[R] Portfolio Optimization

[Enrico Schumann]

I would be biased towards using a heuristic, for instance Threshold 
Accepting (TA), for solving such a problem. (TA is implemented in 
package NMOF. Disclosure: I am the author of that package.) But you will 
not find a ready-to-use solution there.

(1) you need an objective function, ie, a function that maps a given 
vector of holdings (and data like your scenario matrix) into a real 
number; the better the portfolio, the lower the number.

(2) For TA, you need a so-called neighbourhood function. That is a 
function that changes one portfolio vector into another, by changing 
some elements. Examples for simple neighbourhoods are in the package 
vignettes. Do you have a budget constraint? If yes, and you want to work 
with integers, I would suggest using a "cash" variable. (See, eg, 
Algorithm 3 in http://www.swissfinanceinstitute.ch/rp20.pdf )

(3) The constraints can, at least in a first round, be included through 
penalties.


Regards,
Enrico

PS. There is a mailing list dedicated to finance-with-R questions, and 
you may get better answers there.

https://stat.ethz.ch/mailman/listinfo/r-sig-finance



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


Am 13.01.2012 17:06, schrieb Sal Pellettieri:
> Hi,
>
> I'm an R newbie and I've been struggling with a optimization problem for
> the past couple of days now.
>
> Here's the problem - I have a matrix of expected payouts from different
> stock option strategies. Each column in my matrix represents a different
> stock and each row represents the return to the strategy given a certain
> market move. So the rows are not a time series of percentage returns but a
> dollar payout in different expected scenarios, i.e.
>
> Expected Return Matrix (ER) =                   stock1   stock2  .... stockn
>                                                 scenario1   $              $
>                $
>                                                 scenario2   $              $
>                $
>                                                 scenario3   $              $
>                $
>                                                     ...
>
> I want to create an optimal portfolio of these strategies by applying a
> vector of weights. The weights will be the number of contracts of each to
> buy and won't be a percentage weighting. There are a few constraints I need
> it comply with:
>
>     - The weights have to be integers
>     - The minimum portfolio return (ER* Weights) across the scenarios has to
>     be greater than some negative number I specify
>     - There has to be a certain minimum number of stocks in the portfolio so
>     length(weights)>some number I specify.
>
> Any help is GREATLY appreciated since I have tried so many different
> functions and packages. Even if someone can just lead me to the correct
> function to use that would be a great help as I've looked at optim,
> solveLP, ROI package and many others.
>
>
> Thanks,
> S
>