QUESTION 2

Assume the yield curve is flat at 7.5% pa nominal. A cash and $duration-neutral butterfly is to be constructed by selling one thousand 9-year zero coupon bonds and purchasing q_s and q_l zero coupon bonds with maturities 5 and 14 years' respectively. We assume that interest accrues semi-annually. We also assume each bond has a face value of $100.

(a) What is the price of the 5-year bond?

(b) What is the price of the 9-year bond?

(c) What is the price of the 14-year bond?

(d) What is the modified duration of the 5-year bond?

(e) What is the modified duration of the 9-year bond?

(f) What is the modified duration of the 14-year bond?

(g) What is the standardized convexity of the 5-year bond?

(h) What is the standardized convexity of the 9-year bond?

(i) What is the standardized convexity of the 14-year bond?

(j) What is the cash-neutral equation in the system of equations needed to find q_s and q_l?

(k) What is the $Duration-neutral equation in the system of equations needed to find q_s and q_l?

(l): It can be shown that the solution to the system of equations is: q_s = 413.83 and q_l= 642.24. The profit from this strategy if the yield curve shifts upwards by 1% at all maturities is closest to:

(m): What is the modified duration of a portfolio comprising : q_s = 413.83 short-maturity bond and q_l= 642.24 long maturity bonds?

(n): What is the standardized convexity of a portfolio comprising : q_s = 413.83 short-maturity bond and q_l= 642.24 long maturity bonds?