# [R-SIG-Finance] fPortfolio - Maximum Return Portfolio

Diethelm Wuertz wuertz at itp.phys.ethz.ch
Wed May 27 08:31:46 CEST 2009

```Yaakov Moser wrote:
> Can anyone suggest a simple way to find the maximum return portfolio
> on an efficient frontier with fPortfolio?
>
> Without constraints, this is simply the asset with the highest return.
> However, with constraints, it needs to be solved.
>
> The only option I have come up with so far is to use the
> portfolioFrontier function (ideally with a large number of points),
> and then take the end one.
That's true.

It is quite difficult to find the end of the frontier with constraints.
To find the endpoint of the frontier, one has to go along the frontier
with the function portfolioFrontier which can even fail if the constraints
are to restrictive, since then no solution can be found by the solver.

Maybe a nested interval solver can help:  take the return of the minimum
global risk portfolio, the return of the endpoint of the (unconstrained)
frontier, and the point of the return in between. When the intermediate
point exists go up the frontier, otherwise go down the frontier, repeat
this until you have the desired precision. Use the R function try() to
find out if the intermediate point fails or not.
After a few steps one should have reached the endpoint of the frontier.

Has anybody a better and/or faster (more efficient) algorithmic (maybe
analytic) solution to find the frontier endpoint under constraints?

There may be another problem which I often observed, that the solver may
become unstable close to the endpoint of the constrained frontier.
Has anybody a good argument why this may happen and how to circumvent this?

Diethelm

> However, this point varies depending on how many points were selected
> in the Spec...
>
> As far as I can tell, there is no built in functionality equivalent to
> the minriskPortfolio.
That is true, a first implemetation can be done easily along the recipe
given above.
>
> Thanks
>
> Yaakov
>
> _______________________________________________
> R-SIG-Finance at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only.
> -- If you want to post, subscribe first.
>

```