another simpler approach: loss of buy equals to profit of sell
(BPe-BID)*LB=(SPe-ASK)*LS
ASK=SPREAD+BID
then:
(BPe-BID)*LB=(SPe-ASK)*LS
(BPe-BID)*LB=(SPe-SPREAD-BID)*LS
BID*LS-BID*LB=SPe*LS-SPREAD*LS-BPe*LB
BID(LS-LB)=(SPe*LS-BPe*LB)-SPREAD*LS
BID=(SPe*LS-BPe*LB)/(LS-LB)-SPREAD*LS/(LS-LB) --------> OUR ORIGINAL RULE
(BPe-BID)*LB=(SPe-ASK)*LS
ASK=SPREAD+BID
then:
(BPe-BID)*LB=(SPe-ASK)*LS
(BPe-BID)*LB=(SPe-SPREAD-BID)*LS
BID*LS-BID*LB=SPe*LS-SPREAD*LS-BPe*LB
BID(LS-LB)=(SPe*LS-BPe*LB)-SPREAD*LS
BID=(SPe*LS-BPe*LB)/(LS-LB)-SPREAD*LS/(LS-LB) --------> OUR ORIGINAL RULE
Be yourself
7