Q5. Suppose that pension fund PNG has $3.8B in estimated liabilities with duration D = 16 and convexity C = 310 (with respect to BEY). (Note that these are liabilities, and therefore the actual duration and convexity faced by PNG have the opposite sign, i.e., they are negative.) PNG is considering investing in a 30-year 3.10%-coupon bond with yield to maturity 3.40% and a 10-year 4.00%-coupon bond with yield to maturity 2.60%. a) Compute the duration and convexity of the two bonds. [You will definitely need a computer to do this. It suffices to describe how you go about the computation, and report the results.) b) What position in the 30-year bond (and a money-market account) immunizes PNG's liabilities? c) What is the dollar convexity of immunized position computed as immediately above? d) What positions in the two bonds neutralize both the duration and convexity of PNG's liabilities? (This means that you should find the dollar amount invested in each of the two bonds so that, in combination with original liabilities, the overall portfolio has both zero dollar duration and zero dollar convexity.] Make sure that the signs of the positions, i.e., long or short, are clear.] Q5. Suppose that pension fund PNG has $3.8B in estimated liabilities with duration D = 16 and convexity C = 310 (with respect to BEY). (Note that these are liabilities, and therefore the actual duration and convexity faced by PNG have the opposite sign, i.e., they are negative.) PNG is considering investing in a 30-year 3.10%-coupon bond with yield to maturity 3.40% and a 10-year 4.00%-coupon bond with yield to maturity 2.60%. a) Compute the duration and convexity of the two bonds. [You will definitely need a computer to do this. It suffices to describe how you go about the computation, and report the results.) b) What position in the 30-year bond (and a money-market account) immunizes PNG's liabilities? c) What is the dollar convexity of immunized position computed as immediately above? d) What positions in the two bonds neutralize both the duration and convexity of PNG's liabilities? (This means that you should find the dollar amount invested in each of the two bonds so that, in combination with original liabilities, the overall portfolio has both zero dollar duration and zero dollar convexity.] Make sure that the signs of the positions, i.e., long or short, are clear.]