I don't know that gamma translates from options to futures in the way your describing... That or I don't understand what your saying... Typically a correlation is build in relation to the front contract... As opposed to options to their underlying
Well, it could potentially tell you, for any given contract, whether it is rich/cheap vs a "PCA-fitted" strip. Among other things...
Principal components are by construction uncorrelated in the period analyzed as a whole, but we also have the rule of thumb that extremely steep curves are followed by reduction in the level of interest rates. How do I intuitively reconcile those contradictions? For 2 to 30y swaps I get 2nd factor inflection at 4y point for USD (2000-2014) and between 7y and 10y for EUR (2004-2014), and 3rd factor belly point at 10y for EUR and 4y for USD (same periods). If I do PCA on ED gold bundle (2004-2014) I get both inflection and belly at 8th contract - I'd guess it's similar for EURIBOR. Correlation between changes in factors for swaps vs STIRs is meh for USD (0.6 for level and slope, 0.33 for curvature - 2004-2014 period). How would you fundamentally interpret the difference between factors for STIR and for the whole curve?