# Regressing changes in yield/yield curve

If I'm regressing changes in individual points along a yield curve and measures of changes in level/slope/curvature of that yield curve against the returns of some random variable then do I want to use % changes in yields or absolute changes in yields (eg yield change from 1% to 0.95% would be -0.05)?

I am new to fixed income and my experience with volatility tells me that I should use absolute changes since it is already measured in %. For example, the R^2 is much higher when regressing 1-month vix futures changes in points against spx returns than % change against spx returns. However, since I'm new to fixed income I'm running myself in circles (because I don't know what I don't know).

Thanks in advance for any help!

• What I usually see (and do) is working with absolute changes, i.e. $r(t)=R(t)-R(t-1)$. This depends on the rates regime as well, of course. I have seen insurance companies (historically) model their rates with lognormals (r(t)=\ln(R(t)/R(t-1))\$ until 2011/2021, then with a shifted lognormal model until 2018+, and with normals (your suggestion) now.... – Kermittfrog Feb 11 at 8:12
• There's an old RBS piece by Rebonato from 2010, "Dependence of Magnitude of Rate Moves on Rates Levels" which is relevant to your question. At the present time, I would use differences as described by @Kermittfrog. – user42108 Feb 11 at 14:02
• You may find my answers here and here relevant. – Dimitri Vulis Mar 15 at 1:09

The convention in fixed income is for everything to be quoted in yield or basis-point terms, leaving it incumbent on the user to derive a correct price thus. Note that this convention is a convention, that is in no way profit-altering!

As such, it simply seeks to minimise confusion in the face of complexity... which assumes that the tiny majority who are genuinely financially-literate feel the same, which they almost certainly don't ;-) DEM

most rates people speak in terms of basis points and basis point volatility, while some popular products still trade in yield vol (%yield for treasury futures options). Regardless it's an easy conversion between the two. I recommend doing your regressions in basis points. While it's a point of discussion, I'd argue that the fed doesn't work in % of yield and you shouldn't either.

• Options on Treasury futures are based on price vol. – user42108 Feb 13 at 18:37
• that's correct, my mistake. – Edward Watson Feb 13 at 21:17