Advent of Alpha Day 25: Shannons Demon

The last day is here. The delivery schedule wasn’t what I hoped, but I’m glad I got 25 posts out. They’re not all great. At least one is related to an idea that one person claimed has made them seven figures. It’s for you to work it out.

I would say the best has been saved to last.

In Fortune’s Forumula, which is a book by William Poundstone that I’ve mentioned before, there is an account of Claude Shannon - definer of Information Theory, the inspirer of Kelly and his criterion - who gave the World a fascinating insight into the mathematics of portfolio rebalancing.

Here’s the headline takeaway: portfolio rebalancing can make it possible to generate positive returns at the portfolio level, even when all of the portfolio’s individual holdings are expected to produce zero, or even negative, returns over time.

TLDR: if you have multiple uncorrelated strategies and you rebalance banks between them, you can make a profit, even if each strategy in itself is -EV.

It harvests volatility. As one thread on the Quant Stack Exchange explains:

The simplest example starts with a portfolio’s allocation is split between two assets which can be represented as (uncorrelated) martingales or semi-martingales. Assume that trading is costless and frictionless. The allocation changes, however, when prices change. After each period, the allocations are rebalanced back to their original “target” allocation. As a result of the costless and frictionless rebalancing, the portfolio’s expected logarithmic growth rate is greater than the arithmetic mean of the two assets, while its variance is less than (about ~2/3 of) the mean of the variances.

Shannon never rebalanced because he thought that trading fees would kill him, but in an era or environment in which there are no fees or costs in rebalancing (say, two or more strategies running in a betting exchange), by rebalancing you can make it work.

There is nothing more beautiful I’ve seen in my search for alpha: making negative EV positive, with nothing more than reallocation of your banks.

Go carefully, but if there’s one thing I would suggest you look at in 2025, it’s Shannon’s Demon.

Happy Christmas, and see you in 2025!