Has anyone done Practice Problem 8 p. 480 in Reading 66 Intro to Measurement of Interest Rate Risk? The question is about two callable bonds, ABC and XYZ of the same issuer that can be called immediately. Estimated % Change in Price if Int. Rates Change by -50 Bp +50 Bp Bond ABC +2% -5% Bond XYZ +11% -8% They have the same maturity. The coupon rate of one bond is 7% and the other 13%. Suppose the yield for this issuer is flat at 8%. Based on this info, which bond is the lower coupon bond and which is the higher coupon bond? Explain why. I approached this question by calculating the effective duration. I obtained effective duration of 7 for ABC and 9 for XYZ. A bond with lower coupon rate would have higher duration, therefore it is XYZ, which is the low coupon bond. However, the answer provided uses the concept convexity. A high coupon bond will exhibit will exhibit negative convexity and vice versa. ABC is the high coupon bond and XYZ is the low coupon bond. I could not understand the linkage between convexity and coupon rate as I don;t seem to recall this being explained in the Reading and Schweser. Is my approach using effective duration wrong? I thought a combination of duration and convexity would provide a more accurate estimate of the % change in price of a bond, esp. for relatively large changes in yield. As such, I don’t think my approach is incorrect as the % change here is not relatively large even though I did not consider convexity. One more thing - what is the significance of the “Suppose the yield for this issuer is flat at 8%” in the question?

Nuppal, thanks for your help.

My sarcasm meter is broken. If that actually helped then you’re welcome. No thanks needed though, we are all in the same boat, I fully expect I have a question that you may be able to answer, an eye for an eye, I am more than happy to help you out.

Does the answer really say that higher coupon will exhibit negative convexity?

Just laying this out before more confusion ensues: 1) Bonds exhibit negative convexity due to embedded call options. 2) All else equal, the higher the coupon, the low the eff. duration of a bond. Looking at the 50bps shocks, it is easy to tell that ABC is the higher coupon and XYZ is the lower coupon. Also, if i recall correctly, the higher the coupon, the lower the effective convexity in absolute terms.

Ymmt, whereabouts in the CFAI Reading 66 did you come across “the the higher the coupon, the lower the eff. convexity in absolute terms”? This is definitely not covered in Schweser.

I haven’t studied LI in almost 3 years (I passed LIII last year). I’m just explaining to you the basic aspects of bonds. I’m basing this information off empirical evidence. Anything I say that isn’t touched upon in your study notes should be considered unnecessary for the exam. If you have any other questions, feel free to ask. Good luck =)

But thinking more about how convexity changes as we move along the price/yield curve, I think the statement about the convexity/coupon relationship might hinge upon the yield level where convexity changes from positive to negative. I’ll need to look into this more tomorrow.

“Also, if i recall correctly, the higher the coupon, the lower the effective convexity in absolute terms.” Looked into it a little more today and realized this statement is wrong. At certain yield levels, particularly where convexity goes from postive to negative, this relationship does not hold. I was wrongly assuming that the the convexity switched over at same yield level for both high and low coupon bonds. What does happen, it seems, is that convexity changes at a faster rate for lower coupon bonds than for higher coupon bonds.

Yeah, bond with callable option has negative convexity and the two bonds are being called immediately. There are 2 ways of explanation here. First is based on convexity. For a positive convexity, the gain (interest rate decreases) is more than the loss (interest decreases) and vice versa for a negative convexity. Given 50bp change in interest rate, the gain in price of bond ABC is less than the loss, it shows a negative convexity. The assumption in level 1 is clear, bond has negative convexity only when yield