Control number of assets in resulting portfolio with optimizations using package fPortfolio

Dear All,



I am using package fPortfolio to run minimum variance portfolio
optimizations in R. I already know how to set portfolioSpecs, portfolio
objects and constraints. Unfortunately I am not able to set the following
type of constraints.

I have a timeSeries object with returns data for roughly 1.5k assets for 261
subperiods (workingdays) and want to compute the global minimum variance
portfolio, considering following constraints:



-          Leverage = 1 (fully invested)



-          the lower / upper weights constraints (can be done by box
constraints) for individual assets are e.g. +0,01 / +0,04



-          and the problematic part: the minimum weights level for each
asset is +0,01 OR zero (in order to control outcome portfolio size)



? Initially, considering that the minimum weight constraint is +0,01 for
each of the 1.500 assets and the sum of weights constraint (leverage) equals
1 would raise an infeasible problem for the optimizer. Given my additional
restriction that the minimum weight for any asset to get into the portfolio
should be at least 0,01 would solve the target conflict in between minimum
asset weights and the leverage of 1. The iteration path of the optimizer
should consider something like this:



ifelse(min(weight,0,01)<0,01,0,weight)



?during the optimization. (iteratively)



Is there any way to implement that sort of that constraint besides the upper
/ lower weight constraints (box constraints) in order to control for decent
portfolio sizes?



Thx&  Regards,

Alex


	[[alternative HTML version deleted]]

Hi Alex,

I cannot say how to implement such constraints with fPortfolio, but in
general you can use heuristics to solve such problems. An example for
selecting a number of assets from a larger universe is given in a vignette
of the NMOF package (of which I am the author) and in the code examples on
http://nmof.net (even though they do not exactly cover your problem).

Regards,
Enrico


Am 15.02.2012 20:18, schrieb Alexander Erbse:

Dear All,



I am using package fPortfolio to run minimum variance portfolio
optimizations in R. I already know how to set portfolioSpecs, portfolio
objects and constraints. Unfortunately I am not able to set the following
type of constraints.

I have a timeSeries object with returns data for roughly 1.5k assets for
261
subperiods (workingdays) and want to compute the global minimum variance
portfolio, considering following constraints:



- ? ? ? ? ?Leverage = 1 (fully invested)



- ? ? ? ? ?the lower / upper weights constraints (can be done by box
constraints) for individual assets are e.g. +0,01 / +0,04



- ? ? ? ? ?and the problematic part: the minimum weights level for each
asset is +0,01 OR zero (in order to control outcome portfolio size)



? Initially, considering that the minimum weight constraint is +0,01 for
each of the 1.500 assets and the sum of weights constraint (leverage)
equals
1 would raise an infeasible problem for the optimizer. Given my additional
restriction that the minimum weight for any asset to get into the
portfolio
should be at least 0,01 would solve the target conflict in between minimum
asset weights and the leverage of 1. The iteration path of the optimizer
should consider something like this:



ifelse(min(weight,0,01)<0,01,0,weight)



?during the optimization. (iteratively)



Is there any way to implement that sort of that constraint besides the
upper
/ lower weight constraints (box constraints) in order to control for
decent
portfolio sizes?



Thx& ?Regards,

Alex


? ? ? ?[[alternative HTML version deleted]]

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