# [R] generate combination multiset (set with repetition)

G. Jay Kerns gkerns at ysu.edu
Fri Dec 12 05:02:31 CET 2008

```Reuben,

On Thu, Dec 11, 2008 at 9:28 PM, Reuben Cummings <reubano at gmail.com> wrote:
> Good point, I actually thought about doing some kind of sampling
> before, but now I think I don't have a choice. Essentially, what I am
> doing is calculating possible asset allocation possibilities, e.g.
>
> N is the number of available assets and M is the available buckets of
> money to spend on the assets. With N = 3 and M = 2, I am saying I have
> a choice to buy any of 3 three assets and I can afford to make 2 such
> purchases. These combinations are represented below:
>
>        M1      M2
> [1,]    1       1
> [2,]    1       2
> [3,]    1       3
> [4,]    2       2
> [5,]    2       3
> [6,]    3       3
>
> [1,] is saying I spend all of my money buying asset 1.
>
> this produces the following asset allocations
>
>         A1     A2      A3
> [1,]    1       0       0
> [2,]    .5      .5      0
> [3,]    .5      0       .5
> [4,]    0       1       0
> [5,]    0       .5      .5
> [6,]    0       0       1
>
> [1,] again, is saying that my allocation is 100% asset 1.
>
> from here, I plan to run some risk/performance metrics on the
> allocations and then come up with a list of the best allocation
> choices.
>
> The sampling will come in handy to give me random asset allocations.
> I've taken a statistical design of experiments class, so I am familiar
> with generating factorial experiment designs.
>
> So, how would I go about producing the random samples?

rmultinom(10, 2, rep(1,3))/2

Please note that the above assumes a model in which it is equally
likely to choose asset 1, 2, or 3.  You should think about the model
carefully and adjust the "prob" argument accordingly.

> And what # of
> combinations should I use as the cutoff for doing a sampling instead
> of testing every possible combination?

There isn't a definitive answer to that question.  Assuming that it is
desired to find an 'average risk' of some sort, it would be good to
increase the number of samples until the risk estimate stabilizes to a
value with which you are comfortable.

Best,
Jay

***************************************************
G. Jay Kerns, Ph.D.
Associate Professor
Department of Mathematics & Statistics
Youngstown State University
Youngstown, OH 44555-0002 USA
Office: 1035 Cushwa Hall
Phone: (330) 941-3310 Office (voice mail)
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E-mail: gkerns at ysu.edu
http://www.cc.ysu.edu/~gjkerns/

```