0275 
##  8 2013-08-30 -0.0673 
##  9 2013-09-30  0.0277 
## 10 2013-10-31  0.0326 
## # … 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] 0.005506112

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

## [1] 0.04768257

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

# Simulate 
# For Reproducible research 
set.seed(1234)

monte_carlo_sim_51 <- starts %>% 
    
    #Simulate 
    map_dfc(.x = ., 
            .f = ~simulate_accumulation(initial_value = .x, 
                                        N = 120, 
                                        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")

monte_carlo_sim_51

## # A tibble: 6,171 × 3
##    month sim   growth
##    <int> <chr>  <dbl>
##  1     1 sim1     100
##  2     1 sim2     100
##  3     1 sim3     100
##  4     1 sim4     100
##  5     1 sim5     100
##  6     1 sim6     100
##  7     1 sim7     100
##  8     1 sim8     100
##  9     1 sim9     100
## 10     1 sim10    100
## # … with 6,161 more rows

# Find quantiles 
monte_carlo_sim_51 %>%
    
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%
    
    quantile(probs = c(0,0.25, 0.5, 0.75, 1)) %>%
    round(2)

##     0%    25%    50%    75%   100% 
##  58.96 110.21 174.21 252.67 682.09

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_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  682.   174.  59.0

# Step 2 Plot 
monte_carlo_sim_51 %>%
    
    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 $1 over 120 months", 
         subtitle = "Max, Median, and Minimum Simulation")

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?

After 10 years with my $100 investment, I would expect my portfolio to only grow to around $200. The best-case scenario would put my investment over $600 and my worst-case scenario would cut my investment in half, to around $50. This investment is very volatile and would be a risky investment. If I was able to push my investment start data back even further, I would be able to have a better understanding of the market.