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9. Answer the following questions on bond valuation and duration.

1. Calculate the duration of a zero-coupon bond with five years to maturity, face value of $1000, and effective annual yield of 12.1604%. Show your calculations. What does your answer say about the duration of zero-coupon bonds in general?

A zero-coupon bond only has one cash flow and does not pay any coupons, therefore the duration is the same as the years to maturity.

2. Calculate the duration of a coupon bond with the following features. What general conclusion can we make about the duration of coupon bonds relative to their time to maturity? (3 marks)

The duration of the bond will be 3.97 years.

(Hint: The effective annual yield should be 12.1604%.)

3. Duration is a measure of interest rate risk. Specifically, it measures the approximate percentage change in bond price given a small percentage change in interest rate (% bond price change / % interest rate change). For example, for a bond with a duration of five years, a 0.1% change in interest rate would change the bonds price by 5 * 0.1% = 0.5%, approximately.

Suppose that the interest rates on all bonds increase uniformly by 0.1% (this is what is commonly called a parallel upward shift in yields of 10 basis points). What is the percentage change in the price on the coupon bond in part (b)? What is the approximate coupon bond price? Note that bond yield and bond price are inversely related to each other (i.e., an increase in yield should lead to a decrease in bond price). (2 marks)

4. Recalculate the price of the coupon bond with five years to maturity, face value of $1000, coupon rate of 11% paid semi-annually, and a new yield to maturity equaling the original yield in part (b) plus 0.1%. Does it concur with your approximate coupon bond price calculated in part (c)? (Hint: The two answers in parts (c) and (d) should be fairly similar.) (2 marks)