Stock replication

momentumpartners · November 24th, 2009, 4:30 pm

Hi all, I am working on how to replicate a stock with a basket of stocks and I am using the nnls package in R that performs a quadratic optimization program. I was wondering if anybody was familiar with this and wanted to discuss if it was relevant to apply a variance analysis and look at the t-stat, F-stat etc. in this case. Thanks looking forward to your input. Matt

pnrodriguez · November 24th, 2009, 9:07 pm

You want to replicate the returns using linear models? Andrew Lo has a nice paper which replicates hedge funds returns. Although it is not the same application, you can see how restricts the parameters, etc. However, if you dont want to use the linear case, then you will have to decide what is your objective function. For example, explain the charecteristics of the distribution? explain the movements? then I would go for Genetic Algorithms. That way you can find portfolio weights that mimic your stock based on your objective function. Hope this helps!

momentumpartners · November 25th, 2009, 3:06 pm

Thanks pnrodriguez. I've read Lo's paper on HF replication, also Martelini's work is interesting on that same topic. The problem is that some HF like some stocks exhibit non-normal return distributions and this is why I am trying to get away from the linear replication. Linear models fail to replicate some time series properties of asset returns and usually the only thing you manage to replicate is the beta. I am curious about what you said on "Genetic Algorithm" though. I have never heard of it before. Do you any reading recommendation? thanks a lot for your help!