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I've done some PCA analysis of a portfolio consisting of futures on certain commodities. However, I am unsure of how to interpret the output as most of the information found online deals with fixed income/equity markets

Here is the output, the symbol format is Future(product, month contract):

SYMB        factor 1    factor 2
Future1.1   (0.0682)     0.0066 
Future1.2   (0.0681)     0.0066 
Future1.3   (0.0678)     0.0077 
Future1.4   (0.0674)     0.0067 
Future1.5   (0.0672)     0.0077 
Future1.6   (0.0670)     0.0074 
Future1.7   (0.0680)     0.0287 
Future1.8   (0.0681)     0.0267 
Future1.9   (0.0680)     0.0179 
Future1.10  (0.0683)     0.0152 
Future1.11  (0.0682)     0.0111 
Future1.12  (0.0682)     0.0081 
Future2.1    0.0420     (0.0663)
Future2.2    0.0509     (0.1469)
Future2.3    0.0509     (0.1469)
Future2.4    0.0509     (0.1469)
Future2.5    0.0509     (0.1469)
Future3.1   (0.0669)    (0.0368)
Future3.2   (0.0670)    (0.0338)
Future3.3   (0.0671)    (0.0310)
Future3.4   (0.0675)    (0.0415)
Future3.5   (0.0672)    (0.0428)
Future3.6   (0.0670)    (0.0381)
Future3.7   (0.0670)    (0.0373)
Future3.8   (0.0564)    (0.0707)
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So, the interpretation here is fairly straightforward but I don't think it is likely what you are looking for. Looking at the factors above I notice the returns for each future matter, but the month contract doesn't matter as much. You can see that in the first factor whereas the second factor you start to see some of the variation across different contract dates.

The results will likely be very hard to use reasonably as you are mixing two types of motion: between different futures and between different contracts of the same future.

I think you will get more interesting results if you do PCA separately on

  1. A larger space of different futures all with the same rolling contract length. This would be more analogous to doing PCA on stocks.

or

  1. All the contracts for a single future. This would be similar to understanding yield curve dynamics for treasury bonds.
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