Colin Gan
2013-Dec-19 19:04 UTC
[R] ATTN: Problem with Portfolio Optimization converging with Expected Shortfall as risk measure on Asymmetric Generalized Hyperbolic Distribution
Hi there, attached are the necessary code and data. For me, the portfolio
optimization with expected shortfall as risk measure only converges on
gaussian not asymmetric generalized hyperbolic, normal inverse gaussian,
variance gamma and student t distributions. I like to know why. Thank
you.
Sincere Blessings,
--
Colin Gan Cheong Kiat
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BACreturn,BRKBreturn,GEreturn,KOreturn,LOWreturn,MCDreturn,MMMreturn,RFreturn,TGTreturn,WMTreturn,TBillYield,EURUSDreturn,SPYReturn
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-------------- next part --------------
# check code again to ensure it is right
# bond return calculation is wrong except t-bill
# security market line should only have stocks
# Loading generalized hyperbolic distribution facilities
library(ghyp)
library(fPortfolio)
library(stats)
library(timeSeries)
library(fBasics)
library(fAssets)
library(fCopulae)
library(timeDate)
library(robustbase)
library(stabledist)
library(mnormt)
library(sn)
library(quadprog)
library(Rglpk)
library(slam)
library(zoo)
library(PerformanceAnalytics)
library(utils)
library(graphics)
library(ggplot2)
library(plyr)
mydata <- read.csv(file.choose(), header = TRUE, sep = ",")
print(mydata, zero.print = ".")# nicer to read
View(mydata)
ghypmv.fit <- fit.ghypmv(data = mydata, opt.pars = c(lambda = FALSE), lambda
= 2,
control = list(rel.tol = 1e-5, abstol = 1e-5), reltol = 0.01)
summary(ghypmv.fit)
nigmv.fit <- fit.NIGmv(data = mydata, opt.pars = c(alpha.bar = T, mu = T,
sigma = T, gamma = !0), symmetric = F)
summary(nigmv.fit)
vgmv.fit <- fit.VGmv(data = mydata, lambda = 1, opt.pars = c(lambda = T, mu =
T, sigma = T, gamma = !0), symmetric = F)
summary(vgmv.fit)
tmv.fit <- fit.tmv(data = mydata, nu = 3.5, opt.pars = c(lambda = T, mu = T,
sigma = T, gamma = !0), symmetric = F)
summary(tmv.fit)
# only this converges during portfolio optimization
gaussmv.fit <- fit.gaussmv(data = mydata, na.rm = T, save.data = T)
summary(gaussmv.fit)
# Using expected shortfall as risk measure with target return from 0.0001 to
0.0020
g1_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0001,
distr = "return")
print(g1_es)
g2_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0002,
distr = "return")
print(g2_es)
g3_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0003,
distr = "return")
print(g3_es)
g4_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0004,
distr = "return")
print(g4_es)
g5_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0005,
distr = "return")
print(g5_es)
g6_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0006,
distr = "return")
print(g6_es)
g7_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0007,
distr = "return")
print(g7_es)
g8_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0008,
distr = "return")
print(g8_es)
g9_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0009,
distr = "return")
print(g9_es)
g10_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0010,
distr = "return")
print(g10_es)
g11_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0011,
distr = "return")
print(g11_es)
g12_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0012,
distr = "return")
print(g12_es)
g13_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0013,
distr = "return")
print(g13_es)
g14_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0014,
distr = "return")
print(g14_es)
g15_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0015,
distr = "return")
print(g15_es)
g16_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0016,
distr = "return")
print(g16_es)
g17_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0017,
distr = "return")
print(g17_es)
g18_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0018,
distr = "return")
print(g18_es)
g19_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0019,
distr = "return")
print(g19_es)
g20_es <- portfolio.optimize(ghypmv.fit,
risk.measure = "expected.shortfall",
type = "target.return",
level = 0.95,
target.return = 0.0020,
distr = "return")
print(g20_es)
plot(c(g1_es$risk, g2_es$risk, g3_es$risk, g4_es$risk, g5_es$risk, g6_es$risk,
g7_es$risk, g8_es$risk, g9_es$risk, g10_es$risk,
g11_es$risk, g12_es$risk, g13_es$risk, g14_es$risk, g15_es$risk,
g16_es$risk, g17_es$risk, g18_es$risk, g19_es$risk, g20_es$risk),
c(mean(g1_es$portfolio.dist), mean(g2_es$portfolio.dist),
mean(g3_es$portfolio.dist), mean(g4_es$portfolio.dist),
mean(g5_es$portfolio.dist),
mean(g6_es$portfolio.dist), mean(g7_es$portfolio.dist),
mean(g8_es$portfolio.dist), mean(g9_es$portfolio.dist),
mean(g10_es$portfolio.dist),
mean(g11_es$portfolio.dist), mean(g12_es$portfolio.dist),
mean(g13_es$portfolio.dist), mean(g14_es$portfolio.dist),
mean(g15_es$portfolio.dist),
mean(g16_es$portfolio.dist), mean(g17_es$portfolio.dist),
mean(g18_es$portfolio.dist), mean(g19_es$portfolio.dist),
mean(g20_es$portfolio.dist)),
type = "l",
xlab = "Expected shortfall",
ylab = "Expected portfolio return",
main = "Efficient frontier for Gaussian Distribution")