I am working on one quality and value factor, the correlation between a long-only or short only portfolio of these two factors is respectively 0.7 and 0.8, and the correlation between combined long-short portfolio is approx 0.02. I wanted to understand why did it happen and also it would be helpful if someone can explain how to break Corr(L1+L2, S1+S2) into the correlation of Corr(L1, L2) and Corr(S1, S2) and other terms. Thanks a lot for reading this in advance.

  • $\begingroup$ Probably in the long only portfolios you have exposure to the Market factor (since you cannot eliminate that without shorting) and so the two long only portfolios are positively correlated. (The same reasoning for the two short only portfolios, they are both highly negatively exposed to the Market factor). The Long+Short portfolios are closer to "pure" factor portfolios (market neutral), so not much correlation between them. $\endgroup$ – Alex C Aug 22 '19 at 15:50

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