Co-occurrence versus correlation- Still learning about diversification

 

There is a need to deepen our understanding of diversification, but is there a limit to how much we can extract given the basic principles of covariance and correlation? Some in finance are starting to discuss the concept of co-occurrence, which, in the case of asset management, measures the cumulative co-movement of asset pairs during a specific horizon. If, over a particular horizon, the cumulative returns converge to the other returns in the portfolio, you may not have the diversification expected. If we have two assets that, over a one-year horizon, generate similar returns, then you are not diversified. The paths are different, but the two assets end in the same place. 

You can measure the co-occurrence by multiplying the z-scores of two assets and dividing by the average of their squared z-scores. The co-occurrence will fall between -1 and 1, much like the correlation. If the z-score of an asset is zero, then the co-occurrence will be zero. If the z-scores are highly aligned for the tested time period, the co-occurrence will tend toward 1. The determinant of the co-occurrence is the joint informativeness of the two variables, which is essential because the correlation of any two assets is the weighted average of the informativeness with the co-occurrence. So, the co-occurrence tells us something about correlation when we align the return horizon, which we do not do with traditional correlation measures. 

Correlation is useful, but we also want to see how assets move over longer horizons to determine whether there is a pattern of behavior that tells us whether performance diverges or is similar.