Pca-based portfolio properties and trading implications

[Zoho]

As I'm still deeply interested in the topic and really would want to connect with someone who is up to something similar and somehow there's no apparent interest I will try to add some thoughts, sometimes they are not rigorous but the key idea is to get practical results using some kind of analogy which sometimes could be considered as purely theoretical



If we sort stocks based on the whatever forecasting score then eigenvectors of the returns series for the ranked stocks have specific structure: its elements oscillate around zero. So we can interpret this fact the following way: sorted stocks are cointegrated. How one can apply that observation to extract some forecasting power? Lets take some score that is known to posses forecasting power. One can find examples of such scores in the numerous amount of articles. So as the adjacent groups of stocks are going to be cointegrated and we can successfully build long-short portfolios. We can for example take the average value of our score during the long term period, rank according to that score, then get groups based on deciles. Apparently if we succeed in increasing spread between adjacent groups of stocks then we will get better performance of the resulting portfolio. So we can rank stocks within original deciles based on the fresh values of the score. Apparently this ranking within deciles is the same as trying to get zero exposure to the decile group "market". We can attempt to do better if we use portfolio optimization where we specify zero exposure of the resulting portfolio to the portfolio based on long period average score while keeping exposure to the fresh score.



The procedure described above strongly resembles Grinold and Kahn description of estimation of pure factor portfolios returns and also it resembles numerous articles devoted to "surprise in something" scores and their abnormal returns.



Practicle issues with using long period score averaging involves increase of exposure to cross-sectional price momentum. This could be overcome for example by incorporating constraint of zero exposure to momentum into the optimization task.



Hope those ideas would help to bring some interest to the topic. From my point of view it is fascinating to see how purely statistical properties of cross-sectional portfolios could give a rise for the practical ideas.

[Zoho]

Also one can extend the aforementioned ideas and apply improvements to pca like enforcing sparsity like mentioned by EspressoLover. For example one can get the groups of cointegrating stocks and pull residual momentum/reversion using neutralization to the desired factors and for example supervised learning on top of the residuals scores

[Zoho]

implementation of the signals of the "surprise in something"-type that is done with the help of the XTX-style pure-factors could be seen as implementation of the approach by Fernholz who proposed to get smooth information ratio portfolios by hedging frequently rebalanced portfolio with slowly rebalanced portfolio