Uniswap v3 Capital Efficiency (#18)

The 5 largest v3 pools are USDC-WETH 3000 60, USDC-USDT 500 10, WBTC-WETH 3000 60, WETH-USDT 3000 60, UNI-WETH 3000 60. These are not the same as the 5 largest pools in v2, so we will look at the 5 largest v3 pools to give a common frame for comparison. We can define capital efficiency as $ of trade volume per $ of TVL. All 5 of these pools have been more capital efficient in v3 in the last 30 days, but this is most drastic for the USDC-USDT 500 10 pool (.05% fee tier). It is somewhat difficult to reason about the degree of concentration of capital, but one of the most naive metrics is to rank LP positions by the min and max price bounds of their tick range, taking the total amount of liquidity into account. Then, using a running tally of liquidity across these positions it is possible to produce a relationship between a widening lens of price spread inside of which liquidity is provided vs the % of total liquidity within that price spread. Another measure that could be used is Gini coefficient.