[R] how to use solve.QP [SOLVED - ANSWER AVAIL]

[roger bos]

Thanks to Zeileis and Spencer for commenting.  I case anyone wants to
see an example of portfolio optimization using solve.QP directly and
verify that the answer matches that of portfolio.optim, here is the
code:

library(quadprog, lib.loc="C:\\Program Files\\R\\tools")
library(MASS, lib.loc="C:\\Program Files\\R\\tools")
rm(sol)
n<-100	 # number of assets
m<-200			 # number of states of the world
rho<-0.7
sigma<-0.2
mu<-.1
Cov <- matrix(rho*sigma*sigma, ncol=n, nrow=n)
diag(Cov) <- rep(sigma*sigma, n)
S <- 1+matrix(mvrnorm(m, rep(mu, n), Sigma=Cov), ncol=n)


Cov <- var(S) #gives same answer as cov(S)
mu <- apply(S, 2, mean)
mu.target <- mean(mu)
bLo <- rep(0, n)

Amat <- rbind(1, mu)
dim(bLo) <- c(n,1)
bvec <- t(rbind(1, mu.target, bLo))
zMat <- diag(n)
Amat <- t(rbind(Amat, zMat))

Dmat=Cov
dvec=rep(0, nrow(Amat))

#The first two rows of Amat should be equality constraints (so weights sum to 1)
meq <- 2

sol <- solve.QP(Dmat=Dmat, dvec=dvec, Amat=Amat, bvec=bvec, meq)
sol
w.asset <- zapsmall(sol$solution)
par(mfrow=c(1,2))
plot(w.asset, type="n")
lines(w.asset, type="h")
hist(w.asset)

#test to see that we get the same result with portfolio.optim
res<-portfolio.optim(S)
wgt <- zapsmall(res$pw)
cbind(w.asset, wgt) #shows both methods are equal






On Thu, 13 Jan 2005 11:43:46 -0800, Spencer Graves
<spencer.graves at pdf.com> wrote:
>      Also, ' methods("portfolio.optim")' revealed 2 functions for this
> generic:
> 
> [1] portfolio.optim.default portfolio.optim.ts
> 
>      Typing "portfolio.optim.ts" exposes the code for the second one.
> If the class of the first argument "x" is "ts", R dispatches
> "portfiolio.optim(x, ...)" to "portfolio.optim.ts(x, ...)".  Otherwise,
> it is dispatched to "portfolio.optim.default(x,...)".
> 
>      hope this helps.
>      spencer graves
> 
> Achim Zeileis wrote:
> 
> >On Thu, 13 Jan 2005 14:07:29 -0500 roger bos wrote:
> >
> >
> >
> >>Zeileis,
> >>
> >>Thanks, I didn't know about "portfolio.optim".  I wanted to see how it
> >>works, but when I try showMethods, it doesn't show it to me.  Does
> >>that mean I am not allowed to see the inner workings?
> >>
> >>
> >
> >1. All of this is open source, so you are *always* allowed to look
> >   at the sources. (If you haven't got a version of the source package,
> >   then you can always get it from CRAN.)
> >2. showMethods() is for S4 generics, portfolio.optim is an S3 generic.
> >3. Simply typing portfolio.optim.default at the prompt should print the
> >   function.
> >Z
> >
> >
> >
> >>Thanks,
> >>
> >>Roger
> >>
> >>
> >>
> >>>showMethods("portfolio.optim")
> >>>
> >>>
> >>Function "portfolio.optim":
> >><not a generic function>
> >>
> >>
> >>On Thu, 13 Jan 2005 19:58:33 +0100, Achim Zeileis
> >><Achim.Zeileis at wu-wien.ac.at> wrote:
> >>
> >>
> >>>On Thu, 13 Jan 2005 13:44:58 -0500 roger bos wrote:
> >>>
> >>>
> >>>
> >>>>At the risk of ridicule for my deficient linear algebra skills, I
> >>>>ask for help using the solve.QP function to do portfolio
> >>>>optimization.  I am trying to following a textbook example and
> >>>>need help converting the problem into the format required by
> >>>>solve.QP.  Below is my sample code if anyone is willing to go
> >>>>through it.  This problem will not solve because it is not set up
> >>>>properly.  I hope I included enough details for someone to deciper
> >>>>it.  Or does anyone have a good example they can send me?
> >>>>
> >>>>
> >>>You can look at the man page, code and example of the function
> >>>portfolio.optim() in package tseries which does portfolio
> >>>optimization based on solve.QP from quadprog.
> >>>
> >>>hth,
> >>>Z
> >>>
> >>>
> >>>
> >>>>Thanks so much for any hints and suggestions, Roger.
> >>>>
> >>>>
> >>>>
> >>>>library(quadprog, lib.loc="C:\\Program Files\\R\\tools")
> >>>>library(MASS, lib.loc="C:\\Program Files\\R\\tools")
> >>>>n<-100
> >>>>m<-200
> >>>>rho<-0.7
> >>>>sigma<-0.2
> >>>>mu<-0.1
> >>>>Cov <- matrix(rho*sigma*sigma, ncol=n, nrow=n)
> >>>>diag(Cov) <- rep(sigma*sigma, n)
> >>>>S <- 1+matrix(mvrnorm(m, rep(mu, n), Sigma=Cov), ncol=n)
> >>>>
> >>>>#The problem is formulated as minimize t(b) Cov b
> >>>>#subject to cLo <= A <= cUp
> >>>>#and bLo=0 <= w <= 1=bUp
> >>>>
> >>>>Cov <- var(S)
> >>>>mu <- apply(S, 2, mean)
> >>>>mu.target <- 0.1
> >>>>#subject to cLo <= A <= cUp and bLo=0 <= b <= 1=bUp
> >>>>A <- rbind(1,mu)
> >>>>cLo <- c(1, mu.target)
> >>>>cUp <- c(1, Inf)
> >>>>bLo <- rep(0, n)
> >>>>bUp <- rep(1, n)
> >>>>
> >>>>#I convert [cLo <= A <= cUp] to Amat >= bvec and [bLo=0 <= w
> >>>>##<=1=bUp] to
> >>>>Amat <- rbind(-1, 1, -mu, mu)
> >>>>dim(bLo) <- c(n,1)
> >>>>dim(bUp) <- c(n,1)
> >>>>bvec <- rbind(-1, 1, mu.target, Inf, bLo, -bUp)
> >>>>zMat <- matrix(rep(0,2*n*n),ncol=n, nrow=n*2)
> >>>>zMat[,1] <- c(rep(1,n), rep(-1,n))
> >>>>Amat <- t(rbind(Amat, zMat))
> >>>>
> >>>>#So I set Dmat=Cov and set dvec=0
> >>>>Dmat=Cov
> >>>>dvec=rep(0, nrow(Amat))
> >>>>
> >>>>#The first two rows of Amat should be equality constraints (so
> >>>>#weights sum to 1)
> >>>>meq <- 2
> >>>>
> >>>>sol <- solve.QP(Dmat=Dmat, dvec=dvec, Amat=Amat, bvec=bvec, meq)
> >>>>sol
> >>>>
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> >>>>
> >>>>
> >
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> >
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