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Author: Admin | 2025-04-28
That is bad?”, and“Can’t we have AMMs with linear payoffs as they would be better for LPs?”It’s the special kind of non-linearity called concavity or negative convexity, also characterized with negative gamma, that is bad for LPs.2. This kind of non-linearity is present in all reasonable AMMs (as mathematically demonstrated in this paper), not just the Uniswap’s xy=k type of AMM. Therefore it’s usually fine to use the mental shortcuts “linear = beneficial for LPs” and “nonlinear = detrimental for LPs” in this context.There are AMMs with bonding curves that are close to a line for some values of the price. Curve is the most well known of these. However, while Curve offers nice properties for stable swaps, it has higher slippage and risks for LPs at the extremes of the bonding curve, when the price deviate s too much from the stable region. Essentially, Curve reduces the likelihood of losses, but increases the severity of the losses if they do occur.The GreeksLet’s have a quick recap on the Greeks in a financial context.The first derivative of the portfolio’s value function with respect to price is called delta. It represents the rate of change of the portfolio’s value in relation to price.The second derivative is known as gamma. Gamma denotes the rate of change of delta with respect to price.Example values of the Greeks:All HODL portfolios have zero gamma. Delta for HODL portfolios that don’t have loans or leverage ranges from the delta-neutral 0 to +1.All LP positions have negative gamma. In the special case of full-range LP positions the gamma is inversely proportional to — √alpha³, where alpha is the change in price relative to the initial price at which the position was created.Negative gamma payoff: profits decrease when the price rises, and losses amplify when the price declines. https://siamohajer.com/convexity-vs-concavity/Negative gamma is related to the crypto-native concept of impermanent loss, alternatively and more accurately called “divergence loss”.Positive gamma payoff. https://siamohajer.com/convexity-vs-concavity/Positive gamma is the opposite: it signifies value functions that are convex rather than concave. Certain protocols use the term “impermanent gain,” which I’ll admit does sound attractive.Fighting the negative
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