R/cashFlowSimulation.R
In bplloyd/Core:
cashFlowSimulation = function(I0, L0, D0, R0, C0, sig_S, sig_F, mu_S, mu_F, dist_rate=NULL, dd_rate=NULL, rho=0.5, lambda=0.2, v=0.01, n=1000, delta=1/12, t=3) {
if(is.matrix(dist_rate)) {
t = nrow(dist_rate) * delta
n = ncol(dist_rate)
}
#pef = coreActive
#------------------parameter setup for simulation
sig_S = 0.08
mu_S = 0.04
sig_F = 0.16
mu_F = 0.10
rho = 0.4
lambda = 0.2
v = 0.025
n = 10000
delta=1/12
t=8
delta_mu = mu_S - mu_F
delta_var_S = sig_S^2 - sig_S * sig_F * rho
delta_var_F = sig_F^2 - sig_S * sig_F * rho
var_cor = delta_var_F + delta_var_S
noises = c(S = "S", F = "F")
cormat = matrix(c(1, rho, rho, 1), nrow=2)
#------------------historical parameters
y = 2017
lastDate = as.Date.character(paste0(y, "-03-31"))
dists = as_ts(get_series(coreFund, "Distributions_Total", clean = F, end = lastDate))
calls = as_ts(get_series(coreFund, "Calls_Total_Gross", clean = F, end = lastDate))
undrawn = as_ts(get_series(coreActive, "Undrawn", clean = F, end = lastDate))
allocations = allocation_dollars[lubridate::year(allocation_dollars$Date) <= y, ]
hist_weights = as.matrix(allocation_weights[(allocation_weights$Date %in% allocations$Date), c("ILLIQUID", "LIQUID")])
row.names(hist_weights) = as.character(zoo::as.yearmon(allocations$Date))
I0 = as.vector((allocations[(nrow(allocations) - 1):nrow(allocations), "ILLIQUID"]/1000000)[, 1])
L0 = as.vector((allocations[(nrow(allocations) - 1):nrow(allocations), "LIQUID"]/1000000)[, 1])
C0 = as.vector(undrawn)[(length(undrawn)-1):length(undrawn)]
#C0 = as.vector(coreActive@PeriodData[(nrow(coreActive@PeriodData) - 1):nrow(coreActive@PeriodData), "Undrawn"])
#Cm1 = as.numeric(coreFund@PeriodData[nrow(coreFund@PeriodData) - 1, "Undrawn"])
D0 = as.vector(cumsum(calls)[(length(calls)-1):length(calls)])
#Dm1 = as.numeric(cumsum(calls)[nrow(calls) - 1,])
R0 = as.vector(cumsum(dists)[(length(dists)-1):length(dists)])
#Rm1 = as.numeric(cumsum(dists)[nrow(dists) - 1,])
#Pm1 = Im1 + Lm1
P0 = I0 + L0
#wLm1= Lm1 / Pm1
wL0 = L0 / P0
#wIm1 = Im1 / Pm1
wI0 = I0 / P0
#wCm1 = Cm1 / Pm1
wC0 = C0 / P0
date0 = allocations$Date[nrow(allocations)]
month0 = lubridate::month(date0)
#-------------------data, fit, and simulations for distribution rate
dist_rate = as_ts(get_series(coreActive, "DistributionRate", end = lastDate))
lam = forecast::BoxCox.lambda(dist_rate)
#hybrid
# fit_list = list(arima = forecast::Arima(y = dist_rate, order = c(0, 1, 1), seasonal = c(3, 0, 0), lambda = lam),
# stlm = forecast::stlm(y = dist_rate, s.window = 11, method = "ets", etsmodel = "AAN", lambda = lam),
# net = forecast::nnetar(y = dist_rate, p = 1, P = 3, lambda = lam))
#single arima
lam = BoxCox.lambda(dist_rate)
#lam = NULL
fit_stlm = stlm(y = dist_rate, s.window = 13, method = "ets", etsmodel = "ZAN", lambda = lam, biasadj = T)
fit_arima = Arima(y = dist_rate, order = c(0, 1, 1), seasonal = c(3, 0, 0), include.drift = T, lambda = lam, biasadj =T)
sim_hyb = simulate.hybrid(fit_list = list(arima = fit_arima, stlm = fit_stlm), nahead = t*12, N = n, bootErrs = T)
# roll_sims = lapply(X = 2008:2014,function(y){
# rate=window(dist_rate, end = c(y, 12))
# lam=NULL
# fit = forecast::Arima(y = rate, order = c(0, 1, 1), seasonal = c(3, 0, 0), lambda = lam)
# sim1 = forecast::simulate.Arima(fit, nsim = 24, future = T)
# sims = sapply(1:1000, function(j)forecast::simulate.Arima(fit, nsim = 24, future = T))
# ts(sims, start = tsp(sim1)[1], end = tsp(sim1)[2], frequency = tsp(sim1)[3])
# })
#
#
# mean_sims = lapply(roll_sims, function(r)ts(rowMeans(r), start=tsp(r)[1], frequency = tsp(r)[3]))
#
# lam=NULL
#
sim_dist_rate = as.matrix((1/delta) * sim_hyb$hybrid$simulations)
#}
#-------------------data, fit, and simulations for drawdown rate
dd_rate = as_ts(get_series(coreActive, "DrawdownRate", end = lastDate))
fit_dd = forecast::ets(y = window(dd_rate, start = 2006)
#lambda = forecast::BoxCox.lambda(window(dd_rate, start= 2006))
)
sim_dd_rate = (1/delta)*sapply(1:n,
function(i) forecast::simulate.ets(object = fit_dd, nsim = t*12, future = T, bootstrap = T))
########################
set.seed(123)
W = lapply(1:n, function(i) mvtnorm::rmvnorm(n = (t / delta), mean = c(0, 0), sigma = cormat))
Z = lapply(noises, function(z) matrix(data = NA, nrow = t / delta, ncol = n))
for(i in 1:length(W)) {
Z$S[, i] = W[[i]][, 1]
Z$F[, i] = W[[i]][, 2]
}
#L = liquid allocation
L = matrix(data = 0, nrow = nrow(Z$S) + 2, ncol = ncol(Z$S))
row.names(L) = as.character(c(zoo::as.yearmon(allocations$Date[(nrow(allocations)-1):nrow(allocations)]),
zoo::as.yearmon(time(sim_dist_rate))))
redemptions = which(lubridate::month(zoo::as.Date(zoo::as.yearmon(row.names(L)))) %in% c(5, 8, 11, 2))
# wL = matrix(data = 0, nrow = nrow(Z$S) + 1, ncol = ncol(Z$S))
# row.names(wL) = c(row.names(dist_rate$Actual)[nrow(dist_rate$Actual)], row.names(sim_dist_rate))
# redemptions = which(lubridate::month(as.Date(row.names(wL))) %in% c(5, 8, 11, 2))
simulations = array(data = NA_real_,
dim = c(nrow(Z$S) + 2, ncol(Z$S), 6),
dimnames = list(NULL, NULL, c("I", "L", "C", "P", "D", "R")))
#I = liquid allocation
#C = undrawn commitment
#P = total fund nav
#L = illiquid weight
#L = liquid weight
#C = undrawn commitment weight
#D = drawdowns
#R = distributions
simulations[1:2, , "L"] = replicate(expr = L0, n = ncol(simulations))
simulations[1:2, , "I"] = replicate(expr = I0, n = ncol(simulations))
simulations[1:2, , "C"] = replicate(expr = C0, n = ncol(simulations))
simulations[1:2, , "P"] = replicate(expr = P0, n = ncol(simulations))
simulations[1:2, , "D"] = replicate(expr = D0, n = ncol(simulations))
simulations[1:2, , "R"] = replicate(expr = R0, n = ncol(simulations))
for(h in 1:nrow(sim_dd_rate)) {
i = h + 2
#Liquid return
R_L = (mu_S * delta + sig_S * sqrt(delta) * Z$S[h, ])
#Illiquid return
R_I = (mu_F * delta + sig_F * sqrt(delta) * Z$F[h, ])
#Distributions
simulations[i, , "R"] = simulations[i-1, , "R"] + delta * sim_dist_rate[h, ] * simulations[i-1, , "I"]
#Drawdowns
simulations[i, , "D"] = simulations[i-1, , "D"] + delta * sim_dd_rate[h, ] * simulations[i-1, , "C"]
#Undrawn Capital Commitment
simulations[i, , "C"] = simulations[i-1, , "C"] + simulations[i-1, , "P"] * v * delta - (simulations[i, , "D"] - simulations[i-1, , "D"])
#Liquid Allocation
simulations[i, , "L"] = simulations[i-1, , "L"] * (1 + R_L) - (simulations[i, , "D"] - simulations[i-1, , "D"]) + (simulations[i, , "R"] - simulations[i-1, , "R"])
#Subtract redemptions from liquid allocation
if(i %in% redemptions){
simulations[i, , "L"] = simulations[i, , "L"] - 0.25 * lambda * simulations[i-2, , "P"]
}
#Illiquid Allocation
simulations[i, , "I"] = simulations[i-1, , "I"] * (1 + R_I) - (simulations[i, , "R"] - simulations[i-1, , "R"]) + (simulations[i, , "D"] - simulations[i-1, , "D"])
#Total fund NAV
simulations[i, , "P"] = simulations[i, , "L"] + simulations[i, , "I"]
#simulations[i, , "C"] = simulations[i-1, , "C"] + (simulations[i-1, , "P"] * v - sim_dd_rate[h, ] * simulations[i-1, , "C"]) * delta
# simulations[i, , "L"] = simulations[i-1, , "L"] + simulations[i-1, , "L"] * (mu_S * delta + sig_S * sqrt(delta) * Z$S[h, ]) -
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta +
# sim_dist_rate[h, ] * I[i-1, ] * delta
# simulations[i, , "L"] = simulations[i-1, , "L"] + simulations[i-1, , "L"] * R_L -
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta +
# sim_dist_rate[h, ] * I[i-1, ] * delta
# I[i, ] = I[i-1, ] + I[i-1, ] * (R_I - sim_dist_rate[h, ] * delta) +
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta
# I[i, ] = I[i-1, ] + I[i-1, ] * ((mu_F - sim_dist_rate[h, ]) * delta + sig_F * sqrt(delta) * Z$F[h, ]) +
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta
}
sim_dists = ts(diff(simulations[ , , "R"])[2:(nrow(sim_dist_rate) + 1),],
start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
sim_dist_mean = ts(rowMeans(sim_dists), start = tsp(sim_dists)[1], frequency = tsp(sim_dists)[3])
sim_illiq = ts(simulations[3:nrow(simulations),,"I"]/simulations[3:nrow(simulations),,"P"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_illiq = ts(allocations$ILLIQUID/allocations$TOTAL, start = c(2004, 1), frequency = 12)
sim_liq = ts(simulations[3:nrow(simulations),,"L"]/simulations[3:nrow(simulations),,"P"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_liq = ts(allocations$LIQUID/allocations$TOTAL, start = c(2004, 1), frequency = 12)
sim_illiq_NAV = ts(simulations[3:nrow(simulations),,"I"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_illiq_NAV = ts(allocations$ILLIQUID/1e+06, start = c(2004, 1), frequency = 12)
sim_liq_NAV = ts(simulations[3:nrow(simulations),,"L"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_liq_NAV = ts(allocations$LIQUID/1e+06, start = c(2004, 1), frequency = 12)
sim_tot_NAV = ts(simulations[3:nrow(simulations),,"P"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_tot_NAV = ts(allocations$TOTAL/1e+06, start = c(2004, 1), frequency = 12)
sim_dists_cum = ts(simulations[3:nrow(simulations),,"R"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_dists_cum = ts(cumsum(dists), start = c(2004, 1), frequency = 12)
sim_calls_cum = ts(simulations[3:nrow(simulations),,"D"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_calls_cum = ts(cumsum(calls), start = c(2004, 1), frequency = 12)
sim_net_cum = sim_dists_cum - sim_calls_cum
act_net_cum = act_dists_cum - act_calls_cum
# plot.sim(sim_illiq_NAV, actual = act_illiq_NAV, levels = c(80, 95), main = "Private Equity NAV Simulation", ylab = "NAV (millions)", xlab="year")
# plot.sim(sim_liq_NAV, actual = act_liq_NAV, ylim = c(0, 1200),
# levels = c(80, 95),
# main = "Hedge Fund NAV Simulation",
# ylab = "NAV (millions)", xlab="year")
#
# plot.sim(sim_dists_cum, actual = act_dists_cum, levels = c(80, 95), main = "Private Equity Distributions Simulation")
# plot.sim(sim_calls_cum, actual = act_calls_cum, levels = c(80, 95), main = "Private Equity Calls Simulation")
# plot.sim(sim_net_cum, actual = act_net_cum, levels = c(80, 95), main = "Private Equity Net CF Simulation", ylim = c(-300, 350))
#
# plot.sim(sim = sim_dist_rate/12, actual = dist_rate, levels = c(80, 95))
#
# plot.sim(sim_liq, actual = act_liq, levels = c(80, 95), main = "Hedge Fund Weight Simulation", ylab = "weight", xlab="year", ylim = c(0, 1))
plot.sim(sim_illiq, actual = act_illiq, levels = c(80, 95), main = "Private Equity Weight Simulation", ylab = "weight", xlab="year", ylim = c(0, 1))
# wI_std = wI
# wL_std = wL
#
# for(i in 2:nrow(wC)) {
# wC[i, ] = wC[i-1, ] + (v - wC[i-1, ] * (sim_dist_rate[i-1, ] + wL[i-1, ] * mu_S + (1 - wL[i-1, ]) * mu_F)) * delta -
# wC[i-1, ] * sqrt(delta) * (wL[i-1, ] * sig_S * Z$S[i-1, ] + (1 - wL[i-1, ]) * sig_F * Z$F[i-1, ])
#
# wL[i, ] = wL[i-1, ] + (sim_dist_rate[i-1, ] * (1 - wL[i-1, ]) - sim_dd_rate[i-1, ] * wC[i-1, ] + wL[i-1, ] * (1 - wL[i-1, ]) * (delta_mu - wL[i-1, ] * delta_var_S + (1 - wL[i-1, ]) * delta_var_F)) * delta -
# wL[i-1, ] * (1 - wL[i-1, ]) * (sig_F * Z$F[i-1, ] - sig_S * Z$S[i-1, ]) * sqrt(delta)
#
#
# # if(i %in% redemptions){
# # wL[i, ] = wL[i, ] - 0.05 * wL[i - 2, ]
# #
# # }
#
# }
# wI = 1-wL
# row.names(wL) = c(row.names(dist_rate$Actual)[nrow(dist_rate$Actual)], row.names(sim_dist_rate))
#
# sim_dist_tests = vector(mode = "list", length = 6)
# names(sim_dist_tests) = 2010:2015
# sim_dist_tests[[as.character(y)]] = list(mean = sim_dist_mean, fullsim = sim_dists)
#
#
# matplot(simulations[, , "I"]/simulations[, , "P"], type = "l", main = "Illiquid Weight")
# matplot(simulations[, , "L"]/simulations[, , "P"], type = "l", main = "Liquid Weight")
# matplot(simulations[, , "C"]/simulations[, , "P"], type = "l", main = "Undrawn Committed Capital Weight")
#
# matplot(simulations[, , "I"], type = "l", main = "Illiquid NAV")
# matplot(simulations[, , "L"], type = "l", main = "Liquid NAV")
# matplot(simulations[, , "C"], type = "l", main = "Undrawn Commitment")
# matplot(simulations[, , "P"], type = "l", main = "Total Fund Nav")
#
########################
}
bplloyd/Core documentation built on May 13, 2019, 2:24 a.m.
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cashFlowSimulation = function(I0, L0, D0, R0, C0, sig_S, sig_F, mu_S, mu_F, dist_rate=NULL, dd_rate=NULL, rho=0.5, lambda=0.2, v=0.01, n=1000, delta=1/12, t=3) {
if(is.matrix(dist_rate)) {
t = nrow(dist_rate) * delta
n = ncol(dist_rate)
}
#pef = coreActive
#------------------parameter setup for simulation
sig_S = 0.08
mu_S = 0.04
sig_F = 0.16
mu_F = 0.10
rho = 0.4
lambda = 0.2
v = 0.025
n = 10000
delta=1/12
t=8
delta_mu = mu_S - mu_F
delta_var_S = sig_S^2 - sig_S * sig_F * rho
delta_var_F = sig_F^2 - sig_S * sig_F * rho
var_cor = delta_var_F + delta_var_S
noises = c(S = "S", F = "F")
cormat = matrix(c(1, rho, rho, 1), nrow=2)
#------------------historical parameters
y = 2017
lastDate = as.Date.character(paste0(y, "-03-31"))
dists = as_ts(get_series(coreFund, "Distributions_Total", clean = F, end = lastDate))
calls = as_ts(get_series(coreFund, "Calls_Total_Gross", clean = F, end = lastDate))
undrawn = as_ts(get_series(coreActive, "Undrawn", clean = F, end = lastDate))
allocations = allocation_dollars[lubridate::year(allocation_dollars$Date) <= y, ]
hist_weights = as.matrix(allocation_weights[(allocation_weights$Date %in% allocations$Date), c("ILLIQUID", "LIQUID")])
row.names(hist_weights) = as.character(zoo::as.yearmon(allocations$Date))
I0 = as.vector((allocations[(nrow(allocations) - 1):nrow(allocations), "ILLIQUID"]/1000000)[, 1])
L0 = as.vector((allocations[(nrow(allocations) - 1):nrow(allocations), "LIQUID"]/1000000)[, 1])
C0 = as.vector(undrawn)[(length(undrawn)-1):length(undrawn)]
#C0 = as.vector(coreActive@PeriodData[(nrow(coreActive@PeriodData) - 1):nrow(coreActive@PeriodData), "Undrawn"])
#Cm1 = as.numeric(coreFund@PeriodData[nrow(coreFund@PeriodData) - 1, "Undrawn"])
D0 = as.vector(cumsum(calls)[(length(calls)-1):length(calls)])
#Dm1 = as.numeric(cumsum(calls)[nrow(calls) - 1,])
R0 = as.vector(cumsum(dists)[(length(dists)-1):length(dists)])
#Rm1 = as.numeric(cumsum(dists)[nrow(dists) - 1,])
#Pm1 = Im1 + Lm1
P0 = I0 + L0
#wLm1= Lm1 / Pm1
wL0 = L0 / P0
#wIm1 = Im1 / Pm1
wI0 = I0 / P0
#wCm1 = Cm1 / Pm1
wC0 = C0 / P0
date0 = allocations$Date[nrow(allocations)]
month0 = lubridate::month(date0)
#-------------------data, fit, and simulations for distribution rate
dist_rate = as_ts(get_series(coreActive, "DistributionRate", end = lastDate))
lam = forecast::BoxCox.lambda(dist_rate)
#hybrid
# fit_list = list(arima = forecast::Arima(y = dist_rate, order = c(0, 1, 1), seasonal = c(3, 0, 0), lambda = lam),
# stlm = forecast::stlm(y = dist_rate, s.window = 11, method = "ets", etsmodel = "AAN", lambda = lam),
# net = forecast::nnetar(y = dist_rate, p = 1, P = 3, lambda = lam))
#single arima
lam = BoxCox.lambda(dist_rate)
#lam = NULL
fit_stlm = stlm(y = dist_rate, s.window = 13, method = "ets", etsmodel = "ZAN", lambda = lam, biasadj = T)
fit_arima = Arima(y = dist_rate, order = c(0, 1, 1), seasonal = c(3, 0, 0), include.drift = T, lambda = lam, biasadj =T)
sim_hyb = simulate.hybrid(fit_list = list(arima = fit_arima, stlm = fit_stlm), nahead = t*12, N = n, bootErrs = T)
# roll_sims = lapply(X = 2008:2014,function(y){
# rate=window(dist_rate, end = c(y, 12))
# lam=NULL
# fit = forecast::Arima(y = rate, order = c(0, 1, 1), seasonal = c(3, 0, 0), lambda = lam)
# sim1 = forecast::simulate.Arima(fit, nsim = 24, future = T)
# sims = sapply(1:1000, function(j)forecast::simulate.Arima(fit, nsim = 24, future = T))
# ts(sims, start = tsp(sim1)[1], end = tsp(sim1)[2], frequency = tsp(sim1)[3])
# })
#
#
# mean_sims = lapply(roll_sims, function(r)ts(rowMeans(r), start=tsp(r)[1], frequency = tsp(r)[3]))
#
# lam=NULL
#
sim_dist_rate = as.matrix((1/delta) * sim_hyb$hybrid$simulations)
#}
#-------------------data, fit, and simulations for drawdown rate
dd_rate = as_ts(get_series(coreActive, "DrawdownRate", end = lastDate))
fit_dd = forecast::ets(y = window(dd_rate, start = 2006)
#lambda = forecast::BoxCox.lambda(window(dd_rate, start= 2006))
)
sim_dd_rate = (1/delta)*sapply(1:n,
function(i) forecast::simulate.ets(object = fit_dd, nsim = t*12, future = T, bootstrap = T))
########################
set.seed(123)
W = lapply(1:n, function(i) mvtnorm::rmvnorm(n = (t / delta), mean = c(0, 0), sigma = cormat))
Z = lapply(noises, function(z) matrix(data = NA, nrow = t / delta, ncol = n))
for(i in 1:length(W)) {
Z$S[, i] = W[[i]][, 1]
Z$F[, i] = W[[i]][, 2]
}
#L = liquid allocation
L = matrix(data = 0, nrow = nrow(Z$S) + 2, ncol = ncol(Z$S))
row.names(L) = as.character(c(zoo::as.yearmon(allocations$Date[(nrow(allocations)-1):nrow(allocations)]),
zoo::as.yearmon(time(sim_dist_rate))))
redemptions = which(lubridate::month(zoo::as.Date(zoo::as.yearmon(row.names(L)))) %in% c(5, 8, 11, 2))
# wL = matrix(data = 0, nrow = nrow(Z$S) + 1, ncol = ncol(Z$S))
# row.names(wL) = c(row.names(dist_rate$Actual)[nrow(dist_rate$Actual)], row.names(sim_dist_rate))
# redemptions = which(lubridate::month(as.Date(row.names(wL))) %in% c(5, 8, 11, 2))
simulations = array(data = NA_real_,
dim = c(nrow(Z$S) + 2, ncol(Z$S), 6),
dimnames = list(NULL, NULL, c("I", "L", "C", "P", "D", "R")))
#I = liquid allocation
#C = undrawn commitment
#P = total fund nav
#L = illiquid weight
#L = liquid weight
#C = undrawn commitment weight
#D = drawdowns
#R = distributions
simulations[1:2, , "L"] = replicate(expr = L0, n = ncol(simulations))
simulations[1:2, , "I"] = replicate(expr = I0, n = ncol(simulations))
simulations[1:2, , "C"] = replicate(expr = C0, n = ncol(simulations))
simulations[1:2, , "P"] = replicate(expr = P0, n = ncol(simulations))
simulations[1:2, , "D"] = replicate(expr = D0, n = ncol(simulations))
simulations[1:2, , "R"] = replicate(expr = R0, n = ncol(simulations))
for(h in 1:nrow(sim_dd_rate)) {
i = h + 2
#Liquid return
R_L = (mu_S * delta + sig_S * sqrt(delta) * Z$S[h, ])
#Illiquid return
R_I = (mu_F * delta + sig_F * sqrt(delta) * Z$F[h, ])
#Distributions
simulations[i, , "R"] = simulations[i-1, , "R"] + delta * sim_dist_rate[h, ] * simulations[i-1, , "I"]
#Drawdowns
simulations[i, , "D"] = simulations[i-1, , "D"] + delta * sim_dd_rate[h, ] * simulations[i-1, , "C"]
#Undrawn Capital Commitment
simulations[i, , "C"] = simulations[i-1, , "C"] + simulations[i-1, , "P"] * v * delta - (simulations[i, , "D"] - simulations[i-1, , "D"])
#Liquid Allocation
simulations[i, , "L"] = simulations[i-1, , "L"] * (1 + R_L) - (simulations[i, , "D"] - simulations[i-1, , "D"]) + (simulations[i, , "R"] - simulations[i-1, , "R"])
#Subtract redemptions from liquid allocation
if(i %in% redemptions){
simulations[i, , "L"] = simulations[i, , "L"] - 0.25 * lambda * simulations[i-2, , "P"]
}
#Illiquid Allocation
simulations[i, , "I"] = simulations[i-1, , "I"] * (1 + R_I) - (simulations[i, , "R"] - simulations[i-1, , "R"]) + (simulations[i, , "D"] - simulations[i-1, , "D"])
#Total fund NAV
simulations[i, , "P"] = simulations[i, , "L"] + simulations[i, , "I"]
#simulations[i, , "C"] = simulations[i-1, , "C"] + (simulations[i-1, , "P"] * v - sim_dd_rate[h, ] * simulations[i-1, , "C"]) * delta
# simulations[i, , "L"] = simulations[i-1, , "L"] + simulations[i-1, , "L"] * (mu_S * delta + sig_S * sqrt(delta) * Z$S[h, ]) -
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta +
# sim_dist_rate[h, ] * I[i-1, ] * delta
# simulations[i, , "L"] = simulations[i-1, , "L"] + simulations[i-1, , "L"] * R_L -
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta +
# sim_dist_rate[h, ] * I[i-1, ] * delta
# I[i, ] = I[i-1, ] + I[i-1, ] * (R_I - sim_dist_rate[h, ] * delta) +
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta
# I[i, ] = I[i-1, ] + I[i-1, ] * ((mu_F - sim_dist_rate[h, ]) * delta + sig_F * sqrt(delta) * Z$F[h, ]) +
# sim_dd_rate[h, ] * simulations[i-1, , "C"] * delta
}
sim_dists = ts(diff(simulations[ , , "R"])[2:(nrow(sim_dist_rate) + 1),],
start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
sim_dist_mean = ts(rowMeans(sim_dists), start = tsp(sim_dists)[1], frequency = tsp(sim_dists)[3])
sim_illiq = ts(simulations[3:nrow(simulations),,"I"]/simulations[3:nrow(simulations),,"P"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_illiq = ts(allocations$ILLIQUID/allocations$TOTAL, start = c(2004, 1), frequency = 12)
sim_liq = ts(simulations[3:nrow(simulations),,"L"]/simulations[3:nrow(simulations),,"P"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_liq = ts(allocations$LIQUID/allocations$TOTAL, start = c(2004, 1), frequency = 12)
sim_illiq_NAV = ts(simulations[3:nrow(simulations),,"I"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_illiq_NAV = ts(allocations$ILLIQUID/1e+06, start = c(2004, 1), frequency = 12)
sim_liq_NAV = ts(simulations[3:nrow(simulations),,"L"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_liq_NAV = ts(allocations$LIQUID/1e+06, start = c(2004, 1), frequency = 12)
sim_tot_NAV = ts(simulations[3:nrow(simulations),,"P"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_tot_NAV = ts(allocations$TOTAL/1e+06, start = c(2004, 1), frequency = 12)
sim_dists_cum = ts(simulations[3:nrow(simulations),,"R"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_dists_cum = ts(cumsum(dists), start = c(2004, 1), frequency = 12)
sim_calls_cum = ts(simulations[3:nrow(simulations),,"D"], start = tsp(sim_dist_rate)[1], frequency = tsp(sim_dist_rate)[3])
act_calls_cum = ts(cumsum(calls), start = c(2004, 1), frequency = 12)
sim_net_cum = sim_dists_cum - sim_calls_cum
act_net_cum = act_dists_cum - act_calls_cum
# plot.sim(sim_illiq_NAV, actual = act_illiq_NAV, levels = c(80, 95), main = "Private Equity NAV Simulation", ylab = "NAV (millions)", xlab="year")
# plot.sim(sim_liq_NAV, actual = act_liq_NAV, ylim = c(0, 1200),
# levels = c(80, 95),
# main = "Hedge Fund NAV Simulation",
# ylab = "NAV (millions)", xlab="year")
#
# plot.sim(sim_dists_cum, actual = act_dists_cum, levels = c(80, 95), main = "Private Equity Distributions Simulation")
# plot.sim(sim_calls_cum, actual = act_calls_cum, levels = c(80, 95), main = "Private Equity Calls Simulation")
# plot.sim(sim_net_cum, actual = act_net_cum, levels = c(80, 95), main = "Private Equity Net CF Simulation", ylim = c(-300, 350))
#
# plot.sim(sim = sim_dist_rate/12, actual = dist_rate, levels = c(80, 95))
#
# plot.sim(sim_liq, actual = act_liq, levels = c(80, 95), main = "Hedge Fund Weight Simulation", ylab = "weight", xlab="year", ylim = c(0, 1))
plot.sim(sim_illiq, actual = act_illiq, levels = c(80, 95), main = "Private Equity Weight Simulation", ylab = "weight", xlab="year", ylim = c(0, 1))
# wI_std = wI
# wL_std = wL
#
# for(i in 2:nrow(wC)) {
# wC[i, ] = wC[i-1, ] + (v - wC[i-1, ] * (sim_dist_rate[i-1, ] + wL[i-1, ] * mu_S + (1 - wL[i-1, ]) * mu_F)) * delta -
# wC[i-1, ] * sqrt(delta) * (wL[i-1, ] * sig_S * Z$S[i-1, ] + (1 - wL[i-1, ]) * sig_F * Z$F[i-1, ])
#
# wL[i, ] = wL[i-1, ] + (sim_dist_rate[i-1, ] * (1 - wL[i-1, ]) - sim_dd_rate[i-1, ] * wC[i-1, ] + wL[i-1, ] * (1 - wL[i-1, ]) * (delta_mu - wL[i-1, ] * delta_var_S + (1 - wL[i-1, ]) * delta_var_F)) * delta -
# wL[i-1, ] * (1 - wL[i-1, ]) * (sig_F * Z$F[i-1, ] - sig_S * Z$S[i-1, ]) * sqrt(delta)
#
#
# # if(i %in% redemptions){
# # wL[i, ] = wL[i, ] - 0.05 * wL[i - 2, ]
# #
# # }
#
# }
# wI = 1-wL
# row.names(wL) = c(row.names(dist_rate$Actual)[nrow(dist_rate$Actual)], row.names(sim_dist_rate))
#
# sim_dist_tests = vector(mode = "list", length = 6)
# names(sim_dist_tests) = 2010:2015
# sim_dist_tests[[as.character(y)]] = list(mean = sim_dist_mean, fullsim = sim_dists)
#
#
# matplot(simulations[, , "I"]/simulations[, , "P"], type = "l", main = "Illiquid Weight")
# matplot(simulations[, , "L"]/simulations[, , "P"], type = "l", main = "Liquid Weight")
# matplot(simulations[, , "C"]/simulations[, , "P"], type = "l", main = "Undrawn Committed Capital Weight")
#
# matplot(simulations[, , "I"], type = "l", main = "Illiquid NAV")
# matplot(simulations[, , "L"], type = "l", main = "Liquid NAV")
# matplot(simulations[, , "C"], type = "l", main = "Undrawn Commitment")
# matplot(simulations[, , "P"], type = "l", main = "Total Fund Nav")
#
########################
}
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