The Correlation Boundary

A significant amount of time at Newfound is appropriated to quantitative strategy construction. Implicit in mandating quantitative integrity is developing intuition around investment strategy behaviors, throughout the construction process. During one of our strategy deep-dives we discovered a phenomenon that seemed contrary to our initial intuition. Specifically, we assumed that implementing an investment strategy over different time intervals, i.e. daily, weekly, monthly, etc. over the same time horizon, would lead to uncorrelated returns. However, we discovered that no matter the interval the correlation never fell below a certain minimum threshold. We then discovered the same behavior when exploring the joint-behavior of different investment strategies that utilize the same underlying assets.In this paper we mathematically prove the existence of this "correlation boundary." Specifically, we prove that any portfolio will have a correlation to its underlying assets greater than or equal to the minimum pairwise correlation between the assets. We call this minimum correlation level the Correlation Boundary. After proving this boundary, we extend the proof in multiple ways, eventually leading to our ultimate implication: any two investment or trading strategies will always have a correlation to each other that equals or exceeds the minimum pairwise correlation of the set made from the union of their individual underlying assets, no matter the investment horizon of the two strategies