# Reading 29 - Practice Problem #2 - Help Needed

Hi All - I just finished Reading 29 and started to work through the practice problems and I’m not getting the conceptual side of question #2. I don’t really understand (A) or (B), and I think I may understand ©. I feel like © is the swap that gives the lower notional amount because investors would prefer to apply a lower notional amount to the swap compared to a high notional principal (but I’m not even quite sure if this is the correct reason). Please provide any insight or conceptual background that you think might be helpful to aid me in understanding this question.

"Assume that you manage \$100M bond portfolio w/ a duration of 1.5 years. You wish to increase the duration of the bond portfolio to 3.5 years by using a swap. Assume the duration of a fixed rate bond is 75% of its maturity.

(A) Discuss whether the swap you enter into should involve paying fixed, receiving floating or paying floating, receiving fixed. (Is this some sort of general heuristic for increasing (decreasing) duration?)

(B) Would you prefer a 4-year swap w/ quarterly payments or a 3-year swap w/ semi-annual payments? (Is there a formula for determing the modified duration of the swap (MDURs). I didn’t see a formula given in the text but I feel like a lot of questions could easily require this as an input to determine the notional principal required to enter into the swap).

© Determine the notional principal of the swap you would prefer. (I feel like we generally want the swap that requires the lower notional amount instead of the higher notional amount, but I don’t have a great reason on why.)"

Any help is greatly appreciated!!! Thanks in advance!

Hi ,

A)

When we need to reduce the duration of a bond portfolio we need to move along with the interest rate .( as interest rates increase the price of the bond decreases) ie we need to pay fixed and receive floating.( floating rate bond mostly have very low durations and 0 incase of default free bonds).

In this case we need to increase the duration so we add duration by pay floating and receive fixed.

B)The Duration of a 4 year swap with quarterly payments is (Pay floating receive floating )

3 - 0.125= 2.875

Np=100000000{( 3.5 -1.5 )/2.875}=69565217

Duration of a 3 year swap with semi annual payments

2.25 - 0.25=2

Np =100000000{(3.5-1.5)/2}=100000000

so we use the 4 year option

This is what I have understood .Please correct me if I am wrong.

Hi Kirtika,

Your answer looks very similar to the answer from the textbook, can you please elaborate on part A? Specifically: What’s the logic/reason from “we move along with the intereste rate” --> “we need to pay fixed and receive floating”? The link between them doesn’t seem very obvious to me, although I understand what you mean in both the bracktes.

Sorry if my question is too basic. Duration was one of my weaknesses in L2, trying to overcome.

The main idea is that when we want to increase duration we add bonds with higher duration to our portfolio.Similarly when we want to reduce the duartion we add bonds with negative duration.Floating rate bonds mostly have very less duration even negative duration.Therefore if we need to reduce the duration of our portfoilio we opt to receive returns from floating rate bonds and pay fixed rate.

Kirtika, the “main idea” filled the gap of my understanding. So to add bonds with higher duration is equivalent to buy fixed-rate bonds, right? Thanks a lot!

yes

Kirtika - thanks a ton for the response!

Could you please elaborate on the formulas used in (B) to obtain 2.875 and 2.000? I’m not sure where you get the inputs for those equations. Thanks!