[R-SIG-Finance] [R-sig-finance] Newbie Question: Portfolio Optimization with MV, LPM and CVaR constraints

[Brian G. Peterson]

Jonathan Ling wrote:
> Hi there,
>
> I'd start of by apologizing if the following has been answered in previous discussions or materials, so far my searches haven't been resourceful.
>
> I have a project on portfolio optimization to track performances of
> portfolios created under different constraints (mean-variance, LPM, VaR and CVaR). I've used monthly data (for 12 years) for a couple of shares, and I stumbled on fPortfolio which I've been trying out for the last 2 weeks.
>
> I'm having trouble figuring out a couple of things.
>
> 1. Is it possible for fPortfolio to optimize a portfolio constrained by the VaR?
>
>   
No. 

VaR optimization does not have an analytical solution, as VaR is not a 
coherent measure that can be transformed into a linear programming or 
other similar method.  I've previously used a combination of grid search 
and library("Rdonlp2") to do VaR optimization.  fPortfolio development 
code has some support for these methods, but it isn't complete or 
released, to the best of my knowledge.

With only 2 instruments, you can easily do grid search and solve the VaR 
optimization problem via brute force. (with 200 this would obviously be 
computationally infeasible)
> 2. Would it be possible to use the first 10 years of my data to optimize the
> portfolios and track performances at 6 months, 1 year and 2 years after
> that?
>
>   
Yes, in general, you'd set your weights and then float.

Please be aware that the code in fPortfolio used to assume continuous 
rebalancing to maintain your weights.  You'll need to assess whether 
this is still the case.  If the fPortfolio code still uses continuous 
rebalancing, to allow your weights to "float" after the initial 
allocation, the calculation is a little more complicated.  We have some 
code that we haven't quite finished documenting and testing for release 
yet that does this, and I'd be happy to test it on your data and 
allocation weights and share it with you.

> 3. I'm having some trouble with the LPM method of optimization. It's
> spitting out the error below, but only on monthly data, it works fine with
> weekly data.
>   
I've never done LPM optimization, so perhaps another fPortfolio user or 
Diethelm or Yohan can help you out with that part of your query.

Regards,

  - Brian

-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock