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3. Duration An investment fund holds a position in the following three govermnent bonds: Table l: Bond portfolio Information Par value Coupon rate Yield-to-matu rity Market value (USD) Macaulay duration Note the following: Bond A 20,000,000 7.0% 7.21% 2.757 Bond B 9.0% 7.45% 21 4.165 Bond C 6.0% 7.71 % 36,352,583 5.748 - Each bond is on a coupon date so that there is no accrued interest. - Coupons on all 3 bonds are paid semi-annually. YTMs are stated on a semi-annual bond basis. - The Macaulay durations are annualized. - The onesyear spot rate is semi-annually compounded. - You can approximate the modified duration of the portfolio by the weighted av- erage modified duration of the induvidual assets. Answer the following questions: (a) Calculate the portfolio's (annual) modified duration. (b) Using duration, approximate the percentage in the portfolio's market value if the (annual) yield-tomnturity on each bond goes up by 30 bps. (c) Now, supp(se that the fund is expected to pay a fine to the govern- ment in 1 year, i.e., the liability is guaranteed to be paid. How is this going to impact the duration of the portfolio and the fund exposure to interest rate risk? Explain.