Question Regarding Optimization From Ranks (Almgren and Chriss)

[danko]

Good Day,



I am a bit confused about a certain issue after reading "Opitmal Portfolios from Ordering Information" and would appreciate any help.



I am thinking about optimizing a portfolio of currencies and equity indices where I have separate ranks for each asset class.  This problem seems quite similar to the example the authors give of optimizing a portfolio of stocks in which you have some from one sector with its own ranking and others from another sector again with its own ranking but nothing in between.  They also say that this sector problem can be solved using the simple formula they give for approximating the centroid by simply computing separate centroids and optimzing with the total covariance matrix.



However, I am confused as to whether I can use the same method to optimize with equities and currencies.  The first thing that strikes me is that if you had ten equites and ten currencies, the centroid, and thus analogously the expected return, that you plug into the optimizer is the same for the top ranked equity and the top ranked currency.  Given, that the volatility of the equity is a lot higher, it seems like the equity would likely be deemed rather unattractive and the optimizer would not take very large positions in the top ranked equity or any equities for that matter. 



 



So my question is first whether I am not understanding something correcly and this isnt a problem at all (my hope) and second, if it is a problem, does anyone have any ideas on how to solve it.  I've thought about multiplying the equity centroid by some constant but this doesnt feel right.  Also, I was planning on constraining the optimizer so that it takes an equal amount of risk in equities and currencies and constraining individual asset contributions.  It seems like such constraints would help, but it also seems like it would be better to deal with the problem (if one exists) in the first moment.



 



Thanks,



Danko 



 



 



Link:



http://corp.bankofamerica.com/publicpdf/equities/Optimal_Portfolios.pdf

[Veegan]

Constraints would of course work. Or, I assume you have some estimate of expected return that you are using to order your stocks and currencies. If so, why not just normalise each return estimate by dividing by its corresponding volatility to give 'return per unit of risk' and then re-order the [i]entire[/i] set of stocks and currencies based upon this metric so you can use a single centroid?

[quantie]

well you are going to use a covariance matrix in the optimization and if the corrs between the currencies and equities are low then they will enter in to your optimal set. Send me a pm and will send you some stuff on this!.



Also if you do wish to have some equity and currencies necessarily then you can do a sector sort and generate the equivalent centroid.