Problem 1 (25 points total) Suppose the yield curve is flat at 6%. You want to create a barbell-bullet strategy where the available short-term security is an annuity and long-term security is a par bond. You have flexibility to choose the maturity of the medium-term security which is a zero-coupon bond. Overall, your current portfolio will be market-neutral position and will consist of the following investments: The amount of $50 millions in a long position of 8-year annuity. The amount of $179 millions in a long position of 30-year par-coupon bonds. A short position of T-year zero-coupon bonds with position value of $229 millions. (a) (15 points) Determine T, the maturity of the short-positioned bond, such that your strategy overall mimics the barbell-bullet strategy by having total DV01 of the portfolio equal to zero. Round your answer to the nearest multiple of .5, i.e. 1.2 1.0, 1.4 1.5. (b) (7 points) Compute the convexity of each investment in the portfolio. Is the net long-positioned convexity greater than the net short-positioned convexity? (c) (3 points) What does the answer in part (b) imply about the strategy in the case of a parallel shift in the yield curve? Problem 1 (25 points total) Suppose the yield curve is flat at 6%. You want to create a barbell-bullet strategy where the available short-term security is an annuity and long-term security is a par bond. You have flexibility to choose the maturity of the medium-term security which is a zero-coupon bond. Overall, your current portfolio will be market-neutral position and will consist of the following investments: The amount of $50 millions in a long position of 8-year annuity. The amount of $179 millions in a long position of 30-year par-coupon bonds. A short position of T-year zero-coupon bonds with position value of $229 millions. (a) (15 points) Determine T, the maturity of the short-positioned bond, such that your strategy overall mimics the barbell-bullet strategy by having total DV01 of the portfolio equal to zero. Round your answer to the nearest multiple of .5, i.e. 1.2 1.0, 1.4 1.5. (b) (7 points) Compute the convexity of each investment in the portfolio. Is the net long-positioned convexity greater than the net short-positioned convexity? (c) (3 points) What does the answer in part (b) imply about the strategy in the case of a parallel shift in the yield curve
