# Modified duration of treasury futures tracking CTD?

If I know TYU7 contract's CTD is T 2.500 05/15/2024 with modified duration of 6.37. I know futures DV01 is calculated by taking the CTD's DV01 divided by conversion factor as shown here. What is the modified duration of TYU7?

I tried backing out the Mod Dur based on the formula for calculating Mod Dur using DV01 for cash instruments, which is $$Mod Dur = \frac{DV01}{0.01*0.01*Price}$$

Given the future's DV01 and its price, this gave me a Mod Dur for futures which is the same as Mod Dur for cash CTD. Kinda weird, isn't it?

$$D_\text{mod, fut} = \frac{1}{f}\frac{df}{dy} = \frac{1}{F_\text{CTD} / \lambda_\text{CTD}} \cdot \frac{dF_\text{CTD} / dy}{\lambda_\text{CTD}} = \frac{1}{F_\text{CTD}}\frac{dF_\text{CTD}}{dy},$$ where $f$ is the futures price, $F_\text{CTD}$ is the CTD's forward price, and $\lambda_\text{CTD}$ is the CTD's conversion factor. So you're right; under the assumption that futures track its current CTD, then its modified duration is identical to the CTD's (forward) modified duration.