Intuition about interest rate risk being minimized from the formula for Macaulay Duration

[Vaibahvgupta177]

Hey, hi!
I have been reading up on Macaulay Duration for a few days now. One of the few things that keeps cropping up is that, if a bond is held for the duration given by Macaulay Duration, the reinvestment rate risk and market price risk offset each other. In other words, the interest rate risk is nullified.
But, I haven’t been able to develop any intuition or logic for that from the formula (the one which weighs time period with proportion of PV of CFs in bond price). Can anyone help me with that, please?
Thank you.

 

[cpk123]

in a falling rate market - reinvestment return falls - bcos coupons are reinvested at a lower rate.
but price return increases bcos bond increases in value.
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likewise when rates increase - reinvestment return up, price return down.
no need of the macaulay dur formula for this one…

 

[S2000magician]

I believe that he’s asking about the point of indifference: if the YTM changes and you hold the bond for the Macaulay duration (reinvesting coupons at the new YTM), you’ll have the same total value as you would have had had the YTM not changed.

 

[Vaibahvgupta177]

Yes S2000 is right. I want to know how the formula for Macaulay Duration factors this calculation of point of indifference in.
To rephrase my question, how is it that Macaulay Duration acts as the period for which portfolio value remains the same if YTM changes once on the day of the calculation of the Macaulay Duration?