# Position Restriction

The risk ratio $V_{ratio}$ is key value to risk control.

The system does not allow position changes that may lead to high risk ratio, i.e., the risk ratio $V_{ratio}'$ after any position changes shall be lower than the Risk Threshold $\theta$, otherwise the position change order cannot be executed[1].

Assuming that the risk ratio at given moment is $V_{ratio}$ and the position changed is $\Delta p$, the risk ratio after the position change $V_{ratio}'$ is calculated as follows:

$V_{ratio}'=\begin{cases} \dfrac{X_c+Y_c+\Delta p}{X_{all}-Y_{all}+|\Delta p|},&\text{position increase}\\ \\ \dfrac{X_c+Y_c-\Delta p}{X_{all}-Y_{all}-|\Delta p|},&\text{position decrease} \end{cases}$
• $\Delta p$ is positive if the position changed is long, or negative if short.

Then the relationship between $\theta$ and $V_{ratio}'$ can be described as follows:

$-\theta\leq V_{ratio}'\leq\theta,\quad\theta\in(0,1)$

Expand the formula:

$\begin{cases} -\theta\leq\dfrac{X_c+Y_c+\Delta p}{X_{all}-Y_{all}+|\Delta p|}\leq\theta,&\theta\in(0,1),&\text{position increase}\\ \\ -\theta\leq\dfrac{X_c+Y_c-\Delta p}{X_{all}-Y_{all}-|\Delta p|}\leq\theta,&\theta\in(0,1),&\text{position decrease} \end{cases}$

Thus, the formula for restriction on position changed $\Delta p$:

$\begin{cases} \Delta p\leq\dfrac{\theta*(X_{all}-Y_{all})-X_c-Y_c}{1-\theta},&\Delta p>0,&\text{position increase}\\ \\ \Delta p\geq\dfrac{-\theta*(X_{all}-Y_{all})-X_c-Y_c}{1-\theta},&\Delta p<0,&\text{position increase}\\ \\ \Delta p\leq\dfrac{\theta*(X_{all}-Y_{all})+X_c+Y_c}{1+\theta},&\Delta p>0,&\text{position decrease}\\ \\ \Delta p\geq\dfrac{-\theta*(X_{all}-Y_{all})+X_c+Y_c}{1+\theta},&\Delta p<0,&\text{position decrease} \end{cases}$

If the position changed $\Delta p$ failed to satisfy the formula above, the contemplated position change cannot be executed.

Position restriction ensures the risk ratio $V_{ratio}$ shall always be lower than a given risk threshold.

Risk threshold $\theta$ is a changeable constant and can be adjusted via DAO community voting.

[1] Except for liquidation.