# Duration of Fixed vs Floating

Can someone simply explain why a floating rate bond would have lower duration than a fixed rate bond, all else equal?

Having trouble conceptualizing it. I sometimes get confused with the fact that a callable fixed rate bond is more likely to be called in a rising rate environment than a floater, since a floater would adjust to the low rates, and therefore would seemingly have a lower duration than the floater, but I think this is overthinking it.

Think the answer is that a fixed bond won’t adjust to changes in market rates as a floating rate bond will, therefore, its sensitivity to rate moves is higher. But can someone confirm? When a bond, either FRN or FXD is callable, I feel like that logic is reversed.

A floating rate bond is less sensitive to changes in yield than a fixed-rate bond so yes, its duration is lower.

I’m not sure about the 2nd question. Why would an FRN has embedded call option? It just does not make sense when you already had a floating rate to hedge against the changes in rate.

FTFY

The price of a floating-rate bond is less sensitive to changes in yield than the price of a fixed-rate bond. (Assuming a straight, unleveraged floater. Inverse floaters, for example, have extremely long effective durations.)

But the cash flows of a floating-rate bond are more sensitive to changes in yield than the cash flows of a fixed-rate bond. Somethin’s gotta give.

I guess in when talking about duration, we would implicitly understand that it is the change in yield vs. the change in price. And it’s not just effective duration if you recall the formula of approx. modified duration.

Thanks for the correction anyway. It would be helpful in the real exam!

Suppose an issuer issued the callable bond at an interest rate of 8% and is callable after 3 & 7 years. After 3 years the interest rate is now 9%. The issuer won’t do anything because is still cheaper than what was it issued as. But after 7 years the interest rate goes down to let’s say 6%, the bond will be called as the issuer can now refinance its debt at a cheaper percentage than what it was issued as before.

Coming on to your floaters query:

To simplify, forget about call-ability to begin with, it adds unnecessary complexity to the concept. Bullet fixed rate bonds have higher duration than an equivalent bullet floater.

WHY?

Duration measures how sensitive the bond’s PRICE is to changes in rates. A floater has almost no price sensitivity to rates because the coupon resets as rates move. The only reason a floater has any duration at all is because it doesn’t reset continuously (normally it resets every 3 months).

REGARDING CALLABILITY

The ISSUER owns the call option, ALWAYS. If rates go up, the issuer would NOT call a fixed rate bond, all else equal. They’d rather pay the lower rate they are already paying.

If a corp issued a callable floater, it has NOTHING to do with rates, and almost no value based on rates. Again, the coupon resets when rates change. So an issuer would gain nothing from calling the bond due to rate declines, all else equal (they can refinance at lower rates by doing absolutely nothing, b/c the coupon resets automatically). But they might be able to refinance at a lower credit spread, or they may just want to decrease leverage, which is where the option value comes in. A fixed-rate callble bond can be called for any of these reasons, including general rate declines.

This is true with respect to effective duration, but not with respect to, say, spread duration.

It’s not a good idea to try to generalize about all species of duration.

won’t disagree as you are technically correct. But when anyone in the industry refers to duration they are not referring to spread duration. When people refer to spread duration they specifically say “spread duration”, whereas effective duration they say “duration”. They do not say “effective duration”

True enough.

I pointed it out only because we’re talking to candidates here, most of whom are not fixed income practitioners, so I wanted it to be absolutely clear. Candidates often need to be handled carefully, delicately, even.

good points and a good thing for me to keep in mind. It’s helpful to be deliberate and specific when giving technical advice