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

[Brian G. Peterson]

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