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Position Restriction

The risk ratio
VratioV_{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
Vratio′V_{ratio}'
 after any position changes shall be lower than the Risk Threshold
θ\theta
, otherwise the position change order cannot be executed[1].
Assuming that the risk ratio at given moment is
VratioV_{ratio}
 and the position changed is
Δp\Delta p
, the risk ratio after the position change
Vratio′V_{ratio}'
 is calculated as follows:
Vratio′={Xc+Yc+ΔpXall−Yall+∣Δp∣,position increaseXc+Yc−ΔpXall−Yall−∣Δp∣,position decreaseV_{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}
  • ​
    Δp\Delta p
     is positive if the position changed is long, or negative if short.
Then the relationship between
θ\theta
 and
Vratio′V_{ratio}'
 can be described as follows:
−θ≤Vratio′≤θ,θ∈(0,1)-\theta\leq V_{ratio}'\leq\theta,\quad\theta\in(0,1)
Expand the formula:
{−θ≤Xc+Yc+ΔpXall−Yall+∣Δp∣≤θ,θ∈(0,1),position increase−θ≤Xc+Yc−ΔpXall−Yall−∣Δp∣≤θ,θ∈(0,1),position decrease\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
Δp\Delta p
:
{Δp≤θ∗(Xall−Yall)−Xc−Yc1−θ,Δp>0,position increaseΔp≥−θ∗(Xall−Yall)−Xc−Yc1−θ,Δp<0,position increaseΔp≤θ∗(Xall−Yall)+Xc+Yc1+θ,Δp>0,position decreaseΔp≥−θ∗(Xall−Yall)+Xc+Yc1+θ,Δp<0,position decrease\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
Δp\Delta p
 failed to satisfy the formula above, the contemplated position change cannot be executed.
Position restriction ensures the risk ratio
VratioV_{ratio}
 shall always be lower than a given risk threshold.
Risk threshold
θ\theta
 is a changeable constant and can be adjusted via DAO community voting.
[1] Except for liquidation.
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