Newbie Question: Portfolio Optimization with MV, LPM and CVaR constraints
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