Hi all,
I’m looking for some clarification. What is the relationship between coupon bonds and convexity? The books says one thing, and other online sources (I’ve posted one below) says another.
From CFA textbooks Volume 4 Page 131
Coupon-paying bonds have more convexity than zero-coupon bonds of the same duration—a 30-year coupon-paying bond with a duration of approximately 18 years has more convexity than an 18-year zero-coupon bond.6 The more widely dispersed a bond’s cash flows are around the duration point, the more convexity it will exhibit. For this reason, a zero-coupon bond has the lowest convexity
From Investopedia https://www.investopedia.com/ask/answers/052615/what-correlation-between-coupon-rate-and-convexity-given-bond.asp
Generally speaking, convexity decreases as yields increase (geometrically, the yield curve tends to flatten at higher yields). Bonds with lower coupons have higher degrees of convexity, while high-coupon bonds have lower degrees of convexity. Zero-coupon bonds have the highest convexity. These relationships are only valid when comparing bonds that have the same durations and yields to maturity.
This is one of those situations in which you’ll learn more and have a better understanding if you do the work yourself, rather than get an answer from a book or one of us here.
Create a table in an Excel spreadsheet with various coupon rates across the top, various yields along the the left side, and the prices of bonds of a fixed maturity in the body. Using those prices, calculate the convexity of the bonds and see how that changes with coupon and yield.
Can anyone help with this? So do zero coupon bonds have the lowest convexity of all bonds of a given duration?
Thanks in advance!
Once again, this is one of those situations in which you’ll learn more and have a better understanding if you do the work yourself, rather than get an answer from a book or one of us here.
Magician is being Sarcastic. Coupon paying bond should have higher convexity when compared with Zero-coupon bond depending on the price it is trading.
Remember the formula for calculating Effective Convexity {(P- + P+) - 2P} / (P * ΔCurve2)
Where P = Current Price
P-= Price when the curve declines by say 50bp
P+ is the opposite of the above.
Because Coupon paying bond trades at a price § greater than those of Zero-coupon bond, they tend to have higher convexity.
Hope that helps.
No, I’m not.
I’m quite serious: these guys will learn a lot more if they put some numbers into Excel and compute the convexity of a number of bonds themselves.