Question 3 (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 3 years’ time.
(a) Use the current yield curve to determine the present value and also the Macaulay’s
duration 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 modied duration as the liability. To accomplish this task, pick two of the
treasury bonds currently traded in the market, namely GSBU20 and GSBI21, compute
their Macaulay’s durations and determine the dollar amount that should be invested
in each bond. Assume the Macaulay’s duration of your bond portfolio is given by
Dp = w1D1 + w2D2;
where w1 and w2 are the percentage weights invested in each bond.
(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 the percentage change in
the value of the bond portfolio in part (b). Finally, comment on the eectiveness of
the hedge.
(2 marks)

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