What is Shannon's Demon?

The open secret technique to "pump" your returns that no one tells you about

Photo by Antoine Dautry on Unsplash

It is all math.

Suppose you have a portfolio of stock and cash that is evenly split. So let’s say, you invested $200 in the portfolio, the stock and the cash positions are both at $100 each today.

Tomorrow the stock goes up 10%. Now the stock price is $110.

The next day, the stock goes down 9.09%. The stock price becomes $100.

This continues forever.

Let’s look at your portfolio value at the end of day 100.

Assuming you did not buy or sell during this time frame, at the end of day 100 you will have,

Stock worth $100, and,

Cash worth $100

for a total portfolio value of $200.

Your total returns at day 100 were ZERO.

To be more specific, your total geometric returns (CAGR) = (((1+5%) x (1 - 4.545..%) x … x (1 - 4.545..%))^(1/100) - 1) = 0

(Since day 0 your portfolio is worth $200, day 1 it is worth $210, day 2 it is worth $200, and so on).

But the Arithmetic Return is Positive

If you average your daily returns, you get the arithmetic average. In this case it will be (5% - 4.545% + 5% … - 4.545%)/100 = ~0.3%

Why Arithmetic Returns are Dragged Down?

Clearly, you will be happier to get a 0.3% return compared to 0% return. The reason the geometric returns lag the arithmetic returns is due to the volatility in the stock part of your portfolio.

If the stock did not go up and down, but stayed at the same price all this while, your arithmetic and geometric returns will be the same (0%). If the stock steadily rose at a consistent rate, your arithmetic and geometric returns would still be the same.

It is only when volatility is introduced that your portfolio receives a volatility drag. This drags down your CAGR to below what an optimum zero volatility portfolio made up of the same assets can achieve.

This means that if you find a way to reduce volatility in your portfolio, you will increase your returns, even if you keep the portfolio invested in the same assets.

Enter the Demon

Claude Shannon, the inventor of the modern world, outlined a very simple strategy to convert your geometric returns to the higher arithmetic returns.

Follow along with the process below.

Day 0: You start with a 50:50 allocation to stock and cash. You have $100 invested in each

Day 1: Stock rises 10%. Your portfolio is now worth $210. You rebalance it back to 50-50. After the rebalance, you have stock worth $105 and cash worth $105.

Day 2: The stock declines by 9.09%. Your stock is now valued at $100.23 and cash is $105. You rebalance. After the rebalance, your stock is worth $102.61 and cash is worth $102.61. Total portfolio is now valued at $205.23.

Let’s pause here for a moment.

After one cycle of up and down, the stock price is back to where it started. Cash value has not moved. If you had down “buy and hold” your portfolio should be worth $200, same as when you started.

However, because you rebalanced, your portfolio is now worth $205.23 or about 0.26% higher.

You did not change your investments, your stocks did not perform more or less than the earlier case, all that happened is that your Portfolio performed better as you rebalanced. And yes, your portfolio volatility went down.

You just harvested the volatility and added it to your pockets.

You can easily see that if you continue this process for 100 days (or 50 more cycles), your portfolio will continue to compound, compared to a buy and hold portfolio that will stay static.

Sometime during these 100 days, the effect of this extra compounding due to volatility will become visible. This is Shannon’s Demon showing up.

Rebalancing is the Open Secret

All you had to do to get the extra performance boost is to rebalance. The more frequently you rebalance, more you will compound and you will see faster portfolio growth.

In the past, rebalancing was expensive. You lost money in commission and fees. You also were stymied due to the need to buy or sell whole shares. Today, you can do free transactions and buy and share fractional shares at most brokers.

Even better,

if you use Fidelity Baskets or M1 Pies, rebalancing is just a single button click and is done automatically for you.

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Taxes can be a possible reason to avoid doing this. However, if you invest in a tax-advantaged account, this is not a problem. Even in the case of a taxable account, the potential benefits of this can outweigh the potential tax drag.

Read more about this:

Shannon's Demon

The key to making this work is to have assets that are uncorrelated or counter correlated with each other. Additionally you want assets that have high volatility. This will generate frequent rebalancing opportunities and therefore more frequent compounding. Our investment strategy marries Shannon’s Demon to proper stock selection and position sizing to achieve correct mix of correlations and optimal allocations to rebalance around.

Let me know if you find this article though provoking and how you can use this in your investing.

Happy investing!