{"id":4978,"date":"2019-05-31T11:00:27","date_gmt":"2019-05-31T15:00:27","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=4978"},"modified":"2024-05-14T11:30:15","modified_gmt":"2024-05-14T15:30:15","slug":"monte-carlo-simulation-in-r-part-i","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/monte-carlo-simulation-in-r-part-i\/","title":{"rendered":"Monte Carlo Simulation in R &#8211; Part I"},"content":{"rendered":"\n<p><em>Jonathan Regenstein demonstrates running and visualizing Monte Carlo portfolio simulations in R with RStudio. <\/em><\/p>\n\n\n\n<p>Monte Carlo relies on repeated, random sampling, and we will sample based on two parameters: mean and standard deviation of portfolio returns.\u00a0<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">+ SPY (S&amp;P500 fund) weighted 25%\n+ EFA (a non-US equities fund) weighted 25%\n+ IJS (a small-cap value fund) weighted 20%\n+ EEM (an emerging-mkts fund) weighted 20%\n+ AGG (a bond fund) weighted 10%<\/code><\/pre>\n\n\n\n<p>Before we can simulate that portfolio, we need to calculate the historical portfolio monthly returns, which was covered in this article on&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.reproduciblefinance.com\/2017\/10\/12\/introduction-to-portfolio-returns\/\" target=\"_blank\">Introduction to Portfolio Returns<\/a>.<\/p>\n\n\n\n<p>I won\u2019t go through the logic again, but the code is here:&nbsp;<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\"># This is the package we need for today's post.\nlibrary(tidyquant)\nlibrary(tidyverse)\nlibrary(timetk)\nlibrary(broom)\n\nsymbols &lt;- c(\"SPY\",\"EFA\", \"IJS\", \"EEM\",\"AGG\")\n\nprices &lt;- \n  getSymbols(symbols, src = 'yahoo', \n             from = \"2012-12-31\",\n             to = \"2017-12-31\",\n             auto.assign = TRUE, warnings = FALSE) %>% \n  map(~Ad(get(.))) %>%\n  reduce(merge) %>% \n  `colnames&lt;-`(symbols)\n\nw &lt;- c(0.25, 0.25, 0.20, 0.20, 0.10)\n\nasset_returns_long &lt;-  \n  prices %>% \n  to.monthly(indexAt = \"lastof\", OHLC = FALSE) %>% \n  tk_tbl(preserve_index = TRUE, rename_index = \"date\") %>%\n  gather(asset, returns, -date) %>% \n  group_by(asset) %>%  \n  mutate(returns = (log(returns) - log(lag(returns)))) %>% \n  na.omit()\n\nportfolio_returns_tq_rebalanced_monthly &lt;- \n  asset_returns_long %>%\n  tq_portfolio(assets_col  = asset, \n               returns_col = returns,\n               weights     = w,\n               col_rename  = \"returns\",\n               rebalance_on = \"months\")<\/code><\/pre>\n\n\n\n<p>We will be working with the data object&nbsp;<strong>portfolio_returns_tq_rebalanced_monthly<\/strong>&nbsp;and we first find the mean and&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.reproduciblefinance.com\/code\/standard-deviation\/\" target=\"_blank\">standard deviation<\/a>&nbsp;of returns.<\/p>\n\n\n\n<p>We will name those variables&nbsp;<strong>mean_port_return<\/strong>&nbsp;and&nbsp;<strong>stddev_port_return<\/strong>.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">mean_port_return &lt;- \n  mean(portfolio_returns_tq_rebalanced_monthly$returns)\n\nstddev_port_return &lt;- \n  sd(portfolio_returns_tq_rebalanced_monthly$returns)<\/code><\/pre>\n\n\n\n<p>Then we use the&nbsp;<strong>rnorm()<\/strong>&nbsp;function to sample from a distribution with mean equal to&nbsp;<strong>mean_port_return<\/strong>&nbsp;and standard deviation equal to&nbsp;<strong>stddev_port_return<\/strong>. That is the crucial random sampling that underpins this exercise.<\/p>\n\n\n\n<p>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.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">simulated_monthly_returns &lt;- rnorm(120, \n                                   mean_port_return, \n                                   stddev_port_return)<\/code><\/pre>\n\n\n\n<p>Have a quick look at the simulated monthly returns.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">head(simulated_monthly_returns)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">[1]  0.050944351 -0.017579195  0.008322081  0.007901221  0.016835474\n[6] -0.028979050<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">tail(simulated_monthly_returns)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">[1] -0.010568223 -0.033228157 -0.012189181 -0.002823064  0.040136745\n[6] -0.001618285<\/code><\/pre>\n\n\n\n<p>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.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">simulated_returns_add_1 &lt;- \n  tibble(c(1, 1 + simulated_monthly_returns)) %>% \n  `colnames&lt;-`(\"returns\")\n\nhead(simulated_returns_add_1)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\"># A tibble: 6 x 1\n  returns\n    \n1   1.00 \n2   1.05 \n3   0.982\n4   1.01 \n5   1.01 \n6   1.02 <\/code><\/pre>\n\n\n\n<p><em>In the next post, Jonathan will show us how to convert the data into the cumulative growth of a dollar using several R packages.<\/em><\/p>\n\n\n\n<p><em>Jonathan Regenstein, Director of Financial Services, RStudio. <\/em><br><em><a rel=\"noreferrer noopener\" href=\"https:\/\/twitter.com\/jkregenstein\" target=\"_blank\">@jkregenstein<\/a>&nbsp; <a rel=\"noreferrer noopener\" href=\"https:\/\/twitter.com\/rstudio\" target=\"_blank\">@rstudio<\/a>. For additional R scripts, see the \u201cReproducible Finance with R: Code Flows and Shiny Apps for Portfolio Analysis\u201d <a href=\"https:\/\/rviews.rstudio.com\/2018\/10\/29\/reproducible-finance-the-book\/\">article<\/a><\/em>. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jonathan Regenstein demonstrates running and visualizing Monte Carlo portfolio simulations in R with RStudio. <\/p>\n","protected":false},"author":198,"featured_media":5511,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,338,341,352,344,342],"tags":[1047,1043,487,508,1048,1044,1045,1046,2536],"contributors-categories":[13650],"class_list":{"0":"post-4978","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"category-ibkr-quant-news","9":"category-quant-development","10":"category-quant-north-america","11":"category-quant-regions","12":"category-r-development","13":"tag-broom","14":"tag-monte-carlo","15":"tag-r","16":"tag-rstudio","17":"tag-standard-deviation","18":"tag-tidyquant","19":"tag-tidyverse","20":"tag-timetk","21":"tag-visualization","22":"contributors-categories-rstudio"},"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v27.8) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Monte Carlo Simulation in R &#8211; Part I | IBKR Quant<\/title>\n<meta name=\"description\" content=\"Monte Carlo Simulation in R with Jonathan Regenstein. 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