\begin{equation}
    \boxed{\textsf{pos}_t = \textsf{price}_t \times \textsf{signal}_t} \tag{H1}
\end{equation} which corresponds to the case where one decides to hold exactly $\textsf{signal}_t$ shares of the asset at any time\:$t$. Therefore we can deduce the relation between  $\textsf{PnL}_t$, $\textsf{price}_t$ and $\textsf{signal}_t$ : 
