The following is a set of “courses” about the ideas discussed here on the blog. I’ve organized them by the following topics:
The Foundation: Understanding the Geometric Return
Course 2: Portfolio Construction to Maximize Compound Growth
Course 3: The Power of Rebalancing
Course 4: The Geometric Frontier and the Consequences of Errors
Course 5: Ergodicity
Final grades are provided by the markets over the rest of your life. Good luck and study hard.
The Foundation: Understanding the Geometric Return
Investing Games
How random games can fool you and how to take advantage of them.
Ed Thorpe invented the strategy to beat blackjack, a method known today as “card counting”. I first learned of Ed in college when my friends and I spent one summer at the local casinos trying to copy his card counting techniques (I wasn’t very successful). A few months ago, while researching the viability of my…
A Random Market?
Is the market random, and if so how should you invest?
I received a copy of Burton Malkiel’s famous book “A Random Walk Down Wall Street” 15 years ago. The book lays out the case for why stock market investment returns are random and passive investing is preferred over trying to beat the market. It strongly supports the efficient market hypothesis. At least this is why…
The Most Misunderstood Force in the Universe
What is the Geometric Return and how does it apply to compounded randomness?
I once believed Einstein called compound interest the most misunderstood concept in the world. He didn’t. Google claims he actually said, “compound interest is the most powerful force in the universe”.1 Well, I’m going to build on Einstein’s supposed quote and state that: “Random compound interest is the most misunderstood force in the universe.” The…
The Road Not Taken
A story on why compound randomness matters so deeply to investing.
You have a journey to make. You need to head west 15 miles as the crow flies over a mountain ridge, and then go 15 miles down the valley on the other side. So you head out for a drive. The start of the trip entails climbing up and over the ridge, and is full…
Course 2: Portfolio Construction to Maximize Compound Growth
Stocks, Treasuries, and Gold
How to choose assets for portfolio construction.
Everything should be made as simple as possible, but not simpler. -Albert Einstein
How can only three assets plus cash produce such amazing returns? Well, all three assets complement each other in way other assets just can’t. They work so well together, there really isn’t any reason for anything else. Simplify as much as possible,…
How to Balance a Portfolio
How to scale a single asset or a portfolio to maximize compound growth.
Few people balance a portfolio properly. Most have no idea even where to start. In this post, I’m going to show you the proper method to balance a portfolio for the long term. To do this we will analyze the simplest portfolio possible: a risky asset (i.e, stocks) and a risk free asset (i.e cash…
Optimal Portfolios For Two Assets
How to allocate to two assets to maximize compound growth.
Let’s discuss the proper way to mix two risky assets in a portfolio. I explained mixing one risky asset with cash before. Let’s up the complexity. I’m going to continue exploring how to mix assets with the aim of maximizing your long term wealth through the geometric return. If you haven’t read the prior post…
Convergence Time
Thoughts on estimating the inputs required to size portfolios for maximum compound growth.
There’s a saying about prediction models, garbage in/garbage out. All true. This begs the question, how long do you have to sift through garbage until you actually find something useful? The answer depends on what you are looking for. I’m often asked about the “look back” periods in Geometric Balancing. Many investment models use months…
The Ultimate 401k Strategy
How to construct a simple portfolio to maximize growth, and thoughts on how to estimate returns.
Many financial professionals would find the premise behind this post reckless. I’m not going to argue with them. Trading a 401k plan can be a terrible idea. It’s certainly foolish if you’re just using your gut or poor financial signals to time the trades. But would Geometric Balancing work within the confines of a 401k? …
Optimum Portfolio: Two Assets and Cash
Sizing portfolios of two assets and cash for maximum growth.
Time to get to some unfinished business. A few months ago I said I would shortly discuss adding cash to create a small geometrically optimized portfolio. I’ve taken too long to get this post out. So here is the process to maximize the geometric return of two assets and cash. Additionally I’ll show you how…
Course 3: The Power of Rebalancing
Why Market Index Investing Works
Why market index investing beats buy-and hold, and why rebalancing more frequently increases returns.
Why does market index investing work so well? Most say it’s because you can’t beat the market over the long run, so why try? That is nonsense. Index investing works by automatically “rebalancing” multiple assets, and by rebalancing more frequently, you can easily beat the market. Let’s investigate further. The components I’m going to use the…
The Great Age of Rebalancing Begins
An exploration of Shannon’s Demon through trading costs.
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.…
The Shape of Rebalancing: Why Some Studies Don’t Find a Rebalancing Benefit
Expanding Shannon’s Demon beyond equal weight rebalancing to optimal weight rebalancing.
The great age of rebalancing is upon us, and yet many people will ignore this superpower. They will point out some studies claim rebalancing doesn’t help. Those studies are flawed, and I’m going to show you why. By exploring further how rebalancing works, you will see why prior studies on rebalancing may have missed its…
Rebalancing Frequency Affects Portfolio Construction
Evaluating how rebalancing frequency changes the optimum portfolio.
An interesting question which seems unresolved in the investment world: Does investment time horizon affect portfolio construction? If you have longer to invest should you favor riskier assets? This is essentially the time diversification debate, and it’s a complicated one. Too complicated to get deeply into now. But the question of if investment time affects…
Course 4: The Geometric Frontier and the Consequences of Errors
Geometric Frontier
What is the geometric frontier and how does it map to optimizing compound growth?
I fear I have gone past explaining a concept and need to take a step back. Recently I used this chart which has the standard deviation on the x-axis (as opposed to the % of the asset in the portfolio). I want to explain where this chart comes from. To re-cap, the example uses two assets…
If You’re Going To Miss, Aim Left
What is measurement error, and how does it affect portfolio construction?
Engineering college classes teach students early on that all measurements are wrong. Essentially all measurements have some level of error. They are technically just estimates of the true value. Therefore you have to be careful using and extrapolating measurements during calculations. You may think you have precise numbers, but you probably don’t. Here is an example:…
Error Drag: A Lesson in Strategy from Tiger Woods
Understanding how estimation errors impact investing returns.
If Tiger Woods was a investment manager, he would dominate investing just as he dominates golf. Golf is often called a game of misses. Even a professional doesn’t hit most shots to their target. Therefore they try to manage each shot so that the bad ones don’t ruin the round. 2019 Masters re-watching Tiger Woods’…
Factor of Safety
How to construct a portfolio to ensure errors don’t cause failure.
Surprisingly, designing a bridge or building has similarities to constructing an investment portfolio. We’re going to discuss some engineering concepts for a bit. Bear with me, because I will connect each and every one back to the investing world. Imagine you have to design a structural beam. To design this beam the engineer must understand…
Along the Curve
Contemplating why investing at the peak may be sub-optimal for many investors.
A funny thing about the top of a curve: it’s flat. This flatness leads to an interesting investment question: are you willing to give up some return to reduce the bumpiness of the ride?
The Flat Top
When you look at the geometric frontier as a whole and not just the top point by itself,…
Kelly Investing is About Slope
Exploring the characteristics of the partial Kelly portfolios through the geometric frontier .
I left you hanging a few weeks ago, and it’s time to pick the thread back up. In my prior post I explained why factors of safeties are important in engineering and equated the factor of safety to using partial Kelly in investing. But I didn’t explain how to use partial Kelly. What I’m about…
Reflecting At The Milestones: Implementing the Partial Kelly Strategy
Building a model of the partial Kelly portfolio with real world assets.
We’ve taken a long journey together through the world of Geometric Balancing, traveling through some deep concepts together: We’ve learned about the geometric return and why it’s all that matters. We’ve acknowledged that the investing returns look mostly random. We’ve explored why rebalancing improves returns by moving them from the geometric to the higher arithmetic…
Course 5: Ergodicity
Repetition Economics: The Story of the Hunter, the Mammoth, and The Wolves
How human decision making is influenced by compound growth and repetition.
Imagine you’re an early human. When out hunting for food you spot a woolly mammoth in a vulnerable position. Your family hasn’t eaten in days. Much of the tribe is desperate for food as well. Do you attack the mammoth? What would go through an early human’s mind to make this decision? Obviously, bringing down…
A Grand Unified Theory of Market Behavior
Why investing markets react the way they do in a crisis, and why this response is perfectly rational.
In 2013 the Nobel Prize committee gave the economics prize to two academics with fundamentally opposite beliefs.1 On one side they gave Eugene Fama the award for his work developing and expanding the efficient market theory. And on the other side, Robert Shiller won the award for effectively disproving the efficient market theory. If you…
Stochastic Efficiency is Real and It’s Spectacular.
How Ergodicity describes optimal leverage and how it reveals a new perspective on market efficiency.
Have you ever read something, and instantly thought, that just blew my mind. Well this post is about one of those moments for me, and hopefully it will be the same for you as well. I’m also going to introduce you to the brilliance of Ole Peters and Alexander Ademou and their work on Ergodicity.…
What is the Expected Return?
What return do we expect for the future, the arithmetic return or the geometric return?
Everyone agrees on the expected values at the extremes – it’s the middle that confuses people. For a single period, the expected value is the arithmetic average. Over a very long time (infinite), the expected value is the geometric average. But in-between the expected value becomes less obvious. Let’s shed some light on this problem.…
The Arithmetic Return Doesn’t Exist
Why compounding returns through time always trend to the geometric return, not the arithmetic return.
The arithmetic return doesn’t exist. It’s a dream that isn’t real. Like waves crashing against an ocean cliff, the relentlessness of time simply overwhelms the arithmetic return. In the short term the cliff exists. But with enough repetitions, with enough crashes of the waves along its surface, it will grow smaller until ultimately the cliff…
An Ode to Cooperation
How the ideas of repetition, and rebalancing effect our everyday lives and can improve society for the better.
I’m going to show you why giving money to other people may actually make you wealthier in the long run. Not richer in the spiritual or psychological sense, but truly wealthier in a monetary sense. In doing so the whole of society will be better off too. This concept might seem strange but many of…