[R-SIG-Finance] parma - How to optimize a long/short portfolio with sum( abs( weights )) = 1

[u0055 at wolke7.net]

Dear R-SIGs,

I would like to optimize a long/short portfolio and
apply the constraint: sum( abs( weights )) = 1.
The parma package is very close to that,
but I still didn't find a general way,
which works for every input matrix of return values.

Thanks Alexios,
I found the 'parma.tests' with lots of great examples.
I think "parma.test11" "Example 6" "riskType='optimal'"
is the best choice for what I'm looking for.
I'm using that and very often I get warnings:
"In Socp(f, A1, b1, NULL, NULL, N1, x, z1, NULL, control) :
Dual is not in the feasible hyperplane, solution may be wrong.".

1) Why do I get the warnings ?
Is there a work around ?

2) Does anybody have a general solution (R snippet),
which works for every input matrix of return values ?

Thanks in advance,
Uwe


### R snippet begin ###

require( corpcor )
require( parma )

# returns
x=c()
x=c(x,0)#0-0
x=c(x,0.00029801026024799343)#1
x=c(x,0.01923480801352125)#2
x=c(x,0.0046403921153714825)#3
x=c(x,0.03869859235256766)#4
x=c(x,-0.019476139659286133)#5
x=c(x,-0.009050645351487118)#6
x=c(x,0.02984309624005349)#7
x=c(x,0)#0-1
x=c(x,-0.012975945313424369)#1
x=c(x,-0.02407901001552061)#2
x=c(x,0.021245616535913895)#3
x=c(x,0.056956457439674014)#4
x=c(x,-0.06073619413646872)#5
x=c(x,0.0348564722762156)#6
x=c(x,-0.07581515130311306)#7
x=c(x,0)#0-2
x=c(x,0.00029801026024799343)#1
x=c(x,0.01923480801352125)#2
x=c(x,0.0046403921153714825)#3
x=c(x,0.0386985923399131)#4
x=c(x,-0.019476139659286133)#5
x=c(x,-0.009050645351487118)#6
x=c(x,0.029831537955057316)#7
x=c(x,0)#0-3
x=c(x,-0.012975945313424369)#1
x=c(x,-0.02407901001552061)#2
x=c(x,0.021245616535913895)#3
x=c(x,0.05695645745232857)#4
x=c(x,-0.06073619413646872)#5
x=c(x,0.0348564722762156)#6
x=c(x,-0.07580359301811687)#7
x=c(x,0)#0-4
x=c(x,0.00029801026024799343)#1
x=c(x,0.019234808013345154)#2
x=c(x,0.0046403921153714825)#3
x=c(x,0.038698591002771045)#4
x=c(x,-0.019476139659286133)#5
x=c(x,-0.009050645351487118)#6
x=c(x,0.029814537533275967)#7
x=c(x,0)#0-5
x=c(x,-0.012975945313424369)#1
x=c(x,-0.024079010015344522)#2
x=c(x,0.021245616535913895)#3
x=c(x,0.056956458789470615)#4
x=c(x,-0.06073619413646872)#5
x=c(x,0.0348564722762156)#6
x=c(x,-0.07578659259633552)#7
x=c(x,0)#0-6
x=c(x,0.00029801026024799343)#1
x=c(x,0.019234806760933323)#2
x=c(x,0.0046403921153714825)#3
x=c(x,0.03869855234509703)#4
x=c(x,-0.019476139659287156)#5
x=c(x,-0.009050645351487125)#6
x=c(x,0.029790636978526824)#7
x=c(x,0)#0-7
x=c(x,-0.012975945313424369)#1
x=c(x,-0.024079008762932695)#2
x=c(x,0.021245616535913895)#3
x=c(x,0.05695649744714464)#4
x=c(x,-0.0607361941364677)#5
x=c(x,0.0348564722762156)#6
x=c(x,-0.07576269204158638)#7
x=c(x,0)#0-8
x=c(x,0.00029801026025892376)#1
x=c(x,0.01923453220069893)#2
x=c(x,0.004640392115430811)#3
x=c(x,0.03869828542503245)#4
x=c(x,-0.019476139815127035)#5
x=c(x,-0.009050645351487118)#6
x=c(x,0.029768353535081143)#7
x=c(x,0)#0-9
x=c(x,-0.0129759453134353)#1
x=c(x,-0.024078734202698304)#2
x=c(x,0.021245616535854574)#3
x=c(x,0.05695676436720922)#4
x=c(x,-0.060736193980627816)#5
x=c(x,0.0348564722762156)#6
x=c(x,-0.07574040859814071)#7
x=c(x,0)#0-10
x=c(x,0.0002980103179347729)#1
x=c(x,0.01923043617762049)#2
x=c(x,0.004640392486997125)#3
x=c(x,0.03869776965250973)#4
x=c(x,-0.01947619048004869)#5
x=c(x,-0.009050645351487118)#6
x=c(x,0.02975459006868922)#7
x=c(x,0)#0-11
x=c(x,-0.012975945371111148)#1
x=c(x,-0.024074638179619856)#2
x=c(x,0.021245616164288255)#3
x=c(x,0.056957280139731954)#4
x=c(x,-0.06073614331570616)#5
x=c(x,0.0348564722762156)#6
x=c(x,-0.07572664513174876)#7
x=c(x,0)#0-12
x=c(x,0.00029803649043954857)#1
x=c(x,0.019192162723869248)#2
x=c(x,0.004640656340453675)#3
x=c(x,0.0386968409321401)#4
x=c(x,-0.019480064142972733)#5
x=c(x,-0.009050645351488088)#6
x=c(x,0.029743057109602365)#7
x=c(x,0)#0-13
x=c(x,-0.012975971543615924)#1
x=c(x,-0.024036364725868627)#2
x=c(x,0.0212453523108317)#3
x=c(x,0.05695820886010157)#4
x=c(x,-0.06073226965278212)#5
x=c(x,0.03485647227621657)#6
x=c(x,-0.07571511217266193)#7
x=c(x,0)#0-14
x=c(x,0.0002984370859375864)#1
x=c(x,0.019062660408625483)#2
x=c(x,0.00465122630987321)#3
x=c(x,0.038693166438592115)#4
x=c(x,-0.019521858395814863)#5
x=c(x,-0.009050645366251428)#6
x=c(x,0.029737617239541797)#7
x=c(x,0)#0-15
x=c(x,-0.012976372139113963)#1
x=c(x,-0.023906862410624858)#2
x=c(x,0.021234782341412173)#3
x=c(x,0.056961883353649566)#4
x=c(x,-0.06069047539993999)#5
x=c(x,0.03485647229097991)#6
x=c(x,-0.07570967230260134)#7
x=c(x,0)#0-16
x=c(x,0.0002971799298054011)#1
x=c(x,0.018802174294039967)#2
x=c(x,0.0047563932799025285)#3
x=c(x,0.038646702644233005)#4
x=c(x,-0.01969350191625727)#5
x=c(x,-0.00905064913872669)#6
x=c(x,0.02972290172590976)#7
x=c(x,0)#0-17
x=c(x,-0.012975114982981777)#1
x=c(x,-0.023646376296039332)#2
x=c(x,0.021129615371382856)#3
x=c(x,0.057008347148008676)#4
x=c(x,-0.06051883187949758)#5
x=c(x,0.034856476063455176)#6
x=c(x,-0.07569495678896931)#7
x=c(x,0)#0-18
x=c(x,0.0002696431479482309)#1
x=c(x,0.01844955210532226)#2
x=c(x,0.005163748103738864)#3
x=c(x,0.038392434478673985)#4
x=c(x,-0.02006062694298151)#5
x=c(x,-0.009050600101314333)#6
x=c(x,0.02961349117308415)#7
x=c(x,0)#0-19
x=c(x,-0.012947578201124608)#1
x=c(x,-0.023293754107321638)#2
x=c(x,0.02072226054754651)#3
x=c(x,0.057262615313567675)#4
x=c(x,-0.060151706852773344)#5
x=c(x,0.034856427026042816)#6
x=c(x,-0.0755855462361437)#7
x=c(x,0)#0-20
x=c(x,0.00015235255196601426)#1
x=c(x,0.018090134670099473)#2
x=c(x,0.005826010999584576)#3
x=c(x,0.03781096377417702)#4
x=c(x,-0.02051387732871736)#5
x=c(x,-0.009041385295032383)#6
x=c(x,0.029326041084552244)#7
x=c(x,0)#0-21
x=c(x,-0.01283028760514239)#1
x=c(x,-0.02293433667209884)#2
x=c(x,0.02005999765170081)#3
x=c(x,0.057844086018064664)#4
x=c(x,-0.059698456467037496)#5
x=c(x,0.03484721221976086)#6
x=c(x,-0.07529809614761179)#7
x=c(x,0)#0-22
x=c(x,-0.00010016815499999405)#1
x=c(x,0.017581183485064163)#2
x=c(x,0.006409181081122117)#3
x=c(x,0.03703441151715984)#4
x=c(x,-0.020933288820437643)#5
x=c(x,-0.008896102672098314)#6
x=c(x,0.0289138560987212)#7
x=c(x,0)#0-23
x=c(x,-0.012577766898176383)#1
x=c(x,-0.022425385487063534)#2
x=c(x,0.01947682757016327)#3
x=c(x,0.058620638275081835)#4
x=c(x,-0.05927904497531721)#5
x=c(x,0.034701929596826796)#6
x=c(x,-0.07488591116178075)#7
x=c(x,0)#0-24
x=c(x,-0.00045768754116740166)#1
x=c(x,0.016933958174540985)#2
x=c(x,0.006845027226092256)#3
x=c(x,0.036293597180222126)#4
x=c(x,-0.021260198083024463)#5
x=c(x,-0.008159185047229593)#6
x=c(x,0.028743274667077524)#7
x=c(x,0)#0-25
x=c(x,-0.012220247512008975)#1
x=c(x,-0.021778160176540357)#2
x=c(x,0.019040981425193122)#3
x=c(x,0.05936145261201955)#4
x=c(x,-0.05895213571273039)#5
x=c(x,0.033965011971958066)#6
x=c(x,-0.07471532973013709)#7
x=c(x,0)#0-26
x=c(x,-0.0008873151489962878)#1
x=c(x,0.016085311475881815)#2
x=c(x,0.007162773178278581)#3
x=c(x,0.03563186295203474)#4
x=c(x,-0.02153358198952339)#5
x=c(x,-0.006465431369639936)#6
x=c(x,0.028971621313637043)#7
x=c(x,0)#0-27
x=c(x,-0.011790619904180089)#1
x=c(x,-0.02092951347788118)#2
x=c(x,0.0187232354730068)#3
x=c(x,0.06002318684020693)#4
x=c(x,-0.058678751806231465)#5
x=c(x,0.03227125829436841)#6
x=c(x,-0.07494367637669659)#7
x=c(x,0)#0-28
x=c(x,-0.001352039495111673)#1
x=c(x,0.015580897283599052)#2
x=c(x,0.007338821832786869)#3
x=c(x,0.034689872867353914)#4
x=c(x,-0.021986525503168198)#5
x=c(x,-0.004304639325606844)#6
x=c(x,0.02942721457973837)#7
x=c(x,0)#0-29
x=c(x,-0.011325895558064705)#1
x=c(x,-0.020425099285598422)#2
x=c(x,0.018547186818498516)#3
x=c(x,0.06096517692488776)#4
x=c(x,-0.05822580829258665)#5
x=c(x,0.030110466250335324)#6
x=c(x,-0.07539926964279792)#7
x=c(x,0)#0-30
x=c(x,-0.0018626750989563113)#1
x=c(x,0.015036699574173586)#2
x=c(x,0.007650233219604404)#3
x=c(x,0.03305445135619395)#4
x=c(x,-0.022873781833506156)#5
x=c(x,-0.00222238149546775)#6
x=c(x,0.029919947705238273)#7
x=c(x,0)#0-31
x=c(x,-0.010815259954220066)#1
x=c(x,-0.019880901576172963)#2
x=c(x,0.018235775431680975)#3
x=c(x,0.06260059843604772)#4
x=c(x,-0.05733855196224869)#5
x=c(x,0.02802820842019623)#6
x=c(x,-0.07589200276829783)#7
returns = matrix( x, ncol=32 ) # nrow=8

# performs
performs = colMeans( returns )

# C
C = cov( returns )
if( ! is.positive.definite( C ))
	C = make.positive.definite( C, tol=1e-6 ) ## Alexios: tol=1e-2

# spec
spec = parmaspec(
	S = C,
	risk = 'EV', # EV LPM MiniMax
	riskType = 'optimal', # minrisk optimal maxreward
	targetType = 'equality', # equality inequality
	LB = rep( -1, length( performs )),
	UB = rep( +1, length( performs )),
	leverage = 1,
	budget = NULL,
	forecast = performs,
	asset.names = colnames( returns, do.NULL = FALSE ) )

# control
control = list(
	abs.tol = 1e-12,
	rel.tol = 1e-12,
	Nu = 4,
	max.iter = 1250,
	BigM.K = 4,
	BigM.iter = 15 )

# portfolio
portfolio = parmasolve(
	spec,
	solver.control = control,
	type = 'SOCP' )

### R snippet end ###