Monte Carlo Simulation in R – Part I

Jonathan Regenstein demonstrates running and visualizing Monte Carlo portfolio simulations in R with RStudio.

Monte Carlo relies on repeated, random sampling, and we will sample based on two parameters: mean and standard deviation of portfolio returns. 

+ SPY (S&P500 fund) weighted 25%
+ EFA (a non-US equities fund) weighted 25%
+ IJS (a small-cap value fund) weighted 20%
+ EEM (an emerging-mkts fund) weighted 20%
+ AGG (a bond fund) weighted 10%

Before we can simulate that portfolio, we need to calculate the historical portfolio monthly returns, which was covered in this article on Introduction to Portfolio Returns.

I won’t go through the logic again, but the code is here: 

# This is the package we need for today's post.
library(tidyquant)
library(tidyverse)
library(timetk)
library(broom)

symbols <- c("SPY","EFA", "IJS", "EEM","AGG")

prices <- 
  getSymbols(symbols, src = 'yahoo', 
             from = "2012-12-31",
             to = "2017-12-31",
             auto.assign = TRUE, warnings = FALSE) %>% 
  map(~Ad(get(.))) %>%
  reduce(merge) %>% 
  `colnames<-`(symbols)

w <- c(0.25, 0.25, 0.20, 0.20, 0.10)

asset_returns_long <-  
  prices %>% 
  to.monthly(indexAt = "lastof", OHLC = FALSE) %>% 
  tk_tbl(preserve_index = TRUE, rename_index = "date") %>%
  gather(asset, returns, -date) %>% 
  group_by(asset) %>%  
  mutate(returns = (log(returns) - log(lag(returns)))) %>% 
  na.omit()

portfolio_returns_tq_rebalanced_monthly <- 
  asset_returns_long %>%
  tq_portfolio(assets_col  = asset, 
               returns_col = returns,
               weights     = w,
               col_rename  = "returns",
               rebalance_on = "months")

We will be working with the data object portfolio_returns_tq_rebalanced_monthly and we first find the mean and standard deviation of returns.

We will name those variables mean_port_return and stddev_port_return.

mean_port_return <- 
  mean(portfolio_returns_tq_rebalanced_monthly$returns)

stddev_port_return <- 
  sd(portfolio_returns_tq_rebalanced_monthly$returns)

Then we use the rnorm() function to sample from a distribution with mean equal to mean_port_return and standard deviation equal to stddev_port_return. That is the crucial random sampling that underpins this exercise.

We also must decide how many draws to pull from this distribution, meaning how many monthly returns we will simulate. 120 months is 10 years and that feels like a good amount of time.

simulated_monthly_returns <- rnorm(120, 
                                   mean_port_return, 
                                   stddev_port_return)

Have a quick look at the simulated monthly returns.

head(simulated_monthly_returns)

[1]  0.050944351 -0.017579195  0.008322081  0.007901221  0.016835474
[6] -0.028979050

tail(simulated_monthly_returns)

[1] -0.010568223 -0.033228157 -0.012189181 -0.002823064  0.040136745
[6] -0.001618285

Next, we calculate how a dollar would have grown given those random monthly returns. We first add a 1 to each of our monthly returns, because we start with $1.

simulated_returns_add_1 <- 
  tibble(c(1, 1 + simulated_monthly_returns)) %>% 
  `colnames<-`("returns")

head(simulated_returns_add_1)

# A tibble: 6 x 1
  returns
    
1   1.00 
2   1.05 
3   0.982
4   1.01 
5   1.01 
6   1.02 

In the next post, Jonathan will show us how to convert the data into the cumulative growth of a dollar using several R packages.

Jonathan Regenstein, Director of Financial Services, RStudio.
@jkregenstein  @rstudio. For additional R scripts, see the “Reproducible Finance with R: Code Flows and Shiny Apps for Portfolio Analysis” article.