 # interest rate risk questions

Qbank: Which of the following bonds bears the greatest price impact if its yield declines by one percent? A bond with: A) 30-year maturity and selling at 100. B) 10-year maturity and selling at 100. C) 10-year maturity and selling at 70. D) 30-year maturity and selling at 70. Concept Checker Which of the following bonds has the greatest interest rate risk ? A) 5%, 10 year callable bond yielding 4% A) 5%, 10 year putable bond yielding 6% A) 5%, 10 year option free bond yielding 4% A) 5%, 10 year option free bond yielding 6%

Thuderanalyst, Thanks for the great questions. 1) “A” because longer maturity and selling at par. Answer D has a long maturity, but is selling at a discount so the interest rate decrease causes a lesser price impact. 2) “C” because the options in the first two choices lessen the impact of interest changes and the higher coupon rate in the last answer will also lessen the impact. Why are all the answer choices “A” in the second question? I guess that makes it easier to anwer.

Longer maturity or lower coupon = greater volitility

Thats what I thought, but answers are “D” and “C”. Qbank gives some explaination to that too. My thought- Bonds trading at premium side (lower yields) of price-yield curve will have more price volatility compared to the ones trading on discount side of price-yield curve. So selling at par will have more volatility compared to the bond selling at discount (more yield). I just wanted to confirm if I am missing anything. I think Qbank answer is wrong. I’ll post the qbank explaination once I get home from work. Thanks Loscfa and blackjack !!

I agree with the Q-Bank about the first question. Think it this way: Zero coupon bonds, which are pure discount bonds, have the greatest price risk (interest rate risk.) D is a discount bond, so it will have larger price risk than par value bond.

minocfa - coupon rate and interest rate risks are inversely related. Higher coupon —> Low duration/interest rate risk. This is because Price-yield curve has more curvature at premium region compared to discount region where it becomes relatively flat. This the schweser reasoning: There are three features that determine the magnitude of duration: (1) The lower the coupon, the greater the bond price volatility. (2) The longer the term to maturity, the greater the price volatility. (3) The lower the initial yield, the greater the price volatility. The bond with the 30-year maturity will have a greater price impact than the 10-year maturity. The bond selling at the greatest discount will have a large price impact, a discount means that the coupon payments are low or the initial yield is low. So, the bond with the 30-year maturity and selling at 70 will have the greatest price volatility.

When I reached my answer for question 1, I used the following calculations: Answer “A”: before rate change: N = 60, I/Y = 2, PV = -100, PMT = 2, FV = 100 …rates drop 1%: N = 60, I/Y = 1.5, PV = 119.690, PMT = 2, FV = 100 Price Impact : (119.690 - 100)/100 = .1969 0r 19.69% Answer “D”: before rate change: N = 60, I/Y = 3.10, PV = -70, PMT = 2, FV = 100 …rates drop 1 %: N = 60, I/Y = 2.6, PV = -81.62, PMT = 2, FV 100 Price Impact : (81.62-70)/70 = .166 or 16.6% As a percentage, using these hypothetical values, a 1% rate drop has a greater price impact in absolute and relative terms. Will this always hold, or did I happen to choose a unique set of variables for my calculations?