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("SPY", "EFA", "IJS", "EEM", "AGG")

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] "AGG" "EEM" "EFA" "IJS" "SPY"

# 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 AGG        0.25
## 2 EEM        0.25
## 3 EFA        0.2 
## 4 IJS        0.2 
## 5 SPY        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: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0204 
##  2 2013-02-28 -0.00239
##  3 2013-03-28  0.0121 
##  4 2013-04-30  0.0174 
##  5 2013-05-31 -0.0128 
##  6 2013-06-28 -0.0247 
##  7 2013-07-31  0.0321 
##  8 2013-08-30 -0.0224 
##  9 2013-09-30  0.0511 
## 10 2013-10-31  0.0301 
## # … 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] 0.005899134

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

## [1] 0.02347492

6 Simulation function

No need

7 Running multiple simulations

sims <- 51
starts <- rep(100, sims) %>%
    set_names(paste0("sim", 1:sims))

monte_carlo_sim_51 <- starts %>%
    
    map_dfc(.x = .,
            .f =~ simulate_accumulation(initial_value = .x, N = 240, mean_return = mean_port_return, sd_return = stddev_port_return)) %>%
    
    mutate(month = 1:nrow(.)) %>%
    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: 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_sim_51 %>%
    
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%
    
    quantile(probs = c(0, 0.25, 0.50, 0.75, 1)) %>%
    round(2)

##     0%    25%    50%    75%   100% 
## 179.67 320.15 391.89 498.35 847.11

8 Visualizing simulations with ggplot

sim_summary <- monte_carlo_sim_51 %>%
    
    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    
    summarise(max = max(growth), median = median(growth), min = min(growth))
   

monte_carlo_sim_51 %>%
    
    group_by(sim) %>%
    filter(last(growth) == sim_summary$max |
               last(growth) == sim_summary$median |
               last(growth) == sim_summary$min) %>%
    ungroup() %>%
    
    
    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 = "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 20 years? What is the best-case scenario? What is the worst-case scenario? What are limitations of this simulation analysis?

Yo should expect your $100 investment to be in the range of $300 to $500. Best case senario your investment could turn into around the range of $800 to $1000 and in the worst case scenario in the $100 to $200 range. The limitations of this simulation is that the simulation function uses normal distribution of returns when in reality that is usually not the case. Also the data set is from a time period of a raging bull market.