Can someone help me to understand the below question?
Which of the following be the greatest for a putable bond at a relatively high yields?
A) Effective duration of the bond.
B) Macaulay Duration of the bond ignoring the option.
C) Modified duration of the bond ignoring the option.
I understand the Macaulay Duration is the greatest of all of the above but what if it was a straight bond or callable bond instead? Or regardless of embedded option, Macaulay Duration will be the highest in all the cases?
Thanks very much,
Modified\ duration = \frac{Macaulay\ duration}{1 + YTM}
where YTM is the yield to maturity for one coupon period.
Therefore, as long at the YTM is positive, Macaulay duration will be longer than modified duration.
Effective duration can vary all over the map. For callable and putable bonds, effective duration will be less than or equal to modified duration. For interest-only (IO) bonds, when interest rates are low the effective duration can be negative. For floating-rate bonds, the effective duration is close to zero, while for inverse floaters the effective duration can not only be longer than the Macaulay duration, it can be longer than the time to the bond’s maturity.
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thanks millions, very much appreciated!!!