[R] The quadprog package

[Moshe Olshansky]

Hi Thomas,

On my computer the solution is (0,0,1,0,0,0,0) (within
machine accuracy) and it satisfies the constraints.

--- thomas.schwander at mvv.de wrote:

> Hi everybody,
> 
> I'm using Windows XP Prof, R 2.5.1 and a Pentium 4
> Processor.
> Now, I want to solve a quadratic optimization
> program (Portfolio Selection) with the quadprog
> package
> 
> I want to minimize (\omega'%*%\Sigma%*%\omega)
> Subject to
> 	(1) \iota' %*% \omega = 1 (full investment)
> 	(2) R'%*%\omega = \mu (predefined expectation
> value)
> 	(3) \omega \ge 0 (no short sales).
> 
> Where 
> 	\omega is a Nx1 vector of the weights invested in
> each asset
> 	\Sigma is the NxN variance-covariance matrix
> 	\iota is a 1xN vector of 1's
> 	R' is a Nx1 vector of the expected returns
> 	and
> 	\mu is a number, the postualted return of the
> investor
> 
> I've done the following code but it doesn't make
> what I want it to do. The weights aren't all
> positive and the \mu isn't reached. What's wrong
> with my code?
> 
> Require(quadprog)
> Dmat<-diag(1,7,7)
> # muss als quadratische Matrix eingegeben werden
> Dmat
> dvec<-matrix(0,7,1) # muss als Spaltenvektor
> eingegeben werden
> dvec
> mu<-0 # (in Mio. €)
> bvec<-c(1,mu,matrix(0,7,1)) # muss als Spaltenvektor
> eingegeben werden
> bvec
> mu_r<-c(19.7,33.0,0.0,49.7, 82.5, 39.0,11.8)	
>
Amat<-matrix(c(matrix(1,1,7),7*mu_r,diag(1,7,7)),9,7,byrow=T)
> 
> # muss als Matrix angegeben werden, wie sie wirklich
> ist
> Amat
> meq<-2
>
loesung<-solve.QP(Dmat,dvec,Amat=t(Amat),bvec=bvec,meq=2)
> loesung
> 
> # Überprüfen, ob System richtig gelöst wurde
> loesung$solution %*% mu_r
> sum(loesung$solution)
> for (i in 1:7){
> 	a<-loesung$solution[i]>=0
> 	print(a)
> }
> 
> Thanks in advance for your answers.
> 
> ______________________________
> 
> Thomas Schwander
> 
> MVV Energie
> Konzern-Risikocontrolling
> 
> Telefon 0621 - 290-3115
> Telefax 0621 - 290-3664
> 
> E-Mail: Thomas.Schwander at mvv.de .  Internet:
> www.mvv.de
> MVV Energie AG . Luisenring 49 . 68159 Mannheim
> Handelsregister-Nr. HRB 1780, Amtsgericht Mannheim
> Vorsitzender des Aufsichtsrates: Herr Dr. Peter Kurz
> Vorstand: Dr. Rudolf Schulten (Vorsitzender) . 
> Matthias Brückmann . Dr. Werner Dub . Hans-Jürgen
> Farrenkopf 
> 
> 
> 
> 
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> 
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