Hello,
In one of the CFA level 3 chapter on derivatives and risk management, the chapter states that a fixed rate note has a greater modified duration than an otherwise identical FRN.
Can someone explain to me the why behind that statement?
Thx
Modified duration is a measure of the price sensitivity of an asset to a change in the interest rate.
FRN would be a floating rate note. Because the coupon is tied to the interest rate, the price won’t change as much as the price of a fixed rate note.
Modified duration for a fixed-rate bond and for a floating-rate bond should be equal.
Effective durations will be different.
Are you sure that they specified modified duration? Or did they simply say “duration”?
The effective duration of a fixed-rate bond (with more than one period till maturity) will be longer than the effective duration of a comparable floater, but their modified durations will be (or, at least, should be) equal to each other.
They’re mistaken.
They meant effective duration, not modified duration.
I hate this junk.
Thanks for commenting.
Could you explain why would the effective duration should be lower for a floater?
As a simple example, imagine a floating-rate government bond, whose coupon resets at each payment date according to the government par curve. That means that at each coupon date, the price of the bond resets to par (say, $1,000), no matter what happens to interest rates. Therefore, there is very little price change, so the effective duration, which measures the price change when the bond’s YTM changes, will be quite short. In essence, the price of the bond behaves as if the bond’s maturity were the time to the next coupon date.
Makes sense. Thank you.
My pleasure.