# mtp health metric

## Previous Version
At the epoch level, as interest liabilities accumulate, $mtp$ health deteriorates.

$$ h(x) = \frac{x_A}{x_A + x_L}$$

The decline in $h(x)$ affects the steady state interest rate $\beta^*$ as

$$ \beta^{\star} = \frac{K_h}{h(x)} \cdot \frac{K_H}{H(X,Y)}$$

Thus, within an epoch, $\beta^{\star}$ is an *attractor*. In the above equation, the $\frac{K_h}{h(x)}$ term is $mtp$ specific and forms a *local attractor*. Whereas the term $\frac{K_H}{H(X,Y)}$ is akin to a base rate applied to all $mtps$ in the pool and forms a *global attractor*. The local attractor term $\frac{K_h}{h(x)}$ includes interest liabilities $x^I_L$ as $$ h(x) = \frac{x_A}{x_A + x_L}$$ and $$x_L = x^P_L + x^I_L$$

## Update for Margin MVP 1.0
### Requirements
1. Collateral $x_A$ only exists on the $mtp$ holder's balance sheet
2. Need to reflect value held in custody

### Proposed
#### Collateralization Ratio
Oustanding debt on the $mtp$ balance sheet
$debt = x_{li} + x_{lp}$

Current value of custodied position in denominated in x:
$custody_{value} = y_c \cdot P^x_y$
which can be computed using the swap formula on the current state of the pool (**Not actually performing the swap**):
$custody_{value} = f_{swap}(y_c, X, Y)$

The liquidation ratio of the $mtp$ position is:
$LiquidationRatio = \frac{custody_{value}}{debt}$
where a value $LR > 1$ indicates that closing the position would not be a loss to the $mtp$ holder or the pool. A $LR < 1$ means that the pool would have losses and the $mtp$ holder would have lost all of its original deposit.

The liquidation ratio can be queried against a safety factor parameter as a buffer against prices changes too quickly per block:

if LiquidationRatio <= SF:
    then close

$SF$ could be expected to be in the range of $[1.05, 1.50]$.

#### Pro: If close through this pool, you get the exact price from the state of the pool
#### Con: Risky due to oracle manipulation
#### Because custody funds are paying off through swapping, the swap formula (realized price) version is more accurate. If using spot price version is necessary for trade-off considerations, then the safety factor $SF$ shold be increased slightly to account for that difference.