Fixed Income Question Please explain in simple terms following, question, correct

slackeranalyst

Please look at both questions below & explain in simple terms. Thanks!
1) All other things being equal, which one of the following bonds has the greatest volatility?
A) 20year, 15% coupon.
B) 5year, 10% coupon.
C) 20year, 10% coupon.
Your answer: A was incorrect. The correct answer was C) 20year, 10% coupon.
This question is asking: given a change in yield, which of the bonds will exhibit the greatest price change? Of the four choices, the bond with the longest maturity and lowest coupon will have the greatest price volatility.
All else equal, the bond with the longer term to maturity is more sensitive to changes in interest rates. Cash flows that are further into the future are discounted more than nearterm cash flows. Here, this means that one of the 20year bonds will have the highest volatility. Similar reasoning applies to the coupon rate. A lower coupon bond delivers more of its total cash flow (the bond’s par value) at maturity than a higher coupon bond. All else equal, a bond with a lower coupon than another will exhibit greater price volatility. Here, this means that of the 20year bonds, the one with the 10% coupon rate will exhibit greater price volatility than the bond with the 15% coupon.
2) Which of the following 10year fixedcoupon bonds has the most price volatility? All else equal, the bond with a coupon rate of:
A) 6.00%.
B) 5.00%.
C) 8.00%.
Your answer: C was incorrect. The correct answer was B) 5.00%.
If bonds are identical except for the coupon rate, the one with the lowest coupon will exhibit the most price volatility. This is because a bond’s price is determined by discounting the cash flows. A lowercoupon bond pays more of its cash flows later (more of the cash flow is comprised of principal at maturity) than a highercoupon bond does. Longerterm cash flows are discounted more heavily in the present value calculation. Another way to think about this: The relationship between the coupon rate and price volatility (all else equal) is inverse – a greater coupon results in less price volatility. Examination tip: If you get confused on the examination, remember that a zerocoupon bond has the highest interest rate risk because it delivers all its cash flows at maturity. Since a zerocoupon bond has a 0.00% coupon, a low coupon equates to high price volatility.

manchester88

It might help to think of it in terms of a % change of the coupon.
For example, lets go to an extreme and say you have a 40% coupon bond vs. a 1% coupon bond.
If interest rates change by 1% this only affects your 40% coupon bond by 1/40th of its coupon rate where your 1% bond is affected by 100%.
(This may not be 100% technically correct, but it helped me get the concept.)

JRossSter

Reading Chi Paul’s comment ^, if the 40% coupon bond has a maturity of 20 years, and the 1% coupon bond has a maturity of 10 years, then which one of the bond has the most price volatility?

rkapoor

i would say 1%, 10 yr would have more vol