# Swap duration Problem

A bank owns a fixed rate bond with a prsent value of \$450 million and a duration of 8.71 years. Since it perceives increased interest rate risk in the near future ,

It would like to reduce the duration with 2 year swap to 7.81 to meet an overall risk objective.

What is the kind of swap it would be investing in ( i.e. pay-fixed or receive-fixed ) ?

What is the notional on the swap?

swap is semiannual payment or quaterly?

without this info, we wont know the duratioin of the swap.

without duration of swap, we wont know the NP

Sorry , my bad , it is semi-annual payment and usual 75% convention of duration on fixed side .

ok thanks.

then pay fixed.

duration for pay fixed swap:

• (2x0.75-1/2 x 1/2)= -1.25

(Target duration - current duration)/ swap duration x 450 million = NP required

7.81-8.71 ) / 1.25 x 450 million= 324 million

A bank owns a fixed rate bond with a prsent value of \$450 million and a duration of 8.71 years. Since it perceives increased interest rate risk in the near future ,

It would like to reduce the duration with 2 year swap to 7.81 to meet an overall risk objective.

What is the kind of swap it would be investing in ( i.e. pay-fixed or receive-fixed ) ?

a. since it needs to reduce duration - it needs a negative duration swap. So it would be a Pay fixed, receive floating swap.

What is the notional on the swap?it is semi-annual payment

Swap Duration = 0.75 * 2 - 0.5 * 0.5 = -1.25

Swap NP = (7.81 - 8.71)/(-1.25) * 450 Million = 324 Million

cpk and passme are making the curve difficult for the rest of us.