Interpreting Floating-Rate Note Yields and Rate Sensitivity

# How to interpret YTM of FRN when interest rates change?


# How to interpret YTM of FRN when interest rates change?












Say I have a FRN.

If rates go up, then my cashflows are discounted more, but my coupons also go up, so in the end, my bond may be worth the same.

However, if rates go up, then since my price is unchanged but my coupons are higher, my YTM has also gone up.

This doesn't really make sense to me: why is my YTM higher despite the fact that nothing about the bond has actually changed!?

Is there a different way to calculate yield that makes more sense for a FRN?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/72216

While this sounds like a basic question, it does bring up a few nuances that are worth discussing.

First, suppose you have a fixed-coupon bond, rather than FRN. When risk-free rates go up, the coupons stay fixed, but the price goes down and the yield also goes up, same as FRN's yield.

The change in yield means, simply, that we're now in a higher interest rate regime. You invest one dollar risk free, and before the interest rates hike you earned less risk-free interest than after the hike. A risky yield is a sum of a risk-free yield and a risky spread. The risk-free yield is not inatrumwnt-spwcific, but rather characteries the entire market.

Spreads (such as Z-spread, or OAS for callables, discount margin for FRNs...) should change little when risk-free rates move. They measure the extra yield on top of the risk-free yield. They are more useful to look at than yields if you're looking at a particular instrument.

But the FRN that you describe whose coupon is linked exactly to the risk-free index, and whose price therefore has no sensitivity to interest rates, is rather theoretical, and seldom found outside textbooks. A floating leg of an interest rate swap works this way. Real life bonds usually pay something else.

A corporate FRN from a developed market is likely to be paying some spread on top of the index, i.e. coupons are index + spread. In your head, you can decompose such FRN into two instruments: the theoretical FRN with no sensitivity to interest rates, and a fixed swap leg. If this spread is a few percent, then the price of the fixed leg is materially sensitive to interest rates. Thus, in real life, the entire FRN also has sensitivity to interest rates, although less so than a fixed-coupon bond. Sometimes this interest rate sensitivity needs to be measured, monitored, and possibly hedged. Do not blindly assume than FRNs price will not change when interest rates move because your textbook said so.

When interest rates (risk-free yields) go up, this causes the projected floating coupon amounts to go up. But also all cash flows (coupons and principal) are discounted by smaller factors. For a floater, the increase in coupons is approximately offset by smaller discount factors, so the present value (of the whole instrument, not indicidual cash flows) stays approximately the same. Conversely, for fixed cash flows, nothing offsets the smaller discount factors, so the present values just decrease. Whether fixed or floating coupons, the effect of the changing interest rates on the internal rate of return (risky yield of the instrument) is approximately the same.

Also in some other markets, e.g. Brazil, instead of adding a spread to the index, they multiply the index by a "gearing" > 1. A credit-risky bond might be paying, for example, 1.8 * CDI, where CDI is a risk-free index like SOFR. Also some muni FRNs have gearing <1 to compensate for tax benefits. They too have some interest rate sensitivity.