Question

# Consider two Treasury bonds. Both of them have face value of \$1,000 and have four years...

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?

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.

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.