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Is it trading below par ? If yes it can converge to par while keeping the same DM.


You can't really add/subtract the n and t indices. The fact that you didn't use Latex in your question makes it even more confusing :) The $t$ refers to the time of the price and $n$ refers to the time to maturity of the bond, the bond has $n$ periods remaining and matures at ($t+n$). If today's price is $p_t^{(n)}$ then tomorrow's price is $p_{t+1}^{(n-1)}...


You could decompose the portfolio dv01 by buckets (corresponding to the available futures) and hedge each bucket with the appropriate number of contracts.

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