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People often ask me "How did you learn how to hack?" The answer: by reading. This page is a collection of the blog posts and other articles that I have accumulated over the years of my journey. Enjoy!

Uniswap is one of the best Automated Market Makers in the DeFi space. Because of their innovation, they had to create solid mathematical models in order to ensure everyone makes a profit. How did they do this?

In Uniswap, there is a concept of a pool; this is a collection of assets controlled by various individuals. The users provided value or tokens into this are liquidity provdiers (LP). When another user wants to perform a trade, they trade one asset for another asset within the pool. The LPs get rewards in the form of fees put on the users performing trades.

This comes with a problem. The price of the assets in the pool moves randomly. Additionally, it makes the assumption that all traders are informed; meaning that the price gets arbitraged to the proper price threshold. In other words, this means that ever liquidity provider would lose money from impermanent lose on their assets.

Market makers demand a lower price to buy than to sell, they directly profit when assets don't move in price with an even amount of buys in sells. The arbitrager comes in and fixes the cost of the market compared to the real world, stealing value along the way. It seems like the LPs would always lose money. So, where's the magic?

The concept of volatility harvesting comes into play here. It is possible to outperform any static portfolio of two assets by periodically rebalancing them. When the market gets arbitraged, the LPs are paying a fee to the market for the portfolio to be rebalanced. By redistributing the portfolio over time (instead of it being static), it is more accurate to reality.

The next concept is volatility drag. When using multiplication on betting, the results can be devastating. For instance, if we start with $100 and have an equal chance of the asset going up by 75% or dropping by 50%, this sounds like a wonderful deal. However, in reality, it is very hard to recover from a loss.

The expected value of the equation above is 50/2 + 175/2=$112.5 in isolation. But, if we consider the compounding asset to this, it's different. A 50% loss and a 75% gain gives us 87.5% of the value. This is the same in the other direction as well. The effects of compounding on gaining back the wealth are devastating. This is based upon the Kelly Criterion optimal betting strategy.

So, what's the lesson? Keep some of your money in reserve! Don't put all of the eggs in one basket, as they say. Instead of betting all of your money, only bet a portion of it. This way, your positive bet you placed will win in the long run. For instance, keeping $75 and betting $25 with those values will yield different results. A 75% gain then a %50 loss will end up with $131.25 instead of a loss. This is because we kept some of the value in the second step after making money.

In Uniswap, they learned that making the fee as cheap as possible to incentivize rebalancing is important. It pays to an LP vs. simply holding onto the asset in cash if the fee is not zero and the volatility is between (2 * sqrt(fee))/sqrt(3) and 2sqrt(fee). What's going on here? If the asset is too volatile or doesn't move at all, you're better off keeping the asset. Within that middle zone, we can stop volatility drag and make a profit from it though.

This is an interesting post on the finances of the market. I would love to learn more about market making and how the math works behind this in the future. Good read!