Question

CFA Question- Rank the following bonds in order of descending duration

Bond A: coupon 15%, Time to Maturity is 20 years, Yield to Maturity is 10%

Bond B: coupon 15%, Time to Maturity is 15 years, Yield to Maturity is 10%

Bond C: coupon 0%, Time to Maturity is 20 years, Yield to Maturity is 10%

Bond D: coupon 8%, Time to Maturity is 20 years, Yield to Maturity is 10%

Bond E: coupon 15%, Time to Maturity is 15 years, Yield to Maturity is 15%

Answer 1

The zero coupon bond has the highest duration (equal to its maturity) and for all coupon bonds, Duration is less than maturity

Hence Bond C has the highest Duration

Now, Duration of a bond generally increases with the maturity period, other things held constant,

Duration of a bond decreases when the coupon rate increases,other things held constant,

Duration of a bond decreases when the YTM increases,other things held constant,

With these relationships, we can conclude

Duration of Bond A> Duration of Bond B (as maturity period of Bond A is higher)

Duration of Bond D> Duration of Bond A (as coupon rate of Bond A  is higher, so duration is less)

Duration of Bond B> Duration of Bond E (as YTM of Bond E  is higher, so duration is less)

Hence, Durations of the bonds follow the relationship

Duration of C>Duration of D> Duration of A>Duration of B> Duration of E