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("UPS", "FDX", "MSFT")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2017-12-31")

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] "FDX"  "MSFT" "UPS"

# weights
weights <- c(0.5, 0.3, 0.2)
weights

## [1] 0.5 0.3 0.2

w_tbl <- tibble(symbols, weights)
w_tbl

## # A tibble: 3 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 FDX         0.5
## 2 MSFT        0.3
## 3 UPS         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: 60 × 2
##    date       returns
##    <date>       <dbl>
##  1 2013-01-31  0.0732
##  2 2013-02-28  0.0353
##  3 2013-03-28 -0.0185
##  4 2013-04-30  0.0218
##  5 2013-05-31  0.0318
##  6 2013-06-28  0.0105
##  7 2013-07-31  0.0126
##  8 2013-08-30  0.0214
##  9 2013-09-30  0.0432
## 10 2013-10-31  0.102 
## # … with 50 more rows

5 Simulating growth of a dollar

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

## [1] 0.01718291

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

## [1] 0.04269822

6 Simulation function

No need

7 Running multiple simulations

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
    set.seed(1234)
  monte_carlo_sim51 <- 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 months
        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_sim51

## # A tibble: 12,291 × 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 12,281 more rows

monte_carlo_sim51 %>%
    group_by(sim) %>% 
    summarize(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%
    quantile(probs = c(0, 0.25, 0.5, 0.75, 1)) %>%
    round(2)

##       0%      25%      50%      75%     100% 
##  1238.16  3720.59  5744.61  8663.37 15591.95

8 Visualizing simulations with ggplot

sim_summary <- monte_carlo_sim51 %>%
    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 15592.  5745. 1238.

# Step 2, plot
    monte_carlo_sim51 %>%
        
        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 = "Max, Median, 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 20 years? What is the best-case scenario? What is the worst-case scenario? What are limitations of this simulation analysis?

##The best case scenario would be that it turns into close to 15,000. The worst case is that after 20 years it turns into around 1000. Some of the limitations would be if there were a stock market crash. Furthermore, one needs to set the parameters correctly so that it is a true simulation and is fairly acurate.