[R] ATTN: Problem with Portfolio Optimization converging with Expected Shortfall as risk measure on Asymmetric Generalized Hyperbolic Distribution

Colin Gan cgan at caesar.cs.umn.edu
Thu Dec 19 20:04:55 CET 2013


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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0.019736007,-0.005951742,0.022372298,0.004397098,-0.033862412,0.01187398,0.019396356,0.022004817,0.028987537,0.008634277,-2.48E+00,0.001276925,0.015959898

0.044935767,-0.014401296,0.011948933,0.021067834,0.042115554,0.049154172,0.018116667,0.033531722,0.0564157,0.031634269,-2.43E+00,0.004043132,0.018070126

0.006417134,-0.006262843,0.005165004,-0.01341148,-0.017602645,0.005110074,0.002560165,-0.02395081,-0.007986352,0.003055926,-3.09E+00,0.002501438,-0.007385013

0.017801769,0.027279378,0.001151411,-0.014581472,0.015237646,-0.006285623,0.007461761,0.046806573,-0.012609558,0.006140011,-3.21E+00,0.001219182,0.004941924

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0.081625588,0.006761941,0.01573459,0.001359851,0.059329378,0.01062024,0.01242909,0.081531911,0.010349381,0.019324273,-2.87E+00,0.005504349,0.023736847

0.038718031,0.036554103,-0.007606824,-0.032630687,0.100662702,0.000953744,0.003331782,0.04782193,0.071809924,0.033481119,-3.24E+00,0.000828272,-0.010198734

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0.018528579,-0.01137355,0.008211854,0.008276771,0.025760841,0.011713165,0.011788963,-0.002935423,0.010752792,-0.001048328,-5.55E+00,0.006939092,0.008030459

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0.014351861,0.033275632,0.00334635,0.004433241,0.005791522,0.012106685,0.000249377,0.024219145,0.032130486,0.031482138,-6.16E+00,-0.00122691,0.006532722

0.008554816,-0.02291051,0.011236073,0.026390852,0.006799443,0.00680928,-0.000249377,0.004094172,0.019622355,0.020028666,-6.19E+00,-0.001701549,0.010455552

-0.038058482,-0.00519599,-0.02179466,0.004098366,-0.028346842,-0.016506326,-0.011158063,-0.066939483,-0.000816827,-0.012752794,-6.40E+00,-0.001223325,-0.01628026

0.001253919,-0.024923408,0.003877047,0.023331196,0.001422138,0.017032042,-0.007981868,0.002400962,0.018749905,0.018205964,-6.50E+00,-0.000271647,-0.000849558

-0.011229064,-0.021739987,-0.020868412,0.001942062,-0.031748698,-0.015307309,-0.011431476,-0.112641636,-0.030519522,-0.014332493,-6.42E+00,-0.001763908,-0.0248117

-0.00643089,0.00972455,0.001087548,0.01042185,-0.01911756,-0.002930279,-0.000120912,0,0.001211143,-0.011149344,-6.70E+00,0.004415618,-0.000483108

-------------- 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")





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