 # Positive Convexity vs Negative Convexity

Two callable bonds A (7% coupon rate) and B (13% coupon rate) from the same issuer with the same maturity. Suppose the yield curve for this issuer is flat @8%. Based on the following info, tell which one is the lower coupon bond and which one is the higher coupon bond? Why? If interest rate increase 50 bps, estimated percentage price change for A is -5%; for B is -8%. If interest rate decrease 50 bps, estimated percentage price change for A is +2%; for B is +11%. Does high/low coupon bond here mean high/low yield bond? I thought the yield is constant in this case. No??? Thx to share your thoughts.

“Two callable bonds A (7% coupon rate) and B (13% coupon rate) …tell which one is the lower coupon bond and which one is the higher coupon bond” Let’s see… A is the lower coupon bond because you just told me. Something is messed with the question.

Probably it is the current yield they are looking for.

This is exactly one of the practice problems shown at Vol. 5 p. 512 No. 8. You can check it yourself. I did not reword the question. I feel it purposely to confuse me with the description. High coupon rate bond = high coupon bond??? The answer is: Bond A is the higher coupon bond. Why? Because it exhibits negative convexity. A high coupn bond will exhibit negative convexity. Honestly, I’m still not very clear about the above explanation. I know negative convexitty is an important feature of callable bonds. It’s when rates shock a large bp, price gain < price loss. A callable bond exhibits this feature when yield is at low level (compared with its coupon rate). But how to decide btwn two callables which one is high coupon bond?

hyang, in your original wording of the question, you misrepresented it. In the CFAI text, on page 512, it says (last paragraph in question 8), “You are told that both bonds have about the same maturity and the coupon rate of one bond is 7% and the other 13%.” So you need to figure out which coupon rate belongs to which bond.

Really, this problem is messed from the start. Before you look at convexity, you need to look at duration. Bond B surely has a higher duration than Bond A simply because its price changes are much greater for the same interest rate moves. Since they have the same maturity, that means Bond A has a higher coupon rate than Bond B or it’s insensitive to interest rates because it’s going to be called with really high probability (the latter here is neg. convexity sort-of). All things equal, bonds with higher coupons are more likely to be called than bonds with lower coupons.

forumreader Wrote: ------------------------------------------------------- > hyang, in your original wording of the question, > you misrepresented it. In the CFAI text, on page > 512, it says (last paragraph in question 8), “You > are told that both bonds have about the same > maturity and the coupon rate of one bond is 7% and > the other 13%.” So you need to figure out which > coupon rate belongs to which bond. That helps explain things a lot…

I see… Thx to clarify. All else equal, bond B has higher duration than bond A. So should bond B more volatile and risky than bond A?

Absolutely - “duration” and “interest rate risk” are not exactly synonymous in fixed income but really close.