[R-SIG-Finance] SD of simulated index market caps grows too quickly

[James Toll]

Hi,

I'm trying to simulate an indexing strategy on an equity index with  
100 constituents.  I'm using mvrnorm from MASS to generate 10 years  
worth of data.  Because of the difficulty in generating a useable  
covariance matrix for Sigma, I've been trying to get by with a 100x100  
covariance matrix and using that to generate 100 time series.

The problem I'm experiencing is that over a ten year period, the  
standard deviation of the market caps in the index is exploding (e.g.  
200-400% increase, sometimes larger).  I don't have data to support  
this opinion, but I don't think this is very realistic of a typical  
index like, for example, the OEX.

My guess as to the problem is that an index, by its very nature, has a  
kind of built-in mean reversion due to the fact that equities that  
lose a significant amount of market cap will be shortly replaced by  
equities that are growing in market cap.  I believe that this would  
tend to prevent the kind of explosion in SD that I'm seeing in my model.

Short of expanding my matrix, and then periodically rebalancing with  
the largest 100, is there a way to control this expansion of the SD of  
the constituent market caps?

Thank you,

James