When analyzing the structure of a market, one of the commonly leveraged tools is the minimum spanning tree (MST).  Calculated based on the correlation between the return of assets in a market, the MST represents asset clustering and overall structure in an intuitive and graphical way.

    Though this sounds overly abstract and devoid of application, the MST often serves as a good check for portfolio allocation.  In order to obtain optimal portfolios for realistic investment goals, you simply must diversify at least somewhat.  Diversification, however, comes at an additional cost to managing the portfolio.  The constraints here are that you need to achieve reasonable diversification with the least cost possible.

    The best way to do this is to reduce redundancy in your assets.  Carrying redundant assets is essentially adding to costs without adding to diversification.  For instance, if a portfolio's focus isn't technology, it doesn't make sense to hold both a NASDAQ-100 tracker (QQQQ) and another technology ETF (RYT or IXN). 

   So how do you figure this out?  Well, one way is the minimum spanning tree.  The MST gives you the market structure quickly, allowing you to see whether you've accidentally allocated your assets redundantly.  As an example, I've generated an MST for the MSCI ETFs I recently covered.

    An ideal portfolio would pick assets that were not too correlated.  For instance, if you noticed that you held both EWK and EWN, you'd have doubled your costs without really gaining much in terms of diversification.  This goes for any close nodes in the graph, especially those at the fringes.

    So in conclusion, though they may seem unnecessary at first, minimum spanning trees are a great way to get a big picture of a market, and a helpful guide for efficient diversification.