Imagine a government bond with the face value of $100 and 4 years to maturity that:

Pays annual coupons at a rate of 8% per annum; and,

Has a yield to maturity of 7% per annum.

Required

1. What risks would the investor of this bond be exposed to? [5 marks]
2. Would the bond be trading at a premium, at par, or at a discount to face value? Explain why. [5 marks]
3. The Macaulays duration is computed as 3.5847 years, what is the bonds modified duration? Interpret the economic meaning of this modified duration. [5marks]
4. Imagine that the bonds yield to maturity decreases to 6% per annum, estimate the dollar change in the bonds price stemming from the change in its yield using the duration method. [5 marks]
5. The convexity is computed as 8.6234 years. Assume that the bonds yield to maturity decreases to 6% per annum, estimate the dollar change in the bonds price stemming from the change in its yield using the convexity method. [5marks]
6. Using the bond valuation formula, calculate the exact change in bond price following the decrease in the bonds yield to maturity to 6% per annum. [5marks]
7. Are your answers in 4, 5 and 6 the same? Why/Why not? [10 marks]
8. Assume that this bond contract has a call provision at the end of year 2 at a price of $96.529 (right after the coupon payment for year 2). Assume that the yield at the end of year 2 is 9% p.a., would the bond issuer exercise the call provision to buy back the bond at $96.529? Explain why. [10 marks]