I am building a model to value to treasury bond and note futures. I use PCA on the deliverable set to generate interest rate scenarios. I observed that when I regress the actual yield changes of the deliverable set on any particular day to the first 2 factor loadings to find the factor realizations on that day I get an abysmally low correlation (close to 0) though the 2 factors explain close 99% of the variance in the data. Is there anything wrong with my method of computng factor realizations?Thanks

Yes.Let me make sure I understand what you are doing. You compute daily yield changes on the deliverable set of Treasury bonds and notes for some sample of days. One important question is how you identify the "same" security, by time to maturity (which changes every day) or maturity date (which is constant)?Anyway, you used the daily data to compute the correlation matrix of returns, which was all values near 1. You took the principal components and found that the first component was something like the sum of all changes, and the second component was something like the longest instruments minus the shortest.Then you took some new data. On each new day you computed the daily yield changes as before, and then computed the values for factor 1 and factor 2, using the weights from the PC analysis. You did this for a series of days, then regressed individual daily changes for specific securities on the two factor values for each day. You got a low correlation.If this is what you did, there is some error. The correlation should not be low.

AaronBy same security I do mean the same maturity. Actually as you pointed out it was an error in my regression data. The regression does have high correlation.Thanks