As I’m doing my final prep before tomorrow I am taking a few more CFAI practice item sets. In derivatives, the following question came up and I completely unable to think of why a swap of 3.5 years is used. Maybe someone here can help me out? Shouldn’t the two year swap be used since they want to reduce duration by 2 years?
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. **Investment**** Amount **** ( millions) **Risk Measure 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.
EXHIBIT 2
PAY-FIXED INTEREST RATE SWAPS
Swap** Maturity **Duration A 2 years −2.125 B 3 years −3.375 C 3.5 years −3.625
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=20,000,000×3−5/3.625
C is incorrect because 9,412,000=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=20,000,000×2−5/3.375
In the numerator, 2 represents the target reduction in duration, and 5 represents the current duration.
