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CFAI 2014 - Watanbe Q4

Kondo manages a fixed-income portfolio for the Akito Trust. The portfolio’s market value is ¥640 million, and its duration is 6.40. Kondo believes interest rates will rise and asks Watanabe to explain how to use a swap to decrease the portfolio’s duration to 3.50. Watanabe proposes a strategy that uses a pay-fixed position in a three-year interest rate swap with semi-annual payments. Kondo decides he wants to use a four-year swap to manage the portfolio’s duration. After some calculations, Watanabe tells him a pay-fixed position in a four-year interest rate swap with a duration of –2.875 would require a notional principal of ¥683 million (rounded to the nearest million yen) to achieve his goals.

4.) The duration of the swap in Watanabe's first proposal to Kondo is closest to:
Solution:

A pay-fixed (receive-floating) position in an interest rate swap is similar to issuing a fixed-rate bond and buying a floating-rate bond with the proceeds. The duration of the fixed-rate bond is approximately 75% of the maturity, and the swap is short this duration. The duration of the floating-rate bond is approximately half its repricing frequency, and the swap is long this duration. Therefore, the duration of the three-year
swap with semi-annual payments is (0.5 × 0.5) – (0.75 × 3) = –2.00.



@alta12 @RaviVooda‌

Where did he get 75% of the 3 year duration from?

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