When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4?

  • 3
    $\begingroup$ From my experience the higher PC:s have more complex shapes so the interpretation is more complicated as well. Also the above terms are not perfect, e.g. PC1 is not exactly a level factor and can show a weak slope pattern. $\endgroup$
    – fes
    Mar 3, 2022 at 14:34

1 Answer 1


The first 3 PCs have clear geometric interpretations: PC 1 is “level” or “parallel shift”; PC 2 is “slope” or “tilt” or “flatness / steepness” or “twist”; and PC 3 is “curvature”, “bow”, or “butterfly”.

However the higher-numbered components have less intuitive geometric interpretations, such as “double-humps” at varying tenors. Some discussion of PCs beyond 3 can be found in: Richard K. Crump and Nikolay Gospodinov (Federal Reserve Bank of New York). Deconstructing the Yield Curve. Staff Report No. 884 (Revised January 2022).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.