[R-SIG-Finance] solve.QP (for portfolio optimization)

[Christian Prinoth]

If the goal is to build some kind of market neutral position, one could
also take a 2-step approach:

1) build an optimized long portfolio that maximizes some score\expected
return\whatever
2) build a short portfolio that minimizes that same score, while
constraining risk exposure (however defined) to be similar to that of
the long portfolio.

This way it is easier to specify leverage, number of positions etc.

Christian Prinoth
cp at epsilonsgr.it
+39-0288102355


> -----Original Message-----
> From: r-sig-finance-bounces at stat.math.ethz.ch
> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of
> Brian G. Peterson
> Sent: Wednesday, 10 January, 2007 14:06
> To: r-sig-finance at stat.math.ethz.ch
> Subject: Re: [R-SIG-Finance] solve.QP (for portfolio optimization)
>
> On Wednesday 10 January 2007 06:26,
> guillaume.nicoulaud at halbis.com wrote:
> > --- Brian wrote ---
> >
> > "You may find, as many others in the optimization literature have,
> > that the short portfolio requires a different optimization
> approach."
> >
> > I did... and it actually doesn't work! That's why I would like to
> > optimize the whole portfolio instead of doing this
> separatly for longs
> > and shorts (in a Markowitz-like framework *for now*).
>
> Markowitz style optimization will try to minimize variance
> across the entire portfolio.  You *want* the short portfolio
> to decline in value, as much as possible. 
>
> While it should be possible to constrain individual
> instruments to be on the short portfolio, I haven't worked
> with the solve.QP function constraints in enough detail to
> give you any pointers there, and I don't think a minimum
> variance portfolio is really what you want.
>
> Perhaps you can be a little more specific on the problems you
> had with trying to optimize the long and short portfolios separately?
>
> I'll give a couple examples of approaches that could work
> well for your short portfolio (your exact circumstances will
> vary based on the instruments you're constructing a portfolio
> over, of course).  In your short portfolio, you have
> previously made some forecast that the instruments in the
> short portfolio will decline in value.  You need to make some
> decision about how much to short, from the limits you have on
> total short positions in your portfolio. One method of
> choosing how much to short is based on your confidence in
> your price target: higher confidence equals a larger short
> position.  Another method is to use some other appropriate
> measure of risk, like downside deviation or average
> drawdown: larger [downside risk measure] equals larger short
> position, because the instrument tends to move further down in price.
>
> Regards,
>
>    - Brian
>
> --
> http://braverock.com/brian/resume-quant.pdf
>
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