Can someone explain the solution?
Question:
A-rated corporate bonds 20 Duration: 5.0
Lehigh intends to synthetically modify the duration of the corporate bond component of the portfolio to a target of 3.0 in anticipation of rising interest rates. Interest rate swap data are provided in Exhibit 2.
Swap** Maturity **Duration A 2 years −2.125 B 3 years −3.375 C 3.5 years −3.625
Q. Based on the data in Exhibit 2, modifying the duration of the fixed-income allocation to its target will require an interest rate swap that has notional principal closest to:
- $11,030,000.
- $17,777,000.
- $9,412,000.
…
Solution:
A is correct.
NP=B×(MDURT−MDURB)MDURSNP=B×(MDURT−MDURB)MDURS
where
NP = notional principal
B = bond portfolio
MDUR_T_ = duration target of portfolio
MDUR_B_ = duration of bond portfolio
MDUR_S_ = duration of swap
11,030,000=20,000,000×3−5−3.62511,030,000=20,000,000×3−5−3.625
C is incorrect because 9,412,000=20,000,000×2−3−2.1259,412,000=20,000,000×2−3−2.125
In the numerator, 2 represents the target reduction in duration, and 3 represents the new target duration.
B is incorrect because 17,777,000=20,000,000×2−5−3.37517,777,000=20,000,000×2−5−3.375
In the numerator, 2 represents the target reduction in duration, and 5 represents the current duration.
…
Using the formula target duration should be always 3? and bond portfolio duration is always 5? only swap duration should differ between the calculation but I don’t understand their explaination
why are they using different numbers in explaining why it isn’t answer B and C
Please clarify someone, thanks in advance!