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) 20-year, 15% coupon. B) 5-year, 10% coupon. C) 20-year, 10% coupon. Your answer: A was incorrect. The correct answer was C) 20-year, 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 near-term cash flows. Here, this means that one of the 20-year 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 20-year 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 10-year fixed-coupon 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 lower-coupon bond pays more of its cash flows later (more of the cash flow is comprised of principal at maturity) than a higher-coupon bond does. Longer-term 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 zero-coupon bond has the highest interest rate risk because it delivers all its cash flows at maturity. Since a zero-coupon bond has a 0.00% coupon, a low coupon equates to high price volatility.
the explanations you provided seem do an adequate job explaing concepts. longer term bonds will have more exposure to interest rate risk so prices will have opportunity for more volatility. the principal payment for a lower cpn bond will represent a greater % of the total cash flow so changes in price will have greater impact on total yield, YTM. perhapas, you can draw a timeline so you can see cash flows over life of bond for different cpn rates with ending principal repay. this might make it easier to conceptualize.
Long bonds (zero coupon) with low coupons have the highest volitity and duration (interest rate risk). Short bonds with high coupons have the lowest volitity and duration.
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.)
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?
i would say 1%, 10 yr would have more vol
You cant compare bonds using both different terms and interest rates for volatility. I believe that is why they say “all things equal” because they are asking the specific affect of each variable. For your questions, you evalute volatility… C>A and C>B therefore C>A and B, but you cant conclude C>A>B or C>B>A. Maybe you can using derivative analysis, but I am sure that is beyond the scope of this test.