Question

. Assume that a 10-year Treasury bond has a 12% annual coupon, while a 15-year T-bond has an 8% annual coupon. Assume also that the yield curve is flat, and all Treasury securities have a 10% yield to maturity. Which of the following statements is CORRECT?

a. If interest rates decline, the prices of both bonds will increase, but the 10-year bond would have a larger percentage increase in price.

b. If interest rates decline, the prices of both bonds will increase, but the 10-year bond would have a larger percentage increase in price.

c. If the yield to maturity on both bonds remains at 10% over the next year, the price of the 10-year bond would decrease, but the price of the 15-year bond would increase.

d. The 10-year bond would sell at a discount, while the 15-year bond would sell at a premium.

e. The 10-year bond would sell at a premium, while the 15-year bond would sell at par.

Answer 1

Higher the maturity, higher the volatility in price with respect to change in interest rate.

That's why, long term bonds are exposed more to interest rate risk than short term bonds.

Secondly, if coupon rate is higher than YTM, bond will trade at a premium

Thirdly, 15 year bond has coupon rate of 8%, less than YTM =10%, so it trades at a discount and 10 year bond trades at a premium

So if YTM remains at 10%,

The price of 15 year bond will increase and on maturity, it will be equal to face value, that is, at par.

The price of 10 years bond will decrease and on maturity, it will be equal to face value, that is, at par.

so only "c" is correct.

c. If the yield to maturity on both bonds remains at 10% over the next year, the price of the 10-year bond would decrease, but the price of the 15-year bond would increase. [Thumbs up please]