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I have tried to find an answer to this question but have come up with nothing.

So, it is my understanding that to find the duration of a futures contract (assuming no switch risk), all you need to do is find the duration of the CTD in the forward space (by using the delivery date as the settlement date, and by using the invoice price as the price of the CTD), and divide the duration of the CTD by its conversion factor. My questions is, what is the mathematical rationale for dividing the duration of the CTD by its conversion factor, when you are already adjusting the price of the CTD for the conversion factor?

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    $\begingroup$ Assuming you mean mod duration, then you don't have to divide by CF. Does this post help? quant.stackexchange.com/questions/34553/… $\endgroup$
    – Helin
    Nov 2, 2020 at 5:52
  • $\begingroup$ Unfortunately, the post you provided a link to failed to provide an explanation for why we divide by the conversion factor - I understand the steps involved, but I am trying to understand the intuition/reasoning for dividing the forward, conversion factor adjusted modified duration of the CTD by the conversion factor. $\endgroup$
    – basisnerd123
    Nov 2, 2020 at 21:19

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By dividing the duration of the CTD by its conversion factor, we arrive at a number that approximates the sensitivity of the futures price to the yield of the CTD.

Recall that duration of a bond is a measure of its price sensitivity to the change in its yield. Since Futures price is approximately the CTD bond (clean) price divided by the conversion factor (minus carry and any value from its optionality), dividing the duration of the CTD by the conversion factor gives you approximate price sensitivity of the futures to the yield of the CTD.

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