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### Engineering Returns With Multi Asset Universes

Before the engineering starts: Only four months ago, the pageview counter passed the 100,000 milestone. In all likelihood the 200,000 mark will be hit today. Thank you very much for your interest.

The series about Harvesting Momentum (see part I, part II and part III) largely covered pairwise strategies. Now it is time to investigate the performance of more diversified universes to generate returns.

A recent post on CSSA presented Momentum Score Matrices as a tool for predicting the profitability of a given asset universe. Assuming a random walk, the momentum profitability depends on the degree in dispersion of mean returns between the assets in a portfolio. David Varadi states: "A heterogeneous universe of assets such as one containing diverse asset classes will have different sources of returns- and hence greater dispersion- than a homogeneous universe such as sectors within a stock index."

Following a similar, but simplified approach to the cross-sectional dispersion of mean returns, the pairwise momentum score can be calculated as the population average of the squared difference between the momentum values of asset ABC against asset XYZ. Or in "R":

 Dispersion (D) for $IEF -$TIP based on 3 month returns during 2001 - 2014. Average = 8

For an asset collection consisting of 14 assets, this approach results in the below matrix. The calculations can be performed using "R", Excel or AmiBroker. Examples of each are available on the Google Drive connected to this post. AmiBroker has the benefit of exporting the momentum matrix as html-file, which then can be imported into Excel for analysis (and prettifying).

 Dispersion matix based on 3 month returns using synthetic \$ETF's