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If we assume net basis is 0, the bond trades above par, the bond’s yield > than the term repo rate, what is the expected pnl of being Short the ctd vs long futures?

I would have thought the expected pnl is 0. The bond will cheapen vs the future generating pnl in an amount = to the gross basis which = pure carry (coupon income - repo cost).

My confusion is two fold:

  1. what about the pull to par income from being short, is this taken into account above.

  2. The bond yield > repo rate and hence isn’t real carry actually negative and hence the short basis position negative expected pnl?

Please could someone explain intuitively and mathematically why real carry = bond yield - repo rate and why this is equivalent to coupon income - repo cost + pull to par? I am unsure why the former includes pull to par?

Thanks

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