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functions.R
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functions.R
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get_CIB <- function(p, r, n){
# Annual total payments
#p <- 100
#r <- 0.03
#n <- 15
# Payments for principal
a1 <- p / (((1+r)^n - 1)/r)
a <- a1 * (1+r)^((1:n)-1)
# sum(a)
# Payments for interests
int <- numeric(n)
int <- (p - dplyr::lag(cumsum(a), 1, 0))*r
# Total payments
pmt <- a + int
list(pmt_p = a,
pmt_i = int,
pmt_tot = pmt)
}
get_CIB(100, 0.05, 20)
## Function for calculating PVB for retirees Modified
get_PVB_retiree <- function(age_fn, benefit_init, cola_assumed, dr_, decrement = df_decrement, age_max_ = max_age ) {
# calculates actuarial PV for given age, initial benefit,
# cola assumption, and mortality
# This version does not allow for generational mortality
# age_fn: current age
# benefit_init: current benefit payment
# cola_assumed: assumed future annual cola
# i: discount rate
nyear_ret <- age_max_ - age_fn + 1
decrement_fn <- filter(decrement, age >= age_fn)$qxm.post
PVB <- sum(((1 + dr_)^-(0:(nyear_ret - 1))) * c(1, cumprod(1-decrement_fn)[-nyear_ret]) * (benefit_init * (1 + cola_assumed)^(0:(nyear_ret-1))))
}
## Function for calculating PVB for actives
get_PVB_active <- function(age_fn, ea_fn, age_ret, benefit_init, cola_assumed, i, decrement = df_decrement, age_max_ = age_max) {
# calculates actuarial PV for an active plan member.
# age_fn: current age
# benefit_init: benefit payment at age age_ret
# cola_assumed: assumed future annual cola
# i: discount rate
# decrement: decrement table. qxm is the mortality rate for retirees, qxT is the total separation rate for actives (mortality included)
# mortality_ = mortality
# age_max_ = age_max
# i <- 0.075
nyear_ret <- age_max_ - age_ret + 1
decrement_ret <- filter(decrement, age >= age_ret, ea == ea_fn)$qxm
decrement_act <- filter(decrement, age>= age_fn, age< age_ret, ea == ea_fn)$qxT
PVB <- sum(((1 + i)^-(0:(nyear_ret - 1))) * c(1, cumprod(1-decrement_ret)[-nyear_ret]) * (benefit_init * (1 + cola_assumed)^(0:(nyear_ret-1)))) *
((1 + i)^-((age_ret - age_fn)) * prod(1-decrement_act))
}
gaip_inverse <- function(pmt, i, n, g){
# pmt = first-year payment, i=interest rate, n=periods, g=growth rate in payments
# calculating the principle given the first-year payment
# Note: payment at the beginning of period.
#if(end) p <- p*(1 + i)
k <- (1 + g)/(1 + i)
a_sn <- (1 - k^n )/(1 - k)
#pmt <- p/a_sn
p = pmt *a_sn
return(p)
}
#**************************************
# 1. PV of Annuities #####
#**************************************
# 1.1 function calculating temporary annuity values from age x to retirment age (fixed end)
get_tla <- function(px, i, scale = rep(1, length(px))){
# suppose the age corresponding to px runs from a1 to aN, and f = aN + 1 (eg. age 30:64, f = 65)
# The function computes a..{x, f - x} and s_a..{x, f - x}, x runing from a1 to aN.
# The length of px is f - a1
# Note that the last element is redundant, just used as a place holder.
# inputs:
# px: an vector of composite survivial probs from age x to x + n - 1. Length = n
# i: discount rate, scalar
# scale: how the annuity scale up over time. eg:
# 1) salary scale. default is a n vector of 1, meaning no salary scale. used when calculating career based annuity
# 2) simple COLA scale: COLA increasing at a fixed percentage very year.
# cashflow: The cashflow of the annuity can be specified by this argument. This is useful when calculating PV of benefits with COLA.
# output:
# tla: an n vector storing the value of temporary life annuities from age x to age x + n - 1.
tla <- numeric(length(px))
n <- length(tla)
for(j in 1:n){
v <- 1/(1 + i)^(0:(n - j)) # dicount vector
if(j < n) pxr <- cumprod(c(1, px[j:(n - 1)])) else pxr <- 1 # survival probability to retirment at age x. Note that participant always survives at the beginning of age x
SS <- scale[j:n]/scale[j] # scale
tla[j] <- sum(SS * v * pxr) # computing annuity value at j
}
return(tla)
}
get_tlaFixedEnd <- get_tla
# microbenchmark(
# get_tla(rep(0.98, 5), 0.08) # test the function
# )
# 1.1 function calculating temporary annuity values from age x to retirment age (fixed end)
# for a customized cashflow
get_tla_cashflow <- function(px, i, cashflow = rep(1, length(px))){
# suppose the age corresponding to px runs from a1 to aN, and f = aN + 1 (eg. age 30:64, f = 65)
# The function computes a..{x, f - x} and s_a..{x, f - x}, x runing from a1 to aN.
# The length of px is f - a1
# Note that the last element is redundant, just used as a place holder.
# inputs:
# px: an vector of composite survivial probs from age x to x + n - 1. Length = n
# i: discount rate, scalar
# scale: how the annuity scale up over time. eg:
# 1) salary scale. default is a n vector of 1, meaning no salary scale. used when calculating career based annuity
# 2) simple COLA scale: COLA increasing at a fixed percentage very year.
# cashflow: The cashflow of the annuity can be specified by this argument. This is useful when calculating PV of benefits with COLA.
# output:
# tla: an n vector storing the value of temporary life annuities from age x to age x + n - 1.
tla <- numeric(length(px))
n <- length(tla)
for(j in 1:n){
v <- 1/(1 + i)^(0:(n - j)) # dicount vector
if(j < n) pxr <- cumprod(c(1, px[j:(n - 1)])) else pxr <- 1 # survival probability to retirment at age x. Note that participant always survives at the beginning of age x
SS <- cashflow[j:n] # scale
tla[j] <- sum(SS * v * pxr) # computing annuity value at j
}
tla <- as.numeric(tla)
return(tla)
}
get_tla_cashflow(rep(0.98, 5), 0.08, c(1:5)) # test the function
# 1.2 function calculating temporary annuity values from a fixed entry age y to x (fixed start)
get_tla2 = function(px, i, sx = rep(1, length(px))){
# Suppose the age corresponding to px runs from a1 to aN, y = a1 (eg. age 30:65, y = 30)
# This function conputes a..{y, x - y} and s_a..{y, x - y}, x ruuning from a1 to aN.
# Note that when x = a1 = y, we define a..{y, 0} = 0. so the first element is always 0.
# For age x > y, the number of years receiviing annuity is x - y, the resulting annuity value will be placed at age x.
# eg1: x = 31, y = 30, annuity ($1) received only once at age 30, but the resulting annuity value will be placed at age 31.
# eg2: x = 65, y = 30, annuity received from age 30 to 64(total 65 years), the resulting annuity value will be placed at age 65
# Note that the last 2 survival rates and last salary scale are redundant in the calculation, they are just used as place holders.
#(calculating the value of annuity running from 30 to 64 only involves survival rate from 30 to 63,
# because the last annuity payment is paid at the begining of 64. )
# inputs:
# px: an vector of composite survivial probs from age x to x + n - 1. Length = n. The minimum length of px allowed is 2.
# i: discount rate, scalar
# sx: salary scale. default is an n vector of 1, meaning no salary scale.
# output:
# tla: an n vector storing the value of temporary life annuities from age x to age x + n - 1.
tla = numeric(length(px))
n = length(tla)
# tla[1] will be kept as 0, next calculate tla[2:n]:
for(j in 1:(n - 1)){
v <- 1/(1 + i)^(0:(j - 1)) # dicount vector
if(j == 1) pxr <- 1 else pxr <- cumprod(c(1, px[1:(j - 1)])) # survival probability to retirment at age x. Note that participant always survives at the beginning of age x
SS <- sx[1:j]/sx[1] # salary scale
tla[j + 1] <- sum(SS * v * pxr) # computing annuity value at j;
}
return(tla)
}
get_tlaFixedStart <- get_tla2
# 1.2a A simpler implementation of 1.2
get_tla2a <- function(px, i, sx = rep(1, length(px))){
n <- length(px)
tla <- numeric(n)
v <- 1/(1 + i)
tla[-1] <- cumsum(cumprod(c(1,px[1:(n-2)])* v * sx[1:(n - 1)]/sx[1])/v)
return(tla)
}
# microbenchmark(
# get_tla2(rep(0.98, 65), 0.08, rep(1.1, 65)), # test the function
# get_tla2a(rep(0.98, 65), 0.08, rep(1.1, 65))# test the function
# )
# 1.3 PVFB of term costs
get_PVFB <- function(px, v, TC){ # present values of subsets of TC (fixed end)
# This function compute the total present value of TC[j:n] at the beginning of time j, with j running from 1 to n.
# The function can be used to calculate PVFB of term costs of ancillary benefits or retirement benefits with multiple
# retirement ages.
# Inputs
# px: numeric vector of length n. Probability of survival at time 1 through n
# v : numeric. discount factor 1/(1 + i)
# TC: numeric vector of length n. A series of term costs. Term costs are valued at the begninning of period.
# Returns
# PVFBs of fixed end contracting windows of TC.
n <- length(px)
PVFB <- sapply(seq_len(n), function(j) ifelse(j == n, TC[j], sum(cumprod(c(1, (px[j:(n - 1)] * v))) * TC[j:n], na.rm = TRUE)))
return(PVFB)
}
# microbenchmark(
# get_PVFB(rep(0.98, 65), 0.08, rep(1.1, 65))
# )
# 1.4 NC of UC and PUC
get_NC.UC <- function(px, v, TC){
# This function is a variation of get_PVFB. It is used to calculate NC under UC and PUC methods.
# Below we explain the major difference between get_NC.UC and get_PVFB:
# 1. Why TC[(j + 1):n]? Remember NC is the discounted value of benefit accrual. During age x, the individual can
# accrue benefit for age x + 1 to r'', so the corresponding elements in TC are TC[(j + 1):n]. Note that
# TC[j+1] is gx.r(j+1)*qxr(j+1)*ax(j+1) in PUC.
# 2. Why start discounting from the 1st element? Since at j the individual starts accruing benefit from j + 1,
# we need to discount the value in j + 1.
# Note The last elements (at age r'') of the result is NA by construction.
# px must be survival probability from min(age) to r''.
# TC must be defined as
# UC for retirement: gx.r(x) * qxr(x) * ax(x), x running from y (entry age) to r'' (eg. 20 to 65 in Winklevoss book)
# PUC for retirement: Bx(x)/(x - y) * gx.r(x) * qxr(x) * ax(x), x running from entry age (y) to r'' (0 when x = y)
# PUC for vested terms: Bx(x)/(x - y) * gx.r(x) * qxt.a * lead(pxRm) * v^(r.max - age) * ax[age == r.max]
n <- length(px) # n is r''
Fun_NC <- function(j) ifelse(j == n, NA, sum(cumprod(px[j:(n - 1)]) * v^(1:(n-j)) * TC[(j + 1):n]))
NC <- sapply(seq_len(n), Fun_NC)
return(NC)
}
# microbenchmark(
# get_NC.UC(rep(0.98, 65), 0.08, rep(1.1, 65))
# )
# 1.5 AL of PUC
get_AL.PUC <- function(px, v, TC){
# This function is a variation of get_PVFB. It is used to calculate AL under PUC methods.
# Note that the only difference between get_AL.PUC and get_PVFB is that TC[j] is multiplied by (j - 1)
# Note that y(entry age) corresponds to index 1 and age x corresponds to index j, so at age x the individual
# has been accruing benefits for x - y years, which is equal to j - 1 years. (eg. Assuming y = 20, then when x = 21 and j = 2 the
# individual have accrued benefits for 1 year (x - y = 21 - 20 and j - 1 = 2 - 1).
# TC must be defined the same way as in get_NC.UC.
# the first element (age y) should be zero, the last element should be the same as the last element in TC.
n <- length(px) # n is r'' - y + 1
AL <- sapply(seq_len(n),
function(j) ifelse(j == n, TC[j]*(j-1), sum(cumprod(c(1, (px[j:(n - 1)] * v))) * TC[j:n] * (j - 1)))
)
return(AL)
}
# microbenchmark(
# get_AL.PUC(rep(0.98, 65), 0.08, rep(1.1, 65))
# )
#**************************************
# 2. Amortization Functions #####
#**************************************
pmt <- function(p, i, n, end = FALSE){
# amortization function with constant payment at each period
# p = principle, i = interest rate, n = periods.
# end: , if TRUE, payment at the end of period.
if(end) p <- p*(1 + i)
a_n <- (1 - (1 + i)^(-n))/(1 - 1/(1 + i))
pmt <- p / a_n
return(pmt)
}
#pmt(100, 0.02, 10)
gaip <- function(p, i, n, g, end = FALSE){
# p=principal, i=interest rate, n=periods, g=growth rate in payments
# calculating gaip directly
# end: , if TRUE, payment at the end of period.
if(end) p <- p*(1 + i)
k <- (1 + g)/(1 + i)
a_sn <- (1 - k^n )/(1 - k)
pmt <- p/a_sn
return(pmt)
}
# gaip(100, 0.10, 10, 0.04)
# gaip3(100, 0.08, 10, 0.02, end = TRUE)
# Constant dollar amortization method
amort_cd <- function(p, i, m, end = FALSE, skipY1 = FALSE){
# skipY1: if TRUE, payment of year 1 is skipped and then amort. basis is paid off in n-1 non-zero payments.
if(!skipY1) rep(pmt(p, i, m, end), m)
else c(0, rep(pmt(p*(1+i), i, m-1, end), m-1))
}
# Constant percent amortization method
amort_cp <- function(p, i, m, g, end = FALSE, skipY1 = FALSE){
# skipY1: if TRUE, payment of year 1 is skipped and then amort. basis is paid off in n-1 non-zero payments.
if(!skipY1) gaip(p, i, m, g, end)*(g + 1)^(1:m - 1)
else c(0, gaip(p*(1 + i), i, m-1, g, end)*(g + 1)^(1:(m-1) - 1))
}
# Strait line method #
amort_sl <- function(p, i, m, end = FALSE){
# Straitline amortization method
# See Winklevoss(1993, p101)
if(end){
sl <- i*(p - p*(0:(m - 1))/m) + p/m
} else {
d <- 1/(1+i)
sl <- d*(p - p*(1:m)/m) + p/m}
return(sl)
}
# Test the functions
#amort_cd(100, 0.02, 3, F, T)
#amort_cp(100, 0.02, 3, 0.03, F, T)
# amort_sl(100, 0.08, 10, F)
# amort_cp(100, 0.07, 15, 0.03, F, F) # %>% sum # 159.72
# amort_cp(100, 0.07, 15, 0.03, F, T) # %>% sum # 165.33 3.5% higher
#
# amort_cd(100, 0.07, 15, F, F) # %>% sum # 153.92
# amort_cd(100, 0.07, 15, F, skipY1) # %>% sum # 160.08 4% higher
amort_ramp5y <- function(p, i, n, end = FALSE){
# amortization function with 5-year ramp-up period and then constant payments
# p = principle, i = interest rate, n = periods.
# end: , if TRUE, payment at the end of period.
if(end) p <- p*(1 + i)
v <- 1/(1 + i)
a_n <- 0.2 + 0.4*v + 0.6*v^2 + 0.8*v^3 +
v^4 * (1 - v^(n-4))/(1-v)
pmt_full <- p / a_n
pmt_series <- pmt_full * c(0.2, 0.4, 0.6, 0.8, rep(1, n - 4))
return(pmt_series)
}
# Function for choosing amortization methods
amort_LG <- function(p, i, m, g, end = FALSE, method = "cd", skipY1 = FALSE){
# amortize the gain/loss using specified amortization method
switch(method,
cd = amort_cd(p, i ,m, end, skipY1),
cp = amort_cp(p, i, m, g, end, skipY1),
sl = amort_sl(p, i, m, end),
ramp = amort_ramp5y(p, i, m, end)
)
}
#amort_LG(100, 0.07, 15, 0.03, F, "cp", T)
#amort_LG(100, 0.07, 20, 0.03, F, "ramp", T)
#********************************
# 3.Utility functions ####
#********************************
cton <- function (cvar) as.numeric(gsub("[ ,$%]", "", cvar)) # character to numeric, eliminating "," "$" "%". chars will become NA
ht <- function (df, nrecs=6) {print(head(df, nrecs)); print(tail(df, nrecs))} # head tail
memory<-function(maxnobjs=5){
# function for getting the sizes of objects in memory
objs<-ls(envir=globalenv())
nobjs<-min(length(objs),maxnobjs)
tmp<-as.data.frame(sapply(objs, function(x) object.size(get(x)))/1048600)
tmp<-data.frame(name=row.names(tmp), sizeMB=tmp[,1])
tmp<-tmp[order(-tmp$sizeMB),]
tmp$sizeMB<-formatC(tmp$sizeMB,format="f",digits=2,big.mark=",",preserve.width="common")
print(paste("Memory available: ",memory.size(NA),sep=""))
print(paste("Memory in use before: ",memory.size(),sep=""))
print("Memory for selected objects: ")
print(head(tmp,nobjs))
print(gc())
print(paste("Memory in use after: ",memory.size(),sep=""))
}
#na2zero <- function(x){x[is.na(x)] <- 0 ;return(x)}
na2zero <- function(x){replace(x, is.na(x), 0)}
f2n <- function(x) {
if(is.numeric(x)|is.integer(x)) x else
if(!is.factor(x)) stop("Not a factor") else
as.numeric(levels(x)[x])
}
#f2n2 <- function(x) as.numeric(as.character(factor(x))) # much slower than f2n
get_geoReturn <- function(x) {
x <- x[!is.nan(x)]
x <- x[!is.na(x)]
prod(1 + x)^(1/length(x)) - 1}
## spline smoothing
splong<-function(df,fillvar,fitrange=NULL, method = "natural"){
# df should have only 3 columns: fillvar, nonfillvar [in either order], and value
# or just 2 columns, with no nonfillvar
# last column ALWAYS must be the value var
valvar<-names(df)[length(names(df))]
nonfillvar<-setdiff(names(df),c(fillvar,valvar))
f<-function(x) {
if(is.null(fitrange)) fitrange<-min(x[,fillvar]):max(x[,fillvar])
spl<-spline(x[,fillvar], x[,valvar], xout=fitrange, method = method)
dfout<-data.frame(x=spl$x, y=spl$y)
names(dfout)<-c(fillvar,valvar)
return(dfout)
}
if(length(nonfillvar)>0) dfl2<-ddply(df,c(nonfillvar),f) else dfl2<-f(df)
return(dfl2)
}
## Functions for model control
assign_parmsList <- function(paramlist, excludes = NULL, ...){
varNames <- setdiff(names(paramlist), excludes)
assign_var <- function(x) assign(x, paramlist[[x]], ...)
sapply(varNames, assign_var)
}
get_parmsList <- function(rundf, runname) { # don't exclude anything
# Assign the data from the spreadsheet for a single runname to a list. We'll pass the list to the model.
runlist <- as.list(rundf[which(rundf$runname==runname), ])
return(runlist)
}
trans_cont <- function(cont, run){
# Transform the user-defined contribution table to "long" form for the selected "run".
# Before transformation: start, duration, pct_ADC;
# After transformation: year, pct_ADC.
df_cont <- function(start, duration, pct) data.frame(year = start + 0:(duration - 1), pct_ADC = pct)
df <- with(cont %>% filter(runname == run),
mapply(df_cont,
start = start, duration = duration, pct = pct_ADC, SIMPLIFY = FALSE)) %>%
bind_rows
return(df)
}
create_returns <- function(r.mean, r.sd, period){
# Create return series with time varying mean, sd.
# Mean and sd in each period are given by "r.mean" and "r.sd".
# Length of each period is given by "period".
i.r <- unlist(mapply(rnorm, period, r.mean, r.sd)) %>% as.vector # when the length of the arguments is 1, need to convert the reusult to vector from a matrix
}
# rolling window return
get_rollingReturns <- function(returnSeries, rolling_type = c("moving", "expanding"), window){
# calculate moving window or expanding win dow geometric mean return for a return series.
window_width <- switch(rolling_type,
moving = window,
expanding = seq_along(returnSeries))
rollingReturn <- zoo::rollapply(returnSeries, width = window_width, get_geoReturn, fill = NA, align = "right")
return(rollingReturn)
}
getcell <- function(file, sheet, cell) {
require(XLConnect)
value <- readWorksheetFromFile(file, sheet=sheet, header=FALSE, region=cell, colTypes="character")
return(as.character(value))
}
xlrange <- function(file, sheet, cell1, cell2) {
startcell <- getcell(file, sheet, cell1)
endcell <- getcell(file, sheet, cell2)
range <- paste0(startcell, ":", endcell)
return(range)
}
read_ExcelRange <- function(file, sheet, cellStart = "B2", cellEnd = "B3", ...){
require(XLConnect)
range <- xlrange(file, sheet, cellStart, cellEnd)
readWorksheetFromFile(file, sheet = sheet, header=TRUE, region=range, ...)
}
#**********************************************
# 4. Functions for analyzing results ####
#**********************************************
get_quantiles <- function( runName, # character
varName, # character
data = results_all,
year.max = 100,
qts = c(0.1, 0.25, 0.5, 0.75, 0.9)){
# runName = c("R4F1") # character
# varName = "FR" # character
# data = results_all
# year.max = 100
# qts = c(0.1, 0.25, 0.5, 0.75, 0.9)
# runName = "C.ADC_r7.25" # character
# varName = "FR.MA" # character
# data = penSim_results
# year.max = 100
# qts = c(0.1, 0.25, 0.5, 0.75, 0.9)
#
df <- data %>% filter(runname %in% runName, sim >= 1) %>%
select_("runname", "sim","year", varName) %>% spread_("year", varName)
fn <- function(df) {
df_q <- sapply(select(df, -sim, -runname), function(x) quantile(x, qts, na.rm = TRUE)) %>% as.data.frame
df_q %<>% mutate(Quantile = rownames(df_q)) %>% gather(year, Value, -Quantile) %>%
mutate(#year = f2n(year),
Quantile = factor(Quantile)) %>% filter(year <= year.max)
df_q %<>% spread(Quantile, Value)
}
df <- ldply(split(df, df$runname), fn, .id = "runname")
return(df)
}
# get_quantiles2 <- function(varName, # character
# data,
# qts = c(0.1, 0.25, 0.5, 0.75, 0.9)){
#
#
# varName = "maxChg5y" # character
# data = maxChg5y
# qts = c(0.1, 0.25, 0.5, 0.75, 0.9)
#
#
#
# df <- select_(data, "sim", , varName) %>% spread_("year", varName)
#
# fn <- function(df){
# df_q <- sapply(select(df, -sim), function(x) quantile(x, qts, na.rm = TRUE)) %>% as.data.frame
#
# df_q %<>% mutate(Quantile = rownames(df_q)) %>% gather(year, Value, -Quantile) %>%
#
# mutate(#year = f2n(year),
# Quantile = factor(Quantile)) %>% filter(year <= year.max)
#
# df_q %<>% spread(Quantile, Value)
# }
#
# df <- fn(df)
# }
draw_quantiles <- function(runName, # character
varName, # character
data = results_all,
year.max = 80,
qts = c(0.1, 0.25, 0.5, 0.75, 0.9),
ylim = NULL,
EEC_line = 5){
# runName <- c("D1F075-average_gn2","D1F075-average") # character
# varName <- c("C_PR") # character
# data = results_all
# year.max = 80
# qts = c(0.1, 0.25, 0.5, 0.75, 0.9)
# ylim = NULL
# EEC_line = 5
col1 <- colorRampPalette(c("darkgreen","yellowgreen", "dodgerblue4", "orangered", "red4"))
if (varName %in% c("C_PR","ERC_PR")) color_values <- rev(col1(length(qts))) else
color_values <- col1(length(qts))
df_q <- get_quantiles(runName = runName,
varName = varName,
data = data,
year.max = year.max,
qts = qts) %>%
gather(Quantile, Value, -runname, -year) %>%
mutate(Quantile = factor(Quantile, levels = paste0(sort(qts, decreasing = TRUE) * 100, "%")))
plot_q <-
ggplot(df_q, aes(x = year, y = Value, color = Quantile)) + theme_bw() +
geom_point(size = 1.5) + geom_line()+
labs(y = varName, title = paste0("Quantile plots of ", varName))
# scale_color_manual(values = color_values)
if (varName %in% c("C_PR","ERC_PR")) {
df_NC.rate <- data %>% filter(runname %in% runName, sim == 1, year <= year.max) %>% select(runname, year, NC_PR) %>%
mutate(Quantile = "Normal Cost Rate",
runname = factor(runname, levels = runName)) %>%
rename(Value = NC_PR)
plot_q <- plot_q + geom_line(data = df_NC.rate, aes(x = year, y = Value), linetype = 1)+ scale_color_manual(values = c(color_values, "black"))
} else {
plot_q <- plot_q + scale_color_manual(values = color_values)
}
if(length(runName) > 1) plot_q <- plot_q + facet_grid(. ~ runname)
if(!is.null(ylim)) plot_q <- plot_q + coord_cartesian(ylim = ylim)
if(varName == "FR") plot_q <- plot_q + geom_hline(yintercept = 100, color = "black", linetype = 2)
if(varName == "C_PR") plot_q <- plot_q + geom_hline(yintercept = EEC_line,color = "black", linetype = 2)
list(df = df_q, plot = plot_q)
}
draw_quantiles2 <- function(runName, # character
varName, # character
data = results_all,
year.max = 80,
qts = c(0.1, 0.25, 0.5, 0.75, 0.9),
ylim = NULL){
df_q <- get_quantiles(runName = runName,
varName = varName,
data = data,
year.max = year.max,
qts = qts) %>%
gather(Quantile, Value, -runname, -year)
plot_q <-
ggplot(df_q, aes(x = year, y = Value, color = Quantile)) + theme_bw() +
geom_point(size = 1.5) + geom_line()+
labs(y = varName, title = paste0("Quantile plot of ", varName, " in ", runName))
if(length(runName) > 1) plot_q <- plot_q + facet_wrap( ~ runname)
if(!is.null(ylim)) plot_q <- plot_q + coord_cartesian(ylim = ylim)
plot_q
}
get_metrics <- function(runs, year.max, plan_AL, data = results_all ){
# runs = runs_investment
# #runs = "I6F075-5"
# year.max = 30
# include.maxChg = FALSE
# plan_AL = "I6F075-1" # any plan with 7.5% discount rate will do.
#
AL_7.5_v <- results_all %>% filter(runname == plan_AL, sim == 1, year <= year.max) %>% select(AL) %>% unlist
df_TO <- results_all %>% filter(runname %in% runs, year <= year.max, sim > 0) %>%
arrange(runname, sim, year) %>%
group_by(runname, sim) %>%
mutate(AL_7.5 = AL_7.5_v,
FR_MA_7.5 = 100 * MA / AL_7.5) %>%
select(runname, year, sim, AL, AL_7.5, MA, FR_MA, FR_MA_7.5, ERC_PR, C_PR, C, ERC, PR)
## Measures of funded status *********************************************
# 1. Probability of funded ratio falling below X% in 5, 15, 30 years.
# 2. VaR-like measure: 5th percentile of funded ratio in year 5, 15, and 30.
# 3. CVaR-like measure: weighted average of funded ratio below 5th percentile in year 5, 15, and 30.
# question: how to calculate the weight?
df_ruin <-
df_TO %>% group_by(runname, sim) %>%
mutate(FR50 = cumany(FR_MA <= 50),
FR40 = cumany(FR_MA <= 40),
FR50_7.5 = cumany(FR_MA_7.5 <= 50),
FR40_7.5 = cumany(FR_MA_7.5 <= 40)) %>%
filter(year %in% c(15,30,40)) %>%
ungroup %>% group_by(runname, year) %>%
summarise(FR50 = 100 * sum(FR50)/n(),
FR40 = 100 * sum(FR40)/n(),
FR50_7.5 = 100 * sum(FR50_7.5)/n(),
FR40_7.5 = 100 * sum(FR40_7.5)/n()) %>%
gather(variable, value, -runname, -year) %>%
mutate(variable = paste0(variable, "_y", year),
year = NULL) %>%
spread(variable, value)
df_ruin %>% kable(digits = 3)
## Measures of contribution volatility *************************************
df_sd <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
summarise(C_PR.sd = sd(C_PR, na.rm = TRUE), ERC_PR.sd = sd(ERC_PR, na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(median)) %>% select(-sim)
df_sd
df_dsd <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
summarise(C_PR.dsd = sd(diff(C_PR), na.rm = TRUE), ERC_PR.dsd = sd(diff(ERC_PR), na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(med = median(., na.rm = TRUE), q75 = quantile(., 0.75,na.rm = TRUE), q90 = quantile(., 0.9, na.rm = TRUE)), -sim)
# summarise_each(funs(median)) %>% select(-sim)
df_dsd
df_maxC <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
summarise(C_PR.max = max(C_PR, na.rm = TRUE), ERC_PR.max = max(ERC_PR, na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q75 = quantile(., 0.75), q90 = quantile(., 0.9)), -sim)
# summarise_each(funs(median)) %>% select(-sim)
df_maxC
df_minFR <- df_TO %>%
select(runname, year, sim, FR_MA, FR_MA_7.5) %>%
group_by(sim, runname) %>%
summarise(FR_MA.min = min(FR_MA),
FR_MA_7.5.min = min(FR_MA_7.5)) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q25 = quantile(., 0.25), q10 = quantile(., 0.1)), -sim)
# summarise_each(funs(median)) %>% select(-sim)
df_minFR
df_final_C <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
filter(year == max(year)) %>%
rename(C_PR.final = C_PR,
ERC_PR.final = ERC_PR) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q75 = quantile(., 0.75), q90 = quantile(., 0.9)), -sim)
# summarise(C_PR.final = median(C_PR),
# ERC_PR.final = median(ERC_PR))
df_final_C
df_final_FR <- df_TO %>%
select(runname, year, sim, FR_MA, FR_MA_7.5) %>%
group_by(sim, runname) %>%
filter(year == max(year)) %>%
rename(FR_MA.final = FR_MA,
FR_MA_7.5.final = FR_MA_7.5) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q25 = quantile(., 0.25), q10 = quantile(., 0.1)), -sim, -year)
# summarise(C_PR.final = median(C_PR),
# ERC_PR.final = median(ERC_PR))
df_final_FR
df_5yearChg <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
mutate_each(funs(. - lag(., 5)), one_of(c("C_PR", "ERC_PR")) ) %>%
summarise(C_PR.5yChg = max(C_PR, na.rm = TRUE),
ERC_PR.5yChg = max(ERC_PR, na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q75 = quantile(., 0.75), q90 = quantile(., 0.9) )) %>%
select(-starts_with("sim"))
df_5yearChg
df_pctChg <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
mutate_each(funs(. / lag(.) - 1 ), one_of(c("C_PR", "ERC_PR"))) %>%
summarise(C_PR.pctChg = 100 * median(C_PR, na.rm = TRUE),
ERC_PR.pctChg = 100 * median(ERC_PR, na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(med = median(., na.rm = TRUE), q75 = quantile(., 0.75, na.rm = TRUE), q90 = quantile(., 0.9, na.rm = TRUE)), -sim)
df_pctChg
# with(df_5yearChg, df_5yearChg[runname == "A1F075_O30pA5","C_PR.5yChg"] %>% unlist) %>% hist(breaks = 50)
## Present Value of contribution *************************************
df_PVC <- df_TO %>%
select(runname, year, sim, C, ERC, PR) %>%
group_by(sim, runname) %>%
mutate(discount = 1/(1 + 0.075)^(year - 1),
discount_L10 = ifelse(max(year) - year >= 10, 0, discount)) %>%
summarise(PV.C = sum(C * discount),
PV.ERC = sum(ERC * discount),
PV.PR = sum(PR * discount),
PV.C_L10 = sum(C * discount_L10),
PV.ERC_L10 = sum(ERC * discount_L10),
PV.PR_L10 = sum(PR * discount_L10)) %>%
group_by(runname) %>%
mutate(PV.C_PR = 100 * PV.C / PV.PR,
PV.ERC_PR = 100 * PV.ERC / PV.PR,
PV.C_PR_L10 = 100 * PV.C_L10 / PV.PR_L10,
PV.ERC_PR_L10 = 100 * PV.ERC_L10 / PV.PR_L10 ) %>%
summarise_each(funs(med = median, q75 = quantile(., 0.75), q90 = quantile(., 0.9)), -sim)
df_PVC
df_year1 <- df_TO %>%
select(runname, year, sim, FR_MA, FR_MA_7.5, ERC_PR) %>%
filter(year == 1, sim == 1) %>%
rename(FR_MA.y1 = FR_MA,
FR_MA_7.5.y1 = FR_MA_7.5,
ERC_PR.y1 = ERC_PR)
df_year1
df_metrics <- join_all(list(df_ruin,
df_PVC,
df_sd,
df_dsd,
df_maxC,
df_minFR,
df_final_C,
df_final_FR,
df_5yearChg,
df_pctChg,
df_year1))
return(df_metrics)
}
get_metrics_maxChg <- function(runs, year.max, data = results_all){
# This function only calculate 5-year and 10-year max change of ERC rate.
# runs = runs_investment
# year.max = 30
# include.maxChg = FALSE
# prefix = "I1F075-"
df_TO <- results_all %>% filter(runname %in% runs, year <= year.max, sim > 0) %>%
select(runname, year, sim, FR_MA, ERC_PR, C_PR, C, ERC, PR)
## Measures of funded status *********************************************
## Create functions to calculate max changes in 5-year intervals.
maxChgWithin <- function(y, fn, ...){
# max/min change within a single interval.
zoo::rollapply(y, rev(seq_along(y)), function(x) fn(x - x[1], ...), fill = NA, align = "left") %>% fn(., ...)
#y <- outer(x, x, "-")
#y[lower.tri(y)] %>% fn(., ...)
}
roll_maxChg <- function(x, fun, width, ... ){
# For a given vector x, calculate the max/min change WITHIN each interval of the width "width"
zoo::rollapply(x, width, maxChgWithin, fn = fun, ..., fill = NA, align = "right")
}
df_5yearMaxChg <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
mutate(C_PR = roll_maxChg(C_PR, max, 5),
ERC_PR= roll_maxChg(ERC_PR,max, 5)) %>%
summarise(C_PR.5yMaxChg = max(C_PR, na.rm = TRUE),
ERC_PR.5yMaxChg= max(ERC_PR, na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q75 = quantile(., 0.75), q90 = quantile(., 0.9) )) %>%
select(-starts_with("sim"))
df_10yearMaxChg <- df_TO %>%
select(runname, year, sim, C_PR, ERC_PR) %>%
group_by(sim, runname) %>%
mutate(C_PR = roll_maxChg(C_PR, max, 10),
ERC_PR= roll_maxChg(ERC_PR,max, 10)) %>%
summarise(C_PR.10yMaxChg = max(C_PR, na.rm = TRUE),
ERC_PR.10yMaxChg= max(ERC_PR, na.rm = TRUE)) %>%
group_by(runname) %>%
summarise_each(funs(med = median, q75 = quantile(., 0.75), q90 = quantile(., 0.9) )) %>%
select(-starts_with("sim"))
df_maxChg <- join_all(list(df_5yearMaxChg,
df_10yearMaxChg))
return(df_maxChg)
}
maxChgWithin <- function(y, fn, ...){
# max/min change within a single interval.
zoo::rollapply(y, rev(seq_along(y)), function(x) fn(x - x[1], ...), fill = NA, align = "left") %>% fn(., ...)
#y <- outer(x, x, "-")
#y[lower.tri(y)] %>% fn(., ...)
}
roll_maxChg <- function(x, fun, width, ... ){
# For a given vector x, calculate the max/min change WITHIN each interval of the width "width"
zoo::rollapply(x, width, maxChgWithin, fn = fun, ..., fill = NA, align = "right")
}
get_cumAsset <- function(cf, i, year_end = FALSE){
# Given a cash flow and a interest rate, calculates the accumulated asset value each year
# cf: cash flow
# i : interest rate
# cf <- c(10, 20, 30, 50, 90)
# i <- 0.06
n <- length(cf)
i.vector <- (1 + i)^(seq_len(n) - ifelse(year_end, 0, 1))
df <- t(matrix(i.vector, n, n, byrow = T) * cf) %>% as.data.frame()