Currently trying a pairs trading approach using cointegration. Tried both formations:

$$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$

$$P_t^A=P_t^B \hat{\gamma}+\hat{\mu} +\epsilon_t\hspace{2.4cm} (2)$$

However, I am struggling in the calculation of two things: Firstly, the hedge ratio in both models, implies 1 share long (short) of A and $\hat{\gamma}$ short (long) of B or 1 dollar long (short) of A and $\hat{\gamma}$ dollar short (long) of B. Secondly, how should returns be calculated, since I have multiple cointegration vectors: $CV=[1 \hspace{0.3cm}\hat{\gamma}]$. My thought is to calculate daily, in market values the open Long and Short positions, adding the total capital at this point.



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