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Call-put parity writes (to see this, notice that $(S_T-K)^+ - (K-S_T)^+ = S_T - K $ and take the discounted risk-neutral expectation $E^{\mathbb {Q}} [. \vert \mathcal {F}_0 ]$ on both sides): $$ C(K,T) - P(K,T) = DF ( F(0,T) - K ) $$ with $DF = e^{-rT} $ the discount factor, and $F(0,T)$ the fair forward price given by $$ F(0,T) = (S_0 - D^*)e^{rT} $$ ...


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Your return calculation should be on total return, i.e. include dividend income. Your signal, if it is price only, then you should take the price series and not adjust.



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