I know the basics about options greeks, but I heard traders extrapolating the concept to portfolios composed not just of options.

Providing liquidity on Uniswap, an automated market maker (AMM) built on top of the Ethereum blockchain, is said to have negative gamma. The capital deployed would be "impermanently lost" as per the following function:

Impermanent Loss on Uniswap

Uniswap charges a trading fee of 30 bips, so a liquidity provider would make up the loss when there's a lot of volume on the exchange.

Why can you refer to this investment strategy as being "negative gamma"? Is it because volatility harms your portfolio - i.e. concavity?


As per Argyll's comment, I'm adding more details about providing liquidity on Uniswap:

Understanding Uniswap Returns

The strategy is dynamic, in that you provide liquidity once and then people buy and sell assets through the blockchain, using your capital.

The assets that you own may change during the liquidity provision - this is what is dubbed as "impermanent loss" and is explained by the chart above.

The instruments that can be provided can be anything that is minted on Ethereum. (e.g. two USD-backed stablecoins).

The P&L varies according to how much volume there is on Uniswap. The curve from the image above is shifted up by 0.30% * your liquidity / total liquidity in the pool on every trade.

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    $\begingroup$ Yes, when price changes by $\Delta p$ your profit is $\pi =\delta \Delta p + \gamma (\Delta p)^2 + \cdots$. So if you have negative gamma a large price move (in either direction, i.e. a large $|\Delta p|$) harms you. The graph is concave. $\endgroup$ – noob2 Aug 24 '20 at 15:19
  • $\begingroup$ Would you be able to provide the exact formulas of the strategy? From the look of it, it is not a dynamic strategy right? As in, the strategy starts with positions on a number of instruments and will stay with them without modifications, correct? What is the exact basket of instruments? (It's best to ask self-contained questions.) Also, your P&L curve seems to be for the exact moment you checked -- assuming you open the positions right then. It should help to clarify the question by showing P&L at a few future time points, or better, show the surface plot with t as one of the axes. $\endgroup$ – Argyll Aug 24 '20 at 17:38
  • $\begingroup$ Thanks for your guidance, @Argyll, I updated the question body and added more comments. $\endgroup$ – Paul Razvan Berg Aug 24 '20 at 21:06
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    $\begingroup$ I would say this is one of the most interesting questions I have seen on this forum for quite a while now. $\endgroup$ – Hamish Gibson Mar 22 at 13:45

Exact replicating portfolio for constant product AMM here:


It's irritating that people use a new term 'impermanent loss' for something that happens with any option and has been well understood for decades!

  • $\begingroup$ So what is the correct term for that something? "Exact Replicating portfolio for constant product markets"? Maybe it was high-time the term changed to something more succinct. $\endgroup$ – Dimitris Sfounis May 3 at 8:12

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