Question 1 (Bond Pricing) Upon graduation from the UTS Business School, you're now working for a superannuation fund. On your first day at work, your boss has asked you to calculate the prices of the treasury bonds that are currently traded in the market based on the current yield curve, and also find their yield-to-maturities (YTMs).
(a) Based on information provided for the treasury bonds and the ZCYs, compute the bond prices (accurate to 4 decimal places).
(b) Based on the bond prices in part (a), what is the yield-to-maturity (YTM) p.a. (semiannually compounded) for each of the treasury bonds? Note: you will need to use GoalSeek or Solver in Excel to find the YTMs.
(c) Suppose there is a zero-coupon bond (ZCB) with a face value of $100 and 2 years to maturity, which currently trades at $95. Construct an arbitrage portfolio by trading in the ZCB and also in the treasury bonds GSBC17, GSBM17, GSBA18 and GSBS18. Hint: your arbitrage portfolio should have a positive initial cashflow, and then all future cashflows should be zero.
Question 2 (Holding Period Returns) Now your boss is interested in investing in the long-maturity treasury bonds because of their attractive yields, so you're asked to analyse the risks that are involved in this investment.
(a) Suppose you decide to invest in treasury bond GSBK39 for 5 years. Assume coupons can be reinvested at the current YTM of the bond, compute your holding period return (HPR) p.a. (semi-annually compounded) if the YTM increases by 0, 25, 50, 75 and 100 basis points (bps), and if the YTM decreases by the same amount at the end of year 5 when you sell the bond. Plot the relationship between HPR and changes in the YTM.
(b) Repeat part (a) assuming you now decide to also short-sell treasury bond GSBM22 with 5 years to maturity to fund your investment in treasury bond GSBK39.
(c) Repeat part (a) assuming the YTM of the bond remains the same, instead the reinvestment yield of the coupons increases/decreases by 0, 25, 50, 75, and 100 bps. Plot the relationship between HPR and changes in the reinvestment yield.
Question 3 (Hedging interest rate risk) Your boss is impressed with your work efficiency 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 modified duration of the liability.
(b) Now, in order to hedge interest rate risk, you want to invest in a bond portfolio which has the same modified 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 modified 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 modified 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 respectively.
(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 effectiveness of the hedge.
Attachment:- Assignment Data.xlsx