# Understanding Returns

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:

$V(p)=
\begin{cases}
2p*p_{1}-p^{2} & 0\le p\le p_{1}\\
p_{1}^{2} & p > p_{1}
\end{cases}$

The value of a Numoen LP position with p1 as 3