Effect of the reallocation threshold γ on profitability under optimally chosen interval width α

Determine whether varying the reallocation threshold γ in the modified Uniswap v3 liquidity provision strategy—where liquidity is reallocated only when the current square root price falls below the previous lower bound minus γ or exceeds the previous upper bound plus γ—affects the profitability of liquidity provision when the liquidity provision interval width α is chosen optimally.

Background

The study introduces a discrete reallocation strategy for Uniswap v3 liquidity provision that optimizes the interval width parameter α (the relative size of the square root price interval). To assess the timing of reallocation, a modified strategy is considered in which reallocation occurs only when the square root price is sufficiently far outside the previous interval, controlled by a threshold γ.

Empirical results suggest that a positive γ reduces the number of reallocations and can substantially improve profitability for small α, while a negative γ increases liquidity rewards but may reduce overall profitability due to higher reallocation costs. Despite these observations, the authors explicitly note that there is insufficient evidence to determine whether varying γ affects profitability when α itself is optimally chosen, leaving the dependence of profitability on γ under optimal α unresolved.