Hi,
I’m using a previous year’s curriculum text book and was unable to solve question 24 on page 504 of volume 5.
This question is about finding a notional principal for an interest swap to be used for achieving the bond pf duration target.
In the question, the duration of the swap’s fixed pmt is given as 75% of the swap maturity, which is 6 years.
For the duration of the swap’s floating pmt, which I thought would be 0.5 given that it is a semiannual pmt, was actually 0.25 in the answer.
Could anyone please explain why the duration of the semiannual floating pmt in this case is 0.25?
Thank you.
From Seoul
It is half of the reset intervals expressed annually. Semiannual = 0.5*0.5 = 0.25
try and work with it my friend. certainly no time for this questioning…
At the reset date, the price of a floating-rate bond (paying market rate, not market-rate-plus-a-spread) is par. Thus, any price change will occur only between reset dates, and at the next reset date the price returns to par; it’s as if every reset date the bond is paid off and a new bond issued. As an approximation to the duration of a bond that will be paid off as of the next reset date, they use ½ of the time between resets; i.e., ½ of the time between coupon payments. It’s an approximation, but it’s close enough.
For the fixed rate in a swap, the duration will be the duration of the corresponding fixed-rate bond. Again, as an approximation, they use 75% of the time to maturity. It would be better to calculate the duration of that bond from its cash flows, but the approximation is OK for the purposes of the exam.