(20) A portfolio manager invests a nominal amount of $50,000,000 in a bond A whose gross price (in % of the nominal amount), modified duration and $ convexity are 121.65, 4.05 and 2655.15. The nominal amount is $1000.

(a) (6) The portfolio manager would like to hedge his position in bond A with another bond B. Bond B has a gross price (in % of the nominal amount), modified duration and $ convexity are 119.67, 4.63, 3393.14. The nominal amount of B is $1000. Assume the change in yields of bond A and bond B has the following relationship

yA =1.1yB The portfolio manager would like to make his hedged portfolio delta neutral. How many units of Bond B does he has to sell?

b.The portfolio manager would like to make his hedged portfolio self-financed and delta-neutral by including another bond C with gross price, modified duration and $ convexity, 117.91, 5.65, 5042.92 into his portfolio. The nominal amount of C is $1000. As- sume the change in yields of bond A and bond C also has thefollowing relationship:

yA =1.1yC Without calculation, present the formula you use to calculate the

units of B and C.

(c) Now if the portfolio manager wants to have the hedged portfolio both delta-neutral and convexity-neutral but not necessarily self-financed. Present the formula you use to calculate the units of B and C without calculation.