Question 2 (20 Marks) Suppose you observe the following market data on debt securities: Security Coupon (p.a.) Yield to maturity (p.a. continuously compounded) 2.00% 0.00% 6-month Treasury Bill 1-year NZ Government Stock 3.00%, semi-annual 2.50% 1.5-year NZ Government 3.50%, semi-annual 2.75% Stock 2-year NZ Government 2.50%, semi-annual 3.00% Stock Required: (a) Calculate the continuously compounded zero-coupon rates for the maturities above i.e., 0.5, 1.0, 1.5, and 2.0 years. Report your answer in percentage (%) with 4 dps. (8 marks) (b) What are the forward rates for the periods: 6 months to 12 months and 12 months to 18 months, 18 months to 24 months? (3 marks) (c) What is the duration of the following default-free bond portfolio? (4 dps) Time to maturity Number held Coupon rate (p.a.) 8.00% 1 year 2 year 600,000 750,000 6.00% Note: Each bond has a face value of $100.00 and coupons are paid semi-annually. You should assume the zero-coupon rate calculated in part (a) above. Note: Use the following formula to measure the duration of the bond portfolio, i.e., tce DB where ti, Ci, and ridenote for term, cash-flows, and zero-coupon yield for the ce - ith period. (9 marks) 4