Question

Consider two Treasury bonds. Both of them have face value of $1,000 and have four years to maturity, with annual coupon payments. The first bond is a zero-coupon bond and the second bond has 5% coupon rate. The yield is 6% today. Which of the following statements about interest rate risk and duration is false?

Group of answer choices

A. The duration of the zero-coupon bond is four years.

B. The duration of the 5%-coupon bond is larger than the zero-coupon bond.

C. If the yield suddenly drops by 1%, the capital gains from the zero-coupon bond is more than the 5%-coupon bond.

Answer 1

The duration of a zero coupon bond is always equal to its maturity, as the payment isn't made until maturity

The duration of a coupon bond will always be smaller than the zero-coupon bond.

We have found out the duration of the 5% coupon bond as shown in the below table:

time(t)	cash flow(CF)	PV factor	PV of CF	(PV/total)*t
1	50	1.06	47.16981	0.048862967
2	50	1.1236	44.49982	0.092194277
3	50	1.191016	41.98096	0.1304636
4	1050	1.262477	831.6983	3.446208294
Total			965.3489	3.717729137

Here it is found that the duration is 3.71 which is less than 4 years

When the yield drops the capital gains for a coupon bond will always be more than the zero coupon bond

So the correct choice is

B. The duration of the 5%-coupon bond is larger than the zero-coupon bond.