🌏Global Equilibrium Coverage Ratio

The system health of a pool could be measured by the global equilibrium coverage ratio $r^*$, which is the coverage ratio when all tokens return to the equilibrium state.

$$\sum{L_x (r^* - \frac{A}{r^*})} = K$$

If r* is greater than or equal to 1, it indicates the pool has enough asset to cover its liability.

Visualize Wombat

By plotting Wombat’s invariant when the amplification factor is 0.05, we can generate the following visualization:

Wombat Invariant (Red curve) and Constant Function Market Makers (blue curve)

When the pool is close to equilibrium, tokens are exchanged in a way similar to CFMM. Unlimited liquidity is provided near the tail when it deviates from equilibrium.