In the textbook for one of my classes it says, “The sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases.”
I understand why sensitivity increases as maturity increases, but why does it increase at a decreasing rate? I’m thinking it has something to do with the convexity of the price-yield curve.
It has to do with discounting the future cash flows to the present. Suppose that the YTM on a bond is 5%, and it changes to 6%. The effect on the present value of the par payment of a 1-year bond is about $9.00, while the effect on the present value of the par payment of a 10-year bond is about $6.00, simply because the latter payment comes 9 years later.
Thank you! I actually came to that conclusion some time after I made that post, but I’m glad you were able to confirm it.
Also, the quote in your signature is great.
The quote comes from a trigonometry textbook published in 1959.