Réf. : Re: solve.QP (for portfolio optimization)

--- about Christian's two-step approach ---

I've tryed this. The issue is that provided we want to minimize the *overall* portfolio variance we have to manage potential correlations between longs and shorts (e.g. if some of your longs are "anti-correlated" - is that the correct word?
- with some of your shorts). In my tests, simple equally weighted portfolios are less volatiles.

--- Brian wrote ---
" 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. "

I agree. Yet I could think the same way for my long portfolio: I want these stocks to increase in value as much as possible.
So in the end the question is about minimizing variance in general [or not]. At the moment, this is what I'm trying to do (also I agree with your concerns on Markowitz-like frameworks and will keep your suggestions in mind).

G




                                                                                                                           
                                                                                                                           
                                                        Pour :   <r-sig-finance at stat.math.ethz.ch>                         
                                                        cc :                                                               
                                                        Objet :  Re: [R-SIG-Finance] solve.QP (for portfolio optimization) 
             "Christian Prinoth"                                                                                           
             <Christian.Prinoth at epsilonsgr.it>                                                                             
             Envoy? par :                                                                                                  
             r-sig-finance-bounces at stat.math.ethz.                                                                         
             ch                                                                                                            
                                                                                                                           
                                                                                                                           
             10/01/2007 14:35                                                                                              
                                                                                                                           
                                                                                                                           




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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