A floating-rate note has a quoted margin of +20 basis points and a required margin of +30 basis points. If the reference rate is 2.5%, the note’s coupon rate will be reset to ?
2.7 %
2.8%
3.0%
Correct answer is A. I don’t know why ? and what is the relationship between required margin and quoted margin ?
Floating Rate Notes (FRNs) have variable coupon payments (unlike regulard bonds with fixed coupon payments) that vary each period depending on the level of a current reference rate (Libor and the likes, called in Index in the formula below). The most common (and CFA exam relevant ones) often add/subtract a yield spread to that reference rate, depending on the credit risk of the issuer, which is called the quoted margin.
That being said, the coupon is still constant in the sense that it is always reference rate + quoted margin (where the reference rate varies obviousy). So in your case, you are still dealing with a coupon rate of 2.5% +20 bsp =2.7%.
Now the required margin (also called discount margin ) is used to adjust discount the coupon payments of the bond. If QM=DM then FRN is priced at par. If say the credit risk of the issuer increases, the the DM>QM. As in your case above, if the required margin is 30 points this will cause the price of bond to decrease. You’ll find this explained in Reading 54 Chapter 3.4.
The formula is given by:
PV=num/denom+…
num=(Index+QM)/m*FV
denom=(1+Index+DM/m)^N
m is the periodicity of the floating-rate note, the number of payment periods per year