A portfolio value gives the value of a LP share for a given exchange rate. The portfolio value of an AMM can be derived from the trading invariant or vice-versa.
It has been shown that portfolio values of all constant function automated market makers are nondecreasing, non-negative, and concave. This means that without external rewards, providing liquidity is always worse than holding the underlying tokens.
The portfolio value of a PMMP liquidity position is shown below:
The value of a Numoen LP position with p1 as 3