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Show that the value of the bond portfolio at duration date

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Reference no: EM132968244

A firm has a liability due in exactly 15 month's time equal to $125,000. Suppose the firm wishes to manage the interest rate risk of this liability (ie. immunise) using the following two bonds:

  • a 12-month zero coupon paying bond with a $75,000 face value (yield of 2% p.a.) with a duration of 12 months, and
  • a two-year $75,000 face value, 2% coupon bond (yield of 2% p.a.) with a duration of 1.98 years.

Assume both bonds pay annual coupons and that you can invest in fractions of bonds.

Required:

Problem 1: Show that the value of the bond portfolio at the duration date (ie. in 15 month's time) will be sufficient to meet the liability whether interest rates EITHER (i) remain unchanged at 2% p.a., or (ii) increase to 4% p.a. Show all working. Briefly explain your answer.

Reference no: EM132968244

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