[R-SIG-Finance] minimum variance portfolio (no shorts)

[Brian G. Peterson]

On Sat, 2012-02-18 at 17:37 -0500, benn fine wrote:
> I realize this topic has been hashed to death but i think the multitude of
> answers is confusing me.
> 
> I have mu,hat and cov.hat and a time series object of returns.
> I want the minimum variance portfolio without short sales
> 
> Is there a basic function somewhere that does that? I'm finding
> minvariancePortfolio in Fportfolio a little tricky to use.

'a little tricky to use' is hardly reproducible.

> I am trying the optimizeportfolio routine in PortfolioAnalytics. But the
> results seem a bit odd.

PortfolioAnalytics will give the correct result given the correct
objective function, but in any event I wouldn't use a global solver when
a simple closed form solution is available.  Portfolioanalytics, as
stated in the documentation or our seminar slides, is designed for much
more complex objectives for which no closed form solution exists.
 
> I have some code from Eric Zivot's website to compute the global minimum
> variance portfolio (see below).
> When I run it on a simple 4 asset example, I don't get the same result as
> optimize.portfolio, and in
> fact the optimize.portfolio weights give a larger portfolio variance.
>
> Here is the call for optimize.portoflio:
> 
> myconstr=constraint(assets=4, min_sum=1, max_sum=1, min=-100,
> max=100,weight_seq=generatesequence())
> optimize.portfolio(myrets,myconstr)

ouch.  weights are PERCENTAGES.  This is clearly stated in the
documentation, and in all the examples and lecture slides.

You said *without short sales*, yet this is 100x leveraged long/short
portfolio.

> Has someone written a nice wrapper to easily get the min variance portfolio
> wo short sales?

I don't know how much nicer you expect than three lines of code...

> Any ideas why Eric's code (which I trust) gives a different answer from
> opitimize.portfolio?

You put in the wrong constraints.

You also don't show the rest of your objective function here.

Right now, you're using a 100x leveraged long/short portfolio and no
objective...

You'll want to fix your min and max arguments, and have at least one
add.objective call.

Please look at the seminar slides from R/Finance 

http://www.rinfinance.com/agenda/2010/Carl+Peterson+Boudt_Tutorial.pdf

 - Brian

> 
> Thanks! Sorry for the cluelessness.
> 
> globalMin.portfolio <-
> function(er, cov.mat)
> {
>   # Compute global minimum variance portfolio
>   #
>   # inputs:
>   # er				N x 1 vector of expected returns
>   # cov.mat		N x N return covariance matrix
>   #
>   # output is portfolio object with the following elements
>   # call			original function call
>   # er				portfolio expected return
>   # sd				portfolio standard deviation
>   # weights		N x 1 vector of portfolio weights
>   call <- match.call()
> 
>   #
>   # check for valid inputs
>   #
>   asset.names <- names(er)
>   er <- as.vector(er)					# assign names if none exist
>   cov.mat <- as.matrix(cov.mat)
>   if(length(er) != nrow(cov.mat))
>     stop("invalid inputs")
>   if(any(diag(chol(cov.mat)) <= 0))
>     stop("Covariance matrix not positive definite")
>   # remark: could use generalized inverse if cov.mat is positive semi-definite
> 
>   #
>   # compute global minimum portfolio
>   #
>   cov.mat.inv <- solve(cov.mat)
>   one.vec <- rep(1,length(er))
> #  w.gmin <- cov.mat.inv %*% one.vec/as.vector(one.vec %*% cov.mat.inv
> %*% one.vec)
>   w.gmin <- rowSums(cov.mat.inv) / sum(cov.mat.inv)
>   w.gmin <- as.vector(w.gmin)
>   names(w.gmin) <- asset.names
>   er.gmin <- crossprod(w.gmin,er)
>   sd.gmin <- sqrt(t(w.gmin) %*% cov.mat %*% w.gmin)
>   gmin.port <- list("call" = call,
> 		    "er" = as.vector(er.gmin),
> 		    "sd" = as.vector(sd.gmin),
> 		    "weights" = w.gmin)
>   class(gmin.port) <- "portfolio"
>   gmin.port
> }
> 
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> 
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-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock