Apply it to your data 13

How much should you expect from your $100 investment after 20 years?

# Load packages

# Core
library(tidyverse)
library(tidyquant)

# Source function
source("../Desktop/PSU_FIN3100_FinancialAnalytics/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 
## # ℹ 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] 0.005899136

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

## [1] 0.02347491

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

set.seed(1234)

# Simulate
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 the column, month
    mutate(month = (1:nrow(.))) %>%
    select(month, everything()) %>%
   

    # Transform to long form
    pivot_longer(cols = -month, names_to = "sim", values_to = "growth")

monte_carlo_sim_51

## # A tibble: 24,582 × 3
##    month sim         growth
##    <int> <chr>        <dbl>
##  1     1 returns...1    100
##  2     1 growth...2     100
##  3     1 returns...3    100
##  4     1 growth...4     100
##  5     1 returns...5    100
##  6     1 growth...6     100
##  7     1 returns...7    100
##  8     1 growth...8     100
##  9     1 returns...9    100
## 10     1 growth...10    100
## # ℹ 24,572 more rows

# Find quantiles

monte_carlo_sim_51 %>%

    group_by(sim) %>%
    summarise(growth = last(growth)) %>%
    ungroup() %>%
    pull(growth) %>%

    # Find the quantiles
    quantile(probs = c(0,0.25, 0.5, 0.75, 1)) %>%
    round(2)

##     0%    25%    50%    75%   100% 
##   0.96   1.01  90.81 417.64 738.34

8 Visualizing simulations with ggplot

monte_carlo_sim_51 %>%

    ggplot(aes(x = month, y = growth, col = sim)) +
    geom_line() +
    theme(legend.position = "none")

# Simplify the plot

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  738.   90.8 0.957

monte_carlo_sim_51 %>%

    group_by(sim) %>%
    filter(last(growth) == sim_summary$max |
           last(growth) == sim_summary$median |
           last(growth) == sim_summary$min) %>%

    # Plot
    ggplot(aes(month, growth, col = sim)) +
    geom_line() +
    theme()

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?

You should expect anywhere between $750 and $0 as returns. The best case scenario was at $750 at year 20, and the worst case dropped to $0 less than a year in and continued being at $0 until year 20. This simulation is limited because we can not determine a single path that the growth will follow, which makes it hard to say which of these outcomes you will receive.