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 about bonds:

The maturity period is four years Coupon rate 10% Par value $1,000 Coupons on bonds are paid annually Yield to maturity of bonds 11%

i, using the above data, fill in the blanks in the following table:

year(t)	Cash flow (CFt)	CFt/(1+y)t	Wt	t*Wt	t+t^2	(t+t^2) *CFt/(1+y)t
1
2
3
4

Notes:

y = yield to maturity W_t= weight for year t

ii) Based on the calculations in part i, calculate the 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 two per cent

iv) Using the convexity, calculate the change in bond price in dollars when yield to maturity changes by two per cent

Part b

The following data relate to a corporate bond that pays coupons semi-annually: Settlement date 01 March 2022 Maturity date 31 December 2045 Coupon rate 9%

Yield to maturity 10% Face value $1,000 Percentage of face value paid back to the investor on maturity 100% Using the above data, calculate

The flat price of the bond

Accrued interest

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 $24,759 in 8 years. The market interest rate is 12%. The companys portfolio manager wishes to fund the obligation using four-year zero-coupon bonds and perpetuities paying annual coupons.

How can the manager immunise the obligation?

Suppose two years have passed, and the interest rate remains at 12%. Is the position still fully funded? Is it still immunised? If not, what actions are required?