# Load packages

# Core
library(tidyverse)
library(tidyquant)

# Import Excel files
library(readxl)

# time series
library(timetk)

Goal

Simulate future portfolio returns

five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG”

market: “SPY”

from 2012-12-31 to 2017-12-31

1 Import stock prices

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

# 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 x 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

# ?tq_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 x 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 growht of a dollar

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

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

# Construct a normal distribution
simulated_monthly_returns <- rnorm(120, mean_port_return, stddev_port_return)

# Add a dollar
simulated_returns_add_1 <- tibble(returns = c(1, 1 + simulated_monthly_returns))

# Calculate the cumulative growth of a dollar
simulated_growth <- simulated_returns_add_1 %>%
    mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
    select(growth)

# Check the compound annual growth rate
cagr <- ((simulated_growth$growth[nrow(simulated_growth)]^(1/10)) - 1) * 100
cagr
## [1] 5.646367

6 Several simulation functions

simulate_acculation <- function(init_value, N, mean, stdev) {

    tibble(returns = c(init_value, 1 + rnorm(N, mean, stdev))) %>%
        mutate(growth = accumulate(returns, function(x, y) x*y)) %>%
        select(growth)

}

# dump(list = c("simulate_acculation"), file = "00_scripts/simulate_acculation.R")

simulate_acculation(1, 120, mean_port_return, stddev_port_return)
## # A tibble: 121 x 1
##    growth
##     <dbl>
##  1   1   
##  2   1.06
##  3   1.05
##  4   1.07
##  5   1.11
##  6   1.11
##  7   1.12
##  8   1.11
##  9   1.09
## 10   1.09
## # ... with 111 more rows

7 Running multiple simulations

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

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
monte_carlo_sim_51 <- starts %>%

    # Simulate
    map_dfc(simulate_acculation,
            N     = 120,
            mean  = mean_port_return,
            stdev = stddev_port_return) %>%

    # Add the column, month
    mutate(month = seq(1:nrow(.))) %>%

    # Arrange column names
    select(month, everything()) %>%
    set_names(c("month", names(starts))) %>%

    pivot_longer(cols = -month, names_to = "sim", values_to = "growth")

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))


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()

# Calculate the quantiles for simulated values

probs <- c(.005, .025, .25, .5, .75, .975, .995)

monte_carlo_sim_51 %>%

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

    # Find the quantiles
    quantile(probs = probs) %>%
    round(2)
##  0.5%  2.5%   25%   50%   75% 97.5% 99.5% 
##  1.17  1.40  1.84  2.03  2.39  3.18  3.76