Duration An investment fund holds a position in the following three government bonds: Table 1: Bond...

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Duration An investment fund holds a position in the following three government bonds: Table 1: Bond portfolio Information Bond A Bond B Par value Coupon rate Yield-to-maturity Market value (USD) Macaulay duration 2.757 20,000,000 7.0% 7.21% 19,888,485 20,000,000 9.0% 7.45% 21,274,578 4.165 Bond C 40,000,000 6.0% 7.71 % 36,352,583 5.748 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 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 loss in the portfolio's market value if the (annual) yield-to-maturity on each bond goes up by 30 bps. (c) Now, suppose that the fund is expected to pay a $10,000,000 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. Duration An investment fund holds a position in the following three government bonds: Table 1: Bond portfolio Information Bond A Bond B Par value Coupon rate Yield-to-maturity Market value (USD) Macaulay duration 2.757 20,000,000 7.0% 7.21% 19,888,485 20,000,000 9.0% 7.45% 21,274,578 4.165 Bond C 40,000,000 6.0% 7.71 % 36,352,583 5.748 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 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 loss in the portfolio's market value if the (annual) yield-to-maturity on each bond goes up by 30 bps. (c) Now, suppose that the fund is expected to pay a $10,000,000 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.

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a To calculate the portfolios annual modified duration we can use the weighted average modified dura... View the full answer