# Do floating rate bonds always trade near par?

Do we in practice have that floating rate bonds trade only at par?

How is credit spread included in floating rate bonds in practice? The way I see it is two possible ways.

1. The first is that we have a case of floating rate bonds that pays coupons that are calculated by a benchmark rate $$r_i$$, so that each coupon is for example $$Nr_i/K$$, where $$N$$ is the face value of the bond and $$K$$ is the number of coupons each year, and the last payment is $$N(1+r_i/K)$$. Then the price of the bond is lower than par at the reset date, it is lower than what you would get if you got this cashflow from a secure insitution. Do these types of bonds exist in the real world?

2. The second type would be a bond that at each coupon date pays $$N(r_i/K+s)$$, where $$s$$ is something you get extra, and at the last payment you get $$N(1+r_i/K+s)$$. And then these are priced at par at the reset date. Do these type of bonds exist in the real world?

## 1 Answer

A floating rate bond trading at par is more like an academic formulation rather than what you would observe in reality.

If there were only one yield curve and the bond has no credit spread, that in theory (on reset dates) the forwards would exactly match the equivalent discount factors and so compounding and discounting at the same rates would offset each other, resulting in the price of 100 for that bond.

In reality this doesn't quite happen. If you have a bond linked to USD Libor 6M flat (no spread), the forwards would be estimated by that curve (swaps vs 6M) and the bond would mostly likely not be at par, meaning that the "market assessed yield curve" for the issuer is different from the LIBOR curve. If that bond has one payment until maturity and is below par, that means investors require a return higher than Libor for that issuer.

If a bond has a credit spread, then the total rate of the bond would be different from the floating index and that could compensate for the difference in yield curves. However, even if this bond is at par at some point, the spread would be fixed for all coupons while the term structure of that issuer's spread would probably not be flat.

• Thank you very much! Could you please say something about the (estimated) effective duration in those two cases? It is said that the duration of a floating rate note is the time to the next payment, will this be the case when we have a spread involved or when investors yield curve is different from the Libor curve? Note: I am not talking about spread duration, but interest duration of a floating rate bond that has spread. – user394334 Sep 6 '20 at 13:40