1. Consider an 8-year, 4% semiannual-pay bond that matures on September 15, 2021, which is purchased on January 3, 2014. The coupon payments are made on March 15 and September 15 each year. The yield-to-maturity is 6%. Compute the bond's Macaulay duration at time of purchase. 2. Consider a 5-year, annual-pay bond with a par value of $2.5 million. The bond has a modified duration of 4.25, a full price of 102.55 per 100 of par, and a coupon rate of 5%. The market discount rate is 5.5%. What is its Macaulay Duration? 3. An investment fund contains the following 3 fixed-rate government bonds: Bond A Bond B Bond C Par value $20,000,0 $20,000,000 $40,000,000 00 Coupon rate 7.0% 9.0% 6.0% Time-to 3 years 5 years 7 years maturity Yield-to 7.21% 7.45% 7.71% maturity Market value 19,888,48 21,274,578 36,352,583 (USD) 5 Macaulay 2.757 4.165 5.748 duration 1 Each bond is on a coupon date so that there is no accrued interest. The market values are the full prices given the par value. Coupons on all 3 bonds are paid semiannually. The yields-to-maturity are stated on a semiannual bond basis. The Macaulay durations are annualized. a) Calculate the portfolio's (annual) modified duration using shares of market values as weights. b) Estimate the percentage loss in the portfolio's market value if the annual) yield-to-maturity on each bond goes up by 30 bps. 4. Consider the following information regarding a bond with a par value of $100: Initial YTM = 6% PV = $101.7893 Change in yields = 0.0005 PV+ = $101.52 PV = $102.06 ApproxModDur = 5.36 What is the approximate convexity of this bond? 5. Consider the following information regarding a bond with a par value of $100: Initial YTM = 6% PVO = $ 101.7893 Change in yields = 0.0005 PV+ = $101.52 PV_ = $102.06 ApproxModDur = 5.36 What is the estimated percentage price change resulting from a 100 bps increase in the yield-to-maturity