Question

Bond A is a 12 year bond. Bond B is a 10 year bond. Both bonds have the same yield and same duration. Which of the following is true.

a/ Bond A has a lower coupon

b/ Bonds A and B have equal convexity

c/ Bond A has lower convexity

d/ None of the above

Answer 1

a is Correct.

Reasoning

bonds with long maturities and low coupons have the longest durations. These bonds are more sensitive to a change in market interest rates and thus are more volatile in a changing rate environment. Conversely, bonds with shorter maturity dates or higher coupons will have shorter durations. Bonds with shorter durations are less sensitive to changing rates and thus are less volatile in a changing rate environment.
bonds with shorter maturities return investors' principal more quickly than long-term bonds do. Therefore, they carry less long-term risk because the principal is returned, and can be reinvested, earlier.
higher coupon………………………lower duration
longer maturity……………………..higher duration
higher market yield………………..higher duration
First ask yourself, what is duration….

.. it’s the percent change in price to a percent change in yield…

With a low coupon bond, you are going to get a larger percent of your total return through capital appreciation… or more correctly, the change in the price of the bond from the time of purchase to maturity. Therefore, a movement in the interest rate is going to have a pretty big impact on your total yield.

But it you are getting a lot paid out in coupon, that portion of total return mutes the effects of the change in yield somewhat. Therefore, higher coupon, lower duration.

… and consequently, that is why a zero coupon bond has such a high duration (equal to its maturity)

The higher the coupon rate, the lower the duration, and the lower the interest rate risk.
The longer the maturity, the higher the duration, and the greater the interest rate risk. Consider two bonds that each yield 5% and cost $1,000, but have different maturities. A bond that matures faster – say, in one year – would repay its true cost faster than a bond that matures in 10 years. Consequently, the shorter-maturity bond would have a lower duration and less risk.

Coupon rate. A bond’s coupon rate is a key factor in calculation duration. If we have two bonds that are identical with the exception on their coupon rates, the bond with the higher coupon rate will pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the duration, and the lower the interest rate risk