Apply it to your data 13

# Load packages

# Core
library(tidyverse)
library(tidyquant)

# Source function
source("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("BA", "NVTS", "AES", "JPM", "ITA")

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] "AES"  "BA"   "ITA"  "JPM"  "NVTS"

# 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 AES        0.25
## 2 BA         0.25
## 3 ITA        0.2 
## 4 JPM        0.2 
## 5 NVTS       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: 144 × 2
##    date          returns
##    <date>          <dbl>
##  1 2013-01-31  0.0166   
##  2 2013-02-28  0.0428   
##  3 2013-03-28  0.0515   
##  4 2013-04-30  0.0510   
##  5 2013-05-31  0.0238   
##  6 2013-06-28  0.0000673
##  7 2013-07-31  0.0451   
##  8 2013-08-30 -0.0195   
##  9 2013-09-30  0.0585   
## 10 2013-10-31  0.0530   
## # ℹ 134 more rows

5 Simulating growth of a dollar

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

## [1] 0.00673015

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

## [1] 0.06236086

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(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

#Simulate
#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: 12,291 × 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 12,281 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% 
##  0.42  2.15  4.22  7.45 17.71

8 Visualizing simulations with ggplot

Line Plot of Simulations with Max, Median, and Min

monte_carlo_sim_51 %>%
    
    ggplot(aes(x = month, y = growth, color = sim)) +
    geom_line() +
    theme(legend.position = "none") +
    theme(plot.title = element_text(hjust = 0.5)) +
    
    labs(title = "simulating growht of $100 over 240 months")

# 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  17.7   4.22 0.421

#Step 2 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 $100 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?

The maximum return would be $ 1,770, the median $ 422, and the minimum $ 42.10, having a large spread over the 240 month period. this portfolio would benifit from an active portfolio style as it reached its peak value around the 150 month period at around 20.5, but is not shown as the simulation at the end of the period that perfored that best of 17.7, the limitation of this simulation is that it does not consider negative distrabutions allowing only normal distrabution.