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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.Where did he get 75% of the 3 year duration from?
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thx @RaviVooda‌ but the line you highlighted is from the solution and not from the vignette.
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@RaviVooda‌ So a fixed rate duration is always 75% of the bond maturity? It’s a fixed number?
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@RaviVooda‌ got it. Thanks! I’m not sure if it’s even mentioned in schweser. It’s like giving away free points for not knowing 75%. I need to review quicker, I haven’t even get to the second volume. Are u done with all 3 papers on the second volume?
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@RaviVooda‌ @vincentt‌ Not sure if this is mentioned in schweser indeed! I got that question wrong as well.
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@AjFinance not sure about schweser, but was mentioned in text book
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@AjFinance‌ it’s still fine if you forget a formula that you wanted to use, the worse feeling is you have no idea where that formula came from or how did they come up with a magic number 0.75 that’s the most worrying!
But it’s good that we have hardcore candidates like @RaviVooda‌ and @Alta12‌ who uses the underlying text! ^:)^
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@vincentt‌ exactly! I can’t imagine going through the cfai text. Hats off to @RaviVooda‌ and @Alta12‌
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