Stats question - Method for comparing portfolios for similarity given only weights

[CFASouldier]

I've already tried a couple of things, but minimized squared deviations of weights seems the only viable solution, but what is the correct statistical test/threshold to use to define a cutoff? my gut tells me its a chi squared test, but given that i am testing one portfolio at a time versus a suite of model portfolios, i'm not 100% sure how to set it up properly. any thoughts would be helpful.

 

[maratikus]

I don't understand what you are trying to do. First, you want to define some kind of measure of similarity and define it as sum of squared differences of weights (Euclidean measure). Then you try to perform a statistical test. I don't understand what you are trying to test.

 

[bchadwick]

I guess if you only know the weights, then the only way to test portfolios for similarity would be to see how the weights match up against each other, and so a sum of squared differences sounds right. I don't do chi-squared tests all that often (other than the ones embedded in F tests), but it sounds like the right statistic to use for a problem like that. The degrees of freedom would presumably be N-1, where N is the total number of unique assets in all portfolios (so if benchmark portfolio has Asset A and B in it, and your test portfolio has asset A and C in it, N=COUNT(A,B,C)=3, and df=3-1=2)


But usually, the similarity question is more about portfolio performance and tracking error. Are you sure that you don't have any figures for the asset returns in the portfolio? Then you might look at the portfolio returns, given the asset weights and compare that to whatever benchmark you are using with a correlation, or a beta, alpha, and tracking error. That's a more typical problem that you might have.



Edited 1 time(s). Last edit at Thursday, December 2, 2010 at 04:16PM by bchadwick.

 

[jmh530]

bchadwick Wrote:
-------------------------------------------------------

> But usually, the similarity question is more about
> portfolio performance and tracking error. Are you
> sure that you don't have any figures for the asset
> returns in the portfolio? Then you might look at
> the portfolio returns, given the asset weights and
> compare that to whatever benchmark you are using
> with a correlation, or a beta, alpha, and tracking
> error. That's a more typical problem that you
> might have.


I would do this and also look at some factor/sector exposures to see if there are significant differences on that front as well.

Aa rough estimate, you can compare the top 10 largest holdings against each other and the top 20 or so largest bets relative to the benchmark to get a sense of the differences.