Optimizing portfolio allocation weights using Zipf's law?

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When investing you would like to optimize the amounts allocated to each asset. You want to have an optimal return to risk ratio, also known as the Sharpe ratio. Can Zipf's law help?

What is Zipf's Law?

Zipf's law states that the second to most frequent occurence in a natural set ocurs about half as much as the most frequent occurence. Zipf's law only works for occurences that vary in the amount of digits. For example, a city can have 112,000 people living in it (i.e. 6 digits), or 22,300,000 people living in it (i.e. 8 digits). So, Zipf's law does not work for body length: 180 cm vs 120 cm (both have 3 digits).

Investing implementation

According to Ibragimov (2009) diversification is not preferred for extremely heavy-tailed risk of returns. This is similar to what Warren Buffet has done in his portfolio: about half of his investments is allocated to three assets.

When we try to apply Zipf's law in combination with some common sense we can come up with a portfolio allocation for the booming decentralized fintech and blockchain market. The major quote currency is Bitcoin, and the follow-up currency to trade with is Ethereum.

Using a series like 32%, 16%, 8%, 4%, 2%, and 1% would give us a cumulative top 3 diversifying your assets for 56% of the total portfolio. Market swings can be easily rebalance between these three. Be sure to check whether the price history of your top 3 assets show a neutral or negative correlation. Smaller asset allocations of 2% and 1% target weights can be easily rebalanced when they are under-allocated and underbought by selling some of the over-allocated top 3 assets. This kind of diversification is only preferred when the risk of return distributions are moderately heavy tailed.

You have to think about it carefully: What would your portfolio allocation strategy be?