u - 1. A bond is maturing in 30 years and has a Semiannual coupon of 3.5% [for each 5100 of notional $3.5/2 is paid every 6 month}. Suppose the price of this bond is 57-16. a} Calculate the band's Yield to Maturity. b] Suppose you have a position in that bond that has a market value 10 Million. What is the Modied Duration, Macaulay Duration, Convexity and DV'Dl of that portfolio? e) Suppose you have 10 Million of notional ofthat bond. What is the Modied Duration, Macaulay Duration, Convexity and DVOI of that portfolio? 2. Which ofthese bonds is cheaper? Le. which has higher Yield to Maturity? Bond A: Maturity 10yr, Coupon 5.6%, Price 83-1-1L Bond B: Maturity 9yr. Coupon 6% Price 82-15 3. Give the denition of Modied Duration and Convexlty ofa bond and write the relationship between the change in yield and the bond price. 4. A bond is maturing in 10.5 years and has a semiannual coupon of 4.3% and price 9245+. a] Calculate its Yield to Maturity. Show your calculation or explain how you calculated the yield. b] Suppose your market value of this bond is 8 Million. What is Modied Duration, Macaulay Duration. Convexity and {Will of this portfolio? c] Using Modied Duration and Convexity formula approximation calculate bond price if the Yield to Maturity increased 20 Basis Pains. d] Calculate the exact Bond price using the full discount formula. Compare to previous result in part (I. 5. Suppose that the spot interest rates with continuous compounding are: Maturity [years] Rate 91'; 1 1.3 2 2.2 3 2.3 Calculate forward interest rates for second and third years, and for a 2-year period between years 1 and 3. 6. Using bootstrap method calculate zero coupon yield curve from coupon bearing bonds. Coupons are paid every half year. They are shown annualized in percent. Use continuous compounding and then semiannual compounding. Plot tvvo yield curves for continuous and semiannual compounding. Bond Principal Maturity Wears) Coupon Bond Price 100 0.25 t} 99