3. Duration An investment fund holds a position in the following three government bonds: Note the following: - 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 one-year spot rate is 6%, semi-annually compounded. - You can approximate the modified duration of the portfolio by the weighted average modified duration of the induvidual assets. Answer the following questions: (a) Calculate the portfolio's (annual) modified duration. (b) Using duration, approximate the percentage loss in the portfolio's market value if the (annual) yield-to-maturity on each bond goes up by 30bps. (c) Now, suppose that the fund is expected to pay a $10,000,000 fine to the government 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