Sometimes I’m asked why Geometric Balancing hasn’t been invented and implemented already? Well in many ways it was invented decades ago. But there are two main reasons why it hasn’t been implemented in any widespread capacity yet. The first is psychological.1 Rebalancing costs were the second, and more important reason. Let’s explore through the lens of Shannon’s Demon.
Shannon’s Demon
Claude Shannon was an mathematician and electrical engineering professor at MIT, a Bell Labs researcher, and possibly the most influential person in the development of the information technological age. He effectively invented digital circuit design theory, as well as the communication method of information theory. He’s been called the father of the information age.
One of his lesser known “inventions” was Shannon’s Demon, which he developed in the 1940’s. In his study he took an asset which never earned any long term wealth. It just stays flat, moving up and down through time. Shannon showed that by rebalancing this asset’s returns against cash, he could create a portfolio that didn’t stay flat, but increased in wealth.
The base asset’s return stream has a flat geometric return, and a positive arithmetic return. The example above is alternating up 50%, down 33.3%.
1.5 x 0.666 = 1
This is why the returns never go anywhere. There isn’t any geometric return. But of course the arithmetic return is higher and positive:
(1.5+0.666) / 2 = 1.083
Shannon’s Demon rebalances often and in doing so it moves the portfolio’s returns from the lower geometric return toward the higher arithmetic return (see Game 5). This is how it harvests profits out of randomness.
Geometric Balancing is essentially a dynamic version of Shannon’s Demon with 3 uncorrelated assets.2 The foundational ideas I’m using are not new. They are the same ones discovered by possibly the most brilliant engineer of the last 100 years.
Once you understand Shannon’s demon, you will realize it’s found in many places. As an example, Shannon’s Demon underlies the Farmers Fable on cooperation, and much of Ergodicity Economics.
The story behind the Demon’s creation is quite interesting, and has it’s foundation in thermodynamics (which happens to be my main field of engineering). If you want to read more on Shannon’s Demon, check out this, this, this, and read Fortune’s Formula by William Poundstone.
Constraints on Shannon’s Demon
Shannon’s Demon works best under three conditions:
- The assets are volatile. The more volatile the better.
- The assets are not correlated. Uncorrelated is ok. Negatively correlated is best. Shannon used cash in his example which is always uncorrelated.
- Rebalancing doesn’t cost anything.
So now we see the applications of these principles are limited. There are only so many uncorrelated assets to choose from. Shannon’s Demon can work with anything that is not 100% correlated, but the more correlated the assets, the smaller the benefit.
Most traditional assets are not that volatile. Stocks can be volatile, but normally they don’t bounce much from day to day. The lack of volatility constrains the overall benefit as well. However the benefit still exists.
Finally, rebalancing a portfolio certainly isn’t free. There are always transaction costs. And through most of history, these transaction costs were so high they overwhelmed any benefit frequent rebalancing provided.
The Cost of Rebalancing
My simple portfolio of 3 assets rebalanced once a week would require 156 trades each year. Historically this could eat up an enormous amount of profit, causing the rebalancing premium from Shannon’s Demon to disappear. It just simply wasn’t implementable. Let’s run some back of the envelope math to see why.
Commissions
If you go back 40 years, it could cost upwards of $45 to trade stocks. This equates to $45 x 156 = $7020. So a portfolio of $200,000 in the 80’s (not a small amount of money back then) would incur 3.4% of the portfolio value in trading fees. Rebalancing is great, but 3.4% trading costs is a lot to overcome.
Mutual Fund Fees
Geometric Balancing uses the S&P 500, specifically the SPY ETF. But that ETF didn’t exist until 1993. There really wasn’t any option to invest in the S&P 500 until the 1970’s, when mutual funds started following it.
Mutual funds usually came with all sorts of transaction fees. Standard theory encouraged buying and holding, not trading mutual funds. These fees could easily run 1% or more of the funds being bought or sold. With a turnover of potentially 400% because of the frequent rebalancing, you’re looking at a 4%+ hit to the portfolio returns here too. Historically mutual funds didn’t accommodate frequent rebalancing.
Management Fees
Mutual funds, and ETF’s almost all charge management fees to operate the portfolio. Mutual fund fees very commonly would charge a percent or more per year in management fees.
Bid-Ask Spreads
Bid-Ask spreads are silent transaction losses. They aren’t easy to see, but they are there in every stock or ETF transaction. When you buy and sell stocks you are paying someone else for each transaction. You don’t actually buy and sell at the same price. There is a difference between the price at which someone will sell you the stock (higher) and what they will buy a stock from you (lower).
In todays world, these prices are often a penny apart. But 30+ years ago, they were 1/8th of a dollar (12.5 cents) apart. So in the early 90’s the costs for a trade of SPY would have looked like this:
$-0.125/$50 = -0.25%
If the portfolio turns over 400%, you’re going to lose an additional percent each year to trading costs. Stocks with a lower price would incur even more silent losses.
Anyway you look at it, frequent rebalancing of 3 assets would have historically cost you 4%+ per year in trading fees. Rebalance more than three assets, and the costs go up further. Rebalancing more often than once a week increases costs too.
The book Fortunes Formula tells a story of Shannon being asked if he used the system himself. His answer:
“Naw, the commissions would kill you.”
But Today Things Are Different
Today this is all different.3
Values are notional and should not be taken as accurate. True costs depend on what you trade and how often. The chart is meant to show that rebalancing transaction fees are much lower today. Some investment products will have higher fees than listed.
Management fees are near zero on many ETF’s. Many mutual fund fees are near zero. This cost isn’t gone, but it’s very low. The fees for the three ETF’s used by Geometric Balancing:
- SPY- 0.09%
- TLT- 0.15%
- GLD- 0.40%
Much lower than in the past. There are similar ETFs with even lower management fees.
Bid-Ask Spreads are much smaller.
In the early 2000’s the Security Exchange Commission allowed bid-ask spreads to tighten below 1/8th of a dollar. Bid-ask spreads on highly liquid ETF’s are often just 1 cent. So today the math for SPY bid-ask spread costs looks like:
$0.01/$350 = 0.003%
For TLD and GLD the costs would be about 3 times as high because the price of the ETF is lower So let’s just be conservative here, and say bid-ask spreads create a cost of 0.01%. With a 400% turnover, this leads to a 0.04% annual cost from bid-ask spreads.
That’s very manageable.
And then we get to Trading Commissions. This used to be the largest cost and the biggest hindrance to frequent rebalancing.
Today, if you don’t want to pay fees to trade stocks and ETF’s, you don’t have to.4 Many brokerages offer some kind of no commission trading platform. Even if you still want to pay commissions they are often just a few dollars for each trade, a far cry from decades ago.
Trading Commission = $0.
Now each strategy, product and broker are going to lead to different costs. Each year will be different as well. So don’t take any of these numbers to be practices or accurate for your own trading. But I hope you can see that the frictions to rebalancing are much much lower, allowing for the great age of rebalancing to begin.
The Great Age of Rebalancing Begins
The current world of low bid-ask spreads and no commissions opens up an array of strategies aimed at capturing the rebalancing premium. The fees and costs no longer overwhelm the premium. Shannon’s Demon is implementable now.
This blog focuses on a specific method for rebalancing, however Shannon’s Demon, aka the rebalancing premium, is real and should work in a wide variety of strategies. Please take the ideas on the blog as simply an introduction to the benefit of rebalancing. With the fee structures in place today, investors potentially can implement Shannon’s Demon in many, many different strategies without “the commissions killing you” (be careful though, and do your research, there are still plenty of bad investment product out there that would be very costly to rebalance).
It has been said that many of Shannon’s inventions were decades ahead of their time. The world wasn’t ready to implement his ideas until much later. But when it was ready, his inventions revolutionized information technology, computers, and communication systems.
Shannon’s Demon is also one of those inventions the world wasn’t ready for. But it’s ready for the revolution now. Financial professionals are discussing rebalancing more and more these days.5 I believe wide application of rebalancing strategies across the investing world is coming.
The great age of rebalancing begins today. So go forth, keep your costs low, explore the rebalancing demon, and unleash it for your own benefit.
1-That would be this mess.
2-The other important part of Geometric Balancing is the Kelly Criterion. In proof we live in small world, John Kelly worked with Claude Shannon at Bell Labs. The Kelly Criterion and Shannon’s Demon are very much linked. And to go even deeper, Shannon taught Ed Thorpe (from this post) at MIT and they worked together in taking on the casinos. And deeper, Elwin Berlekamp studied under Claude Shannon and then went on to work at Bell Labs. Berlekamp later took over the investment reign of a struggling fund at Renaissance Technologies, promptly redesigned their investment implementation, and began the greatest stretch of investment returns the world has ever seen.
3-On my post on the unlevered strategy, I put a column on the expected trading costs. These costs included the bid-ask spreads calculated similar to above (but always in today’s valuations and a 2 cent bid ask spread to be conservative) and interactive brokers trading costs or minimum commissions and rebalancing around every other day. It ended up around 0.15% in costs per year (every years is different, so this is just an average). But since then, with the advent of no-fees trading, this number now seems too high.
Simply put, the weight of fees from frequent rebalancing used to be overwhelming but is now quite manageable with the correct implementation.
4-These no-commissions cost platforms are not always the best option for making trades. They don’t always get a great price depending on what you’re trading, meaning the bid-ask losses could be higher. I’m not endorsing them with this post, as they may not work for everyone.
5-Evidence is coming out that most factor premiums are actually the result of a rebalancing and not because of “factors” (you heard it here first). Once this realization takes hold (this won’t happen overnight), huge chunks of the investing industry will change. I believe the ideas on this blog will move to the forefront when it does.
Good post! One thing I’d suggest adding is a note about Shannon’s Demon – it works even when the asset moves up and down unpredictably – from the graph it shows it moving up and down regularly, which may confuse people who think the benefit is from timing the market.
Very good point and I can see how some would misinterpret my chart because of that.
Check out M1 Finance. It’s a broker dealer with automatic and one-click rebalancing
Great post, great concept. Any thoughts on the typical tax related impacts related to rebalancing frequency?
For a start: https://breakingthemarket.com/the-certainty-of-death-and-taxes/
Crypto currencies have the volatility (almost) that Shannon dreamed of.
This mess by Samuelson is really incredible, No wonder why Taleb calls him that
Two questions:
In the video, the farmers sow every year, sometimes yielding less than they sow, sometimes more. What if one of the farmers only ever produced exactly as much wheat as they sowed? Would the math still hold up? Because that is where cash is now, at 0.001% interest or so. There is no exponential growth in cash.
Common wisdom says rebalancing once a year is enough. Does this mean we should be rebalancing more often?
This is the math that creates the farmers fable. :
https://breakingthemarket.com/optimal-portfolios-for-two-assets
In your example, just set the volatility to zero for one of them to figure out what to rebalance too. And yes, rebalancing more often should produce a higher growth rate, but you have to consider transactions costs, which would become overwhelming at some frequency. See this post. https://breakingthemarket.com/why-market-index-investing-works/
Whats the difference between the Kelly Criterion and Shannon´s Demon? It seems by the two examples they achieve the same thing.
They are essentially the same, they just are solving it from different directions.