What is the economic interpretation of z

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Reference no: EM133712960

Problem

This question refers to the impermanent loss you'd incur when you provide liquidity to a DEX. Suppose the initial composition of the liquidity pool is 100 units of ETH and d units of DAI. Suppose you provide liquidity by adding another 100 units of ETH and d units of DAI to this pool. Suppose, in the next 10 days, no new liquidity provider comes, and no existing liquidity provider withdraws. Suppose, at the end of the 10th day, the market price of ETH is US$z/ETH. Suppose you withdraw your liquidity from this pool at this moment. What is the impermanent loss (expressed in terms of d and z) you have incurred within these 10 days? Since z is the price of ETH in US dollars, it cannot be negative. Among all strictly positive numbers, which z (expressed in terms of d) will give you the smallest possible impermanent loss? Let z∗ denote your answer. What will be your impermanent loss if you are so lucky that z happens to be exactly z∗? What is the economic interpretation of z∗?

Reference no: EM133712960

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