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", "BABA", "JNJ", "GE", "AMZN")

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] "AMZN" "BABA" "GE"   "JNJ"  "LLY"

# weights
weights <- c(0.3, 0.15, 0.15, 0.2, 0.2)
weights

## [1] 0.30 0.15 0.15 0.20 0.20

w_tbl <- tibble(symbols, weights)
w_tbl

## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AMZN       0.3 
## 2 BABA       0.15
## 3 GE         0.15
## 4 JNJ        0.2 
## 5 LLY        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: 156 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0535 
##  2 2013-02-28  0.0189 
##  3 2013-03-28  0.0233 
##  4 2013-04-30 -0.0163 
##  5 2013-05-31  0.0170 
##  6 2013-06-28 -0.00219
##  7 2013-07-31  0.0645 
##  8 2013-08-30 -0.0476 
##  9 2013-09-30  0.0344 
## 10 2013-10-31  0.0703 
## # ℹ 146 more rows

5 Simulating growth of a dollar

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

## [1] 0.01358603

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

## [1] 0.04558117

6 Simulation function

No need

7 Running multiple simulations

# Create a vector of 1s as starting point
sims <- 51
starts<- rep(1, sims) %>%
    set_names(paste0("sim", 1:sims))

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)
monte_carlo_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")

monte_carlo_sim_51

## # A tibble: 12,342 × 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 12,332 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% 
##  4.65 15.13 24.18 37.45 70.18

8 Visualizing simulations with ggplot

Line Plot of Simulations with Max, Median, and Min

# 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  70.2   24.2  4.65

# Plot
monte_carlo_sim_51 %>%
    # filter for max, median and 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 $1 over 240 months", 
         subtitle = "Maximum, Median, and Minimum Simulation")

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?

I would expect the $100 investment return over 4 times the initial value. The best case scenario is over 7 times and the worst case scenario is a little under 2 times. This analysis shows consistent growth of this portfolio and it is likely to provide positive returns.