Hedging interest rate risk

Question (Hedging interest rate risk – 5 marks)
Your boss is impressed with your work eciency and now the real challenging task comes

  • you need to implement a hedging strategy to ensure that the fund has enough capital to
    meet a liability. The superannuation fund will need to pay $100 million in 5 years’ time.
    (a) Use the current yield curve to determine the present value and also the modi ed du-
    ration of the liability.
    (1 mark)
    (b) Now, in order to hedge interest rate risk, you want to invest in a bond portfolio which
    has the same modi ed duration as the liability. To accomplish this task, pick two of
    the treasury bonds currently traded in the market, Bond A and Bond B, compute their
    modi ed durations and determine the dollar amount that should be invested in each
    bond. Note that you need to determine which two bonds are most suitable and explain
    your choice. Also, assume the modi ed duration of your bond portfolio is given by
    Dp = wADA + wBDB;
    where wA and wB are the percentage weights invested in Bond A and Bond B respec-
    tively.
    (2 marks)
    (c) Now suppose the entire yield curve shifts down by 100 bps. Calculate the percentage
    change in the present value of the liability in part (a) and also of the value of the bond
    portfolio in part (b). Comment on the e ectiveness of the hedge.
    (2 marks)

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