Retirement : simulating wealth with random returns, inflation and withdrawals – Shiny web application

April 6, 2013
By

(This article was first published on Systematic Investor » R, and kindly contributed to R-bloggers)

Today, I want to share the Retirement : simulating wealth with random returns, inflation and withdrawalsShiny web application (code at GitHub).

This application was developed and contributed by Pierre Chretien, I only made minor updates. This is application is a great example of how easy it is to convert your R script into interactive Shiny web application.

Please see below the sample script to simulate wealth random returns, inflation and withdrawals:

#-------------------------------------
# Inputs
#-------------------------------------

# Initial capital
start.capital = 2000000

# Investment
annual.mean.return = 5 / 100
annual.ret.std.dev = 7 / 100

# Inflation
annual.inflation = 2.5 / 100
annual.inf.std.dev = 1.5 / 100

# Withdrawals
monthly.withdrawals = 10000

# Number of observations (in Years)
n.obs = 20

# Number of simulations
n.sim = 200

#-------------------------------------
# Simulation
#-------------------------------------

# number of months to simulate
n.obs = 12 * n.obs


# monthly Investment and Inflation assumptions
monthly.mean.return = annual.mean.return / 12
monthly.ret.std.dev = annual.ret.std.dev / sqrt(12)

monthly.inflation = annual.inflation / 12
monthly.inf.std.dev = annual.inf.std.dev / sqrt(12)


# simulate Returns
monthly.invest.returns = matrix(0, n.obs, n.sim)
monthly.inflation.returns = matrix(0, n.obs, n.sim)
  
monthly.invest.returns[] = rnorm(n.obs * n.sim, mean = monthly.mean.return, sd = monthly.ret.std.dev)
monthly.inflation.returns[] = rnorm(n.obs * n.sim, mean = monthly.inflation, sd = monthly.inf.std.dev)

# simulate Withdrawals
nav = matrix(start.capital, n.obs + 1, n.sim)
for (j in 1:n.obs) {
	nav[j + 1, ] = nav[j, ] * (1 + monthly.invest.returns[j, ] - monthly.inflation.returns[j, ]) - monthly.withdrawals
}

# once nav is below 0 => run out of money
nav[ nav < 0 ] = NA

# convert to millions
nav = nav / 1000000

#-------------------------------------
# Plots
#-------------------------------------
layout(matrix(c(1,2,1,3),2,2))

# plot all scenarios    
matplot(nav, type = 'l', las = 1, xlab = 'Months', ylab = 'Millions', 
	main = 'Projected Value of initial capital')

# plot % of scenarios that are still paying
p.alive = 1 - rowSums(is.na(nav)) / n.sim

plot(100 * p.alive, las = 1, xlab = 'Months', ylab = 'Percentage Paying', 
	main = 'Percentage of Paying Scenarios', ylim=c(0,100))
grid()	

# plot distribution of final wealth
final.nav = nav[n.obs + 1, ]
	final.nav = final.nav[!is.na(final.nav)]

plot(density(final.nav, from=0, to=max(final.nav)), las = 1, xlab = 'Final Capital', 
	main = paste('Distribution of Final Capital,', 100 * p.alive[n.obs + 1], '% are still paying'))
grid()	

plot1

The corresponding Shiny web application consists of two files:

  • ui.r – User Interface
  • server.r – R simulations and calculations

Following is the user interface (ui.r) that maps and describes required inputs for the retirement simulation:

# Define UI for application that plots random distributions 
shinyUI(pageWithSidebar(

  # Application title
  headerPanel("Retirement : simulating wealth with random returns, inflation and withdrawals"),

  # Sidebar with a slider input for number of observations
  sidebarPanel(
    sliderInput("n.obs", 
                "Number of observations (in Years):", 
                min = 0, 
                max = 40, 
                value = 20),

    sliderInput("start.capital", 
                "Initial capital invested :", 
                min = 100000, 
                max = 10000000, 
                value = 2000000,
                step = 100000,
                format="$#,##0",
                locale="us"),

    sliderInput("annual.mean.return", 
                "Annual return from investments (in %):", 
                min = 0.0, 
                max = 30.0, 
                value = 5.0,
                step = 0.5),

    sliderInput("annual.ret.std.dev", 
                "Annual volatility from investments (in %):", 
                min = 0.0, 
                max = 25.0, 
                value = 7.0, 
                step = 0.1),

    sliderInput("annual.inflation", 
                "Annual inflation (in %):", 
                min = 0, 
                max = 20, 
                value = 2.5,
                step = 0.1),

    sliderInput("annual.inf.std.dev", 
                "Annual inflation volatility. (in %):", 
                min = 0.0, 
                max = 5.0,
                value = 1.5,
                step = 0.05),

    sliderInput("monthly.withdrawals", 
                "Monthly capital withdrawals:", 
                min = 1000, 
                max = 100000, 
                value = 10000,
                step = 1000,
                format="$#,##0",
                locale="us",),
                
    sliderInput("n.sim", 
                "Number of simulations:", 
                min = 0, 
                max = 2000, 
                value = 200)
                
  ),

  # Show a plot of the generated distribution
  mainPanel(
    plotOutput("distPlot", height = "600px")
  )
))

The last step is modify the retirement simulation logic to use user inputs:

library(shiny)

# Define server logic required to generate and plot a random distribution
#
# Idea and original code by Pierre Chretien
# Small updates by Michael Kapler 
#
shinyServer(function(input, output) {

  # Function that generates scenarios and computes NAV.
  getNav <- reactive({ 
	#-------------------------------------
	# Inputs
	#-------------------------------------
	
	# Initial capital
	start.capital = input$start.capital
	
	# Investment
	annual.mean.return = input$annual.mean.return / 100
	annual.ret.std.dev = input$annual.ret.std.dev / 100
	
	# Inflation
	annual.inflation = input$annual.inflation / 100
	annual.inf.std.dev = input$annual.inf.std.dev / 100
	
	# Withdrawals
	monthly.withdrawals = input$monthly.withdrawals
	
	# Number of observations (in Years)
	n.obs = input$n.obs
	
	# Number of simulations
	n.sim = input$n.sim
	
	#-------------------------------------
	# Simulation
	#-------------------------------------
	
	# number of months to simulate
	n.obs = 12 * n.obs
	
	
	# monthly Investment and Inflation assumptions
	monthly.mean.return = annual.mean.return / 12
	monthly.ret.std.dev = annual.ret.std.dev / sqrt(12)
	
	monthly.inflation = annual.inflation / 12
	monthly.inf.std.dev = annual.inf.std.dev / sqrt(12)
	
	
	# simulate Returns
	monthly.invest.returns = matrix(0, n.obs, n.sim)
	monthly.inflation.returns = matrix(0, n.obs, n.sim)
	  
	monthly.invest.returns[] = rnorm(n.obs * n.sim, mean = monthly.mean.return, sd = monthly.ret.std.dev)
	monthly.inflation.returns[] = rnorm(n.obs * n.sim, mean = monthly.inflation, sd = monthly.inf.std.dev)
	
	# simulate Withdrawals
	nav = matrix(start.capital, n.obs + 1, n.sim)
	for (j in 1:n.obs) {
		nav[j + 1, ] = nav[j, ] * (1 + monthly.invest.returns[j, ] - monthly.inflation.returns[j, ]) - monthly.withdrawals
	}	
	
	# once nav is below 0 => run out of money
	nav[ nav < 0 ] = NA
	
	# convert to millions
	nav = nav / 1000000
	
	return(nav)  
  })
  
  # Expression that plot NAV paths. 
  output$distPlot <- renderPlot({
	nav = getNav()

	layout(matrix(c(1,2,1,3),2,2))
	
	# plot all scenarios    
	matplot(nav, type = 'l', las = 1, xlab = 'Months', ylab = 'Millions', 
		main = 'Projected Value of initial capital')

		
	# plot % of scenarios that are still paying
	p.alive = 1 - rowSums(is.na(nav)) / ncol(nav)
	
	plot(100 * p.alive, las = 1, xlab = 'Months', ylab = 'Percentage Paying', 
		main = 'Percentage of Paying Scenarios', ylim=c(0,100))
	grid()	

		
	last.period = nrow(nav)
  	
	# plot distribution of final wealth
	final.nav = nav[last.period, ]
		final.nav = final.nav[!is.na(final.nav)]
	
	if(length(final.nav) ==  0) return()		
	
	plot(density(final.nav, from=0, to=max(final.nav)), las = 1, xlab = 'Final Capital', 
		main = paste('Distribution of Final Capital,', 100 * p.alive[last.period], '% are still paying'))
	grid()	
  })
		
})

We all done now!!! Shiny is amazing in the way it allows you to convert your script into interactive web application with just two simple steps.

Please play around with the Retirement : simulating wealth with random returns, inflation and withdrawalsShiny web application (code at GitHub).

Have a good weekend


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