Retirement : simulating wealth with random returns, inflation and withdrawals – Shiny web application
April 6, 2013
By systematicinvestor
http://www.r-bloggers.com
Today, I want to share the Retirement : simulating wealth with random returns, inflation and withdrawals – Shiny 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:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
|
#-------------------------------------
# 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()
|
- 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:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
# 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:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
|
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="" span="">
#-------------------------------------
#
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="" span="">
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
withdrawals – Shiny web
application (code at GitHub).
Have a good weekend
No hay comentarios:
Publicar un comentario