Is the general goal to find a swap with the lowest notional prinicple?
Here’s an example:
Duration target = 3
Current duration = 5
Bond Portfolio = $20M
The following swaps are given:
SWAP A : Maturity: 3 years and Duration:-2.125
SWAP B: Maturity: 4 years and Duration: -2.8175
SWAP C: Maturity: 5 and Duration: -3.625
Question: Based on this data, modifying the duration of the fixed income allocation to its target will require an interest rate swap which has notitional principle closest to:
a) $6,956,000
b) $11,030,000
c) $18,823,000
Using the usual formula [(Dtarget - Do)/Dswap]*portfolio value, a) and c) are plauible answers. My intution was to choose the swap A (notional principle then equals $18.8M) because swap A has a duration closest to the desired change in duration (3-5 = -2) and the swap A has a duration = -2.125.
However, the correct answer is C, a notional principle of $11.0M, which is the result of using SWAP C.
Is the general idea to use a swap that has the lowest notional principle, all else equal?
Thanks