The constant product equation does not hold under thee conditions a) selloffs b) reduction in value of asset n and c) when transaction fees for liquidity utilization increases beyond a percentage of the network’s value.
The constant product nature of automated liquidity makers make these products amenable to a V = mxn formulation wherein V is the total value held in a pool in USD and m is the value of asset 1 and n is the value of asset 2. However, when shorts of m happen or massive selloffs of n happen. i.e., when the ration of m/n change and/or the ratio of m to the dollar or n to the dollar changes, this constant product need not necessarily be valid, amidst massive selloffs. the value of m and n would continuously decrease as will the product mXn as liquidity reduction happens in the market. Similarly, despite increasing liquidity in markets if the exchange rate of m or of n decreases then V decreases significantly.
Liquidity farming, another trend in today’s marketplace wherein in addition to pool fees, users can stake their liquidity tokens into centralized pools to earn interest on the liquidity token. Such staking activity can earn the investor interests in the liquidity token through either proof of stake or through a guaranteed value mechanism. That however, could again be subjected to both entry (staking) and exit( unstaking) fees that are large.
When ethereum is still maturing the crypto ecosystem is fraught with inconsistencies that are market dependent. To name a few, recent increases in transaction fees from about 1$ to about 30$ for smart contract transactions have made liquidity pool investing siginficantly difficult for small investors.
Aave another protocol, similar to uniswap but different in terms of risk monitoring provides an interesting set of guidelines for analyzing risks with respect to liquidity pools and tokens available. With uniswap the philosophy has consistently been – that as a protocol, it is upto the users or services that are built atop uniswap to disclose or discover risks through disclosure of their mechanisms. Aave built atop uniswap and other decentralzied exchanges provide some amount of visibility into various risks faced by staked tokens. Aave has created this risk matrix that summarizes the overall risks a market faces.