# [R-SIG-Finance] comparing solve.pq and nloptr for min variance portfolio

Alec Schmidt aschmid1 at stevens.edu
Fri Mar 18 15:39:45 CET 2016

```Hi Enrico,
Many thanks for your interest. I attach my script and input file with asset tickers. Sorry for lots of unrelated stuff - it's a working draft.

Alec
________________________________________
From: Enrico Schumann <es at enricoschumann.net>
Sent: Friday, March 18, 2016 10:25 AM
To: Alec Schmidt
Cc: R-SIG-Finance at r-project.org
Subject: Re: [R-SIG-Finance] comparing solve.pq and nloptr for min variance portfolio

On Fri, 18 Mar 2016, Alec Schmidt <aschmid1 at stevens.edu> writes:

> I'm puzzled that I cannot reproduce results for asset weights using
> solve.pq and nloptr even in the case of just three assets.  E.g. if I
> use NLOPT_LD_SLSQP and start with initial weights of 1/3, I may obtain
> (0.47, 0, 0.53) vs (0.52, 0, 0.47).  If I start with (0.52, 0, 0.47),
> I do get (0.52, 0, 0.47)...
>
> When I use NLOPT_GN_ISRES or other nloptr solvers that permit equality
> constraint sum(weights)=1 with initial weights of 1/3, I obtain
> (almost) the same initial weights after 20000 iterations with
> xtol_rel=1.0e-8...
>
> I remember from my MC simulations of protein structures (20 years ago)
> that sampling is key due to multiple local minimums but is it so bad
> for a simple portfolio?
>
>
> I'll greatly appreciate relevant comments.
>
> Alec

[...]

Unless your covariance matrix is 'broken' in some way, a
minimum-variance portfolio with only a budget constraint should be
fairly easy to compute (no multiple local minima, smooth objective
function, ...). Please provide a reproducible example.

Kind regards,
Enrico

--
Enrico Schumann
Lucerne, Switzerland
http://enricoschumann.net
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