Q2
Assume that you manage a 100mil bond port with duration of 1.5year. You wish to increase the bond duration to 3.5 year using swap. Assume the duration of fixed rate bond is 75% of its maturity.
A (answer) we enter as a receiver fixed rate swap
B. Would you prefer a four-year swap with quarterly payment or 3 year swap with semiannual payment???
WTF is the question? any one explain the reason why ?
Don’t have the books in front of me, but here’s the general technique
D-Swap = D-Fix - D-Flo
D-Fix = 4*0.75 = 3 D-Flo = 0.125 D-Swap = 2.875 -----------------------
D-Fix = 3*0.75 = 2.25 D-Flo= 0.25
D-Swap = 2 -----------------
Increase duration = fixed receiving, pay floating.
Fixed rate swap duratiion of .75 x 4 = 3
Floating side is 1/4 * .5 = .125
Swap = 3 - .125 = 2.875
OR
Fixed rate swap duration is 75% of time, or .75 x 3 = 2.25
Floating side is 1/2 * .5 = .25
Swap = 2.25 - .25 = 2.00
Your bond is at 3.5…you want 1.5. Subtract 1.5 from 3.5 and you have your answer which swap you want 
Remember these key pointers:
To calculate fixed duration it’s 75% of time unless stated otherwise (never seen it otherwise, but I’m not going to be God here)
Floating duration is 1/2 the next payment interval. For example
Quarterly payment: 1/4 * .5 = .125
Semiannual: 1/2 * .5 = .25
Annual: 1/2 + .5 = .5
On the floating side it doesn’t matter about the length, just the payment interval.
Hope this helps
Why should there be a preference for one swap over the other? Both could get the job done, just with different nominals.
Thanks L3, the question they asked is which one you prefer to the other?
The answer CFAI says is 4 years quartly payment. However, I dont the reason why they prefer the swap to 3 year semi swap.
my cal:
if we use 4 year, the notional is 100*(3.5-1.5)/2.875 = 69.59
3 year: 100 *(3.5-1.5)/2 = 100
The diff btw 2 strategy is diff notional 100 and 69 mil. Is that the reason for their choice? why?
yes using 4 years quarterly payments lower ur notional principal of swap
Thanks all guys
Rah: What is the difference btw 2 notional p? What i can think about now is the difference of credit risk if any. However, with nondelivery (or exchange?, i dont remember the term) principal swap, the situation (credit risk ) is the same. Interest payment (risk) in both case is also same. For example, if interest rate increase 1%, both fixed-ers pay float-ers
1% * 69.59 * 2.875 = 1%* 100 * 2
We bin it and answer what CFAI says
Why am I still awake?! Here’s the deal - receive floating, pay fixed lowers duration. Receive fixed, play floating increases duaration. Don’t get fixated on the NP, worry about the relative direction, and then the net duration.
It’s 1:30am in the states (Chicago time) - crazy to think it’s morning out east. Sorry for my drunk ignorance in advance, but I have tomorrow off and my study time begins at noon, so I’m enjoying the night/morning.
Thanks Biz, i appreciate your answers. I think all people here got how a swap works. But WTF CFAI asking is which swap we prefer over the other? What i am thinking is their characters seem to be the same.
Whatever, forget it and enjoy your time…
text says
choose Swap with longer absolute duration which also reduces your NP amount
I think I remember this question, and it asks to shorten duration (not lengthen it). In that case you want to shorten it by receive floating, pay fixed. With that you can delete two of the four options. Then it comes down to calculating the net duration (as I posted earlier). You don’t need to calculate the NP to figure the right choice - just the closest one. If I recall, one gives a net decrease of 1/4 bps while the other was more substantial to the target of .3 bps. Current duration + swap duration = net duration.
BTW, you’d be surprised how many peeps don’t understand how a swap works…even at L3. Sad but true. Many will pass too. I wouldn’t say it unless I’ve seen it.
It is an exact question on CFAI book 5, reading 38 page 530
After calculate the 2 swap duration of 2.875 and 2, they give the reason that “Because the objective is to increase the duration of the bond port, the 4year…is the better choice”
Ruh: actually, they do not mention about NP as a reason…
I’ll have to look at it Tuesday. I’m out of the office tomorrow, but a pay floating, receive fixed will increase duration. My prior comments stand true.