Hi David,
I have a small doubt.
Holding yield constant , the bond with lower coupon would have higher duration and greater convexity.
But I read somewhere that by keeping both yield and duration constant, the bond with lower coupon has lower convexity.Convexity is a measure of dispersion of cash flows.Could you please explain the same.
If possible could you upload an excel working for this if possible.
Regards,
Sunil

Hi Sunil,

A way to think about convexity (courtesy of the experts at fixedincomerisk.com) is: as (Macualay) duration is the weighted average time to cash flows of a bond, convexity is the weighted average maturity-squared of a bond, where the weights are the present value of the bond’s cash flows. In this way, a zero-coupon bond has high convexity; e.g., a 5-year zero coupon bond, with only the one cash flow at 5 years, has convexity of 5^2 = 25.

Now with higher coupons, the weights are being dispersed to interim maturities, and the maturity-squared must come down; i.e., high coupon implies lower convexity (in this case, add coupons, and convexity will be < 25). Just like, in Tuckman, the barbell has higher convexity than the bullet portfolio because the squaring increases the impact of long-term cash flows.

I don’t have an XLS - it is good idea for next season....

Thanks, David