7 votes

Principal components in treasuries: spot vs futures

It is preferable to use constant maturity yields (ideally par yields) for running PCA analyses. Using constant maturity par yields has several advantages: By definition, the yields are of constant ...
Helin's user avatar
  • 11.7k
5 votes

Principal Component Analysis of yield curve change

To put things in context, if $\{{\bf X}_i\}_{i=1}^n$ is a set of variables and $\{{\bf Y}_j\}_{j=1}^n$ denote the principal components of ${\bf X}$ then $$ {\bf X}_j = \mu_j + \sum_{k=1}^n{\bf Y}_k ...
caverac's user avatar
  • 311
4 votes

Principal Component Analysis of yield curve change

We can calculate the principal components by finding the eigenvalues and eigenvectors of the covariance matrix. The largest eigenvalue represents the largest variance, second largest eigenvalue the ...
RRG's user avatar
  • 1,024
4 votes

Principal components in treasuries: spot vs futures

This is an interesting exercise and would be compelled to see the results of your data gathering. The principal purpose of treasury note (cash bond) analysis is for yields and the cross-asset class ...
rrg's user avatar
  • 969
4 votes

Applications of PCA to yield curve analysis

You can see my remark above for some more words on PCA for the yield curve and an interesting paper. About the question whether it helps us to creat a risk model: PCA on the yield curve changes (!) ...
Richi Wa's user avatar
  • 13.7k
3 votes

Can PCA be used to transform a ladder of interest rate risk?

PCA is a mathematical transformation from a certain basis representation, i.e. 1y,2y,3y,4y, into another representation PC1, PC2, PC3 and PC4. In its raw form it is not a dimension reduction procedure....
Attack68's user avatar
  • 10.2k
3 votes

PO (Principal only) mortgage bonds - Does Price or yield go up when interest rates go down?

Prices go up. For 2 reasons a) just like any bond, prices go up when rates go down and b) faster prepayments are expected , which means the maturity of the bond becomes earlier than previously ...
dm63's user avatar
  • 17k
2 votes

Low-rank approximation techniques for portfolio optimisation

I don't think that PCA works how you think it does. In coming up with orthogonal vectors (i.e. the eigenvectors of the covariance matrix), Principal Component Analysis generally ends up with each ...
David Kozak's user avatar
1 vote

How do you optimize an all equity portfolio while getting around the multicollinearity issue?

This is a matter of your preference aka utility function. Perhaps the simplest reasonable approach would be the constrained Markowitz allocation $$ w=argmax(w^T\mu - kw^T\Sigma w)\quad s.t.\quad w_i\...
Michael Isichenko's user avatar
1 vote

Difference between par value and principal?

Usually both principal and par value refer to payment from a bond on its maturity. Sometimes term nominal is used for this as well. There can a little difference, however. Principal is used for a ...
Martin Vesely's user avatar

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