Case study 2 Part a

You are the portfolio manager of a large company that invests in many securities including corporate bonds. You have been assigned the task of bond portfolio management. You are provided with the following data in relation to bonds:

Maturity period 6 years Coupon rate 10% Par value $1,000 Coupons on bonds are paid annually Yield to maturity of bonds 12%

Required: i) Fill in the blanks in the following table Year (t) Cash flow (CFt) CFt/(1+y) t Wt t*W t t+t^2 (t+t^2)*CFt/(1+y) t

Year (t)	Cash flow (CFt)	CFt/(1+y) t	Wt	t*W t	t+t^2	(t+t^2)*CFt/(1+y)
1
2
3
4
5
6
Notes y = yield to maturity Wt= weight for year t

ii) Based on the calculations in part i, calculate modified duration and convexity of the bond iii) Using the modified duration, calculate the change in bond price in dollars when yield to maturity changes by one percent iv) Using the convexity, calculate the change in bond price in dollars when yield to maturity changes by one percent Part b The following data relate to a corporate bond which pays coupons semi-annually: Settlement date 01 March 2022 Maturity date 31 December 2042 Coupon rate 10% Yield to maturity 9% Face value $1,000 Percentage of face value paid back to the investor on maturity 100% Using the above data, calculate i. The flat price of the bond ii. Accrued interest iii. Invoice price of the bond

Note: Show the assumptions, if any, you made in your calculations.

Part c A company must make a payment of $31,384 in 12 years. The market interest rate is 10%. The companys portfolio manager wishes to fund the obligation using four-year zero-coupon bonds and perpetuities paying annual coupons. How can the manager immunize the obligation? Suppose that three years have passed, and the interest rate remains at 10%. Is the position still fully funded? Is it still immunized? If not, what actions are required?