CFA Practice Question

An investor is comparing two bonds issued by the same entity. The first bond has a coupon of 4.35% and a duration of 5.75. The second bond has a coupon of 4.25% with the same duration of 5.75. Their convexities are 44.37 and 47.95 respectively. The investor would MOST likely choose ______.
A. the 4.35% coupon bond
B. the 4.25% coupon bond
C. He would be indifferent about the two bonds.
Explanation: The two bonds have the same duration so this is not a discriminator. Since convexity is a desirable property in a bond as it shields an investor against a steep price drop, the bond with the higher convexity will be preferred. This is the second bond with 4.25% coupon. Its convexity (47.95) is greater than the convexity of the first bond (44.37).

User Comment
danlan But 4.35% gives a higher coupon, why not choose this?
Dancho The coupon is already incorporated in the duration. Therefore the convexity is the indicator
jcrichton If yields stay constant, would the 4.35% coupon bond not be preferred?
patsy not necessarily - remember it doesn't say the two bonds are identical - one may be more junior than the other and other and therefore of a lesser credit quality.
rgat why is higher convexity better?
steved333 Higher convexity is better
twotwo lol convexity is a desirable property in a bond as it shields an investor against a steep price drop, the bond with the higher convexity will be preferred.
sambra Price% variation = -D.dR + Ce.dr^2
note that if price drops, since dr is positive ( interest increase >>from low to high), convexity reduces the drop decrease, conversely if interest decreases price variation is amplified.
Kuki A higher convexity indicates that if yields ìncrease, the price of a bond will decline but at a declining rate.
jackwez duration includes the coupon... so esentially you get the same investment which will hold up better to interest rate flucs... so go with more convexity... (I got this wrong as well..)
akjohn1 why would an investor care about protecting against a steep price drop if they were going to hold it to maturity? Unless you can infer from the data presented in the problem that the 4.25 coupon bond has a higher ytm that the 4.35 coupon bond, there isn't enough info to make the correct decision.
jpducros The 4,35% coupon bond has a higher reinvestment risk, so it can be a reason to prefer the 4,25% bond.
mstroh314 I think the logic of the question goes like this: Even though the coupon of the first bond is higher, this does not mean that the YTM is higher, because both are issued by the same entity. Since duration for both is the same, choose the bond with higher convexity. So far so good. BUT if you think about it, the assumption that both bonds have the same expected return would imply free convexity (buy the bond with higher convexity, sell the bond with lower convexity). Or am I missing something?
ibewonjae This is explained well on page 557
mlaique When there a duration/convexity related question, have the Price-Yield graph in your mind.

1. As the yield gets lower, we move towards the more steeper side of the curve > therefore, the price of the bond increases at a faster rate.

2. Vice versa, as the yield increases, we move to a point on the curve where it is flatter > therefore, the price of the bond decreases at a slower rate.

Point (1) and (2) combined is the beauty of a normal bond's convexity and why investors like convexity.

To summarize, when yields drop, the price of the bond increases at a faster rate RELATIVE to when yields increase the price of the bond decreases at a slower rate. It is a win-win situation when you have positive convexity.