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1) Suppose I have 5, products, the #1 PCA is [a,b,c,d,e], what should be the rations of the positions of each contract to be hedged?2) Suppose I have the top 3 PCAs, i.e. eigenvectors of the covariance matrix. What is the formula for the hedge coefficients then? 3) Suppose I am hedging with respect to the first PCA only, shouldn't my hedge coefficients be very close to those I get with OLS?

You need deltas.

Explanation please? And to what part of my question this refers?

My humble understanding:PCA is just a linear transformation (more exactly, a linear projection); basically, it could be use to map from, say, 5 dimensions space (A,B,C,D,E) to a new set of variables (a new space) , say (X, Y) where: X =f(A,B,C,D,E) & Y= g((A,B,C,D,E).thus, you need to understand what are X & Y EXACTLY in order to propose hedging with them, right?Please anyone feel free to correct me.

1) You don't need ratios for EACH contract. You need 2 contracts to hedge the first factor, 3 contracts for the first two, 4 for the first three, and so on. 2) 2 simultaneous equations (for three instruments a, b, c of your choice).w'*PC1 = 0, w'*PC2 = 0, < this hedges against first two factors.where w' = (weight_a, weight_b, weight_c),PC1' = (eigenvector1_a, eigenvector1_b, eigenvector1_c), then for PC2Use those weights on your DV01, then convert to notionals.3) Depends on purpose. If you are the textbook example of a corporate treasurer hedging interest rate risk of an upcoming bond issue, you're probably fine with OLS. If it's about taking a view on the second factor, then slight difference might matter. Second factor explains normally at least ten times less variance, so basically hedging 95% of pc1 still means your exposure is split 50-50 between PC1 and PC2.

Thanks a lot for your responses, can you please look at http://wilmott.com/messageview.cfm?cati ... ARTPAGE=16) Is PCA practical as a pricing model, to be used on the fly for generating signals? How many PCs should I use and how often should I sample if I want holding times of a few minutes?

Erm, I think you need to do some more reading on the subject. I can send you two papers that I found most useful. In short, PCA wouldn't really work systematically with a holding period of a few minutes.

Ok, please send me the papers.What should the holding times be then?