Just would like to clarify methodology on trades like 4-8-12 "PCA based Fly".lets supposed we are paying 8y swap rate on 100m notional, and we are solving notional receivingon wings 4y & 12y, resp. Alpha and Beta.Which Principal Component Analysis has to be done ?Once done, how do you translate results into finding Alpha & Beta specifically?There were a few threads on this in the forum , but this point wasn't addressed.For instance, I would think that one wants to pick alpha&beta to reducevariance and take advantage of a "mean-reverting" relation between 4y/8y/12y. Someone suggested to maximize the variance, but I would disagree as we dont want the trade to be sensitive to parallel shifts,etc?

hey chesscorner just saw your post. Maybe we can transfer this to the original thread. If you tell me what you are trying to achieve with the fly...then I will be able to tell you how to construct it. I started the thread because I didn't know what is the use of the PCA fly anyway so we put up some hypothesis on how it can be used. So since you know what you want to achieve with it maybe you should explain it to the rest of us too. Are you a trader btw?

lets call s4(i) , s8(i), s12(i) the 4y,8y,12y daily swap rates observations over 10y.I am trying to compute the wing weights such that the fly is not sensitive to parralel shift and flattening/steepening moves. there are many ways to proceed but i'd like to try a PCA method.currently i am doing the followinga) compute s4(i)-s4(i-1), s8(i)-s8(i-1),etc on three columns.b) compute the correlation matrix ( 3x3) on these 3 columns.c) PCA on matrix from b.the first vector obtain is clearly a parallel shift of yield curves.the second vector is something like (0.75,-0.26,-0.65), clearly a steepening move.the third vector is (a,b,c)if 8 years is the belly (qty =1) , does that mean that a/b is my 4y weight, and c/b is my 12y weight ?since people seem to have used similar methodologies, the question is :do people use variations for step a) or something else ?do people use the ratio a/b, c/b for the fly ?what is the most widespread methodology on this , based on what was suggested above ?of course, after that, there's an another step which inclues views onthe yield curve, what pillars to take, do it on treasuries or spreads or rates, etc.etctrying here to focus on the financial application of the pca method.thx

lets call s4(i) , s8(i), s12(i) the 4y,8y,12y daily swap rates observations over 10y.I am trying to compute the wing weights such that the fly is not sensitive to parralel shift and flattening/steepening moves. there are many ways to proceed but i'd like to try a PCA method.currently i am doing the followinga) compute s4(i)-s4(i-1), s8(i)-s8(i-1),etc on three columns.b) compute the correlation matrix ( 3x3) on these 3 columns.c) PCA on matrix from b.the first vector obtain is clearly a parallel shift of yield curves.the second vector is something like (0.75,-0.26,-0.65), clearly a steepening move.the third vector is (a,b,c)if 8 years is the belly (qty =1) , does that mean that a/b is my 4y weight, and c/b is my 12y weight ?since people seem to have used similar methodologies, the question is :do people use variations for step a) or something else ?do people use the ratio a/b, c/b for the fly ?what is the most widespread methodology on this , based on what was suggested above ?of course, after that, there's an another step which inclues views onthe yield curve, what pillars to take, do it on treasuries or spreads or rates, etc.etctrying here to focus on the financial application of the pca method.thx

b) i meant covariance matrix ( and not correlation).