I recently read, that yield changes during a short time window can be approximated by dividing the returns of futures on the bond by its Duration. Has anybody heard this before and can shed some light on why this works?

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    $\begingroup$ The duration allows you to approximate change in bond price from change in yield and vice versa, based on $\Delta P \approx -P \cdot ModD \cdot \Delta y$. Source: en.wikipedia.org/wiki/Bond_duration This is why ModD or modified duration is useful in working with bonds. This is not particularly linked to futures. $\endgroup$
    – nbbo2
    Commented Jun 12, 2021 at 15:55
  • $\begingroup$ Does that mean you could apply the same formula with the Futures Duration? I intuitively understand Duration as the time it takes to recover the present value of all future cash flows, so I'm having a hard time understanding what the Duration of a Future contract would represent. $\endgroup$ Commented Jun 12, 2021 at 16:38
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    $\begingroup$ For Futures people use the Duration of the bond that will be delivered at futures maturity (the "CTD bond"). That's the most common concept of bond futures duration, there are several posts here on this topic (search for Futures Duration). $\endgroup$
    – nbbo2
    Commented Jun 12, 2021 at 16:41

1 Answer 1


In general it's not a good idea to calculate some sort of delta and then use it to estimate price sensitivity. It's better to calculate

Value 1 @ price 1, then Value 2 @ price 1 + some small price diff

so that delta = Value 2 - Value 1

It's a lot less complicated that understanding how to derive a formula for 1st derivative wrt to price.


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