The following is a U.S. Treasury quote from the WSJ on Oct. 15, 2003

Rate = 7.1250

Maturity = Oct 15, 2005

Ask = 102;08

Change = -1

Ask yield = 5.9156

Here, the Rate is the coupon rate. Ask is the current market price (for buying), quoted in percentage of the face value. In addition, Treasuries are quoted on 32nds after the :, so 102:8 = 102 + (8/32) = 102.25, per US$100 face value of this Treasury. Ask yield is the yield (discount rate). Change is the price change from previous reporting date, but this information will not be used for this question. Both coupon and discount rates are reported in annual rates. Treasury is a non-amortizing bond. (You dont need to remember all these as I will provide such information in the exam.)

1. A) In reality, U.S. Treasury pays interest semi-annually. What are the duration and modified duration of this Treasury? (2 marks)

2. B) If you expect the annual yield to go down by 2 percentage points, what is the price change of this Treasury (with face value US$100) using duration approximation? (2 marks)

3. C) The convexity of this Treasury is 17.23 when the change in yield is per period change; or equivalently, 4.3075 when the change in yield is in annual frequency. What is the approximate price change (per face value US$100) when taking the convexity into account? (2 marks)

4. D) What is the accurate price change using the exact price formulas when the yield goes down by 2% (per fave value US$100)? (2 marks)

5. E) Keep the original coupon rates and original yield, but suppose now the payment frequency of this bond is monthly instead of semi-annually. What is the price (per fave value US$100) for this Treasury for this new payment frequency? (2 marks)

6. F) What are the duration and modified duration of the bond in question (e)? (2 marks)