# Variable Rate LIBOR

If choosing between a fixed-rate loan and a variable loan structured as 1-year treasury rate plus x basis points, would it be reasonable to use the treasury yield curve to extrapolate implied forward rates for each of the years in the term of the loan and then compare the total yield on the fixed-rate loan to the total yield of the variable loan based on the implied forward rates? If this makes sense, is there a way to translate the methodology so that it is applicable to LIBOR-based variable loans? Specifically, my problem is that, since the maximum LIBOR maturity is 1 year, there is no yield curve applicable to the entire term of the loans I would like to compare.

As a technical point, you would be using the Treasury yield curve to interpolate implied forward rates, not to extrapolate. And, yes, it soule be reasonable to do so.

You can do the same with LIBOR rates. Beyond one year, you would have to extrapolate the curve, perhaps using a constant or linearly changinging spread over the US Treasury curve.

Thank you. Any thoughts on what would be a reasonable spread? One possibility is to switch from interpolating 1-year forward rates over the 5-year period to 3-month forward rates over the 5-year period and then adding the current TED spread to those 3-month rates.

I was thinking merely of extrapolating the LIBOR/Treasury spread. If there’s a clear trend in the spread from 1 month maturity to 12 months maturity, then you could incorporate that trend. Otherwise, you might just use the 12-month spread unchanged. It’s pretty much a guess either way.

I learned of another potential solution that I wanted to share with any who are interested in this thread. Instead of using treasuries as a base for the calculation, I used the various tenors of interest rate swaps published in the FRB’s H.15 publication. The swap rates are the rates received by the fixed leg of an interest rate swap in return for paying three-month LIBOR. This data is relatively easy to use to bootstrap a forward curve. Let me know if you see any drawbacks to this approach.