# Bond Immunization, Duration, and Convexity Project

Bond Immunization, Duration, and Convexity Project

Immunization

You are the CFO of a major real-estate firm. Your firm has just won a contract to build a tower that will

be twice as tall as the Burj Khalifa, currently the world’s tallest building. Your firm has borrowed \$10

billion dollars, to be re-payed in 15 years. The market interest rate is 12%, so the present value of this

obligation is \$1,826,962,613. You decide to fund the obligation using five-year zero-coupon bonds and

perpetuities that make annual coupon payments.

1. How can you immunize the obligation? (Here, you need to construct an immunized portfolio that

consists of the zero-coupon bonds and the perpetuities.)

2. Now suppose that one year has passed and that the market rate is still 12%. You need to ensure that

the obligation is still fully-funded and immunized. Is the obligation still fully-funded and immunized? If

not, show the steps that you need to take to fully fund and immunized the obligation?

Duration

1. What is the duration of a 15-year, 8.5% semi-annual bond if the market rate on bonds of similar

quality is 8.7%?

2. Now suppose that the yield to maturity has changed to 8.71%. Using Macaulay duration, what is the

approximate percent change in the price of the bond? (You do not need to recalculate Macaulay

duration using 8.71%. Use the duration value that you found in Problem 1.)

3. Using duration, what is the approximate percent change in the price of the bond? Also, what is the

approximate dollar change in the price? (Use the same Macaulay duration value that you used in

Problems 1 and 2.)

4. Using duration and convexity, what is the percent change in the bond? Also, what is the approximate