Entropy as a diversification measure?

[agentq]

As an example, this:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1358533



At my firm, we've recently started considering using this metric as an additional limit on some of our portfolios. I'm working on applying the basic idea of this paper (PCA, shannon entropy) to some of our more complex bond portfolios.



Anybody else have any ideas of using this in practice?

[hedgeQuant]

Problem with diversification: everything works until it does not. If you know the future correlations among assets, the problem can be solved in a variety of ways. The problem is knowing the future correlations.



IMHO the main focus should be on estimating correlations and trying to do some analysis of worst case scenarios: what if correlation is +1 or -1? How would the portfolio do?

[agentq]

Not disagreeing with you, but assuming we have good covariance estimation techniques and care about the diversification of the portfolio right now is the main concern. What you've said could apply to anything

[sv507]

It seems unclear why you would want to put a limit based on your current estimate of covariance rather than some worst case, but I guess this can be added in later.



I don't know enough about portfolio diversification, but I would say it sounds pretty suspect.





you ought to understand your covariance estimate. do you have confidence intervals? maybe consider a worst case correlation



PCA - the directions depend on the scaling of the variables. some people normalise by the variance before PCA(some term like sphering ) - ie to highlight directions of maximum correlation rather than covariance.



when you do PCA, you typically only keep the first few components, ( if they explain the majority of movements) the others are "noise" - do you want to do that? ie normalise by the retained variance...





the entropy idea ( normalising the portfolio factor variances to generate a "probability") has no statistical justification. Isn't there a metric with a clearer "goal"?



whether this metric is a good idea perhaps depends perhaps on whether your data is highly correlated or not - I guess it makes sense when each factor explains equal amounts of variance, not when the factors are grossly unequal: do you really want to have a portfolio that has equal weightings for parallel shifts of the yield curve, tilts and other more complicated deformations (corresponding to the last components) - I don't think so. whereas parallel shifts, currency, stock moves make more sense. This all depends on having the right scaling...

sean

[tgruhn]

People constantly say "you need to diversify". It would help to

know how to calculate diversity (diversification index).

I have several papers bookmarked that show how to do this.



Also, think of your portfolio (IRA, bond fund etc) as a closed

ecosystem. The stocks/bonds are the animals. You can also

use "Brillouins H". In either method, you need to weight the

securities. Think of Chipotle Mexican Grill(CMG) or Priceline(PCLN)

as alpha predators and Ram Resources(RAMJF) as zooplankton.

[nikol]

just recalled from physics.



gzip test of entropy in data



following this one can monitor entropy of portfolio by simply zipping historical data weighted with respective current portfolio weights.



accordingly, one can optimize weights by finding maximum entropy. result will be the most diversified portfolio.

[Nonius]

Thanks for the link. I see that mofo studied under Jim crutchfield, one of the guys at Santa Cruz who reinvented classical physics with Packard, farmer et al.