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:
Measurement Error
Take a meter stick and measure the radius of a circle so you can calculate its area.
The meter stick is marked in millimeters. You measure 436 mm.
You calculate the area: 436 mm2 * pi = 597204.197077 mm2
Is that right? No its not.
The “correct” answer is 597000 mm2
The measurement had no “visibility” of anything beyond millimeters. Therefore, you have no idea If the real radius is 436.3 or 436.1. You’re confident the first 3 digits are correct but after that, who knows? Because of this ambiguity, your calculation of the area becomes way too confident. The 204.197077…. part is actually just a guess. It’s likely not accurate.
This is the concept of significant digits, and it is violated all the time.
But I’m not trying to point out how people report far too specific data leading to over-confidence. That is a real problem, but I want you to focus on how all measurements have error. And if simple measurements have errors, what does that mean about estimations?
Investment Errors
The entire investment “problem” revolves around errors. Think about it. If we could forecast the future with very little error, then this stuff would be fairly straightforward. But our forecasts of the future are generally really, really terrible.
Investors lose money because they lacked a good estimation of what the future would hold. Their forecasts are loaded with errors.
Up to this point in the blog, I have explained investing math as a “game” with understood parameters (except for here). Real life investing doesn’t have understood parameters. All the parameters are estimates.
Investing at the Peak
In prior posts about selecting a portfolio, I’ve focused on the Kelly maximum point, and described how to invest at the top.
This is a perfectly logical, defensible place to invest and it’s where I started in my own quest. As I’ve shown, it can perform extremely well often outperforming other investing strategies.
However, the inputs into these formulas are measurements and estimations. They are full of errors.
It’s not that they might not be correct, I’m 100% positive they are not correct. This leads to the realization that the “chosen portfolio” looks more like this:
If you are “measuring” the market, and estimating the future properties of the market, there will be errors. Combining those errors into a portfolio can compound those errors.
Past the Peak
Aim for the Kelly maximum and around half of the outcomes will end up past the peak. Portfolios “past the peak” are not the best places to invest.
All portfolios past the peak have a “better” corresponding portfolio. Some portfolios with less volatility receive more return. Some portfolios with much less volatility, still receive an identical return. Both portfolios are an improvement over a portfolio “past the peak”. Therefore it’s sometimes called “insane” to invest past the peak.
A portfolio past the peak will be sub-optimal. I don’t want that. I don’t like the idea of half of my investments being in the “insane” range. I’d rather invest somewhere along the aggressive to conservative part of the curve.
Logically then, maybe you should aim to the “left” of the Kelly maximum point. When aiming left of the peak, more of the outcomes end up in a desirable part of the curve.
If You’re Going to Miss, Aim Left
As stated above, you are going to miss. You will have errors. There are no perfect measurements. There are even fewer perfect estimates. So miss conservatively. Aim Left.
The specifics of how to aim left become complicated and are a conversation for another time. This post serves as an introduction to a new string of thought that moves the framework away from known probabilities, toward the much cloudier, murkier true reality of markets. One that acknowledges errors in our measurements and estimates, and examines the impact of these errors.
Because of these errors, maybe it makes sense to aim a bit left of the peak.
I’m an engineer and one of my past bosses used to say engineers weigh things on hay scales and then correct for barometric pressure.
Is this your way of saying that one should invest in multiple
portfolios/parameter sets along the aggressive/consiervative
continuum?
No, its my was of saying. That instead of investing at say 80/20 you should invest at 75/25. I’m going to expand on this in future posts.
Interesting premise. Your portfolio seems to follow your implied goal of minimizing volatility as well. You have a high weighting in U.S. Treasuries, cash, and gold.