CFA CFA Level 3 Fixed Income: Calculating Duration with Leverage

Fixed Income: Calculating Duration with Leverage

  • This topic has 6 replies, 2 voices, and was last updated Sep-17 by vincentt.
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    • RaviVooda
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      Have a doubt in the below question

      Bond A Bond B Bond C
      Par Value $50,000 $60,000 $40,000
      Market Value $52,000 $61,000 $40,000
      Effective Duration 8.2 6.8 5

      Richards wishes to investigate the use of leverage to increase return. Cupp says Richards should consider doubling her position in Bond C to $80,000 using the proceeds from a loan. Richards asks about sources of funds for such a leveraged position. Cupp says Richards could use the proceeds from a 3-month repurchase (repo) agreement, or Richards could sell short zero-coupon bonds with a duration of 3. Richards asks Cupp to estimate the value of the leveraged portfolio in each case after a 25 basis point downward parallel shift in the yield curve.

      Q1: Using the repo agreement, what is the effective duration of the equity invested? A) 8.05. B)8.28. C)6.22.
      Answer: (A) The repo agreement described has a duration of 0.25. Duration of bond positions = (52/193) × 8.2 + (61/193) × 6.8 + (80/193) × 5 = 6.43 The duration of the equity invested can be found as: D E = (D i I -D B B)/E where: D E = duration of equity D i = duration of invested assets D B = duration of borrowed funds I = amount of invested funds B = amount of borrowed funds E = amount of equity invested Using the information provided in the question: D E = [(6.43)(193,000) − (0.25)(40,000)] / 153,000 = (1,230,990 − 10,000) / 153,000 = 8.05 (Study Session 10, LOS 22.a & b)

      Doubt here is why did he use duration of 0.25 when the question specifies duration as 3?

      Q2) If Richards uses the zero-coupon bonds to leverage her portfolio, what is the change in value of the leveraged portfolio for a 25 basis point change in interest rates? A)$4,300. B)$3,100. C)$2,803

      Answer: (C) Change in Bond A = $52,000 × 8.2 × 0.0025 = $1,066
      Change in Bond B = $61,000 × 6.8 × 0.0025 = $1,037
      Change in Bond C = $80,000 × 5 × 0.0025 = $1,000
      Change in zero-coupon bond = $40,000 × 3 × 0.0025 = $300
      Total change in the portfolio = $1,066 + $1,037 + $1,000 − $300 = $2,803

      Doubt: Why should we subtract change from zero coupon bond. Is it because there is leverage here?


      @Alta12
      , @sophie , @marc, @vincentt‌ please help

    • RaviVooda
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      For the second question, please ignore I have the answer, since it is leverage and there is shift of 25bps, the bond value will increase and we will be paying less so we deduct from total change.

    • vincentt
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      As far as i can see the repo agreement is like a zero coupon as payment is made (return) at maturity, hence 3 months repo = 3/12 = 0.25 duration.

      If you still remember, for zero coupon bond the maturity is the duration.

    • RaviVooda
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      @vincentt, thank you. I was thinking the same. However in the same problem consider we are given a floating rate bond with the duration of 3, and we are using it for 3 months. Then should we consider the duration as average of (0+.25)/2?

    • vincentt
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      @RaviVooda‌ I’m not sure if you can use a 3 years zero coupon bond for 3 months, but otherwise the duration should be 0.25 for 3 months ( multiply with 3 / 36).

      What’s the average duration you are taking?

    • RaviVooda
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      @vincentt, in portfolio management, if you remember when we do a swap from fixed to floating where we calculate swap duration, we use average duration for floating rate bonds? I am not sure if I am confusing between the two concepts

    • vincentt
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      As far as I remember when it comes to these calculation I don’t think it will be as straightforward as taking an average of the two, but I could be wrong. By any chance, you know which reading you’re specifically referring to? Can’t find it within R31.

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