Monday, May 17, 2010

Math, Physics, & Investing

Below are some principles that, at least for me, are very relevant to investment process but just happen to come from math and physics.

1) Enrico Fermi - Believed the ability to effectively estimate was an important skill for physicists. A good way to solve physics, and other difficult problems, was by coming up with simple, approximate, but meaningful estimates (over precise calculations) to verify if he was on the right track. After that is done well, that one could later decide if a bigger effort to measure something with more precision was warranted.

Fermi was known for his ability to make good approximate calculations with little or no actual data, hence the name. One well-documented example is his estimate of the strength of the atomic bomb detonated at the Trinity test, based on the distance traveled by pieces of paper dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons. - Wikipedia

In investing, becoming good at making quick, meaningful, approximations (of valuation, market size etc.) using simple assumptions is more important than complex spreadsheet analysis. If you need a spreadsheet to see a mispricing then you shouldn't be buying it. The mispricing should be plainly obvious.

Prior post: Enrico Fermi's Rule

2) Richard Feynman

"The first principle is you must not fool yourself, and you are the easiest person to fool." - Richard Feynman

Whether aware of it or not, heuristics (mental shortcuts) and cognitive biases exist in our mental wiring that can lead to misjudgments.

...heuristics are simple, efficient rules... These rules work well under most circumstances, but in certain cases lead to systematic errors or cognitive biases. - Wikipedia

So these shortcuts, for example, can be helpful but, in the context of investing, can cause the potential and risks of an investment to be misjudged; they can also cause an investor to become overconfident or maybe overestimate how well a particular investment is understood. Consider confirmation bias, which just happens to be one of many cognitive biases. The way it works against the investor is that, once a purchase has been made, there can be a tendency to seek information that confirms the wisdom of that action. Well, that behavior, done consistently over time, inevitably will lead to blind spots and potentially expensive misjudgments.

One way to counteract this tendency is to consciously spend more time and energy thinking about why an investment thesis may be wrong; to seek out opposing views instead of reading or listening to those who might have a view that mostly conforms to your own.

"If you want to avoid irrationality, it helps to understand the quirks in our own mental wiring..." - Charlie Munger

3) Kurt Godel - Showed that any system of mathematics complex enough to contain basic arithmetic must always be either inconsistent or incomplete. A quick way to begin understanding the first of his two incompleteness theorems is through its relationship to the liar paradox.

"When I was young everybody was excited by Gödel who came up with proof that you couldn't have a mathematical system without a lot of irritating incompleteness in it. Well, since then my betters tell me that they've come up with more irremovable defects in mathematics and have decided that you're never going to get mathematics without some paradox in it. No matter how hard you work, you're going to have to live with some paradox if you're a mathematician. 

Well, if the mathematicians can't get the paradox out of their system when they're creating it themselves, the poor economists are never going to get rid of paradoxes, nor are any of the rest of us. It doesn't matter. Life is interesting with some paradox. When I run into a paradox I think either I'm a total horse's ass to have gotten to this point, or I'm fruitfully near the edge of my discipline. It adds excitement to life to wonder which it is." - Charlie Munger

So even the simplest systems can have paradox. If the simple ones have it, you can be pretty sure the more complex stuff does.

Occasionally, you will find an investment surrounded by contradiction, paradox or what is just generally counterintuitive.

This should not deter further investigation since the confusion caused can sometimes help an asset become mispriced.


This site does not provide investing recommendations as that comes down to individual circumstances. Instead, it is for generalized informational, educational, and entertainment purposes. Visitors should always do their own research and consult, as needed, with a financial adviser that's familiar with the individual circumstances before making any investment decisions. Bottom line: The opinions found here should never be considered specific individualized investment advice and are never a recommendation to buy or sell anything.
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