If a bond's yield to maturity increases, what specific effect does this have on its duration, assuming all other factors remain constant?

Generally, if a bond's yield to maturity (YTM) increases, its duration decreases, assuming all other factors remain constant. Duration measures a bond's price sensitivity to changes in interest rates; it's the approximate percentage change in a bond's price for a 1% change in yield. A higher YTM implies that future cash flows are discounted at a higher rate. This higher discount rate reduces the present value of those future cash flows, especially those occurring further in the future. Because duration is a weighted average of the times until those cash flows are received, weighting the later cash flows less heavily due to the higher discount rate reduces the overall duration. Mathematically, the relationship between YTM and duration is inverse, but not perfectly linear. For bonds with embedded options, such as callable bonds, the relationship can become more complex, and the duration may increase with increasing yields at certain points due to the changing probability of the bond being called. However, for a plain vanilla bond, an increase in YTM will predictably result in a decrease in duration.