If we determine that our portfolio's returns are dependent on the
market via this relation
then we can take out a short position in SPY to try to cancel out this
risk. The amount we take out is −βV where V is the total value of our
portfolio. This works because if our returns are approximated by
α+βXSPY, then adding a short in SPY will make our new returns be
α+βXSPY−βXSPY=α. Our returns are now purely alpha, which is
independent of SPY and will suffer no risk exposure to the market.
I get that the return we get from the new portfolio is independent of the return from SnP, say, but is there a way to eliminate Beta from the return as well?