A Basic Primer on Dynamic Portfolio Management

There was a recent tweet in the crypto-Twitter sphere (can’t seem to find now) which discussed constant-mix – a well known, albeit simplistic, dynamic portfolio management technique – in the context of Uniswap and impermanent loss. What surprised me about that thread is that people seemed unaware of constant-mix. The matter of the fact is that constant-mix has been known and used since 1985, potentially much earlier. Yep, you read that right! There’s awesome journals from Perold et. al on this topic since back then. In fact, part of this post will be from those papers.

[2]: https://sekniqi.com/functionalization-theory/ “Functionalization Theory” –>

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Functionalization Theory

Market evolution (or innovation) is often catalyzed from a multitude of mechanisms. Software digitizes and streamlines archaic business models, technological breakthroughs give birth to whole new markets, etc. In this post, and the main topic of discussion, I wanted to take the time to formalize an important driving force of market innovation, called functionalization (not to be confused with the similar term used in materials science, which means something very different). This will be the first post in (hopefully) a series of posts formalizing what I call “innovation theory”, or the formal framework which describes precisely what makes companies valuable.

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This is a brief intro to the Azuma-Hoeffding concentration inequality. It can be viewed as a generalization of the Chernoff bound. For those that are unfamiliar, concentration inequalities specify how concentrated around some mean a particular random variable is. This is useful to quickly demonstrate that a particular random process doesn’t deviate from some expected outcome by more than some bounded amount.

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